DEPARTMENT OF THE INTERIOR

FRANKLIN K. LANE, Secretary

UNITED STATES GEOLOGICAL SURVEY

GEORGE OTIS SMITH, Director tfj v

Bulletin 650

GEOGRAPHIC 

TABLES AND FORMULAS

FOURTH EDITION

COMPILED BY '

SAMUEL S. GANNETT

WASHINGTON

GOVERNMENT PRINTING OFFICE 

1916
ADDITIONAL COPIES

OF THIS PUBLICATION MAY BE PROCURED FROM

THE SUPERINTENDENT OF DOCUMENTS

GOVERNMENT PRINTING OFFICE

WASHINGTON, D. C.

AT

25 CENTS PER COPY
CONTENTS.

Rules ior solution of right-angled triangles................................

Reduction to center............................................. c ........

Graphic reduction to center..............................................

Solution of triangles, two sides and included angle being given............

Three-point problem ......................................................

Given the three sides of a triangle to find the angles.......................

Graphic solution of the 'three-point problem................................ 11

Micrometer alidades determination of constant and value of division ....... 12

Method of fixing a meridian at any time by hour angle...................... 14

Table 1. Polaris: azimuth at elongation ................................... 16

2. Polaris: azimuths and altitudes at different hour angles............. 17

3. Convergence of meridians..........:..................'........... 27

4. Values in feet of seconds of latitude and longitude................. 29

5. Offsets, in feet, from secant to parallel............................ 32

Example of use of projection tables............................. 34

6. Projections for large areas........................................ 36

7. Projections: scale r^ns, latitudes 0° to 80°...................... 48

8. Projections: scale fl5 ^g 0 , latitudes 0° to 80°....................... 58

9. Projections: scale Tnrcw, latitudes 25° to 50°...................... 70

10. Projections: scale ;njwff> latitudes 25° to 65°...................... 76

11. Projections: scale 24 ooO) latitudes 0° to 25°....................... 90

12. Projections: scale y^^ny, latitudes 25° to 50°...................... 99

13. Areas of quadrilaterals; 1° extent, latitudes 0° to 90°.............. 108

14. Areas of quadrilaterals; 30' extent, latitudes 0° to 90°.............. 110

15. Areas of quadrilaterals; 15' extent, latitudes 0° to 90°............. 113

16. Areas of quadrilaterals; 1CK extent, latitudes 0° to 90°............. 119

17. For conversion of arc into time.,.......:.......................... 124

18. For conversion of time into arc................................... 125

19. For conversion of mean time into sidereal time.................... 126

20. For conversion of sidereal time into mean time.................... 127

21. For interconversion of feet and decimals of a mile................. 128

22. For conversion of chains into feet................................. 129

23. For conversion of feet into chains................................. 129

24. For conversion of wheel revolutions into hundredths of a mile...... 130

25. Five-place logarithms of natural numbers......................... 140

26. Natural sines and cosines ........"................................. 162

27. Five-place logarithms of circular functions expressed in arc and time. 171

28. Geodetic position computations .................................. 216

29. Values of log sec $ (A <P) ......................................... '291

30. Corrections to longitude for difference in arc and sine.............. 292

31. Log m, for use in computing spherical excess...................... 29

32. Logarithms and factors for converting latitudes and departures in feet

to seconds of latitude and longitude ............................ 295

33. Mean refraction ................................................. 334

3
CONTENTS.

Table 34. Corrections for curvature and refraction .......................... 335

35. For obtaining differences of altitude ............................. 336

36. Horizontal distances and elevations from stadia readings ....... .. 353

37. For converting metric into United States measures................ 362

38. For converting United States measures into metric................ 363

39. For interconversion of miles and logarithms of meters............. 364

 Convenient equivalents................................................... 376

Table 40. Ratios for map scales............................................ 378

Base line computations................................................... 379

Errors in elevations....................................................... 380

Errors in leveling ........................................................ 380

Errors in plumbing rods.................................................. 380

Comparison of'Centigrade and Fahrenheit degrees........................... 381

Constants.................................................. v ............ 382

Linear expansion of metals ...............................'................ 382

Salary tables ............................................................ 383

Index................................................................... 387

ILLUSTRATIONS.

Page.

FIGURE 1. Solution of right-angled triangles................................ 5

2. Reduction to center............................................ 6

3. Solution of triangles; two sides and included angle given......... 8

4. Three-point problem; computation.............................. 10

5. Three-point problem; graphic solution.......................... 12

6. Aspects of Polaris.............................................. 14

7. Offsets from secant to parallel................................... 33

8. Construction of polyconic projection............................. 34
GEOGRAPHIC TABLES AND FORMULAS.

Compiled by S. S. GANNETT.

RULES FOB SOLUTION OF BIGHT-ANGLED TBIANGLES.

The "parts" of the figures are 

H=hy pothenuse, 

P=perpendicular, 

B=base, 

and the six circular functions of the angle a at the base of the triangle.

Secant

Cosecant

\

\ Tangent \

i

Sine

Cotangent

Cosine

FIG. 1. Solution of right-angled triangles.

RULE I. The product of two opposite parts = 1, .'. either is the 

reciprocal of the other.

Example: Tan a X cot or = 1, tan ac= ^

Rule 11. Each part=adjacent part divided by the following -part, 

.*. each part=the product of the adjacent parts.

Example: Sin a = , ^ sin ^^TJ' B=Hxcos a.

5
GEOGRAPHIC TABLES AND FORMULAS.

REDUCTION TO CENTER.

In fig. 2 let

P=place of instrument;

C=center of station;

Q=measured angle at P between two objects, A and B;

y=angle at P between C and the left-hand object, B;

r=distance CP;

C'=unknown and required angle at C; 

D=distance AC;

. (r and D must be reduced to same unit, usually meters.) 

G distance BC; 

A=angle at A between P and C; 

B=angle at B between P and C.

FIG. 2. Keduction to center.

Then0, from the relation between the parts of the triangle,

G : r :; sin y : sin B; 

hence

. _ r sin v sm B = Q-*-

As the angles at A and B are very small, their sines may be regarded 

as equal to A sin 1" and B sin 1", respectively; hence

and

T» / i \ n y B=(m seconds^ sin j,,

sin (Qrfay) r sin y 

Dsinl" Gsinl"'
GEOGRAPHIC TABLES AND FORMULAS.

In the use of this formula, proper attention should be paid to the 

signs of sin (Q+y) and sin y; for the first term will be positive only 

when (Q+y) is less than 180° (the reverse with sin ?/); D being the 

distance of the right-hand object, the graduation of the instrument 

running from left to right.

T being relatively small, the lengths of D and G are approximately 

computed with the angle Q.

The following quantities must be known in addition to the measured 

angles in order to find the correction for reducing to center:

1. The angle measured at the instrument, P, between the center of 

the signal or station, C, and the first-observed station to the right of 

it, A.

2. The distance from the center of the instrument to the center of 

the station = r.-

* 3. The approximate distances, D, G, etc., from the station occupied 

to the stations observed. The latter may be computed from the 

uncorrected angles. 

Example: Reduction to center from P to C.

Constants: a. c. log sin 1" =5. 31443 

log feet to log meters =9. 48402

log constant (for any station) 4. 79845 

r=6.5 feet: log =0.81291

log constant for this station 5. 61136

correction to angle B P A=4".08 +5^.12 =9". 20.

Angle Q-Y 

(CPA) 23° 40'

9. 6036

5. 3954

5. 6114

0.6104

4". 08

Angle 

Y 

(BPC) 37°14' 

or 322° 46'

9. 7818

5.3162

5. 6114

0. 7094

5". 12
8 GEOGRAPHIC TABLES AND FORMULAS.

GRAPHIC REDUCTION TO CENTER,

Approximate closure errors of triangles may be tested in the field 

before distances have been computed by scaling from the plot the 

distances between stations in miles and the perpendicular distance in 

feet from signal to line joining instrument and distant station.

Then, since 1 foot at a distance of 40 miles subtends an angle of 1" 

(nearly),

length of perpendicular in feet X 40 .. . , 

- i £ r- z - = correction in seconds, 

number of miles

Example: Station P. Correction for swing on line B P, 30 miles 

in length from instrument to signal

= 3.8 feet mX 40 K ,, , =5 - 1'

correction for swing on line A P, 25 miles in length, 

_2.6 feet x 40 _ . 

 25 - * -4

and correction to angle B P A = Q to reduce from instrument to signal = 5.1" + 4.2" = 9.3", agreeing closely with the exact computation.

APPROXIMATE SPHERICAL EXCESS IN SECONDS.

This may be obtained -by dividing the area of the triangle in square 

miles by 75.5.

SOLUTION OP TRIANGLES.

Given two sides and included angle, to solve the triangle:

FIG. 3. Solution ol triangles; two sides and included angle given.

Let x be an auxiliary angle; then

tan X ^TI or log tan x=\og a log J;

tan i (A-B) = tan («-45°) tan \ (A+B);

i (A+B)-H (A-B) = A; 

. i (A+B)-i (A-B) = B; 

from which remaining parts can be computed.
GEOGRAPHIC TABLES AND FORMULAS.

Example:

Given log 0=4.3666779 

Given log &=4.2050498

(1) tan i=0.1616281 

1=55° 25'25". 49

~-

(5) Log tan (i-45°)=10° 25' 25". 49=9.2647300

(6) Log tan 79 22 33 .00=0.7268100

Given C (spherical angle) 21° 14' 54". 

Given J sph. exc. .

C (planeangle) = 21 14 54.00 (?)

180°-C=A+B=15S 45 06.00;:.! 

J(A+B)= 79° 22'3?" JO (4)

(7) 9.9915400= tan £ (A-B)

(10)

44 26 31 .11

sum=A=123°49'04" 

clifference=B= 34 56 01

11 (8) 

89 (9)

Check.

A=123° 49' 04". 11 a. c. 

A= 34 56 01 .89 ' 

C= 21 14 54 .00

log 'a =4.3666779 

log sin A=0. 0804975

log sin B=9. 7578744

log sin C=9. 5592012

Sum=180 00 00 .00 log c =4. 0063766 

log b =4. 2050498

THREE-POINT PROBLEM.

If three points, forming a triangle of which the sides and angles are 

known or can be computed, be visible from a fourth point, P, it is 

required to determine the position of P.

Set up the theodolite at P and measure the two angles subtended 

by any two of the given sides.

This problem is of use in cases where, the regular triangulation having been completed, additional points are required for the topographic 

survey, or are needed for special service. The angles should be carefully measured, and in the computations the logarithms should be carried to seven places1 of decimals.

Three cases of its application are given, as in others, such as when 

P falls upon one or another of the sides of the known triangle, or on 

the prolongation of either, the case resolves itself into the solution of 

a simpk triangle with one side and the angles given; or the problem 

is indeterminate, as when P is situated on the circumference of the 

circle passing through the three known points a contingency which 

rarely occurs.

In making the computations, first prepare a plat of the various 

lines on such a scale that the shortest line will be about 2 inches in 

length, letter the plat the same as above, write by each line (a, &, c) 

the log of its length, and place in the proper positions the values for 

the angles A, P', P". The computations for Case III differ only in
10 GEOGRAPHIC TABLES AND FORMULAS.

the method of combining P', P", and A to find S. Blank forms for 

this computation are provided.

CASE II. CASE III.

Bf « 7C

FIG. 4. Three-point problem; computation.

P' .............. 50 06 12

P".............. 43 50 38

A............... Ill 10' 54

sum.............. 205 07 44

i sum.... 1......... 102 33 52

S=180°-i sum.......... 77 26 08

, sum................

A ................

A sum...............

S=£ (A sum) ....

Computation.

logc.... 3.7975307

log sin P'.... 9.8849100

(add) cologfc.... 6.1373320

colog sin P".... 0.1594574

log tan Z....' 9.9792301

Z.... 43 37 49.6 

Z+45 0 .... 88 37 49.6

log cot (Z+45°).... 8. 3785397 

(add) log tan S.... 0. 6519386

log tan e.... 9. 0304783 (sign +) 

e.... 6 07 21.7

S.... 77 26 08.0

(When tan eis +) 

S+e-AB P....- -----

S-e-ACP ....

0

BPA..... 43 

ABP..... 83 

PAB..... 52

180

50 38 

33 29.7 

35 52.3

00 00.0

83 33 

71 18

APC 

ACP 

CAP

29.7 

.46.3

(When ta 

S-a=ABP

S+e=A C P

50 06 12 

71 18 46.3 

58 35 01.7

180 00 00. 0

01 « is )

BPC.... 

PCB.... 

CPB....

As all the angles and a side in each triangle are now known, the 

other sides, or the distances from P to the three given points, can be 

readily computed.

P B ............. 7194.87

PA............. 8999. 89

PC............. 8107. 98

PA............. 8999. 89

P B ............. 7194. 94

PA............. 1388. 54

PC............. 8107. 91

PA............. 1388. 54

The results are verified when both triangles give the same value for 

the line P A.

P B ............. 5256. 29

PA............. 2609. 75

PC............. 6203. 63

PA.............. 2609. 75
GEOGRAPHIC TABLES AND FORMULAS. 11

GIVEN THE THREE SIDES OF A TRIANGLE TO FIND THE

ANGLES. ' ' ,.

Let Y be an auxiliary quantity and 

S the half sum of the three sides; 

Y== / (S-a) (S-Z>) (S-c) /

V s

Y Y Y

 tan i B = Q r tan 4 C = Q a 2 S 6 2 S c

Example:

Given a=43. 75C6 

6=40. 8954 

c= 4.1908

sum=88. 8428 

S=44. 4214

S-a= 0.6648 log=9. 8226910

8-6=3.5260 log=0.5472823

S-c=40. 2306 log=l. 6045564

log of product=l. 9745297 

log of S =1. 6475922

log of Y2 =0. 3269375=log of quotient, 

log of Y =0.1634688

log Y =0.1634688 

log S-a =9.8226910

log tan £ A =0. 3407778 (quotient)

} A =65° 28' 27" A=130° 56' 54"

log Y =0.1634688 

logS-6 =0.5472823

log tan £ B =9. 6161865

£B =22°27/ 06// B=44°54'12"

log Y =0.1634688 

log S c =1. 6045564

log tan \ C =8. 5589124

-JO = 2° 04' 27" C= 4° 08' 54"

180° 00'00" 

GRAPHIC SOLUTION OF THE THREE-POINT PROBLEM.

1. When new point is within the triangle formed by the three 

points, point sought is within the triangle of error.

2. When new point is on or near the circle passing through the 

other points, the location is uncertain.

3. When new point is within either of the three shaded segments of 

the circle (see diagram below), orient on middle point; then the line 

from middle point lies between true point and point of intersection 

of lines from other two points.
12 GEOGRAPHIC TABLES AND FORMULAS.

4. When new point is without the circle, orient on most distant 

point; then the point sought is always on the same side of the line 

from most distant point as the point of intersection of the other two 

lines.

NOTE. Since a location can be made from any three points, whether 

correctly plotted or not, therefore always check such locations by 

means of a fourth point if possible.

FIG. 5. Three-point problem; graphic solution.

MICROMETER ALIDADES DETERMINATION OF CONSTANT 

AND VALUE OF DIVISION.

R', R" = readings of micrometer screw. 

R =R' R" = difference of readings.

d = value in seconds of arc of 1 division of micrometer head.

A = angle subtended by targets in seconds of arc.

C = micrometer constant or ratio.

H = distance to targets, supposed at right angles to line of

sight. 

B = length of base, or distance between targets.

(1) d =

(2) C =

B

HR sin 1" 

1 HR

dsm B
GEOGRAPHIC TABLES AND FORMULAS. 13

EXAMPLE.

Readings taken on two targets 21.25 feet apart at right angles to 

the line of sight and at a measured horizontal distance of 2859.5 feet 

from the point of observation.

R' R" R

550.0-88.0 = 462.0

540.5-76.5 = 464.0

etc. etc. etc.

Computation of d by formula (1): 

B =21.25 ft. __: ..log. 1.32736 

H= 2859.5ft_ _. colog. 6.54371 

sin 1".........colog. 5.31443

R = 462.075 div. colog. 7.33528

462.075 mean of 20 readings.

Computation of C by formula (2): 

B = 21.25ft....colog. 8.67264 

H = 2859.5 ft....log! 3.45629 

R = 462.075 div..log. 2.66472

C = 62180 .......log. 4.79365

d =3".317-------log. 0.52078

For computing distances use this formula:

(V (3; H M= BC^

When the base is not at right angles to the line of sight as at &, or 

at the same elevation as the point of observation, the factors sin a 

and cos V must be introduced, a, being the angle between the base 

and line of sight and V the vertical angle at A.

The full formula for' distances then becomes 

(4) H =

&C sin a cos V 

R

The plotted position of the base & should be prolonged on the field 

sheet in order to permit the measurement of the angle a with a large 

paper or other protractor, with greater accuracy.
14 GEOGRAPHIC TABLES AND FORMULAS.

METHOD OF FIXING A MERIDIAN AT ANY TIME BY HOUR

ANGLE.

[Extracted from United States Land Survey Manual.]

The annexed diagram (fig. 6) will show in their proper relation the 

various aspects of Polaris in its daily apparent motion around the. 

north-polar point.

This must be carefully studied, as the illustration of Table 1, for 

finding at any hour the hour angle and azimuth of Polaris, and the 

resulting meridian, at times when more direct methods are not available.

Hour angle of Polaris. In fig. 6 the full vertical line represents a 

portion of the meridian passing through the zenith Z (the point 

directly overhead), and intersecting the northern horizon at the north 

point N, from which, for surveying purposes, the azimuths of Polaris

W.elong.5

FIG. 6. Aspects of Polaris.

are reckoned east or west. The meridian is pointed out by the plumb 

line when it is in the same plane with the eye of the observer and 

Polaris on the meridian, and a visual representation is also seen in the 

vertical wire of the transit, when it covers the star on the meridian. 

When Polaris crosses the meridian it is said to culminate; above the
GBOGEAPHIO TABLES A"ND FOEMULAS. 15

pole (at.S), the passage is called the upper culmination, in contradistinction to the lower culmination (at S').

In the diagram which the surveyor may better understand by holding it up perpendicular to the line of sight when he looks toward the 

pole Polaris is supposed to be on the meridian, where it Avill be 

about noon on April 14 of each year. The star appears to revolve 

around the pole, in the direction of the arrows, once in every 23h 56m.l 

of mean solar time; it consequently comes to and crosses the meridian, 

or culminates, nearly four minutes earlier each successive day. The 

apparent motion of the star being uniform, one quarter of the circle 

will (omitting fractions) be described in 5h 59m , one half in llh 58m, and 

three quarters in 17h 5Ym. For the positions S15 S2 , S3 , etc., the angles 

SPsn SPs2 , SPs3 , etc., are called hour angles of Polaris, for the instant 

the star is at S1? s2 , or s3", etc., and they are measured by the arcs Ssn 

Ss2 , Ss3 , etc., expressed (in these instructions) in mean solar (common 

clock) time, and are alwaj7 s counted from the upper meridian (at S), to 

the west, around the circle from Oh Om to 23h 56m.l, and may'have any 

value between the limits named. The hour angles, measured by the 

arcs Ss15 Ssa , Ss3 , Ss4 , Ss6 , and Ss6 , are approximately lh 8mv 5U 55m , 

9h 4m, 14:h 52^, 18h Olm, and 22h 48m, respectively; their extent is also 

indicated graphically by broken fractional circles about the pole.

Suppose the star observed at the point S3 ; the time it was at S (the 

time of upper culmination), taken from the time of observation, will 

leave the arc Ss3 , or the hour angle at the instant of observation; 

similar relations will obtain when the star is observed in any other 

position; therefore, in general:

Subtract the time of upper culmination from the correct local mean 

time of observation; the remainder will be the hour angle of Polaris 

expressed in time.

The observation may be made at any instant when Polaris is visible, 

the exact time being carefully noted.

The General Land Office publishes annually the Ephemeris of the 

Sun and Polaris and Tables of Azimuths of Polaris.

The azimuth of Polaris at any hour angle on any day in the year 

may be obtained from this table by a very simple computation. This 

publication replaces tables formerly printed on pages 16 to 25 of 

Geographic Tables and Formulas.
16 GEOGRAPHIC TABLES AND FORMULAS.

TABLES.

TABLE 1. Azimuth of Polaris when at elongation for any year between 1916 and 1924.

Latitude.

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

1916

1 09.6

09.9

10.1

10.4

10.7

11.0

11.4

11.7

12.1

12.5

13.0

13.5

14.0

14.5

15.1

15.7

16.3

17.0

17.7

18.4

19.2

20.0

20.9

21.8

22.7

23.7

24.8

25.9

27.0

28.2

29.5

30.9

32.3

33.8

35.3

37.0

38.7

40.6

42.5

44.5

1 46.7

1917

1 09.3

09.6

09.8

10.1

10.4

10.7

11.0

11.4

11.8

12.2

12.7

13.1

13.6

14.2

14.7

15.3

16.0

16.6

17.3

18.1

18.8

19.7

20.5

21.4

22.4

23.3

24.4

25.3

26.6

27.8

29.1

30.4

31.9

33.4

34.9

36.6

38.3

40.1

42.0

44.1

1 46.2

1918

1 09.0

09.2

09.5

09.8

10.0

10.4

10.7

11.1

11.5

11.9

12.3

12.8

13.3

13.8

14.4

15.0

15.6

16.3

17.0

17.7

18.5

19.3

20.1

21.0

22.0

23.0

24.0

25.1

26.2

27.5

28.7

30.0

31.5

32.9

34.5

36.1

37.8

39.7

41.6

43.6

1 45.7

1919

1 08.7

08.9

09.2

09.4

09.7

10.0

10.4

10.8

11.1

11.6

12.0

12.5

' 13.0

13.5

14.1

14.7

15.3

15.9

16.6

17.4

18.1

18.9

19.8

20.7

21.6

22.6

23.6

24.7

25.9

27.1

28.3

29.6

31.0

32.5

34.1

35.7

37.4

39.2

41.1

43.1

1 45.3

1920

1 08.4

08.6

08.9

09.1

09.4

09.7

10.1

10.4

10.7

11.2

11.7

12.2

12.6

13.2

13.7

14.3

14.9

15.6

16.3

17.0

17.8

18.6

19.4

20.3

21.2

22.2

23.3

24.3

25.5

26.7

27.9

29.1

30.6

32.1

33.6

35.3

37.0

38.8

40.7

42.7

1 44.8

1921

1 08.1

08.3

08.6

08.8

09.1

09.4

09.8

10.1

10.5

10.9

11.4

11.8

12.3

12.8

13^4

14.0

14.7

15.2

15.9

16.6

17.4

18.2

19.1

19.9

20.9

21.8

22.9

24.0

25.1

26.3

27.5

28.8

30.2

31.8

33.2

34.8

36.5

38.3

40.2

42.2

1 44.3

1922

1 07.8

08.0

08.2

08.5

08.8

09.1

09.4

09.8

10.2

10.6

11.0

11.5

12.0

12.5

13.0

13.6

14.2

14.9

15.6

16.3

17.0

17.9

18.7

19.6

20.5

21.5

22.5

23.6

24.7

25.8

27.1

28.4

29.8

31.2

32.8

34.4

36.1

37.9

39.8

41.7

1 43.8

1923

107.4

07.7

07.9

08.2

08.5

08.8

09.1

' 09.5

09.8

10.2

10.7

11.2

11.6

12.2

12.7

13.3

13.9

14.6

15.2

16.0

16.7

17.5

18.3

19.2

20.1

21.1

22.1

23.2

24.3

25.5

26.7

28.0

29.4

30.8

32.4

34.0

35.6

37.4

39.3

41.3

1 43.4

1924

1 07.2

07.4

07.6

07.8

.08.2

08.5

08.8

.09.2

09.5

09.9

10.4

10.8

11.3

11.8

12.4

13.0

13.6

14.2

14.9

15.6

16:4

17.2

18.0

18.8

19.8

20.7

21.7

22.8

23.9

25.1

26.3

27.6

29.0

30.4

31.9

33.5

35.2

37.0

38.8

40.8

1 42.9

The above table was computed with the mean declination of Polaris 

for each year. A more accurate result will be had by applying to 

the tabular values the following correction, which depend on the 

difference of the mean and the apparent place of the star. The 

deduced azimuth will, in general, be correct within 0'.3.

For middle of 

February..........

April..............

June..............

Correction.

-0.5

-0.4

-0.3

0.0

+0.1

+0.2

For middle of 

July...............

August. ............

September........

October............

November....... . .

Correction.

/ 

+0.2

+0.1

-0.1

-0.4

-0.6

-0.8
GEOGKAPHIC TABLES AND FORMULAS. 17

TABLE 2. AZIMUTH AND APPARENT ALTITUDE OF POLAHIS AT DIFFERENT HOUR ANGLES. 

[From U. S. Coast and Geodetic Survey Report for 1895.]

The accompanying tables are intended for field use, to facilitate 

placing an instrument in the meridian. They are also suitable for 

determining the approximate latitude or meridian. They contain the 

azimuth of Polaris at intervals of fifteen minutes in hour angle for 

each degree of north latitude from 30° to 60°, and the apparent altitude at the same intervals and for each fifth degree of latitude. 68 The 

tables are computed for the declination of Polaris 88° 46', but the rate 

of change in both azimuth and altitude is given with the argument V 

increase in declination. 6 The tables are intended to be used in connection with the American Ephemeris, where are given the apparent 

right ascension and declination of Polaris for each day in the year.

The approximate local time will in general be known with sufficient

accuracy from standard time and the approximate longitude of the 

place. The following example explains the use of the tables and the 

deriyation of the hour angle of Polaris:

Position, latitude 36° 20' N., longitude 5h 20m 30s W. of Greenwicli.

h. m. s.

Time of observation, July 10,1895, standard (75th naer.) mean time 8 52 40 p. m. 

Reduction to local time 20 30

Local mean time 8 32 10

Reduction to sidereal time (Table III, Amer. Ephem.) + 1 24

Sidereal time mean noon, Greenwich, July 10,1895 7 12 38

Correction for longitude, 5" 20m 30s (Table III, Amer. Ephern.) + 0 53

Local sidereal time ' 15 47 05

Apparent right ascension of Polaris, July 10,1895 . 1 20 18

Hour angle before upper culmination 9 33 13 

"The tables were computed with the following formulas:

_ _ _ __ __ _ tan a = co~s ,p tan"8~sin <p cost' 

sin h = sin <p sin S + cosy cos & cos t, 

cos S

cos 4= cot S tan <p;

where a = azimuth from true north, 

t = hour angle, 

<p = latitude, 

S = declination, 

h = true altitude, 

a0 = azimuth at elongation, 

tc = hour angle at elongation.

& As the corrections are given with proper sign for increase in declination over 88° 46', they are to 

be applied with reversed sign while the declination is less than 88° 46', as it will be until near the 

close of the century. v

41623° 16 2
18 GEOGRAPHIC TABLES AND FORMULAS.

Declination of table 88 46 

Apparent declination, July 10,1895 " 88 44 47

Increase in declination 1 13= 1''2

o /

Values from tables (interpolated) azimuth 0 54 12, apparent altitude 35 21.8 

Correction for 1'.2 increase in declination +52 1.0

0 55 04 35 20.8 

East of north

It is to be remembered that Polaris is east of the meridian for twelve 

hours before upper culmination, and west of the meridian for twelve 

hours after. By setting the instrument at the apparent altitude and 

sweeping near the meridian Polaris can ordinarily be found and the 

instrument placed in the meridian some time before dark. With 

transit instruments not provided with horizontal arc, the value of the 

azimuth adjusting screw may be readily determined and used.

Without the American Ephemeris these tables may be conveniently 

used for obtaining the approximate meridian or latitude, in connection 

with Bulletin 14, United States Coast and Geodetic Survey, where 

are given the approximate mean times of culminations of Polaris, and 

the mean declinations for various epochs.

20 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 2. Azimuth and apparent altitude

Hour angle before 

or after upper 

culmination.

h. m.

0 15

0 30

0 45

"1 00

1 15

1 30

1 45

2 00

2 15

2 30

2 45

3 00

3 15

3 30

3 45

4 00

4 15

4 30

4 45

5 00

5 15

5 30

5 45

6 00

6 15

6 30

6 45

7 00

7 15

7 30

7 45

8 00

8 15

8 30

8 45

9 00

9 15

9 30

9 45

10 00

10 15

10 30

10 45

11 00

11 15

11 30

11 45

Elongation: 

Azimuth . . .

Hour angle.

Azimuth of Polaris computed for declination 88° 46'.

Latitude 30°.

0 / II

0 05 40

0 11 18

0 16 53

0 22 23

0 27 48

0 33 05

0 38 13

0 43 12

0 47 58

0 52 32

0 56 52

1 00 58

1 04 47

1 08 19

. 1 11 33

1 14 28

1 17 04

1 19 19

1 21 14

1 22 48

1 24 00

1 24 51

1 25 20

1 25 27

1 25 12

1 24 34

1 23 36

1 22 16

1 20 35

1 18 34

1 16 13

1 13 33

1 10 34

1 07 17

1 03 43

0 59 54

0 55 49

0 51 31

0 46 59

0 42 16

0 37 23

0 32 20

0 27 09

0 21 51

0 16 28

0 11 01

0 05 31

1 25 27

h. m. s.

5 57 09

Latitude 31°.

0 ' //

0 05 43

0 11 25

0 17 04

0 22 38

0 28 06

0 33 26

0 38 38

0 43 40

0 48 29

0 53 06

0 57 29

1 01 37

1 05 28

1 09 02

1 12 18

1 15 15

. 1 17 52

1 20 09

1 22 05

1 23 40

1 24 53

1 25 44

1 26 13

1 26 19

1 26 04

1 25 27

1 24 27

1 23 06

1 21 25

1 19 22

1 16 59

1 14 17

1 11 16

1 07 57

1 04 22

1 00 30

0 56 23

0 52 01

0 47 27

0 42 42

0 37 45

0 32 39

0 27 25

0 22 04

0 16 38

0 11 08

0 05 34

1 26 20

h. m. s.

5 57 02

Latitude 32°.

o / n

0 05 47

0 11 33

0 17 15

0 22 53

0 28 25

0 33 49

0 39 04

0 44 09

0 49 02

0 53 42

0 58 07

1 02 18

1 06 12

1 09 48

1 13 06

1 16 05

1 18 44

1 21 02

1 22 59

1 24 35

1 25 48

1 26 40

1 27 09

1 27 15

1 26 59

1 26 21

1 25 21

1 23 59

1 22 16

1 20 12

1 17 48

1 15 04

1 12 01

1 08 40

1 05 02

1 01 07

0 56 58

0 52 34

0 47 57

0 43 08

0 38 08

0 32 59

0 27 42

0 22 18

0 16 48

0 11 14

0 05 38

1 27 16

h. m. s.

5 56 55

Latitude 33°.

0 1 II

0 05 51

0 11 41

0 17 27

0 23 09

0 28 45

0 34 13

0 39 32

0 44 40

0 49 36

0 54 19

0 58 48

1 03 01

1 06 58

1 10 36

1 13 56

1 16 57

1 19 37

1 21 57

1 23 55

1 25 32

1 26 46

1 27 38

1 28 07

1 28 14

1 27 57

1 27 19

1 26 18

1 24 55

1 23 10

1 21 05

1 18 39

1 15 53

1 12 48

1 09 25

1 05 44

1 01 47

0 57 34

0 53 08

0 48 28

0 43 36

0 38 33

0 33 20

0 28 00

0 22 32

0. 16 59

0 11 22

0 05 42

1 28 14

h. m. 8.

5 56 48

Latitude 34°.

0 ' //

0 05 55

0 11 49

0 17 40

0 23 26

0 29 06

0 34 38

0 40 00

0 45 12

0 50 12

0 54 59

0 59 30

1 03 46

1 07 46

1 11 27

1 14 49

1 17 52

1 20 34

1 22 55

1 24 55

1 26 32

1 27 47

1 28 39

-1 29 09

1 29 15

1 28 59

1 28 19

1 27 17

1, 25 53

1 24 08

1 22 00

1 19 33

1 16 45

1 13 37

1 10 12

1 06 29

1 02 29

0 58 13

0 53 43

0 49 00

0 44 05

0 38 59

0 33 43

0 28 18

0 22 47

0 17 10

0 11 29

0 .05 45

1 29 16

h. m. s.

5 56 40

Latitude 35°.

0 / II

0 06 00

0 11 58

0 17 53

0 23 44

0 29 28

0 35 04

0 40 30

0 45 46

0 50 50

0 55 40

1 00 15

1 04 34

1 08 36

1 12 20

1 15 45

1 18 50

1 21 34

1 23 57

1 25 57

1 27 36

1 28 51

1 29 44

1 30 14

1 30 20

1 30 03

1 29 23

1 28 20

1 26 55

1 25 08

1 22 59

1 20 29

1 17 39

1 14 29

1 11 01

1 07 0 15

1 03 12

0 58 54

0 54 21

. 0 49 34

0 44 35

0 39 26

0 34 06

0 28 38

0 23 03

0 17 22

0 11 37

0 05 49

1 30 20

h. m. s.

5 56 33
GEOGRAPHIC TABLES AND EORMULAS.

of Polaris at different hour angles.

21

Azimuth of Polaris computed for declination 88° 46'.

Latitude 36°.

o / //

0 06 05

0 12 08

0 18 07

0 24 02

0 29 51

0 35 31

0 41 02

0 46 22

0 51 29

0 56 23

1 01 02

1 05 24

1 09 29

1 13 16

1 16 43

1 19 50

1 22 36

1 25 01

1 27 03

1 28 42

1 29 59

1 30 52

1 .31 21

1 31 27

1 31 10

1 30 30

1 29 26

1 27 59

1 26 11

1 24 00

1 21 28

1 18 36

1 15 24

1 11 53

1 '08 04

1 03 58

0 59 37

0 55 00

0 50 10

0 45 08

0 39 54

0 34 30

0 28 59

0 23 19

0 17 35

' 0 11 46

0 05 53

1 31 28 '

h. m. s.

5 56 25

Latitude 37°.

o / //

0 06 10

0 12 18

0 18 22

0 24 22

0 30 15

0 36 00

0 41 35

0 47 00

0 52 11

0 57 09

1 01 51

1 06 17

1 10 25

1 14 14

1 17 44

1 20 54

1 23 42

1 26 08

1 28 12

1 29 52

1 31 09

1 32 03

1 32 33

1 32 39

1 32 21

1 31 40

1 30 35

1 29 07

1 27 17

1 25 04

1 22 30

1 19 36

1 16 21

1 12 48

1 08 56

1 04 47

1 00 22

0 55 42

0 50 48

0 45 42

0 40 24

0 34 57

0 29 20

0 23 37

0 17 48

0 11 54

0 05 58

0

1 32 40

h. m. s.

5 56 17

Latitude 38°.

O > H

0 06 15

0 12 28

0 18 38

0 24 43

0 30 41

0 36 31

0 42 11

0 47 39

'0 52 55

0 57 57

1 02 43

1 07 12

1 11 24

1 15 16

1 18 49

1 22 01

1 24 51

1 27 19

1 29 24

1 31 06

1 32 24

1 33 18

1 33 48

1 33 54

1 33 36

1 32 54

1 31 48

1 30 18

1 28 26

1 26 12

1 23 36

1 20 39

1 17 22

1 13 45

1 09 50

1 05 38

1 01 09

0 56 25

0 51 27

0 46 17

0 40 55

0 35 24

0 29 43

0 23 55

0 18 02

0 12 04

0 06 02

1 33 55

h. m. s.

5 56 09

Latitude 39°.

o r H

0 06 20

0 12 39

0 18 54

0 25 04

0 31 08

0 37 02

0 42 47

0 48 21

0 53 41

0 58 47

1 03 37

1 08 10

1 12 25

1 16 21

1 19 57

1 23 11

1 26 03

1 28 33

1 30 40

1 32 23

1 33 42

1 34 37

1 35 07

1 35 13

1 34 54

1 34 11

1 33 04

1 31 33

1 29 39

1 27 23

1 24 45

1 21 45

1 18 25

1 14 45

1 10 47

1 06 31

1 01 59

0 57 11

0 52 09

0 46 54

0 41 28

0 35 52

0 30 07

0 24 14

0 18 16

0 12 13

0 06 07

1 35 14

h. m. s.

5 56 00

Latitude 40°.

o / //

0 06 26

0 12 50

0 19 11

0 25 27

0 31 36

0 37 36

0 43 26

0 49 04

0 54 29

0 59 40

1 04 34

1 09 12

1 13 30

1 17 29

1 21 08

1 24 25

1 27 20

1 29 52

1 32 00

1 33 44

1 35 04

1 35 59

1 36 30

1 36 35

1 36 16

1 35 32

1 34 24

1 32 52

I 30 56

1 28" 38

1 25 57

1 22 54

1 19 31

1 15 48

' 1 11 47

1 07 27

1 02 51

0 57 59

0 52 53

0 47 34

0 42 03

0 36 22

0 30 32

0 24 35

0 18 31

0 12 23

0 06 12

1 36 36

h. TO. 8.

5 55 52

Correction for 1' increase in declination of Polaris.

Latitude 30°.

«

- 5

- 9

 14

-18

-23

-27

-31

-35

-39

-43

-46

-50

-53

-56

 58

-61

-63

-64

-66

-68

-69

-69

-70

-70

-69

-68

-67

-66

-65

-64

-62

-60

-57

-54

-51

-48

-45

 42

-38

-34

-30

-26

-22

-18

-13

- 9

- 4

-69

8.

+ 2

Latitude 40°.

ii - 5

-10

-16

-21

-26

-31

-36

-40

-45

-49

-53

' -57

-60

-63

-66

-69

-72

-74

-75

. -76

_ 77

-78

-78

-78

-78

-77

-76

-75

-73

-72

-69

-66

-64

-61

-58

-54

-50

-46

-42

-38

-34

-29

-24

-20

-15

-10

 5

-78

8.

+ 3

Hour 

angle 

before 

or after 

upper 

culmi- . 

nation.

h. TO. : 0 15 .

0 30 

0 45 '

1 00

1 15

1 30

1 45

2 00 .

2 15

2 30

2 45 3' 00 '

3 15 i

3 30 !

3 45

4 00

4 '15 I 4 30 :

4 45

5 00

5 15 '

5 30

5 45 ,

6 00

6 15

6 30

6 45

7 00 

7f5 : 7 30 :

7 45 '

8 00

8 15 :

8 30 !

8 45 j

9 00 i

9 15 '

9 30 ;

9 45 1 1000 ;

10 15 <

10 30

10 45 ,

11 00

11 15

11 30 .

11 45

i
22 GEOGEAPHIO TABLES AND FOEMULAS.

TABLE 2. Azimuth and apparent altitude

Hour angle before

or after upper

culmination.

h. m. 

0 15

0 30

0 45

1 00

1 15

1.30

1 45

2 00

2 15

2 30

2 45

3 00

3 15

3 30

3.45

4 00

4 15

4 30

4 45

5 00

5 15

5 30

5 45

6 00

6 15

6 30

6 45

700

7 15

7 30

7 45

8 00

8 15

8 30

8 45

9 00

9 15

9 30

9 45

10 00

10 15

30 30

10 45

11 00

11 15

11 30

11 45

Elongation:

Azimuth . . .

Hour angle.

Azimuth of Polaris computed for declination 88° 46'.

Latitude 40°.

0 06 26

0 12 50

0 19 11

0 25 27

0 31 36

0 37 36

0 43 26

0 49 04-

0 54 29

0 59 40

1 04 34

1 09 12

1 13 30

1 17 29

1 21 08

,1 24 25

1 27 20

1 29 52

' 1 32 00

1 33 44

1 35 04

1 35 59

1 36 30

1 36 35

1 36 16

1 35 32

1 34 24

1 32 52

1 30 56

1 28 38

1 25 57

1 22 54

1 19 31

1 15 48

1 11 47

1 .07 27

1 02 51

0 57 59

0 52 53

0 47 34

0 42 03

0 36 22

0 30 32

0 24 35

0 18 31

0 12 23

0 06 12

1 36 36

h. m. s.

5 55 52

Latitude 41°.

0 06 32

0 13 03

0 19 30

0 25 51

0 32 05

0 38 11

0 44 07

0 49 50

0 55 20

1 00 35

1 05 34

1 10 16

1 14 38

1 18 41

1 22 23

1 25 43

1 28 40

1 31 14

1 33 24

1 35 10

1 36 30

1 37 26

1 37 57

1 38 02

1 37 43

1 36 58

1 35 48

1 34 15.

1 32 17

1 29 56

1 27 13

1 24 07

1 20 41

1 16 55

1 12 49

1 08 26

' 1 03 45

0 58 49

0 53 39

0 48 15

0 42 39

0 36 53

0 30 58

0 24 56

0 18 47

0 12 34

0 06 18

1 38 03

h. m. s.

5 55 43

Latitude

.42°.

0 06 39

0 13 15

0 19 48

0 26 16

0 32 36

0 38 48

0 44 50

0 50 39

0 56 14

1 01 34

1 06 38

1 U 24

1 15 50

1 19 57

1 23 42

1 27 05

1 30 04

1 32 41

1 34 53

1 36 40

1 38 02

1 38 58

1 39 29

1 39 34

1 39 14

1 38 28

. 1 37 17

1 35 42

1 33 42

1 31 19

1 28 33

1 25 24

1 21 55

1 18 05

1 13 55

1 09 28

1 04 43

0 59 42

0 54 27

0 48 58

0 43 18

0 37 26

0 31 26

0 25 18

0 19 04

0 12 45

0 06 23

1 39 35

h. m. s.

5 55 34

'Latitude 43°.

0 06 45

0 13 29

0 20 08

0 26 43

0 33 09

0 39 27

0 45 35

0 51 29

0 57 10

1 02 36

1 07 44

1 12 35

1 17 06

1 21 16

1 25 04

1 28 31

1 31 33

1 34 12

1 36 25

1 38 14

1 39 37

1 40 34

1 41 05

1 41 10

1 40 49

1 40 03

1 38 50

1 37 13

1 35 11

1 32 46

1 29 56

1 26 45

1 23 12

1 19 18

1 15 05

1 10 33

1 05 43

1 00 38

0 55 18

0 49 44

0 43 58

0 38 01

0 31 55

0 25 42 .

0 19 22

0 12 57

0 06 29

1 41 11

h. m. s.

5 55 24

Latitude 44°.

0 06 52

0 13 43

0 20 29

0 27 10

0 33 44

0 40 09

0 46 22

0 52 23

0 58 10

1 03 41

1 08 54

1 13 50

1 18 25

1 22 39

1 26 32

1 30 01

1 33 07

1 35 48

1 38 04

1 39 54

1 41 18

1 42 16

1 42 47

1 42 51

1 42 30

1 41 42

1 40 28

1 38 49

1 36 45

1 34 17

1 31 25

1 28 10

1 24 33

1 20 35

1 16 18

1 11 41

1 06 47

1 01 37

0 56 11

0 50 32

0 44 40

0 38 38

0 32 26

0 26 06

"0 19 40

0 13 09

0 06 36

0

1 42 53°

h. m. s.

5 55 14

Latitude 45°.

0 07 00

0 13 58

0 20 52

0 27 40

0 34 21

0 40 52

0 47 12

cO 53 19

0 59 12

1 04 49

1 10 08 .

1 15 09

1 19 49

1 24 08

1 28 04

1 31 37

1 34 45

1 37 29

1 39 47

1 41 38

1 43 04

1 44 02

] 44 34

1 44 38

1 44 16

1 43 27

1 42 12

1 40 31

1 38 24

]. 35 53

1 32 58

1 29 40

1 25 59

1 21 57

1 17 35

1 12 54

1 07 54

1 02 38

0 57 07

0 51 22

0 45 25

0 39 16

0 32 58

0 26 32

0 20 00

0 13 23

0 06 42

1 44 40

h. m. s.

5 55 04
GEOGKAPHIC TABLES AND FOKMULAS.

of Polaris at different hour angles Continued.

23

Azimuth of Polaris computed for declination 88° 46'.

Latitude 46°.

0 / //

0 07 08

0 14 13

0 21 15

0 28 11

0 34' 59

0 41 38

0 48 05

0 54 19

1 00 18

1 06 01

1 11 26

1 16 .32

1 21 17

1 25 40

1 29 41

1 33 17

1 36 29

1 39 15

1 41 35

1 43 29

1 44 55

1 45 54

1 46 26

1 46 31

1 46 08

1-45 18

1 44 01

1 42 18

1 40 09

1 37 35

1 34 36

1 31 14

1 27 29

1 23 23

1 18 56

1 14 10

1 09 05

1 03 44

0 58 07

0 52 16 '

0 46 12

0 39 57

0 33 32

0 27 00

0 20 20

0 13 36

0 06 49

1 46 32

h. m. s.

5 54 53

Latitude 47°.

0 I II

0 07 16

0 14 30

0'21 40

0 28 44

0 35 40

0 42 26

0 49 01

0 55 22

1 01 28

1 07 17

1 12 48

1 18 00

1 22 50

1 27 18

1 31 23

1 35 03

1 38 18

1 41 08

1 43 30

1 45 25

1 46 53

1 47 53

1 48 25

1 48 29

1 48 05

1 47 14

1 45 56

1 44 10

1 41 59

1 30 21

1 36 19

1 32 53

1 29 04

1 24 53

1 20 21

1 15 30

1 10 19

1 04 52

0 59 09

0 53 12

0 47 01

0 40 40

0 34 08

0 27 28

0 20 42

0 13 51

0 06 56

1 48 31

h. m. s.

5 54 42

Latitude 48°.

o t it

0 07 25

0 14 48

0 22 06

0 29 18

0 36 23

0 43 17

0 49 59

0 56 28

1 02 41

1 08 38

1 14 15

1 19 33

1 24 29

1 29 02

1 33 11

1 36 55

1 40 14

1 43 06

1 45 31

1 47 28

1 48 57

1 49 58

1 50 30

1 50 34

1 50 10

1 49 17

1 47 56

1 46 09

1 43 54

1 41 14

1 38 08

1 34 38

1 30 44

1 26 28

1 21 51

1 16 54

1 11 38

1 06 04

1 00 15

0 54 11

0 47 53

0 41 25

0 34 46

0 27 59

0 21 05

0 14 06

0 07 04

1 50 36

h. m. s.

5 54 31

Latitude 49°.

O 1 II

0 07 34

0 15 06

0 22 33

0 29 55

0 37 08

0 44 11

0 51 02

0 57 38

1 03 59

1 10 03

1 15 47

1 21 11

1 26 13

1 30 51

1 35 05

1 38 54

1 42 16

1 45 11

1 47 39

1 49 38

1 51 08

1 52 10

1 52 43

1 52 46

1 52 21

1 51 27

1 50 04

1 48 14

1 45 57

1 43 13

1 40 03

1 36 29

1 32 30

1 28 09

1 23 26

1 18 23

1 13 01

1 07 21

1 01 24

0 55 13

0 48 49

0 42 12

0 35 26

0 28 31

0 21 29

0 14 22

0 07 12

1 52 48

h. m. s.

5 54 20

Latitude 50°.

Oil'

0 07 44

0 15 25

0 23 02

0 30 33

0 37 56

0 45 08

0' 52 07

0 58 52

1 05 21

1 11 32

1 17 24

1 22 54

1 28 02

1 32 46

1 37 06

1 40 59

1 44 25

1 47 24

1 49 54

1 51 55

1 53 27

1 54 30

1 55 03

1 55 06

1 54 40

1 53 44

1 52 20

1 50 27

1 48 06

1 45 19

1 42 05

1 38 26

1 34 22

1 29 55

1 25 07

1 19 57

1 14 28

1 08 41

1 02 38

0 56 19

0 49 47

0 43 02

0 36 08

0 29 05

0 21 55

0 14 39

0 07 21

1 55 08

h. m. s.

5 54 07

Correction for 1' increase in declination of Polaris.

Latitude 40°.

- 5

-10

-16

 21

-26

-31

-36

 40

-45

-49

-53

-57

-60

-63

-66

-69

-72

-74

-75

-76

-77

-78

-78

-78

-78

-77

-76

-75

-73

-72

-69

-66

-64

-61

-58

-54

-50

-46

 42

-38

-34

-29

-24

-20

-15

-10

- 5

-78

8.

+ 3

Latitude 50°.

- 6

-13

-19

-25

-32

-38

-43

-49

-54

-59

-64

-68

-72

-76

 80

-83

-86

-88

-90

-91

-92

-93

-94

-93

-93

-92

-91

-89

-87

-85

-82

-79

-76

-72

-68

-64

-59

-55

-50

-45

-40

-34

-29

-23

-18

-12

- 6

-93

8.

+ 5

Hour 

angle 

before 

or after 

upper culmination.

ft. m.

0 15

0 30

0 45

1 00

1 15

1 30

1 45

2 00

2 15

2 30

2 45

3 00

3 15

3 30

3 45

4 00

4 15

4 30

4 45

5 00

5 15

5 30

5 45

6 00

6 15

6 30

6 45

7 00

7 15

7 30

7 45

8 00

8 15

8 30

8 45

9 00

9 15

9 30

9 45

10 00

10 15

10 30

10 45

11 00

11 15

11 30

11 45
24 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 2. Azimuth and apparent altitude

Hour angle before 

or after upper 

culmination.

h. m.

0 15

0 30

0 45

1 00

1 15

1 30

1 45

2 00'

2 15

2 30

2 45

3 00

3 15

3 30

3 45

4 00

4 15

4 30

4 45

5 00

5 15

5 30

5 45

6 00

6 15

6 30

6 45

7 00

7 15

7 30

7 45

8 00

8 15

8 30

8 45

9 00

9 15

9 30

9 45

10 00

10 15

10 30

10 45

11 00

11 15

11 30

11 45

Elongation : 

Azimuth . . .

Hour angle.

Azimuth of Polaris computed for declination 88° 46'.

Latitude 50°.

0 / II

0 07 44

0 15 25

0 23 02

0 30 33

0 37 56

0 45 08

0 52 07

0 58 52

1 05 21

1 11 32

1 17 24

1 22 54

1 28 02

1 32 46

1 37 06

1 40 59

1 44 25

1 47 24

1 49 54

1 51 55

1 53 27

1 54 30

1 55 03

1 55 06

1 54 40

1 53 44

1 52 20

1 50 27

1 48 06

1 45 19

1 42 05

1 38 26

1 34 22

1 29 55

1 25 07

1 19 57

1 14 28

1 08 41

1 02*33

0 56 19

0 49 47

0 43 02

0 36 08

0 29 05

0 21 55

0 14 39

0 07 21

1 55 08

h. m. s.

5 54 07

Latitude 51°.

O 1 II

0 07 54

0 15 46

0 23 33

0 31 14

0 38 47

0 46 08

0 53 17

1 00 11

1 06 48

1 13.08

1 19 07

1 24 44

1 29 59

1 34 49

1 39 14

1 43 12

1 46 42

1 49 44

1 52 17

1 54 21.

1 55 54

1 56 58

1 57 31

1 57 34

1 57 06

1 56 09

1 54 42

1 52 47

1 50 23

1 47 32

1 44 13

1 40 29

1 36 20

1 31 48

1 26 53

1 21 37

1 16 01

1 10 06

1 03 55

0 57 28

0 50 48

0 43 56

0 36 52

0 29 41

0 22 22

0 14 57

0 07 30

1 57 36

h. m. s.

5 53 54

Latitude 52°.

O 1 II

0 08 05

0 16 08

0 24 06

0 31 58

0 39 40

0 47 12

0 54 31

1 01 34

1 08 21

1 14 48

1 20 55

1 26 41

1 32 02

1 36 58

1 41 29

1 45 32

1 49 07

1 52 13

1 54 49

1 56 54

1 58 29

1 59 34

2 00 08

2 00 10

1 59 41

1 58 43

1 57 14

1 55 15

1 52 48

1 49 52

1 46 29

1 42 40

1 38 25

1 33 47

1 28 45

1 23 22

1 17 38

1 11 36

1 05 17

0 58 42

0 51 53

0 44 52

0 37 39

0 30 18

0 22 50

0 15 16

0 07 39

2 00 13

h. m. s.

5 53 41

Latitude 53°.

O I II

0 08 17

0 16 31

0 24 41

0 32 44

0 40 38

0 48 20

. 0 55 49

1 03 03

1 09 59

1 16 35

1 22 51

1 28 44

1 34 13

1 39 16

1 43 52

1 48 01

1 51 40

1 54 50

1 57 29

1 59 37

2 01 15

2 02 20

2 02 53

2 02 56

2 02 26

2 01 25

1 59 54

1 57 52

1 55 21

1 52 21

1 48 53

1 44 58

1 40 38

1 35 52

1 30 44

1 25 1.3

1 19 22

1 13 12

1 06 44

1 00 00

0 53 02

0 45 51

0 38 29

0 30 58

0 23 20

0 15 37

0 07 49

2 02 59

h. m. s.

5 53 27

Latitude 64°.

0 / //

0 08 29

0 16 56

0 25 18

0 33 33

0 41 38

0 49 32

0 57 12

1 04 37

1 11 43

1 18 29

1 24 54

1 30 55

1 36 32

1 41 42

1 46 25

1 50 39

1 54 23

1 57 37

2 00 20

2 02 31

2 04 10

2 05 16

2 05 50

2 05 52

2 05 21

2 04 18

2 02 44

2 00 39

1 58 04

1 5459

'1 51 26

1 47 25

1 42 58

1 38 06

1 32 50

1 27 11

1 21 12

1 14 53

1 08 16

1 01 23

0 54 15

0 46 54

0 39 22

0 31 41

0 23 52

0 15 58

0 08 00

2 05 55

h. m. s.

5 53 12

Latitude 

. 55°.

O / II

0 08 42

0 17 22

0 25 57

0 34 25

0 42 43

0 50 49

0 58 41

1 06 16

1 13 33

1 20 30

1 27 04

1 33 15

1 39 00

1 44 18

1 49 07

1 53 27

1 57 16

2 00 35

2 03 21

2 05 35

2 07 16

2 08 23

2 08 58

2 08 58

2 08 26

2 07 22

2 05 45

2 03 36

2 00 57

1 5747

1 54 08

1 50 01

1 45 27

1 40 28.

1 35 04

1 29 17

1 23 08

1 16 40

1 09 53

1 02 50

0 55 32

0 48 01

0 40 18

0 32 26

0 24 26

0 16 21

0 08 11

2 09 02

h. m. s.

5 52 57
GEOGEAPHIC TABLES AND FOEMULAS.

of Polaris at different hour angles Continued.

25

Azimuth of Polaris computed for declination 88° 46'.

Latitude 56°.

Q 1 II

0 08 56

0 17 50

0 26 39

0 35 21

0 43 52

0 52 11

1 00 16

1 OS 03

1 15 31

1 22 39

1 29 23

1 35 43

1 41 37

1 47 03

" 1 52 00

1 56 26

2 00 21

2 03 44

2 06 34

2 OS 51

2 10* 34

2 11 42

2 12 17

2 12 17

2 11 44

2 10 37

2 08 57

2 06 44

2 04 00

2 00 45

1 57 00

1 52 47

1 48 06

1 42 58

1 37 26

1 31 30

1 25 12

1 18 34

1 11 37

1 04 23

0 56 54

0 49 12

0 41 18

0 33 14

0 25 02

0 16 45

0 08 23

2 12 21

h. m. s.

5 52 41

Latitude 57°.

O 1 II

0 09 12

0 18 20

0 27 24

0 36 20

0 45 06

0 53 39

1 01 56

1 09 57

1 17 37

1 24 56

1"31 52

1 38 22

1 44 25

1 50 00

1 55 04

1 59 37

2 03 38

2 07 06

2 10 00

2 12 20

2 14 05

2 15 14

2 15 50

2 15 49

2 15 14

2 14 05

2 12 21

2 10 05

2 07 16

2 03 55

2 00 04

1 55 43

1 50 54

1 45 39

1 39 57

1 33 51

1 27 24

1 20 36

1 13 28

1 06 03

0 58 22

0 50 27

0 42 21

0 34 05

0 25 41

0 17 10

0 08 36

2 15 54

h. m. s.

5 52 24

Latitude 58°.

0 1 II

0 09 28

0 18 53

0 28 12

0 37 23

0 46 24

0 55 12

1 03 44

1 11 58

1 19 52

1 27 24

1 34 31

1 41 12

1 47 25

1 53 08

1 58 21

2 03 01

2 07 09

2 10 42

2 13 40

2 16 03

2 17 50

2 19 01

2 19 36

2 19 35

2 18 59

2 17 47

2 16 00

2 13 39

2 10 45

2 07 18

2 03 20

1 58 52

1 53 54

1 48 30

1 42 39

1 36 23

1 29 44

1 22 45

1 15 25

1 07 48

0 59 55

0 51 48

0 43 28

0 34 59

0 26 21

0 17 38

0 08 50

2 19 40

h. m. s.

5 52 06

Latitude 59°.

O / II

0 09 45

0 19 27

0 29 03

0 38 31

0 47 48

0 56 52

1 05 40

-1 14 08

1 22 16

1 30 01

1 3721

1 44 13

1 50 37

1 56 30

2 01 51

2 06 40

2 10 54

2 14 32

2 17 35

2 20 02

2 21 51

2 23 04

2 23 39

' 2 23 37

2 22 59

2 21 44

2 19 53

2 17 27

2 14 27

2 10 54

2 06 49

2 02 12

1 57 06

1 51 32

1 45 31

1 39 05

1 32 14

1 25 03

1 17 31

1 09 41

1 01 34

0 53 14

0 44 40

0 35 57

0 27 05

0 18 07

0 09 04

2 23 43

h. m. s. 5 51 47

Latitude 60°.

o / //

0 10 03

0 20 04

0 29 58

0 39 44

0 49 19

0 58 40

1 07 44

1 16 28

1 24 51

1 32 50

1 40 23

1 47 28

1 54 03

2 00 07

2 05 37

2 10 34

2 14 55

2 18 39

2 21 47

2 24 17

2 26 09

2 27 23

2 27 58

2 27 56

2 27 15

2 25 57

2 24 03

2 21 32

2 18 26

2 14 46

2 10 32

2 05 47

2 00 32

1 54 47

1 48 35

1 41 57

1 34 55

1 27 30

1 19 45

1 11 41

1 03 20

0 54 45

0 45 57

0 36 59

0 27 51

0 18 38

0 09 20

2 28 02

h. m. s.

5 51 27

Correction for I' increase in declination of Polaris.

Latitude 50°.

// - 6

-13

-19

-25

-32

-38

-43

-49

-54

-59

-64

-68

 72

-76

-80

-83

-86

-88

-90

-91

-92

-93

-94

-93

-93

-92

-91

-89

-87

-85

-82

-79

-76

-72

-68

-64

-59

-55

-50

-45

-40

-34

-29

-23

-18

-12

- 6

-93

8.

+ 5

Latitude CO0.

- 8

- 17

- 25

- 33

- 41

- 49

- 57

- 64

- 71

- 78

- 84

- 89

- 94

- 99

-104

-108

-111

-114

-116

-118

-119

-120

-120

-120

-119

-118

-116

-114

-111

-108

-104

-100

- 96

- 91

- 86

- 80

- 75

- 69

- 63

- 56

- 50

- 43

- 36

- 29

- 22

- 14

- 7

-120

8. +- 7

Hour 

angle 

before 

or after 

upper culmination.

h. m.

0 15

0 30

0 45

1 00

1 15

1 30

1 45

2 00

2 15

2 30

2 45

300

3 15

3 30

3 45

4 00

4 15

4 30

4 45

5 00

5 15

5 30

5 45

6 00

6 15

6 30

6 45

7 00

7 15

7 30

7 45

8 00

8 15

8 30

8 45

9 00

9 15

9 30

9 45

10 00

10 15

10 30

10 45

11 00

11 15

11 30

11 45
26 GEOGKRAPHIC TABLES AND FOEMULAS.

TABLE 2. Azimuth and apparent altitude of Polaris at different hour angles Continued.

Hour 

angle 

before 

or after 

upper culmination.

h. m.

000

015 030'

045;

100

115

130

145

200

215

230

245

300

315

330

345

400

415

430

445

500

515

530

545

600

615

630

645

700

715

730

745

800

815

830

845

900

915

930

945

1000

1015

1030

1045

1100

1115

1130

1145

1200

Apparent altitude of Polaris, computed for declination 88° 46' and 

mean refraction.

Latitude 30°.

0 /

31 15.6

31 15.4

31 14.9

31 14.2

31 13.0

31 11.6

31 09.9

31 07.9

31 05.6

31 03.0

31 00.1

30 57.0

30 53.7

30 50.1

30 46.4

30 42.4

30 38.3

30 34.0

30 29.6

30 25.0

30 20.4

30 15.6

Latitude 35°.

o /

36 15.3

36 15.2

36 14.7

36 13.9

36 12.8

36 11.3

36 09.6

36 07.6

36 05.3

36 02.7

35 59.8

35 56.7

35 53.4

35 49.8

35 46..0

35 42.1

35 38.0

35 33.6

35 29.2

35 24.6

35 20.0

35 15.3

30 10.8 35 10.4

30 06.0

30 01.2

29 56.4

29 51.6

29 46.8

39 42.1

29 37.5

29 33.0

29 28.6

29 24.4

29 20.3

29 16.4

29 12.7

29 09.2

29 05.9

29 02.8

29 00.0

28 57.5

28 55.3

28 53.3

28 51.6

28 50.2

28 49.2

28 48.4

28 47.9

28 47.7

35 05.6

35 00.8

34 56.0

34 51.2

34 46.4

34 41.7

34 37.1

34 32.6

34 28.2

34 24.0

34 19.9

34 16.0

34 12.3

34 08.8

34 05.5

34 02.5

33 59.7

33 57.2

33 55.0

33 53.0

33 51.3

33 49.9

33 48.9

33 48.1

33 47.6

33 47.4

Latitude 40°.

o /

41 15.1

41 14.9

41 14.5

41 13.7

41 12.5

41 11.1

41 09.4

41 07.3

41 05.0

41 02.4

40 59.5

40 56.5

40 53.1

40 49.5

40 45.7

40 41.8

40 37.6

40 33.3

40 28.9

40 24.3

40 19.7

40 14.9

40 10.1

40 05.3

40 00.5

39 55.6

39 50.8

39 46.0

39 41.4

39 36.8

39 32.3

39 27.9

39 23.7

39 19.6

39 15.7

39 12.0

39 08.5

39 05.3

39 02.2

38 59.4

38 56.9

38 54.7

38 52.8

38 51.1

38 49.7

38 48.6

38 47.8

38 47.4

38 47.2

Latitude 45°.

o /

46 14.9

46 14.8

46 14.3

46 13.5

46 12.3

46 10.9

46 09.2

46 07.2

46 04.8

46 02.2

45 59.3

45 56.2

45 52.9

45 49.2

45 45.5

45 41.5

45 37.4

45 33.0

45 28.5

45 24.0

45 19.4

45 14.6

45 09.9

45 05.0

45 00.2

44 55.3

44 50.5

44 45.7

44 41.1

44 36.4

44 32.0

44 27.6

44 23.4

44 19.3

44 15.4

44 11.7

44 08.3

44 05.0

44 02.0

43 59.2

43 56.7

43 54.5

43 52.5

43 50.8

43 49.5

43 48.4

43 47.6

43 47.1

43 47.0

Latitude 50°.

O 1

51 14.8

51 14.6

51 14.2

51 13.3

51 12.2

51 10.8

51 09.0

51 07.0

51 04.6

51 02.0

50 59.1

50 56.0

50 52.6

50 49.0

50 45.2

50 41.3

50 37.1

50 32.8

50 28.3

50 23.7

50 19.1

50 14.3

50 09.6

50 04.7

49 59.9

49 55.0

49 50.2

49 45.5

49 40.8

49 36.2

.49 31.7

49 27.3

49 23.1

49 19.0

49 15.2

49 11.5

49 08.1

49 04.8

49 01.8

48 59.0

48 56.6

48 54.3

48 52.4

48 50.7

48 49.4

48 48.2

48 47.5

48 47.0

48 46.8

Latitude 55°.

O 1

56 14.6

56 14.4

56 14.0

56 13.2

56 12.0

56 10.6

56 08.8

56 06.8

56 04.4

56 01.8

55 58.9

55 55.8

55 52.3

55 48.8

55 45.0

55 41.0

55 36.8

55 32.5

55 28.0

55 23.4

55 18.8

55 14.0

55 09.2

55 04.4

54 59.5

54 54.7

54 49.9

54 45.1

54 40.4

54 35.8

54 31.4

54 27.0

54 22.8

54 18.8

54 14.9

54 11.2

54 07.9

54 04.5

54 01.5

53 58.8

53 56.4

53 54.1

53 52.1

53 50.5

53 49.1

53 48.0

53 47.2

53 46.8

53 46.7

Latitude 60°.

o /

61 14.5

61 14.3

61 13.8

61 13.0

61 11.9

61 10.4

61 08.6

61 06.6

61 04.2

61 01.6

60 58.7

60 55.5

60 52.1

60 48.5

60 44.7

60 40.7

60 36.5

60 32.1

60 27.6

60 23.0

60 18.4

60 13.6

60 08.8

60 04.0

59 59.1

59 54.3

59 49.6

59 44.8

59 40.1

59 35.4

59 31.0

59 26.7

59 22.5

59 18.4

59 14.6

59 11.0

59 07.6

59 04.3

59 01.3

58 58.6

58 56.1

58 53.9

58 52.0

58 50.3

58 49.0

58 47.9

58 47.1

58 46.7

58 46.6

Correction forl' 

increase ndecination of Polaris.

/

-1.0

-1.0

-1.0

-1.0

-1.0

-0.9

-0.9

-0.9

-0.8

-0.8

-0.8

-0.7

-0.7

-0.6

 0.6

-0.5

-0.5

-0.4

-0.4

-0.3

-0.2

-0.2

-0.1

0.0

0.0

+0.1

+0.1

+0.2

+0.3

+ 0.4

+0.4

+0.5

+0.5

+0.6

+0.6

+0.7

+0.7

+0.8

+0.8

+0.8

+0.9

+0.9

+0.9

+0.9

+1.0

+1.0

+1.0

+1.0

+1.0

Hour

before 

or after 

upper culmination.

ft. m.

000

015

030

045

100

115

130

145

200

215

230

245

300

315

330

345

400

415

430

445

500

515

530

545

600

615

630

645

700

715

730

745

800

815

830

845

900

915

930

945

1000

1015

1030

1045

1100

1115

1130

1145

1200
TABLE 3. Convergence of meridians and arc for each statute mile on the 

[Formula: Convergence in minutes=arc of parallel in minutes X 

[Prepared by E. M. Douglas.]

Latitude.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

. 23

24

25

26

27

28

29

30

31

32

33

34

35

Arc for 

1 mile on ° 

parallel.

0 52.0

0 52.0

0 52.1

0 52.1

0 52.2

0 52.2

0 52.3

0 52.4

0 52.6

0 52.7

0 52.8

0 53.0

0 53.2

0 53.4

0 53.6

0 53.9

0 54.1

0 54.4

0 54. 7

0 55.0

0 55.4

0 55.7

0 56.1

0 56.5

0 56.9

0 57.4

0 57.9

0 58. 4

0 5S.9

0 59.5

1 00.1

1 00.7

1 01.3

1 02.0

1 02.8

1 03.5

Convergence.

1 mile.

0 00

0 00.9

0 01.8

0 02.7

0 03.6

0 04.6

0 05.5

0 06.4

0 07.3

0 08.2

0 09.2

0 10.1

0 11.1

0 12.0

0 13.0

0 13.9

0 14.9

0 15.9

0 16.9

0 17.9

0 18.9

0 20.0

0 21.0

0 22.1

0 23.2

0 24.3

0 25.4

0 26.5

0 27.7

0 28.8

030.0

0 31.2

0 32.5

0 33.8

0 35.1

0 36.4

2 miles.

0 00

0 01.8

0 03.6

0 05.5

0 07. 3

009.1

0 10.9

0 12.8

0 14.6

0 16.5

0 18.3

0 20. 2 

0 22.1

0 24.0

0 25.9

0 27.9

0 29.8

0 31.8

0 33.8

0 35.8

0 37.9

0 40. 0

0 42.0

0 44. 2

0 46.3

0 48.5

050.7

0 53.0

0 55.3

0 57.6

1 00.0

1 02.5

1 05.0

1 07.5

1 10.1

1 12.8

3 miles.

0 00

0 02.7

0 05.5

0 08.2

0 10.9

0 13.7

0 16.4

0 19.2

0 21.9

0 24.7

0 27.5

030.3

0 33. 2

0 36.0

0 38.9

041.5

0 44.8

0 47.7

0 50.7

0 53.7

0 56.8

0 59.9

1 03.1

1 06.2

1 09.5

1 12.8

116.1

1 19.5

1 23.0

1 26.5

1 30.1

1 33.7

1 37.5

1 41.4

1 45.2

1 49.2

4 miles.

0 00

0 03.6

0 07.3

0 10.9

0 14.6

018.2

0 21.9

0 25.6

0 29.2

0 33.0

0 36.7

0 40.5

0 44. 2

0 48.0

0 51.9

0 55.8

0 59.7

1 03.6

1 07.6

1 11.7

1 15.7

1 19.8

1 24.1

1 28.3

1 32.6

1 37.0

1 41.4

1 46.0

1 50.6

1 55.3

2 00.1

2 05.0

2 10.0

2 15.1

' 2 20.3

2 25.6

5 miles.

0 00

0 04.5

0 09.1

0 13.7

0 18.2

0 22.8

0 27.4

0 32.0

0 36.6

. 041.2

0 45.9

0 50.6

0 55.3

1 00.1

1 04.9

1 09. 7

1 14.6

1 19.5

1 24.5

1 29.6

1 34.7

1 30.8

1 45.1

1 50.4

1 55.8

2 01.3

206.8

2 12.5

2 18.3

2 24.1

2 30.1

236.2

242.5

2 48.9

2 55.4

3 02.1

6 miles.

0 00

0 05.4

0 10.9

0 16.4

0 21.8

0 27.3

0 32.8

0 38.3

0 43.9

0 49.5

0 55.0

1 00.7

1 06.3

1 12.1

1 17.8

1 23.7

1 29.5

1 35.4

1 41.4

1 47.5

1 53.6

1 59.8

2 06.1

2 12.5

2 19.0

2 25.5

2 32.2

2 39.0

2 45.9

2 52.9

3 00.1

3 07.5

3 14.9

3 22.7

3 30.4

3 38.4
TABLE 3. Convergence of meridians and arc for each statute mile on the par

[Formula: Convergence in minutes=arc of parallel in minutes X 

[Prepared by E. M. Douglas.]

Latitude.

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

Arc for 

1 mile on 

parallel.

1 04.3

. 1 05. 1

1 06.0

1 06.9

1 07. 9

1 08.9

1 09.9

1 11.0

1 12.2

1 13.5

1 14.7

1 16.2

1 17.6

1 19.1

1 20.8

1 22.6

1 24.4

1 26.3

1 28.3

1 30.5

1 32.9

1 35.4

1 38.0

1 40.8

1 43. 9

1 47.' 1

1 50.6

1 54. 3 

1 58.4

2 02.8

2 07.6

2 12.8

2 18.5

2 24.8

2 31.7

Convergence.

1 mile.

0 37.8

0 39.2

0 40.6

0 42.1

0 43. 6

0 45.2

0 46.8

0 48.5

0 50.2

0 52.0

0 53.8

0 55.7

0 57.7

0 59.8

1 01.9

1 04.1

1 06. 5

1 08.9

1 11.5

1 14.2

1 17.0

1 20.0

1 22.1

1 26.4

1 29.9

1 33.7

1 37.6

1 41.9

1 46.4

1 51.3

1 56.6

2 02.3

2 08.4

2 15.2

2 22.6

2 miles.

1 15.5

1 IS. 3

1 21.2

1 24.2

1 27.2

1 30.3

1. 33. 6

1 36.9

1 40.4

1 43.9

1 47.6

1 51.4

1 55.4 o

1 59.5

2 03.8

2 08.3

2 12.9

2 17.8

2 22.9

2 28.3

2 34.0

2 39.9

2 44.2

2 52.8

2 59.8

3 07.3

3 15.3

3 53.7

3 32.8

3 42.6

3 53.1

4 04.5

4 16.9

4 30.3

4 45.1

3 miles.

1 53. 3

1 57.5

2 01.8

2 06.3

2 10.1

2 15.5

2 20.4

2 25.4

2 30,5

2 35.9

2 41.4

2 47.1

2 53.1

2 59.3

3 05.7

3 12.4

3 19.4

3 26.7

3 34.4

3 42.5

3 50.9

3 59.9

4 06.3

4 19.2

4 29.8

4 41.0

4 52.9

5 05.6

5 19.2

5 33.9

5 49.7

6 06.8

6 25.3

6 45.5

7 07.7

4 miles.

2 31.1

236.7

2 42.4

2 48.4

2 54.4

3 00.7

3 07.2

3 13.8

3 20.7

3 27.8

3 35.2

3 42.8

3 50.8

3 59.0

4 07.6

4 16.6

4 25.9

4 35.7

4 45.9

4 56.6

5 07.9

5 19.8

' 5 28. 4

5 45.6

5 59. 7

6 14.6

6 30. 5

6 47.5

7 05.6

7 25.2

7 46.2

8 09.1

8 33.7

9 00.7

9 30.2

5 miles.

3 08.8

3 15.8

3 23.0

3 30.4

3 38.0

3 45.9

3 53.9

4 02.3

4 10.9

- 4 19.8

' 4 29.0

4 38.6

4 48. 5

4 58.8

5 09.5

5 20.7

5 32.4

5 44.6

5 57.4

6 10.8

6 24.9

6 39.8

6 50.4

7 12.0

7 29.6

7 48. 3

8 OS. 1

8 29.3

8 62.0

9 16.5

9 42.8

10 11.3

10 42. 2

11 15.9

11 52. 8

6 miles.

3 46.6

3 55.0

4 03.6

4 12.5

4 21.6

4 31.0

4 40.7

4 50.7

5 01.1

5 11.7

5 22.8

5 34.3

5 46. 2

5 58. 5

6 11.4

6 24.8

6 38.8

6 53.5

7 08. 8

7 25.0

7 41.9

7 59.7

8 12.5

8 38.4

8 59. 5

9 21.9

9 45.8

10 11.2

10 38. 5

11 07. 8

11 39.4

12 13. 6

12 50.6

13 31.0

14 15.4
TABLE 4. Values in feet of seconds of latitude and 

[Prepared by E. M. Douglas.]

 3

3

8

O.

"5

«

3

g

PM

Meridional

arcs.

2"3

£

ft

"3

CO

1CO

s

ft.

Meridional

arcs.

Minutes of

latitude.

0

5

10

15

20

25

30

35

40

45

50

55

60

Mean value

of 1" of

latitude . .

0

5

10

15

20

25

30

35

40

45

50

55

60

Mean value

of 1" of

latitude . .

Latitude of arc. (Values in feet for sin

0°

101. 45

.45

.45

.45

.45

.45

.45

.44

.44

.44

.44

.44

101. 44

100. 76

15°

98.02

97.98

.94

.90

.86

.82

.79

.75

.71

.66

.62

.58

97. 55

100.83

1°

101.44

.43

.43

.43

.42

.42

.42

.41

.41

.40

.40

.40

101. 39

100.76

16°

97.55

.51

.47

.42

.38

.34

.30

.26

.22

.17

.13

.09

97.05

100.85

2°

101. 39

.38

.38

.38

.37

.37

.36

.35

.34

.34

.33

.32

101.31

100.77

17°

97.05

97.00

96.96

,92

.88

.83

.78 .

.74

.70

.65

.61

.56

96.52

100.86

3°

101. 31

.30

.30

.29

.28

.27

.27

.26

.25

.24

.23

.22

101. 21

100. 77

18°

96.52

.47

.42

.38

.33

.29

.24

.19

.15

.10

.06

.01

95.96

100.87

4°

101. 21

.20

.19

.17

.16

.15

.14

.13

.12

.11

.09

.09

101. 07

100. 77

19°

95.96

.91

.87

.82

.77

.72

.67

.62

.57

.52

o.47

.43

95.37

100.88

5°

101. 07

.06

.04

.03

.01

101. 00

100.98

.97

.96

.95

.93

.92

100.90

100. 77

20°

95.37

.32

.27

.22

.17

.12

. .07

95.01

94.96

.91

.86

.81

94.76

100.89

6°

100.90

.89

.87

.85

.84

.82

.80

.79

.77

.75

.74

.72

100. 70

100.77

21°

94.76

.70

.65

.59

.54

.49

.44

.38

.32

.27

.22

.16

94.11

100.90

7°

100.70

.68

.66

.65

.63

.61

.59

.57

.55

.53

.51

.49

100.47

. 100. 78

22°'

94.11

.05

94.00

93.94

.88

.83

.77

 .71

.66

.61

.55

.49

93.43

100.92

8°

100.4

.4

.4

.4

.3

.3

.3

.3

.3

.2

.2

.2

100.

100. 

23°

93.4

.3

.3

.2

.2

.1

.0

93.0

92.9

.9

.8

.8

92.7

100.9
TABLE 4. Values in feet of seconds of latitude and long

3s

1

"o

1fH

o

P=H

Meridional

arcs.

2"c3

£

A

"o

s

§

o

PL,

Meridional

arcs.

Minutes of

latitude.

0

5

10

15

20

25

30

35

40

45

50

55

60

Mean value

of 1" of

latitude..

0

5

10

15

20

25

30

35

40

45

50

55

60

Mean value

of 1" of

latitude . .

Latitude of arc. (Values in feet for sing

30°

87.93

.86

.79

.72

.64

.57

.49

.41

.34

.27

.19

.11

87.04

101. 03

45°

71.86

.75

.65

.55

.44

.34

.23

.13

71.02

70.91

.80

.70

70.60

101.29

31°

87.04

86.96

.89

.81

.73

.65

.58

.51

.43

.35

.27

.19

86.12

101. 04

46°

70.60

.49

.39

.28

.17

70.06

69.96

.86

.75

.64

.53

..42

69.32

101.31

32°

86.12

86.04

85.96

.89

.81

.73

.65

.57

.49

.41

.33

.25

85.17

101. 05

47°

69.32

.21

.11

69.00

68.89

.78

.67

.56

.45

.34

.23

.12

68. 01

101. 32

33°

85.17

.09

85.01

84.93

.85

.77

.68

.60

.52

.44

.36

.28

84.20

101. 08

48°

68.01

67.90

.79

.68

.57

.46

.35

.24

.13

67.02

66.91

.80

66. 69

101. 34

J34 0

84.20

.11

84.03

83.95

.86

.78

.70

.61

.53

.44

.37

.28

83.20

101. 09

49°

66.69

.57

.46

.35

.24

.13

66.02

65.90

.79

.68

.56

.45

65.34

101. 36

35°

83.20

.11

83.02

82.95

.86

.77

.69

.60

.51

.43

.34

.26

82.17

101.11 

50°

65.34

.23

.12

65.01

64.89

.78

.66

.55

.44

.32

.21

64.09

63.98

101. 38

36°

82.17

.09

82.00

81.91

.82

.74

.65

.56

.48

.39

.30

.21

81. 12

101. 13

51°

63.98

.86

.75

.63

.52

.41

.29

.18

63.06

62.94

.82

.70

62.59

101. 39

37°

81.12

81.03

80.94

.85

.77

.68

.59

.50

.41

.32

.23

.14

80.05

101. 14

52°

62.59

.48

.36

.24

.13

62.01

61.89

.78

.66

.54

.42

.30

61.19

101. 41

38°

80.05

79.96

.87

.78

.68

.59

.50

.41

.32

.23

.13

79.04

78.95

101. 16

53°

61.19

61.07

60.95

.83

.72

.60

.48

.36

.24

.12

60.00

59.88

59.76

101. 43
2103ao

 K)Os£Pn

Meridional

arcs. 21a"3wo 

>3

C3sPH

Meridional

Of/lC

05

10

15

20

25

30

35

40

45

50

55

60

Mean value

of 1" of

latitude.- 05

10

15

20 -

25

30 .

35

40

45

50

55

60

Mean value

of 1" of

latitude. .

63°

50.85

.73

.60

.47

.34

.22

50.09

49.96

.83

.71

.57

.44

49.31

101. 55

75°

26.34

.20

26.06

25.91

.77

.62

.48

.34

.20

25.05

24:91

.76

24.62

101.73

61°

49.31

.18

49.05

48.92

.79

.66

.54

.41

.28

.15

48.02

47.89

47.76

101.56

76°

24.62

.48

.34

.19

24.05

23.90

.76

.62

.47

.33

.18

23.04

22. 89

101. 73

62°°

47.76

.63

' .49

.36

.23

.10

46.97

.84

.71

.57

.44

.31

46.18

, 101.57

77°

22.89

.75

.60

.46

.32

.17

22.03

21.88

.74

.59

.45

.31

21.16

101. 74

63°

46.18

46.05

45.92

.79

.66

.52

.39

.26

45.13

44.99

.86

.72

44.59

101.59

78°

21.16

21.02

20.87

.73

.58

.44

.30

.15

20.00

19.85

.71

.57

19.42

101. 75

64°

44.59

.46

.33

.19

44.06

43.93

.80

.66

.53

.40

.26

43.13

42.99

101.60

79°

19.42

.28

.13

18.98

.84

.69

.55

.40

.26

18.11

17.97

.82

17.68

101. 76

- 65°

42.99

.86

.73

.59

.46

.32

.19

42.05

41.92

.78

.65

.52

41.38.

101.62

80°

17.68

.53

.38

.24

17.09

16.95

.80

.65

.51

.36

.21

16.07

15.92

101. 76

66°

41.38

.25

41.11

40.98

.84

.70

.57

.44

.30

.16

40.03

39.89

39.76

101.63

81°

15.92

. 77

.63

.49

.34

.19

15.05

14.90

.75

.61

.46

.31

14.17

101. 77

67°

39.76

.62

.48

.34

.21

39.07

38.94

.80

.66

.52

.39

.25

38.12

101.64

S2°

14.17

14.02

13.87

.73

.58

.43

.29

13.14

12.99

.85

.70

.55

12.'41

101. 77

68°

38.12

37.98

.84

.70

.57

.43

.29

.15

37.01

36.88

.74

.60

36.46

101.66

83°

12.41

.26

12.11

11.96

.82

.67

.52

.38

.23

11.08

10.94

.79

10.64

101. 78
32 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 5. Offsets, in feet, from the secant to the parallel. 

[Prepared by E. M. Douglas.]

Latitude.

Deyrees.

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

o.

Feet.

1.6

1.6

1.7

1.8

1.8

1.9

2.0

2.1

2.2

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.6

3.7

3.8

4.0

4.1

4.3

4.4

4.6

4.7 '

4.9

5.1

- 5.3

5.5

5.8

6.0

6.3

6.6

6.9

7.1

7.5

7.9

8.3

8.7

9.1

£ mile.

Feet.

0.7

.7

.8

.8

.8

.9

.9

.9

1.0

1.0

1.0

1.1

1.1

1.2

1.2

1.3

1.3

1.4

1.4

1.5

1.5

1.6

1.6

1.7

1.7

1.8

1.8

1.9

2.0

2.1

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

3.0

3.1

3.2

3.4

3.6

3.7

3.9

4.1

1 mile.

Feet.

0.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

- .0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

1£ miles.

Feet.

0.5

.6

.6

.6

.6

.7

.7

.7

.8

.8

.8

.8

.9

.9

.9

1.0

1.0

1.0

1.1

1.1

1.2

1.2

1.3

1.3

1.4

1.4

1.4

1.5

1.6

1.6

1.7

1.7

1.8

1.9

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

 2.8

2.9

3.0

3.2

2 miles.

Feet.

0.9

r.o

1.0

. 1.0

1.1

1.1

1.2

1.2

1.3

1.3

1.4

1.5

1.5

1.6

1.6

1.7

1.7

1.8

1.8

1.9

2.0

2.1

2.2

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

 3.1

3.2

3.3

3.4

3.6

3.8

3.9

4.1

4.3

4.5

4.8

5.0

5.2

5.5

2£ miles.

Feet.

1.2

1.2

1.3

1.3

1.4

1.4

1.5

1.6

1.6

1.7

1.8

1.8

1.9

2.0

2.0

2.1

2.2

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.6

3.7

3.9

4.0

4.2

4.3

4.5

4.7

4.9

5.1

5.'3

5.6

5.9

6.2

6.5

6.8

3 miles.

Feet.

1.2

1.3

1.4

1.4

1.5

1.5

1.6

1.7

1.7

1.8

1.9

1.9

2.0

2.1

2.2

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.6

3.7

3.8

4.1' 4.0

4.3

4.4

4.6

4.8

5.0

5.3

5.5

5.7

6.0

6.3

6.7

7.0

7.3

COMPUTATION OF OFFSETS FROM SECANTS TO PARALLELS.

The formulas for computing geodetic coordinates and azimuths 

may be used to compute the offsets or azimuths for a secant line as 

follows: The distance, s (for metric measures), in the formula will be 

the distance lc or cd, figure 7, to the intersection of the parallel and 

secant from the central meridian. The azimuth of the secant at the 

central meridian c will be 90° or 270°. - The latitude to be used in 

finding the constants A, B, C, etc., may (without appreciable error) 

be taken as that of the parrallel. As the cosine of 90° is 0 the first 

term of the latitude computation will be 0, and us the sine of 90°
GEOGRAPHIC TABLES AND FORMULAS. 33

equals 1, the second term will reduce to $2C. The third and fourth 

terms will in all cases be negligible. Therefore, the seconds of latitude found from the second term when reduced to feet or other unit 

will be the offset eg. The azimuth of the secant where it intersects 

the parallel will be 90° plus or minus s (reduced to seconds of longitude) multiplied by the sine of the latitude, or

log s (in seconds) + log sine <£ = log Aa (in seconds).

The azimuth of the secant at its intersection with the parallel having been found, the offsets for any distance along the secant may be 

found by using values derived from both the first and second terms 

of the formula. These should be added for points to the left of & or 

the right of d and subtracted for points between & and d.

For distances in miles, the computation may be shortened'by using 

Table 3. The azimuth of the secant where it intersects the parallel

is 90° plus or minus the convergence for the distance 5c from the 

central meridian.

FIG. 7. Offsets from secant to parallel.

The angle ce/between two adjoining secants of the same length is 

the convergence for the total length of the secant at the given latitude; 

this angle may be found from Table 3. The azimuth of a secant line 

from either end is 90° plus or minus the convergence given in the 

table for a distance equal to half of the length of the secant.

TANGENTS TO A PARALLEL OFFSETS AND AZIMUTHS.

The Initial Azimuth of tangent is 90° or 270°. The change in azimuth in seconds for any distance from the initial point is = difference 

of longitude in seconds X sine of latitude (approximately, the error 

being less than one-tenth second for a distance of 60 miles).

The offset in seconds for any distance in meters from initial point 

is = square of distance X C, C being the factor C in Table 28. The 

resulting seconds may be changed to feet by using values given in 

Table 4 for 1 second of latitude.

41623° 16 3
34 GEOGRAPHIC TABLES AND FORMULAS. 

b

~

c-

-

TV

g 2.908

CO

>0 

N

e

2.911

\

'

r

0) 

N

f

Z.9J5

00 

CO 

">

h.

8.723

z

8-734

y

6.745 m,

^ k 2.919 j 8.75S I

.006" 

' 40°15'

.006"

' 10'

*

.006" 

' 05'

 °06 " , 

40QO

8O°15' 10' 07*72' 05' 90°00'

FIG. 8. Construction of polyconic projection. 15'of latitude and longitude; scale 1:48000. Construction lines (to be drawn in pencil) dotted; final projection lines full.

EXAMPLE OF USE OP PROJECTION TABLES.

Let it be required to construct a projection for the area between parallels of 40° 0(K 

arid 40° 15' and meridians 90° 00/ and 90° 15' on a scale of 1:48000 (4,000 feet=l inch). 

For this scale it is customary to show meridians or parallels at intervals of 5 minutes, 

though any other desired interval may be adopted.

Through the center of the paper (see diagram, fig. 8) draw two fine pencil lines 

a-b and c-d exactly perpendicular to each other. The vertical line will be the meridian of 90° 07' 30" and the intersection of the horizontal line with the vertical line 

will be a point on the parallel of 40° 07' 30". From the column headed '' Meridional 

distance," Table 10, page 81, opposite 40° in column "Latitude of parallel," take
GEOGRAPHIC TABLES AND FORMULAS. 35

the value of a latitude interval of 5', which is 7.588 inches; lay off half of this interval 

or 3.794 inches, on the central meridian above and below the horizontal line; these 

distances will give points e and/, on the parallels of 40° 10' and 40° 05/, respectively. 

The distance, 7.588 inches, laid off above and below the latter points will give points 

g and h for latitudes 40° 15' and 40° 00'. Through each of these points draw a line 

parallel to the horizontal line and perpendicular to the vertical line first drawn.

In a similar manner lay off points on the horizontal lines through e, f, g, h, by measuring from the central meridian east and west distances obtained from columns headed 

"Abscissas of developed parallel" in Table 10, page 81, for the appropriate latitudes 

and for the longitude intervals of 2y and 7$'. Thus, for 40?, the tabular value for 2$' 

is 2.919 inches, for 5' it is 5.837 inches, and for 7J' it is 8.755 inches, which fix the 

points i, j, k, and 1. In order to find corner points of the 5-minute area take from the 

columns headed "Ordinatesof developed parallel" in Table 10, on .the same page, 

opposite the latitude, the distances for the "Longitude intervals" 2$' and 7$' (the 

value of 2y for the 1:48000 scale is inappreciable, being less than 0.001 inch); lay 

these distances off perpendicularly northward from the horizontal lines, giving points 

x, y, z, etc., the required corners, and through these points draw curves of the parallel 

concave toward the north and meridional lines joining corresponding points as x, y, z

on each parallel. After testing the accuracy of the plotting by comparing the length 

of the diagonals/ i=f l, h m=h n, etc., the projection may be inked in.

In a similar manner projections may be constructed for other scales or areas. Table 

8, for the scale of 1:63360 (1 mile to 1 inch), may be used for any even fraction or multiple 

of a mile. The distance between parallels being found from column "Meridional 

distance"; distances not given may be found by simple proportion except for "Ordinates of developed parallel," which increase as the square of the distance from the 

central meridian, or actually as the vers sin of angle of convergence. For scales of 

any number of thousands of feet to 1 inch use suitable fractions of the distance given 

for scale 1:12000 (1,000 feet to 1 inch) in Table 12.

For maps of large areas Table 6 gives the actual or full scale distances in meters. 

These may be divided by the proper scale ratio and the distances so found platted 

with a metric scale or reduced to feet by the table on page 291. The first part of this 

table gives the actual lengths of arcs of 1° along the meridian for each degree of latitude as its middle point (see p. 36), the second part gives the lengths of arcs of the 

parallels for 1° of longitude for each degree of latitude (see p. 37), and the third 

part gives lengths of the arcs of the parallel for V of longitude. The remainder of 

Table 6 entitled " Coordinates of curvature " (see pp. 39-47) is for use in making polyconic projections; these are rectangular coordinates of the curves of parallels. The 

X values are the distances measured east and west from the central meridian, each 

to be taken for the proper latitude, and the corresponding Y values give the offsets 

at right angles to the horizontal lines to fix intersection points of the curved parallels 

with the other meridians. For projections of large extent the meridians differ sensibly from straight lines and they as well as the parallels must be drawn as curves.
36 GEOGEAPHIC TABLES AFD FOEMULAS.

TABLE 6. For projection of maps of large areas.

[The ratio of the yard to the meter as stated by Clarke, namely, 1 meter = 1.093623 yards = 39.370432 

inches, is that used in the table.]

LENGTHS OF DEGREES OP THE MERIDIAN.

Latitude.

O

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

' 3837

39

40

41

42

43

44

45

Meters, a

110, 567. 2

110, 567. 6

110, 568. 6

110, 570. 3

110, 572. 7

110, 575. 8

110, 579. 5

110, 583. 9

110, 589. 0

110, 594. 7

110, 601. 1

110, 608. 1

110, 615. 8

110, 624. 1

110, 633. 0

110, 642. 5

110, 652. 6

110, 663. 3

110, 674. 5

110, 686. 3

110, 698. 7

110,711.6

110, 725. 0

110, 738. 8

110, 753. 2

110, 768. 0

110, 783. 3

110,799.0

110, 815. 1

110, 831. 6

110, 848. 5

110, 865. 7

110, 883. 2

110, 901. 1

110, 919. 2

110, 937. 6

110, 956. 2

110, 975. 1

110, 994. 1

111, 013. 3

111, 032. 7

111, 052. 2

111, 071. 7

111, 091. 4

111, 111. 1

111, 130. 9

Statute 

miles.

68. 704

68. 704

68. 705

68. 706

68. 708

68. 710

, 68.712

68. 715

68. 718

68. 721

68. 725

68. 730

68. 734

68. 739

68. 744

68. 751

68.757

68. 764

68. 771

68. 778

68. 786

68. 794

68. 802

68. 811

68. 820

68. 829

68. 839

68. 848

68. 858

68. 869

68. 879

68. 890

68. 901

68. 912

68. 923

68. 935

68. 946

68. 958

68. 969

68. 981

68. 993

69. 006

69. 018

69. 030

69. 042

69. 054

Latitude.

O

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

Meters, a

111, 130. 9

111, 150. 6

111, 170. 4

111, 190. 1

111, 209. 7

111, 229. 3

111, 248. 7

111,268.0

111, 287. 1

111,306.0

111, 324. 8

111, 343. 3

111, 361. 5

111, 379. 5

111,397.2

111, 414. 5

111,431.5

111, 448. 2

111, 464. 4

111, 480. 3

111, 495. 7

111, 510. 7

111,525.3

111, 539. 3

111, 552. 9

111, 565. 9

111, 578. 4

111,590.4

111,601.8

111,612.7

111, 622. 9

111, 632. 6

111,641.6

111, 650. 0

111, 657. 8

111, 664. 9

111, 671. 4

111, 677. 2

111, 682. 4

111, 686. 9

111, 690. 7

111, 693. 8

111, 696. 2

111, 697. 9

111, 699. 0

111, 699. 3

Statute 

miles.

69. 054

69. 066

69. 079

69. 091

69. 103

69. 115

69. 127

69.139

69. 151

69. 163

69. 175

69. 186

69. 197

69. 209

69. 220

69. 230

69. 241

69. 251

69. 261

69. 271

69. 281

69. 290

69. 299

69. 308

69. 316

69. 324

69. 332

69.340

69. 347

69. 354

69. 360

69. 366

69. 372

69. 377

69. 382

69. 386

69. 390

69. 394

69. 397

69. 400

69. 402

69. 404

69. 405

69. 407

69. 407

69. 407

a These quantities express the number of meters and statute miles contained within an arc of which 

the degree of latitude named is the middle; thus, the quantity 111,032.7, opposite latitude 40°, is the 

number of meters between latitude 39° 30' and latitude 40° 30'.
GEOGRAPHIC TABLES AND FORMULAS. 37

TABLE 6. For projection of maps of large areas Continued.

[Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Report for 1884.]

LENGTHS OP DEGREES OF THE PARALLEL.

Latitude.

0

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

36

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

Meters.

111,321 !

111, 304

111, 253

111, 169

111,051

110, 900

110, 715

110, 497

HO, 245

109, 959

109,641

109, 289

108, 904

108, 486

108, 036

107, 553

107, 036

106, 487

105, 906

105, 294

104, 649

103, 972

103, 264

102, 524

101,754

100, 952

100, 119

99, 257

98, 364

97, 441

96, 488

95, 506

94, 495

93, 455

92, 387

91, 290

90, 166

89, 014

87, 835

86, 629

85, 396

84, 137

82, 853

81,543

80, 208

78, 849

Statute 

miles.

69. 172

69. 162

69. 130

69. 078

69. 005

68. 911

68. 795

68. 660

68. 504

68. 326

68. 129

67.910

67. 670

67. 410

67. 131

66. 830

66. 510

66. 169

65. 808

65. 427

65. 026

64. 606

64. 166

63. 706

63. 228

62. 729

62. 212

61. 676

61. 122

60. 548

59. 956

59. 345

58. 716

58. 071

57. 407

56. 725

56. 027

55. 311

54. 579

53. 829

53. 063

52. 281

51. 483

50. 669

49. 840

48. 995

Latitude.

o 

45

46

47

48

49

50

51

52

53

54

55 '

56

57

58

59

60

61

62

63

64.

65

66

67

68

69

70

7172 '

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

Meters.

78, 849

77, 466

76, 058

74, 628

73, 174

71, 698

70, 200

68, 680

67, 140

65, 578

63, 996

62, 395

60, 774

59, 135

57, 478

55, 802

54,110

52, 400

50, 675

48, 934

47, 177

45, 407

43, 622

41, 823

40, 012

38, 188

36, 353

34, 506

32, 648

30, 781

28, 903

27, 017

25, 123

23, 220

21, 311

19, 394

17,472

15, 545

13, 612

11, 675

9,735

7,792

5,846

3,898

1,949

0

Statute 

miles.

48. 995

48. 136

47. 261

46. 372

45. 469

44. 552

43. 621

42. 676

41.719

40. 749

39. 766

38. 771

37. 764

36. 745

35. 716

34. 674

33. 623

32. 560

31. 488

30. 406

29. 315

28. 215

27. 106

25. 988

24. 862

23. 729

22. 589

21. 441

20. 287

19. 127

17. 960

16. 788

15. 611

14. 428

13. 242

12. 051

10. 857

9. 659

8.458

7.255

6.049

4.842

3.632

2.422

1.211

0.000
38 GEOGEAPHIC TABLES AND FORMULAS.

TABLE 6. For projection of maps of large areas Continued.

[Extracted from Appendix No. 6, U. S. Coast and Geodetic Survey Report for 1884.]

ARCS OF THE PARALLEL IN METERS.

Latitude.

o /

24 00

10

20

30

40

50

25 00

10

20

30

40

50

26 00

10

20

30

40

50

27 00

10

20

30

40

50

28 00

10

20

30

40

50

29 00

10

20

30

40

50

30 00

10

20

30

40

50

31 00

10

20

30

40

50

32 00

10

20

30

40

50

Value of 1'..

1695. 9

1693. 7

1691.5

1689.3

1687. 0

1684. 8

1682. 5

1680. 3

1678. 0

1675. 7

1673. 3

1671. 0

1668. 7

1666. 3

1663. 9

1661. 5

1659. 1

1656. 7

1654. 3

1651. 8

1649. 4

1646. 9

1644. 4

1641. 9

1639. 4

1636. 9

1634. 3

1631. 8

1629. 2

1626. 6

1624. 0

1621.4

1618.8

1616. 1

1613.5

1610.8

1608. 1

1605.4

1602.7

1600. 0

1597. 3

1594.5

1591. 8

1589. 0

1586. 2

1583. 4

1580. 6

1577. 8

1574.9

1572. 1

1569. 2

1566. 3

1563. 4

1560. 5

Latitude.

o /

33 00

10

20

30

40

50

34 00

10

20

30

40

50

35 00

10

20

30

40

50

36 00

10

20

30

40

50

37 00

10

20

30

40

50

38 00

10

20

30

40

50

39 00

10

20

30

40

50

40 00

10

20

30

40

50

41 00

10

20

30

40

50

Value of 1'.

1557. 6

1554. 7

1551. 7

1548. 7

1545. 8

1542. 8

1539. 8

1536. 8

1533. 7

1530. 7

1527. 6

1524. 6 

1521. 5

1518. 4

1515. 3

1512. 2

1509. 1

1505. 9

1502. 8

1499. 6

1496.4

1493. 2

1490. 0

1486. 8

1483. 6

1480. 3

1477. 1

1473. 8

1470. 5

1467. 2

1463. 9

1460.6

1457.3

1453. 9

1450.6

1447.2

1443. 8

1440. 4

1437.0

1433. 6

1430. 2

1426. 7

1423. 3

1.419.8

1416.3

1412. 8"

1409. 3

1405. 8

1402. 3

1398. 8

1395. 2

1391.6

1388.1

1384. 5

Latitude.

o /

42 00

10

20

30

40

50

43 00

10

20

30

40

50

44 00

10

20

30

40

50

45 00

10

20

30

40

50

46 00

10

20

30

40

50

47 00

10

20

30

40

50

48 00

10

20

30

40

50

49 00

10

20

30

40

50

50 00

10

20

30

40

50

Value of 1'.

1380. 9

1377. 3

1373. 7

1370.0

1366. 4

1362. 7

1359. 1

1355. 4

1351. 7

1348. 0

1344. 3

1340. 5

1336. 8

1333. 1

1329. 3

1325. 5

1321.7

1318.0

1314. 2

1310. 3

1306. 5

1302. 7

1298. 8

1295. 0

1291.0

1287. 2

1283. 3

1279. 4

1275. 5

1271.6

1267. 6

1263. 7

1259. 7

1255. 8

1251.8

1247. 8

1243. 8

1239.8

1235. 8

1231. 7

1.227. 7

1223. 6

1219. 6

1215. 5

1211.4

1207.3

1203. 2

1199.1

1.195. 0

. 1190.8

1186. 7

1182.5

1178.4

1174. 2
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 6. For projections of maps of large areas Continued. 

COORDINATES OF CURVATURE.

Natural scale. Values of X and Y in meters.

Latitude 24°.

Longitude.

o / 

1 00

2 00

3 00

4 00

6 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

101,753

203, 500

. 305,237

406, 959

508, 660

610, 336

711,981

813, 590

915,159

1, 016, 681

1; 118, 152

1,219,566

1,320,919

1,422,205

1,523,420

1,624,558

1,725,614

1, 826, 583

1, 927, 460

2, 028, 240

2, 128, 918

2,229,488

2,329,946

2,430,287

2,530,505

2,630,596

2,730,554

2, 830, 374

2,930,052

3,029,582

Y

361

1,445

3,250

6,778

9,028

13, 001

17,695

23, 109

29,245

36, 102

43, 679

51,977

60,994

70, 731

81,186

92, 360

104, 251

116,859

130, 184

144,225

158, 981

174, 451

190, 634

207, 530

225, 138

243,458

262, 487

282, 225

302, 671

323, 825

Latitude 25°.

Longi- 

' tude.

o / 

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

.14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

100, 951

201, 896

302, 831

403, 749

504, 645

605, 514

706, 349

807, 146

907, 899

1,008,603

1,109,252

1,209,841

1,310,364

1,410,815

1,511,190

1,611,483

1,711,688

1,811,800

1, 911, 813

2,011,722

2, 111, 522

2,211,207

2, 310, 771

2,410,210

2,509,518

2, 608, 689

2, 707, 718

2, 806, 600

2, 905, 329

3,003,900

Y

372

1,489

3,351

5,957

9,307

13, 401

18, 239

23, 821

30, 146

37,215

45, 026

53, 578

62,873

72,909

83,685

95,202

107, 458

120, 453

134,186

148,656

163, 862

179,805

196,482

213,894

232,038

250, 914

270, 521

290,859

311,925

333, 718

Latitude 26°.

Longitude.

o / 

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

100, 118

200, 231

300, 332

400,416

500,476

600,506

700, 501

800, 456

900, 364

1,000,218

1,100,015

1, 199, 747

1,299,409

1,398,994

1,498,498

1,597,914

1,697,237

1, 796, 460

1,895,578

1,994,585

2, 093, 475

2, 192, 243

2, 290, 882

2, 389, 387

2, 487, 753

2, 585, 973

2,684,042

2,781,953

2,879,702

2, 977, 281

' Y

383

1,532

.3,447

6,128

 9, 574

13, 786

18, 763

24, 505

31,011

38,282

46, 316

55, 114

64, 675

74,998

86,082

97,928

110,534

123, 899

138,023

152, 905

168, 544

184, 939

202, 089

219, 993

238, 650

258,061

278, 222

299, 132

320, 788

343, 197
40 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 6. For projections of maps of large areas Continued. 

COORDINATES OF CURVATURE.

Natural scale. Values of X and Y in meters.

Latitude 27°.

Longitude.

0 /

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

80 00

X

99,256

198,505

297, 742

396, 960

496, 154

595, 316

694,440

793, 522

892,554

991,529

1,090,442

1, 189, 287

1,288,057

1, 386, 746

1,485,348

1, 583, 857

1, 682, 267

1,780,570

1, 878, 762

1, 976, 836

2, 074, 786

2, 172, «06

2, 270, 289

2, 367, 830

2, 465, 222

2, 562, 459

2, 659, 535

2, 756, 445

2, 853, 181

2,949,739

Y

393

1,573

3,539

6,291

9,829

14,154

19,264

25, 159

31,839

39, 303

47, 551

56, 583

66,398

76, 995

88, 374

100, 534

113, 474

127, 193

141,690

156, 966

173,018

189,845

207, 447

225, 823

244, 970

264,889

285, 577

307, 035

329, 259

352,249

Latitude 28°.

Longitude.

O 1

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

98,363

196,719

295, 062

393, 385

49] , 682

589, 945

688, 168

786, 347

884,472

982,537

1,080,537

1, 1 78, 464

1, 276, 312

1,374,075

1,471,745

1,569,315

1,666,781

1, 764, 135

1,861,371

1,958,481

2, 055, 460

2, 152, 302

2, 248, 998

2, 345, 544

2,' 441, 932

2, 538, 156

2,634,210

2, 730, 087

2,825,779

2,921,284

Y

403

1,612

3,627

6,447

10,073

14, 505

19, 741

25, 782

32, 827

40, 276

48, 728

57, 983

68,040

78, 899

90, 558

103,017

116,2/5

130, 331

145, 185

160, 835

177. 280

194,518

212, 550

231, 374

250, 988

271,391

292, &82

314, 559

337, 321

360, 866

Latitude 29°.

Longitude.

o / 

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00 ,

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

97,439

194, 872

292, 291

389, 689

487,059

584, 394

681,687

778, 931

876, 120

973,246

1,070,302

1,167,282

1,264,178

1,360,983

1,457,691

1,554,295

1, 650, 787

1,747,161

1,843,410

1,939,527

2, 035, 505

2, 131, 338

2, 2i7, 020

2,322,539

2, 417, 893

2,513,074

2, 608, 075

2, 702, 890

2,797,511

2,891,931

Y

412

1,649

3,710

6,595

. 10,305

14,838

. 20.194

26,374

33, 376

41, 199

49, 845

59,313

69, 601

80,706

92, 631

105, 375

118, 935

133, 311

148,602

164,506

181,324

198, 953

217, 392

236, 640

256, 695

277,558

299, 224

321, 694

344, 964

369, 036
GEOGRAPHIC TABLES AND FORMULAS. 41

TABLE 6. For projections of maps of large areas Continued. 

COORDINATES OF CURVATURE.

Natural scale. Values of X and Y in meters.

Latitude 30°.

Longitude.

o / 

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

31 00

32 00

13 00

14 00

15 00

1C 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

. 28 00

29 00

30 00

X

96, 487

192, 967

289, 432

385,875

482,288

578, 665

674, 998

771, 279

867,502

963, 658

1,059,741

3,155,744

1,251,658

1,347,477

1,443,193

1,538,800

3,634,290

1,729,654

1,824,887

1,919,982

2,014,930

2, 109, 725

2, 204, 359

2, 298, 825

2,393,116

2, 487, 224

2, 581, 144

2,674,867

2, 768, 385

2,861,694

Y

421

1,684

3,789

6,735

10, 523

15,153

20, 623

26,934

34,084

42, 074

50,903

60, 570

71,074

82,415

94, 591

107, 603

321,449

136, 127

151,637

167,977

185, 147

203, 143

221, 966

243,616

262,089

283, 383

305, 498

328, 432

352, 383

376, 749

Latitude 31°.

Longitude.

0 /

1 00

2 00

3 00

4 00

5 00

'6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

39 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

95, 505

191,002

286,484

381, 943

477, 371

572, 760

668, 103

763,392

858, 619

953,777

1,048,858

3,143,854

3,238,758

1,333,561

1,428,257

3,522,837

1, 617, 294

1,713,621

3,805,810

1,899,852

1, 993, 740

2,087,468

2,181,027

2, 274, 411

2, 367, 610

2,460,638

2, 553, 427

2, 646, 029

2, 738, 418

2, 830, 585

Y

429

3,717

3,863

6,867

10, 729

15, 450

.21,027

27, 461

34, 751

42,897

51,898

61, 753

72,462

84, 024

96, 437

309, 701

123, 815

138, 777

154, 586

171,241

188, 741

207, 085'

226, 270

246, 295

267,159

288, 860

313,396

334, 765

358, 966

383, 997

Latitude 32°.

Longitude.

o / 

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

94,494

388,980

283,449

377,894

472, 307

566, 680

663,004

755, 272

849, 475

943,605

1,037,655

1,131,616

1,225,480

1,319,239

1,412,885

1,506,411

1,599,808

1, 693, 067

1, 786, 382

3,879,144

1,971,946

2,064,579

2, 157, 035

2, 249, 305

2, 341, 385

2,433,264

2,524,935

2, 616, 390

2, 707, 621

2, 798, 621

Y

437

3 , 748

3,933

6,991 .

10,922

15, 727

21, 404

27,954

35, 375

43, 667

52, 821)

62, 861

73, 763.

85, 529

98, 164

311,664

126, 029

141,256

357, 346

174,296

192,305

210, 772

230, 295

250, 672

271, 901

293, 981

316, 910

340, 080

365, 307

390, 770
42 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 6. For projections of maps of large areas Continued. 

COORDINATES OF CURVATURE.

Natural scale. Values of X and Y in meters.

^

Latitude 33°.

Longitude.

o / 

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30' 00

X

93, 454

186,899

280, 328

373,731

467, 100

560, 428

653,704

746, 922

840,072

933, 146

1,026,136

1,119,033

1,211,829

1, 304, 515

1,397,083

1,489,526

1,581,834

1,673,998

1, 766, Oil

1,857,866

1,949,553

2,041,062

2, 132, 387

2,223,521

2,314,453

2,405,175

2, 495, 680

2, 585, 961

2, 676, 007

2, 765, 812

Y

444

1,777

3,997

,7, 106

11, 102

15, 986

21,757

28, 414

35,957

44,385

53,697

63, 893

74,971

86, 931

99, 771

113,491

128,089

143, 564

159,914

177, 138

195,234

214, 201

234,037

254, 740

276; 309

298, 741

322,034

346, 187

371, 197

397,061

Latitude 34°.

Longitude.

o / 

1 00

2 00

3 00

4 00

5 00

-6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

 22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

92,385

184,762

277, 121

360,454

461,751

554,004

646, 205

738,344

830, 413

922,403

1, 014, 305

1,106,110

1,197,809

1,289,395

1,380,858

1,472,190

1,563,381

1,654,423

1,745,308

1, 836, 026

1, 926, 569

2,016,929

2, 107, 097

2, 197, 065

2,286,823

2, 376, 363

2, 465, 677

2,554,756

2, 643, 591

2, 732, 175

Y

451

1,803

4,057

7,212

11,268

16,225

22,082

28,839

36, 494

45,048

54,499

64,846

76, 089

88,227

101,258

115, 180

129, 993

145, 696

162, 287

179, 763

198, 124

217, 368

237, 493

. 258, 497

230,378 .

303, 134

326, 763

351, 262

376, 629

402, 863

Latitude 35°.

Longitude.

o / 

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 OC

30 00

X

91,289

182,568

273, 830

365, 064

456,261

547,412

638,509

729,542

820, 501

911,379

1,002,165

1,092,850

1,183,426

1,273,884

1,364,214

1, 454, 407

1,544,454

1,634,347

1,724,076

1,813,632

1,903,006

1,992,190

2, 081, 174

2,169,949

2,258,507

2, 346, 838

2, 434, 934

2,522,787

2, 610, 386

2, 697, 724

Y

457

1,828

4,112

7,310

11,421

16, 445

22,381

29,229

36, 987

45, 656

55, 234

65,721

7.7, 115

89,415

102, 619

116, 728

131,738

147, 650

164, 460 -

182, 168

200, 772

220, 268

240, 657

261, 936

284, 102

307, 154

331,089

355, 905

381,598

408,168
GEOGRAPHIC TABLES AND FORMULAS. 43

TABLE 6. For projections of maps of large areas Continued. 

COORDINATES OF CURVATURE.

Natural scale. Values of X and Y meters.

Latitude 36°.

Longitude.

o / 

1 00

2 00

3 00

4 00

6 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

1C 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

90, 164

180, 319

270,455

360, 562

450, 631

540, 653

630, 618

720, 517

810,340

900,078

989, 720

1, 079, 259

1,168,684

1,257,987

1, 347, 156

1,436,184

1,525,061

1, 613, 777

1, 702, 324

1, 790, 691

1,878,870

1,966,851

2,054,625

2,142,183

2, 229, 516

2, 316, 613

2,403,467

2,490,068

2, 676, 407

2, 662, 475

Y

462

1,850

4, 162

7,399

11, 560

16, 645

22,652

29, 583

37, 435

46,209

55, 903

06, 515

78,046

90,494

103, 856

118, 133

133, 323

149,423

166, 433

184,350

203, 173

222, 899

243, 527

265,055

287, 479

310, 798

335, 009

360, 111

386, 099

412, 971

Latitude 37°.

Longitude.

O 1

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00'

29 00

30 00

X

89, 012

178, 015

266, 997

355, 951

444,865

533, 730

622, 536

711,273

799,932

888,503

976, 975

1, 065, 340

1,153,587

1,241,707

1, 329, 690

1,417,526

1,505,206

1, 592, 721

1,680,059

1, 767, 211

1, 854, 169

1,940,922

2, 027, 462

2,113,777

2, 199, 860

2,285,699

2,371,287

2, 456, 612

2,541,667

2,626,441

Y

467

1,870

4,207

7,479

11, 685

16, 824

22,896

29,901

37,838

46,706

56, 503

67,229

78,882

91,462

104, 967

119, 395

134,745

151,015

168, 203

186, 307

205, 326

225, 258

246, 099

267, 849

290, 503

314,061

338, 519

363, 874

390, 125

417,267

Latitude 38°.

Longitude.

o / 

1 00

2 00

3 00'

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

87, 833

175, 656

263,458

351,230

438, 962

526, 643

614,263

701,812

789, 280

876,657

963, 933

1,051,098

1,138,141

1,225,053

1,311,823

1,398,441

1,484,899

1,571,185

1,657,289

1,743,202

1,828,914

1,914,415

1,999,694

2,084,743

2, 169, 551

2,254,109

2,338,406

2,422,433

2, 506, 181

2, 589, 639

Y

472

1,888

4,247

7,549

11,795

16, 983

23,112

30,183

38,195

47,145

57,034

67,860

79, 622

92, 319

105,949

120,511

136,002

152, 421

169,767

188,037

207,229

227, 341

248, 370

270, 315

293, 172

316, 939

341,613

367, 192

393, 672

421,050
44 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 6. For projections of maps of large areas Continued. 

COORDINATES OF CURVATURE.

Natural scale. Values of X and Y in meters.

Latitude 39°.

Longitude.

o /

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

10 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

86. 627

173, 213

259, 8b9

346, 403

432,925

519,396

605, 803

692, 138

778, 388

864, 545

950, 598

1,036,536

1,122,349

1,208,027

1,293,559

1,378,934

1,464,144

1,549,177

1,634,023

1, 718, 671

1, 803, 113

1, 887, 337

1,971,333

2, 055, 091

2, 138, 602

2,221,854

2,304,838

2, 387, 545

2,469,963

2, 552, 084

Y

476

1,903

4, 281

7,611

11,891

17, 121

23, 300

30, 428

38,504

47,527

, 57,496

68, 409

80,266

93,064

106, 802

121,479

137, 093

153, 642

171, 124

189, 537

208, 878

229, 146

250, 337

272, 450

295, 481

319,429

344, 289

370, 059

396, 736

424, 317

Latitude 40°.

Longitude.

0 /

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

85,394

170, 778

256, 140

341, 470

426, 757

511,990

597, 158

682, 252

767,260

852, 171

936, 975

1,021,661

1,106,218

1, 190, 636

1,274,904

1, 359, 012

1, 442, 949

1, 526, 704

1,610,267

1,693,628

1,776,775

1,859,698

1,942,387

2, 024, 833

2, 107, 023

2, 188, 948

2, 270, 597

2,351,961

2, 433, 029

2, 513, 790

Y

479

1,916

4,311

7,663

11,972

17,238

23,460

30,637

38, 768

47,852

67,888

68,875

80,811

93, 695

107,525

122, 300

138, 017

154, 675

172, 272

190, 805

210, 272

230, 671

251,998

274, 252

297, 430

321,528

346,543

372,473

399, 314

427,063

Latitude 41°.

Longitude.

O 1

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00'

29 00

30 00

; x

84,136

168, 260

252,363

336, 432

420,457

504, 428

588, 332

672, 159

755,897

839, 537

923, 067

1,006,475

1, 089, 752

1, 172, 886

1,255,866

1,338,681

1,421,321

1, 503, 775

1,586,031

1, 668, 079

1,749,909

1,831,509

1, 912.-869

1,993,978

2, 074, 826

2, 155, 402

2,235,695

2,315,695

2, 395, 392

2,474,774

Y

482

1,927

4,335

7,706

12, 039

17, 335

23, 591

30, 807

38, 983

48,118

58, 209

69, 256

81,258

94,212

108,117

122, 971

138, 773

155, 520

173, 210

191,841

211, 409

231, 914

253, 352

275,719

299, 014

323,233

348, 374

374, 432

401, 404

429,287
GEOGRAPHIC TABLES AND FORMULAS. 45

TABLE 6. For projections of maps of large areas Continued.

COORDINATES OF CURVATURE.

Natural scale. Values of X and Y in meters.

Latitude 42°.

Longitude.

0 /

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

82,851

165,691

248, 508

331,292

414,030

496,712

579,325

661,861

744,305

826,648

908, 879

990, 985

1,072,956

1, 154, 781

1,236,449

1,317,948

1,399,267

1, 480, 395

1,561,321

1,642,035

1, 722, 524

1,802,779

1,882,.788

1,962,540

2, 042, 024

2, 121, 230

2,200,146

2, 278, 762

2,357,067

2, 435, 052

Y

484

1,935

4,354

7,739

12, 092

17, 410

23, 693

30, 941

39, 152

48,325

58,459

69, 553

81, 605

94, 614

108,577

123,493

139, 360

156, 175

173, 937

192, 642

212, 289

232,874

254,396

276,850

300, 234

324,544

349, 778

375, 932

403, 002

430, 985

Latitude 43°.

Longitude.

0 /

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

81,541

163,071

244,578

326, 050

407, 476

488, 844

570, 143

651,361

732, 486

813,608

894,415

975, 195

1,055,837

1, 136, 329

1, 216, 661

1,296,820

1,376,795

1,456,575

1,536,148

1,615,505

1,694,632

1,773,519

1,852,155

1,930,528

2,008,628'

2, 086, 443

2, 163, 963

2,241,176

2,318,071

2, 394, 639

Y

485

1,941

4,367

7,763

12, 129

17, 464

23,766

31,036

39,272

48,474

58,639

69, 766

81,854

94,901

108, 905

123,864

139, 777

156, 640

174,451

193,209

212,909

233, 551

255,129

277, 642

301,087

325,459

350, 750

376, 974

404,109

432, 157

Latitude 44°.

Longitude.

O 1

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00.

9 00

10 00

11 00

12 00

13 00

14 00

16 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

80,206

160, 401

240, 572

320, 708

400, 797

480, 827

560, 786

640, 662

720,445

800,122

879, 681

959, 110

1,038,399

1,117,535

1, 196, 507

1,275,303

1, 353, 911

1, 432, 320

1,510,519

1,588,496

1,666,240

1,743,738

1,820,930

1,897,955

1,974,650

2, 051, 055

2,127,159

2, 202, 950

2,278,417

2, 353, 550

Y

486

1,945

4,375

7,778

12, 152

17, 496

23,811

31,094

39, 345

48,563

58, 746

69,893

82,002

95,072

109,100

124,084

140,023

156, 913

174, 753

193,540

213, 270

233, 942

255,552

278, 096

301,572

325, 977

351, 306

377, 555

404, 722

432,801
46 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 6. For projections of maps of large areas Continued. 

COORDINATES OF CURVATURE.

Natural scale. Values of X and Y in meters.

Latitude 45°.

Longitude.

o / 

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

. 24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

78,847

157, 682

236,493

315, 269

393, 996

472, 663

551,258

629, 769

708,184

786,492

864, 679

942, 735

1; 020, 647

1,098,404

1,175,994

1, 253, 404

1, 330, 624

1,407,640

1,484,443

1,561,019

1, 637, 358

1,713,447

1,789,276

1,864,831

1, 940, 103

2,015,079

2, 089, 749

2, 164, 100

2, 238, 121

2, 311, 802

Y

486

1,946

4,378

7,783

12, 160

17,508

23,826

31,114

39, 370

48,594

58, 782

69, 936

82,051

95, 127

109, 162

124, 153

140, 099

156,996

174, 842

193, 635

213, 371

234, 048

255, 663

278,211

301,690

326,097

351,427

377, 676

404,841

432, 918

Latitude 46°.

Longitude:

0 '

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

15 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

77, 464

154, 915

232, 342

309,732

387,074

464,354

541, 562

618, 684

695, 708

772,623

849,416

926, 075

1,002,588

1, 078, 943

1,155,128

1,231,131

1,306,940

1,382,543

1,457,928

1,533,083

1,607,997

1,682,657

1,757,052

1,831,170

1,904,999

1, 978, 528

2,051,745

2, 124, 639

2, 197, 197

2, 269, 410

Y

486

1,945

. 4,376

7,779

12, 153

17,498

23,813

31,096

39, 347

48, 565

58, 747

69, 893

82,000

95, 067

109,091

124,071

140, 003

156,887

174, 718

193, 494

213,212

233, 869

255, 462

277,987

301,441

325, 820

351,120

377, 337

404,468

432, 507

Latitude 47°.

Longitude,

0 <

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

76,056

152,100

228,119

304, 101

380,034

455,904

531, 700

607,410

683,020

758,520

833,895

909, 135

984,227

1, 059, 158

1,133,917

1, 208, 491

1,282,868

1,357,036

1, 430, 984

1,504,697

1,578,166

1,651,377

1,724,320

1,796,982

1,869,351

1,941,415

2,013,163

2,084,583

2, 155, 663

2,220,392

Y

'485

1,942

4,368

7,765

12, 131

17, 467

23, 770

31,040

39, 276

48, 477

58,640

69,765

81,849

94, 890

108, 887

123,837

139, 738

156,587

174,381

193, 118

212, 793

233, 405

254,950

277, 425

300, 824

325, 146

350, 386

376, 539

403, 602

431,569
GEOGRAPHIC TABLES AND FORMULAS. 47

TABLE 6. For projections of maps of. large areas Continued. 

COORDINATES OF CURVATURE.

Natural scale. Values of X and Y in meters.

Latitude 48°.

Longitude.

o / 

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

.12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

74,626

149, 239

223, 827

298, 377

372,877

447,314

521, 677

595, 951

670, 125

744, 186

818, 123

891, 921

965,570

1,039,056

1,112,367

1,185,491

1,258,416

1,331,129

1,403,618

1,475,871

1,547,876

1, 619, 620

1,691,091

1,762,279

1,833,170

1,903,752

1,974,015

1 2, 043, 945

2, 113, 531

2, 182, 762

Y

484

1,936

4,355

7,742

12, 095

17, 414

23,698

30,946

39, 167

48,329

58,461

69,552

81, 598

94,598

108,551

123,453

139,302

156,096

173, 832

192,506

212, 116

232,658

254,128

276,524

299,842

324,077

349, 225

375, 283

402,245

430, 107

Latitude 49°.

Longitude.

O I

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

73, 172

146,331

219,465

292,561

365, 606

438,588

511,493

584,310

657, 026

729,627

802,102

874, 438

946, 622

1,018,642

1,090,485

1,162,138

1,233,591

1, 304, 829

1,375,840

1,446,613

1,517,135

1,5*7,394

1,657,378

1,727,073

1,796,470

1,865,554

1,934,315

2,002,740

2,070,817

2,138,536

Y

482

1,928

4,337

7,709

12, 044

17, 340

23,598

30,815

38, 991

48,123

58, 212

69,254

81,248

94, 191

108,082

122, 918

138,697

155,416

173, 071

191, 660

211, 180

231,627

252, 998

275, 288

298, 495

322,614

347, 640

373,570

400, 399

428, 123

Latitude 50°.

Longitude.

0 /

1 00

2 00

3 00

4 00

5 00

6 00

7 00

8 00

9 00

10 00

11 00

12 00

13 00

14 00

15 00

16 00

17 00

18 00

19 00

20 00

21 00

22 00

23 00

24 00

25 00

26 00

27 00

28 00

29 00

30 00

X

71,696

143, 379

215,037

286, 656

358,224

429, 727

501,154

572,492

643, 727

714,847

785,839

856, 691

927, 389

997, 922

1,068,277

1,138,440

1,208,400

1,278,144

1,347,660

1,416,934

1,485,956

1,554,711

1, 623, 189

1,691,377

1,759,262

1, 826, 833

1,894,077

1, 960, 983

2,027,538

2, 093, 731

Y

479

1,917

4,313

7,667

11,978

17,246

23, 469

30, 646

38, 777

47,859

57,891

68, 872

80, 798

93, 669

107,482

122,234

137, 923

154,546

172,099

190,581

209,987

230, 314

251,559

273,717

296, 785

320, 758

345, 633

371,404

398,068

425, 619
48 GEOGRAPHIC TABLES AND FOBMULAS.

TABLE 7. Coordinates for projection of maps (scale xy 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

o / 

0 00 

10 

. 20 

30 

40 

50

1 00 

10 

20 

30 

40 

50

2 00 

10 

20 

30 

40 

50

3 00 

10. 

20 

30 

40 

50

4 00 

10 

20 

30 

40 

50

5 00 

10 

20 

30 

40 

50

6 00 

10 

20 

30 

40 

50

7 00 

10 

20 

30 

40 

50

8 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.

5.804 

11. 608 

17. 412 

23. 216 

29. 020

. 5.840 

11. 608 

17.412 

23.216 

29. 020

5.804 

11. 608 

17. 412 

23. 216 

29. 020

5.804 

11. 608 

17.413 

23. 217 

29. 021

5.804 

11. 609 

17. 413 

23.217 

29. 022

5.804 

11. 609 

17. 414 

23.218 

29. 022

5.805 

 11. 609 

17.414 

23. 219 

29. 024

5.805 

11.610 

17. 415 

23. 220 

29. 025

Abscissas of developed parallel.

5' longitude.

Inches. 

2.922 

2.922 

2.922 

2.922 

2.922 

2.921

2.921 

2.921 

2.921 

2.921 

2.920 

2.920

2.920 

2.920 

2. 919 

2.919 

2.918 

2.918

2.918 

2.917 

2.917 

2.916 

2.916 

2.915

2.915 

2.914 

2.913 

2.913 

2^912 

2. 911

2.911 

2.910 

2.909 

2.908 

2.908 

2.907

2.906 

2.905 

2.904 

2.903 

2. 902 

2.901

2.900 

2.899 

2.898 

2.897 

2. 896 

2.895

2. 894

10' longitude.

Indies. 

5.844 

5.843 

5.843 

5.843 

5.843 

5.843

5.843 

5.842 

5.842 

5.841 

5.841 

5.840

5.840 

5.839 

5.839 

5.838 

5.837 

5.886

5. 836 

5.835 

5.834 

5.832 

5. 831 

5.830

.5.829 

5.828 

5.827 

5.825 

5.824 

5..S23

5. 822 

5.820 

5.818 

5.817 

5.815 

5.813

5.812 

5.810 

5.808 

5.806 

5.804 

5. 802

5.800 

5.798 

5.796 

5.794 

5.791 

5.789

5.787

15' longitude.

Inches. 

8.765 

8.765 

8.765 

8.765 

8.764 

8.764

8.764 

8.763 

8.763 

8.762 

8.761 

8.761

8.760 

8.759 

8.758 

8.757 

8.756 

8.755

8.753 

8.752 

8.750 

8.749 

8.747 

8.746

8.744 

8. 742 

8.740 

8.738 

8.736 

8.734

8.732 

8.730 

8.727 

8.725 

8.722 

8.720

8.718 

8.715 

8.712 

8.709 

8.706 

8.703

8.701 

8.697 

8. 694 

8.6% 

8.687 

8.684

8.680

20' longitude.

Inches. 

11. 687 

11.687 

11.686 

11. 686 

11. 686 

11.686

11.685 

11. 684 

11. 684 

11. 683 

11.682 

11. 681

11. 680 

11.678 

11. 677 

11. 676 

 11.674 

 11.673

11. 671 

11. 669 

11. 667 

11. 665 

11.663 

11.661

11. 659 

11. 656 

11.654 

11. 651 

11. 648 

11. 646

11. 643 

11. 640 

11. 636 

11.633 

11. 630 

11. 627

11. 624 

11.620 

11. 616 

11. 612 

11. 608 

11. 604

11. 601 

11.596 

11. 592 

11.587 

11. 583 

11. 578

11. 574

25' longitude.

Indies. 

14. 609 

14.608 

14. 608 

14. 608 

14. 608 

14. 607

14. 606 

14. 606 

14. 604 

14. 604 

14. 602 

14. 601

14. 600 

14.598 

14. 596 

14. 594 

14. 592 

14. 591

14.589 

14.586 

14.584 

14.581 

14. 578 

14. 576

14. 574 

14. 570 

14. 567 

14.564 

14. 560 

14. 557

14.554 

14. 550 

14.546 

14. 542 

14. 538 

14. 534

14.530 

14.524 

14.520 

14.515 

14.510 

14. 506

14.501 

14. 496 

14.490 

14. -184 

14.478 

14. 473

14. 468

30' longitude.

Inches. 

17. 531 

17. 530 

17. 530 

17.530 

17. 529 

17.528

17. 528 

17. 527 

17. 525 

17. 524 

17.522 

17. 521

17.520 

17.518 

17.616 

17.513 

17. 511 

17. 509

17. 507 

17. 504 

17. 501 

17.497 

17. 494 

17.491

17. 488 

17. 484 

17. 480 

17. 476 

17. 473 

17. 468

17.465 

17. 459 

17. 455 

17. 450 

17. 445 

17.440

17. 435 

17. 429 

17.424 

17.418 

17.413 

17.407

 17.401 

17. 395 

17.387 

17 381 

17. 374 

17.3b8

17.361

Ordinates of developed 

parallel.

Longitude interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20

25 

30

5 

10 

15 

20 

25 

30

0°

Inches. 

0.000 

.000 

.000 

.000 

.000 

.000

2°

0.000 

.000 

.001 

.001 

.002 

.003

40

0.000 

.001 

.001 

.002 

.004 

.005

6°

0.000 

.001 

.002 

.004 

.006 

.008

8°

0.000 

.001 

.003 

.005 

. .007 

.010

1°

Inches. 

0.000 

.000 

.000 

.001 

.001 

.001

3°

0. 000 

.000 

.001 

.002 

.003 

.004

5°

0.000 

.001 

.002 

.003 

.005 

.007

7°

0.000 

.001 

.002 

.004 

.006 

.009
GEOGEAPHIC TABLES AND FOEMULAS. 49

TABLE 7. Coordinates for projection of maps (scale rWinnr) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

O '

8 00 

10 

20 

30 

40 

50

9 00 

10 

20 

30 

40 

50

10 00 

10 

20 

30 

40 50'

11 00 

10 

20 

30 

40 

50

12 00 

10 

20 

30 

40 

50

13 00 

10 

20 

30 

40 

50

14 00 

10 

20 

30 

40 

50

15 00 

10 

20 

30 

40 

50

16 00

Meridional distances 

from 

even 

degree 

parallels

Inches.

a. 805 

11. 610 

17.416 

23. 221 

29. 026

5.806 

11.611 

17. 417 

23.222 

29. 028

5.806 

11. 612 

17. 417 

23. 223 

29.029

5.806 

11.612 

17. 419 

23. 225 

29. 031

5. 807 

11.613 

17.420 

23. 226 

29. 033

5.807 

11.614 

.17.421 

23. 228 

29. 035

5.808 

11.615 

17. 422 

23. 230 

29. 038

5.808 

11.616 

17. 424 

23. 232 

29. 040

Abscissas of developed parallel.

5' longitude.

Inches. 

2.894 

2.892 

2.891 

2.890 

2.888 

2. 887

2. 886 

2.885 

2.883 

2.882 

2.881 

2.879

2.878 

2. 876 

2.875 

2.873 

2.872 

2.870

2.869 

2.867 

2.865 

2.864 

2. 862 

2.860

2.858 

2. 857 

2.855 

2.853 

2. 851 

2. 849

2.847 

2.846 

2. 844 

2. 842 

2.840 

2. 838

2. 836 

2. 834 

2.831 

2.829 

2.827 

2.825

2. 823 

2. 821 

2.818 

2.816 

2.814 

2. 812

2.809

10' longitude.

Inches. 

5.787 

5.784 

5.782 

5.779 

5. 777 

5.775

5.772 

5.769 

5.767 

5.764 

5.761 

5.758

5.755 

5.752 

5.749 

5. 746 

5.743 

5.740

5. 737 

5.734 

5.730 

5. 727 

5.724 

5. 720 .

5.717 

5. 713 

5.709 

5.706 

5.702 

5.698

5.695 

5. 691 

5. 687 

5. 683 

5.679 

5.675

5. 071 

5.667 

5. 663 

5.658 

5. 654 

5.650

5. 646 

5.641 

5. 637 

5.632 

5. 628 

5.623

5. 619

15' longitude.

Indies. 

8.680 

8.677 

8.673 

8.669 

8.666 

8.662

8.658 

8.654 

8.650 

8.646 

8.642 

8.637

8.633 

8.628 

8.624 

8.619 

8.614 

8.610

8.606 

8.601 

8.596 

8.590 

8.585 

8.580

8.575 

8.570 

8.564 

8.559 

8.553 

8.548

8.542 

8.536 

8.530 

8. 524 

8.519 

8.513

8.507 

8.500 

8.494 

8. -188 

8.481 

8.475

8.469 

8.462 

8.455 

8.448 

8.441 

8.435

8.428

20' longitude.

Inches. 

11. 574 

11. 569 

11. 564 

11.559 

11. 554 

11.549

11.544 

11.639 

11.533 

11.628 

11.522 

11.516

11. 511 

H.,504 

J1.498 

11. 492 

11.486 

11. 480

11. 474 

11. 468 

11.461 

11.454 

11. 447 

11. 440

11.434 

11. 426 

11.419 

11.412 

11. 404 

11.397

11. 390 

11. 382 

11. 374 

11. 366 

11. 358 

11.350

11. 342 

11.334 

11. 326 11.317' 

11. 308 

11. 300 ,

11.292 

11. 282 ' 

11.274 

11.264 

11.255 

11. 246

11.237

25' longitude.

Inches. 

14. 468 

14. 461 

14.455 

14.448 

14.442 

14. 436

14. 430 

14. 424 

14. 416 

14.410 

14.402 

14.396

14. 388 

14. 380 

14.373 

14. 366 

14.358 

14. 350

14. 342 

14. 334 

14. 326 

14.318 

14. 309 

14. 300

14.292 

14.282 

14. 274 

14. 264 

14. 256 

14. 246

14. 237 

14. 228 

14. 218 

14. 208 

14. 198 

14. 188

14. 178 

14. 168 

14.157 

14. 146 

14. 136 

14. 125

14.114 

14. 103 

14. 092 

14, 080 

14. 069 

14. 058

14.046

30' longitude.

Inches. 

17. 361 

17. 353 

17.346 

17. 338 

17. 331 

17.324

17.317 

17.308 

17.300 

17. 291 

17.283 

17.275

17. 266 

17.257 

17.248 

17.239 

17. 229 

17. 220

17.211 

17. 201 

17. 191 

17. 181 

17. 171 

17. 161

17.150 

17. 139 

17.128 

17. 117 

17. 107 

17. 095

17. 084 

17. 073 

17. 061 

17. 049 

17.038 

17. 026

17. 014 

17. 001 

16.988 

16. 975 

16.963 

16. 950

16. 937 

16.924 

16.910 

16. 897 

16.883 

16. 870

16.856

Ordinates of developed 

parallel.

Longitude . 

interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

' 5 

10 

25 

20 

25 

30

5 

10 

15 

20 

25 

30

8°-

Inches. 

0.000 

.001 

.003 

.005 

.007 

.010

10<?

0.000 

.001 

.003 

.006 

.009 

.013

12°

0.000 

.002 

.004 

.007 

.011 

.016

14°

0.000 

.002 

.004 

.008 

.012 

.018

16°

0.001 

.002 

.005 

.009 

.014 

.020

9°

Inches. 

0.000 

.001 

.003 

.005 

.008 

.012

11°

0.000 

.002 

.004 

.006 

.010 

.014

13°

0.000 

.002 

.004 

.007 

.012 

.017

15°

0.001 

.002 

.005 

.009 

.013 

.019

41623° 16-
50 GEOGKAPH10 TABLES AND FORMULAS.

TABLE 7. Coordinates for projection of maps (scale TirjWtf) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

. o /

: is oo

10 

: 20 

30 

40 

 50

' 17 : 00

 10

20 

' 30 ' ' 40 

50

i 18- 00 

10 

20 

T 30 

" 40 

 . 50

19 00 

. 30 

20 

30 

40 

50

20, 00 

. 10 

20 

' 30 

40 

50

21 00 

10

: 20

30 

40 

50

22' 00 

10 

20 

30 

40 

50

23 00 

10 

20 

30 

40

: 50

. 24 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.

5.809 

11.617 

17. 426 

23. 234 

29. 043

5.809 

 11.618 

17. 427 

 23.236 

29.046.

5. 810' 

11.619 

17. 429 

23. 239 

29. 049

5.810 : 

11.621 

17. 431 

: 23,242 

29.052'

'"s.'sii"

, 11.622 

17. 433 

. 23.244 

29.055

5. 812 

11.623 

17. 435 

23. 247 

' 29.058

5. 812 

11. 625 

17.437 

23. 250 

29. 062

5.813 

11.626 

17.439 

23.252 

29. 066

Abscissas of developed parallel.

5' longitude.

Inches. 

2.809 

2.807 

2.804 

2. 802 

2.800 

2.797

2.795 

2. 792 

2.790 

2. 787 

2.785 

2.782

2.780 

2.777 

2. 774 

2.772 

2.769 

2. 760

2.764 

2. 761 

2. 758 

2.755 

2.752 

2.750

2.747 

2. 743 

2.741 

2. 738 

2.735 

2. 732

2.729 

2. 72G 

2. 723 

2.720 

2.717 

2.714

2. 710

2. 707 

2.704 

2.701 

2.697 

2. 694

2. 691 

2.688 

2. 684 

2. 681 

2. 677 

2.674

2. 671

10' longitude.

Inches. 

5. 619 

5.614 

5.609 

5.604 

5.599 

5. 595

5.590 

5.585 

5.580 

5.575 

5.570 

5.564

5.559 

5.554 

5.549 

5.543 

5.538 

5.533

5. 527 

5. 522 

5.516 

5.510 

5.505 

5.499

5. 493 

5.487 

5.482 

5. 476 

5.470 

5.464

5.458 

5. 462 

5.445 

5.439 

5.433 

5.427

5.414 

5.408 

5.401 

5. 395 

5.388

5.382 

5. 375 

5.368 

5.362 

5. 355 

5.348

5.341

15' longitude.

Inches. 

8.428 

8.421 

8.414 

8.406 

8.399 

8.392

8.385 

8.377 

8.369 

8.362 

8.354 

8.347

8.339 

8.331 

8.323 

8.315 

8.307 

8.299

8.291 

8.282 

8. 274 

8.266 

8.257 

8. 249

8.240 

8.231 

8. 222 

8.213 

8.204 

8.196

8.187 

8. 177 

8.168 

8.159 

8.150 

8.141

8.131 

8.122 

8.112 

8.102 

8.092 

8.083

8. 073 

8. 063 

8.053 

8.042 

8.032 

8.022

8.012

20' longitude.

Inches. 

11.237 

11.228 

11. 218 

11.208 

11. 199 

11. 189

11. 180 

11.170 

11.159 

11. 149 

11.139 

11. 129

11.119 

11. 108 

11. 097 

11. 087 

11. 076 

11.065

11.054 

11.043 

11.032 

11.021 

11.009 

10. 998

10. 987 

10. 975 

10. 963 

10. 951 

10.939 

10. 928

10.916 

10. 903 

10. 891 

10.878 

10. 866 

10.854

10. 842 

10.829 

10. 816 

10. 802 

10.790 

10. 777

10. 764 

10. 750 

10. 737 

10.723 

10. 710 

10. 696

10. 683

25' longitude.

Inches., 

14.046 

14. 034 

14. 022 

14. 010 

13. 998 

13. 986

13. 974 

13. 962 

13. 949 

13. 936 

13.924 

13.911

13. 898 

13. 885 

13. 872 

13. 859 

13. 845 

13.832

13. 818 

13. 804 

13.790 

13. 776 

13. 762 

13. 748

13. 734 

13.719 

13. 704 

13. 689 

13. 674 

13. 660

13. 645 

13. 629 

13. 614 

13. 598 

13. 583 

13.568

13. 552 

13. 536 

13. 520 

13. 503 

13.487 

13.471

13. 455 

13.438 

13. 421 

13.404 

13.387 

13. 371

13.354

30' longitude.

Inches. 

16.856 

16.841 

16. 827 

16. 813 

16.798 

16.784

16. 769 

16. 754 

16. 739 

16.724 

16. 709 

16. 693

16. 678 

16. 662 

16. 646 

16. 630 

16.614 

16. 698

16. 582 

16. 565 

16. 548 

16. 531 

16. 514 

16. 497

16. 480 

16.462 

16.445 

16. 427 

16. 409 

16. 391

16. 373 

16. 355 

16. 336 

16. 318 

16.300 

16.281

16. 262 

16.243 

16.223 

16. 204 

16.184 

16. 165

16.145 

16. 125 

16. 105 

16.085 

16. 064 

16. 045

16. 024

Ordinates of developed 

parallel.

Longitude interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

 20 

25 

30

5 

10 

15 

20 

25 

30

16°

Inches. 

0.001 

.002 

.005 

.009 

.014 

.020

18°

0.001 

.002 

.006 

.010 

.016 

.022

20°

0.001 

.003 

.006 

.011 

.017 

.025

22°

0.001 

.003 

.007 

.012 

.018 

.027

24°

0.001 

.003 

.007 

.013 

.020 

.028

17°

Inches. 

0.001 

.002 

.005 

.010 

.015 

.021

19°

0.001 

' .003 

.006 

.010 

.016 

.024

21°

0.001 

.003 

.006 

.011 

.018 

026

23°

0.001 

.003 

.007 

.012 

.019 

.028
GEOGRAPHIC TAJ3LES AND FORMULAS. 51

TABLE 7. Coordinates for projection of maps (scale TToVoir)"" Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

o / 

24 00 

10 

20 

30 

-10 

50

25 00 

10 

20 

30 

40 

50

26 00 

10 

20 

30 

40 

50

27 00 

. 10 

20 

30 

40 

50

28 00 

10 

20 

30 

40 

50

29 00 

10 

20 

30 

40 

50

30 00 

10 

20 

30 

40 

50

31 00 

' 10 

20 

30 

40 

50

32 00

Meridional distances 

from 

even 

degree 

parallels

Inches.

5.814 

11. 628 

1.7. 442 

23. 256 

29. 069

5.815 

11.629 

17.444 

23.259 

29. 074

5.816 

11.631 

17. 446 

23. 262 

29. 077

5.816 

11.633 

17.449 

23. 265 

29. 082

5.817 

11. 634 

17.451 

23. 268 

29. 086

5. 818 

11. 636 

17. 454 

23. 272 

29. 090

5. 819 

11. 638 

17.457 

23. 276 

29. 094

5.820 

11. 640 

17. 460 

23. 280 

29. 100

Abscissas of developed parallel.

5' longitude.

Inches. 

2.671 

2. 667 

2.664 

2. 660 

2.657 

2.653

2. 650 

2. 646 

2. 642 

2.639 

2.635 

2.631

2.628 

2.624 

2.620 

2. 616 

2.613 

2.609

2. 605 

2. 601 

2.597 

2. 593 2.589' 

2.586

2.582 

2.578 

2.574 

2.570 

2.566 

2.562

2.558 

2.553 

2.549 

2.545 

2.541 

2. 537

2.533 

2.528 

2. 524 

2.520 

2.515 

2.611

2.507 

2.502 

2.498 

2.493 

2.489 

2.485

2.480

10' longi 

tude.

Inches. 

5.341 

5.334 

5.327 

5.320 

5. 313 

5.306

5.299 

5. 292 

5.285 

5. 278 

6.270 

5.263

5.256 

5.248 

5.240 

5. 233 

5.225 

5 218

5. 210 

5.203 

5.195 

5.187 

5.179 

5.171

5.163 

6. 155 

5.147 

5.139 

5. 131 

5.123

5. 115 

5.107 

5.098 

5. 090. 

5.082 

5.073

5.065 

5.056 

5. 048 

5.039 

5.031 

5. 022

5. 014 

5.005 

4.996 

4.987 

4.978 

4.969

4.960

15' longi 

tude.

Indies. 

8. 012 

8.002 

7.991 

7.981 

7.970 

7.960

7.949 

7.938 

7.927 

7.916 

7.905 

7.894'

7.883 

7. 872 

7.861 

7.849 

7.838 

7.827

7.816 

7.804 

7.792 

7.780 

7.768 

7.757

7.745 

7.733 

7.721 

7.709 

7.697 

7.685

7. 673 

7.660 

7. 648 

7. 635 

7.622 

7. 610

7.598 

7.585 

7.572 

7. 559 

7.546 

7.533

7.520 

7.507 

7.494 

7.480 

7.467 

7.454

7.441

20' longi 

tude.

Inches. 

10. 683 

10. 669 

10. 655 

10. 641 

10. 627 

10. 613

10. 599 

10. 584 

10.570 

10.555 

10.540 

10.526

10. 511 

10. 496 

10. 481 

10. 466 

10. 451 

10.436

10. 421 

10. 405 

10.390 

10. 374 

10. 358 

10. 342

10;327 

10.311 

10. 294 

10. 278 

10. 262 

10. 246

10. 230 

10.213 

10.197 

10.180 

10.163 

10. 146

10. 130 

10. 113 

10. 096 

10. 078 

 10. 061 

10.044

10.027 

10. 009 

9.992 

9.974 

9.956 

9.938

9.921

26' longi 

tude.

Inches. 

13.354 

13. 336 

13. 319 

13. 301 

13.284 

. 13. 266

13. 249 

13. 231 

13.212 

13. 194 

13. 176 

13. 157

13. 139 

13. 120 

13. 101 

13.082 

13. 063 

13. 045

13. 026 

13. 006 

12.987 

12.967 

12. 947 

12.928

12. 909 

12. 889 

12. 868 

12.848 

12.828 

12.808

12. 788 

12. 767 

12.746 

12. 725 

12. 704 

12. 683

12. 662 

12. 641 

12. 620 

12. 598 

12. 577 

12. 555

12. 53-i 

12. 512 

12. 490 

12. 467 

12. 445 

12. 423

12. 401

30' longi 

tude.

Inches. 

16. 024 

16. 003 

15. 982 

15. 961 

15. 940 

15. 919

15.898 

.15.877 

15. 85-1 

15. 833 

.15:811 

15.788

15. 767 

15.744 

15. 721 

15. 698 

15. 676 

15. 654

15. 631 

15. 608 

15.584 

15. 560 

15. 537 

15. 514

15. 490 

15. 466 

15.442 

15. 418 

15. 394 

15. 369

15.345 

15. 320 

15. 295 

15.270 

15. 245 

15. 220

15. 195 

15.169 

15. 143 

15.118 

15. 092 

15. 066

15. 040 

15. 014 

14. 987 

14. 960 

14. 934 

14.908

14.881

Ordinates of developed 

parallel.

Longitude interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10. 15' 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

24°

Iiichcu. 

0.001 

.003 

.007 

.013 

.020 

.028

26°

0. 001 

.003 

.008 

.013 

.021 

.030

28°

0. 001 

.004 

.008 

. 014 

.022 

.032

30°

0. 001 

.004 

.008 

.015 

.023 

.033

32°

0.001 

.004 

.009 

.015 

.024 

.034

25°

Inches. 

0.001 

.003- 

.007 

. 0.13 

.020 

.029

 27°

0.001 

.003 

.008 

.014 

.022 

.031

29°

0.001 

.004 

.008 

.014 

.023 

.032

31°

0. 001 

.004 

.008 

. 015 

.023 

.034
52 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 7. Coordinates for projection of maps (scale TTSTRRF) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

o / 

32 00 

10 

20 

30 

40 

50

 33 00 

10 

20 

30 

40 

50

34 00 

10 

20 

30 

40 

50

35 00 

10 

20 

30 

40 

60

30 00 

10 

20 

30 

40 

50

37 00 

10 

20 

30 

40 

50

38 00 

10 

20 

30 

40 

50

39 00 

10 

20 

30 

40 

60

40 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.'

5.821 

11.642 

17. 462 

23.283 

29. 104

5. 822 

11.643 

17. 465 

23.287 

29.109

5.823 

11.645 

17.468 

23. 291 

29. 113

5.824 

11.647 

17. 471 

23.294 

29. 118

5.824 

11. 649 

17. 473 

23. 297 

29. 122

5.826 

11. 651 

17. 477 

23. 302 

29.128

5.827 

11. 653 

17.480 

23. 306 

29. 133

5.828 

11.655 

17.483 

23.310 

29.138

Abscissas of developed parallel.

5' longitude.

Inches. 

2.480 

2.476 

2.471 

2.467 

2.462 

2.458

2.453 

2.448 

2.444 

2.439 

2.434 

2.429

2.425 

2.420 

2.415 

2.410 

2.406 

2.401

2.396 

2.391 

2.386 

2.381 

2.377 

2.372

2.367 

2.362 

2.357 

2.351 

2.346 

2.341

2.336 

2. 331 

2.326 

2.321 

2. 316 

2. 311

2.305 

2.300 

2.295 

2.290 

2.284 

2.279

2.274 

2.268 

2. 263 

2.258 

2.252 

2.247

2.241

10' longitude.

Inches. 

4.960 

4.951 

4.942 

4.933 

4.924 

4.915

4.906 

4.896 

4.887 

4.878 

4.868 

4.859

4.850 

4.840 

4.830 

4.821 

4.811 

4.802

4.792 

4. 782 

4.773 

4.763 

4.753 

4.743

4.733 

4. 723 

4.713 

4.703 

4.693 

4.683

4.673 

4.662 

4.652 

4.642 

4.631 

4.621

4. 611 

4.600 

4.590 

.4.579

4.568 

4.558

4.548 

4.537 

4.526 

4.515 

4.504 

4.493

4.483

15' longitude.

Inches. 

7.441 

7.427 

7.413 

7.400 

7.386 

7. 373

7.359 

7.345 

7.331 

7.316 

7.302 

7.288

7.274 

7.260 

7.246 

7.231 

7.217 

7.203

7.188 

7.174 

7.159 

7.144 

7.130 

7.115

7. 099 

7.085 

7.070 

7.055 

7.039 

7.024

7.009 

6.994 

6. 978 

6.963 

6.947 

6.932

6.916 

6.900 

6.884 

6.869 

6.853 

6.837

6.821 

6.805 

6.789 

6.773 

6.756 

6.740

6.724

20' longitude.

Inches. 

9.921 

9.903 

9; 884 

9.866 

9.848 

9.830

9.812 

9.793 

9.774 

9.755 

9.736 

9.718

9.699 

9.680 

9.661 

9.642 

9. 622 

9.604

9.584 

9.565 

9.545 

9.526 

9.506 

9.486

9.466 

9.446 

9.426 

9.406 

9.386 

9.366

9.345 

9.325 

9.304 

9.284 

9.263 

9.242

9.222 

9.200 

9.179 

9.158 

9.137 

9.116

9.095 

9.073 

9.052 

9.030 

9.008 

8.987

8.965

25' longitude.

Inches. 

12. 401 

12.379 

12. 355 

12. 333 

12.310 

12. 288

12.265 

12. 241 

12.218 

12. 194 

12.171 

12. 147

12. 124 

12. 100 

12. 076 

12. 052 

12.028 

12.004

11. 980 

11. 956 

11.932 

11. 907 

11.883 

11.858

11.833 

11.808 

11.783 

11.757 

11. 732 

11.707

11. 682 

11. 656 

11. 630 

11.605 

11.579 

11.553

11. 527 

11. 501 

11. 474 

11. 448 

11.421 

11. 395

11. 369 

11. 342 

11.315 

11.288 

11. 261 

11. 234

11. 207

30' longitude.

Inches. 

14.881 

14. 854 

14.827 

14.800 

14. 772 

14. 745

14. 717 

14. 689 

14. 661 

14.633 

14. 605 

14.576

14.549 

14.520 

14. 491 

14.462 

14.434 

14. 405

14. 376 

14. 347 

14.318 

14.288 14.259' 

14. 230

14.200 

14. 170 

14. 139 

14.109 

14. 078 

14. 048

14. 018 

13. 987 

13. 956 

13. 925 

13.894 

13.864

13. 832 

13. 801 

13. 769 

13. 737 

13. 705 

13. 673

13. 642 

13. 610 

13. 577 

13. 545 

13. 513 

13. 480

13.448

Ordinates of developed 

parallel.

Longitude interval.

. 5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

32°

Inches. 

0.001 

.004 

.009 

.015 

.024 

.034

34°

0.001 

.004 

.009 

.016 

.025 

.036

36°

0.001 

.004 

.009 

.013 

.025 

.036

38°

0.001 

.004 

.009 

. .017 

.026 

.037

40°

0.001 

.004 

.009 

.017 

.026 

.038

33°

Inches. 

0.001 

.004 

.009 

.016 

.024 

.035

35°

0.001 

.004 

.009 

.016 

.025 

.036

37°

0.001 

.004 

.009 

.016 

.026 

.037

39°

0.001 

.004 

.009 

.017 

.026 

.037
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 7. Coordinates for projection of maps (scale T^fVrnj) Continued. 

[From Smithsonian Geographical Tables.]

53

Latitude of 

parallel.

0 /

' 40 00 

10 

20 

30 

40 

50

41 00 

10 

20 

30 

40 

50

42 00 

10 

20 

30 

40 

50

43 00 

10 

20 

30 

40 

50

44 00 

10 

20 

30 

40 

50

45 00 

10 

20 

30 

40 

50

46 00 

10 

20

, 30 

40 

50

47 00 

10 

20 

30 

40 

50

48 00

Meridional distancesfrom 

even 

degree 

parallels

Inches.

5.829 

1.1. 657 

17. 486 

23. 314 

29. 143

5.830 

11. 659 

17. 489 

23.319 

29.149

5.831 

11. 661 

17. 492 

23. 323 

29.154

5.832 

11. 663 

17. 495 

23. 327 

29. 159

5.833 

11.666 

17. 498 

23. 331 

29. 164

5.834 

11. 668 

17. 501 

23. 335 

29. 169

5.835 

11. 670 

17.504 

23. 339 

29. 174

5.836 

11. 672 

17. 508 

23. 344 

29. 180

Abscissas of developed parallel.

5' longitude.

Inches. 

2. 241 

2.236 

2.230 

2.225 

2.219 

2.214

2.208 

2.203 

2. 197 

2.192 

2.186 

2.180

2.175 

2.169 

2.163 

2.157 

2. 152 

2.146

2.140 

2. 135 

2.129 

2. 123 

2.117 

2.111

2.105 

2.099 

2.093 

2.087 

2.081 

2.076

2.070 

2.064 

2.057 

2.051 

2.045 

2.039

2.033 

2.027 

2.021 

2. 015 

2.009 

2.003

1. 996 

1.990 

1.984 

1.978 

1.971 

1.965

1.959

10' longitude.

Inches. 

4.483 

4.472 

4.461 

4.450 

4.439 

4.428

4.417 

4.406 

4.394 

4.383 

4.372 

4.360

4.349 

4.338 

4.326 

4.315 

4. 303 

4.292

4.281 

4.269 

4. 257 

4.246 

4.234 

4.222

4.210 

4.199 

4.187 

4. 175 

4.163 

4.151

4. 139 

4.127 

4.115 

4.103 

4.091 

4.079

4.067 

4.054 

4.042 

4.030 

4.017 

4.005

3.992 

3.980 

3.968 

3.955 

3.943 

3.930

3.917

15'longi 

tude.

Indies. 

6.724 

6.707 

6.691 

6.674 

6.658 

6.641

6.625 

6.608 

6.591 

6.575 

6.558 

6.541

6.524 

6.507 

6.490 

6.472 

6.455 

6.438

6.421 

6.403 

6.386 

6.368 

6.351 

6.333

' 6.316 

5.298 

6.280 

6.262 

6.244 

6. 227 c

6.209 

6.191 

6.172 

6.154 

6.136 

6. 118

6.100 

6.081 

6.063 

6.044 

6.026 

6.008

5.989 

5.970 

5.951 

5.933 

5.914 

5.895

5.876

20'longi 

tude.

Indies. 

8.965 

8.943 

8. 923.

8.899 

8.877 

8.855

8.834 

8.811 

8.788 

8.766 

8.744 

8.721

8.698 

8.676 

8.653 

8.630 

8.607 

8.584

8. 561 

8.538 

8.514 

H.491 

8.468 

8.444

8.421 

8.397 

8.373 

8.350 

8. 326 

8.302

8.278 

8.254 

8.230 

8.206 

8.181 

8.157

8.133 

8.108 

8.084 

8.059 

8.034 

8.010

7.985 

7.960 

7.935 

7.910 

7.885 

7.860

7.835

25'longi 

tude.

Inches. 

11.207 

11. 179 

11. 152 

11. 124 

11.097 

11. 069

11.042 

11. 014 

10. 985 

10. 958 

10. 929 

10.901

10. 873 

10. 844 

10. 816 

10.787 

10.759 

10. 730

10. 702 

10. 672 

10. 643 

10. 614 

10.585 

10. 556

10.526 

10. 496 

10. 467 

10. 437 

10. 407 

10.378

10.348 

10. 317 

10. 288 

10. 257 

10. 226 

10. 197

10. 166 

10. 136 

10. 104 

10. 074 

10. 043 

10. 013

9.981 

9.951 

9. 919 

9.888 

9.857 

9.826

9.794

30'longi 

tude.

Inches. 

13. 448 

13.415 

13. 382 

13. 349 

13.316 

13.283

13. 250 

13. 217 

13. 183 

13.149 

13. 115 

13.081

13. 048 

13. 013 

12. 979 

12.945 

12. 910 

12. 876

12. 842 

12. 807 

12. 772 

12. 737 

12. 701 

12. 667

12. 631 

12. 596 

12. 560 

12. 524 

12.489 

12. 453

12. 417 

12. 381 

12.345 

12. 308 

12. 272 

12.236

12.199 

12. 163 

12. 125 

12. 089 

12. 052 

12. 015

11. 978 

11.941 

11. 903 

11. 866 

11. 828 

11. 791

11.752

Ordinates of developed 

paralle .

Longitude interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

40°

Inches. 

0.001 

.004 

.009 

.017 

.026 

.038

42°

0.001 

.004 

.010 

.017 

.026 

.038

44°

0.001 

.004 

.010 

.017 

.027 

.038

46°

0.001 

.004 

.010 

.017 

.027. 

.038

48°

0.001 

.004 

.010 

.017 

.026 

.038

41°

Inches. 

0.001 

.004 

.009 

.017 

.026 

.038

48°

0. 001. 

.004 

.010 

.017 

.027 

.038

45°

0.001 

.004 

.010 

.017 

.027 

.038

47°

0.001 

.004 

.010 

.017 

.027 

.038
54 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 7. Coordinates for projection of maps (scale Tsrfrrnr) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

o / 

48 00 

10 

20 

30 

40 

50

49 00 

10 

20 

30 

40 

50

50 00 

10 

20 

30 

40 

50

51 00 

10 

20 

30 

40 

50

52 00 

10 

20 

30 

40 

50

53 00 

10 

20 

30 

40 

50

54 00 

10 

20 

30 

40 

50

55 00 

10 

20 

30 

40 

' 50

66 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.

5.837 

11. 674 

17. 511 

23. 348 

29. 185

5.838 

11. 676 

17. 514 

23. 352 

29. 190

5.839 

11. 678 

17.517 

23. 356 

29. 191

5.840 

11. 080 

17. 520 

23. 360 

29. 200

5.841 

11. 682 

17. 523 

23. 364 

29.204

5.842 

11. 684 

17. 526 

23. 368 

29.210

. 5.843 

11. 686 

17. 529 

23. 372 

29. 214

5.844 

11. 688 

17.532 

23. 376 

29. 220

Abscissas of developed parallel.

5' longitude.

Inches. 

1.959 

1.952 

1.946 

1.940 

1.933 

1.927

1.921 

1.914 

1.908 

1.901 

1.895 

1.888

1.882 

1.875 

1.869 

1.862 

1.856 

1.849

1.842 

1. 836 

1.829 

1.823 

1.816 

1.809

1.803 

1.796 

1.789 

1.782 

1.776 

1.769

1.762 

1.755 

1.748 

1.742 

1.735 

1.728

1. 721 

1.714 

1.707 

1.700 

1.694 

1.687

1.680 

1.673 

1. 666 

1.659 

1.652 

1.645

1.638

10' longitude.

Inches. 

3.917 

3.905 

3.892 

3.879 

3.867 

3.854

3.841 

3.828 

3.815 

3.803 

3.790 

3.777

3.764 

3.750 

3.737 

3.724 

3.711 

3.698

3.685 

3.672 

3.658 

3.645 

3.632 

3.618

3.605 

3.592 

3.578 

3.565 

3.551 

3.538

3.524 

3.511 

3.497 

3.483 

3.470 

3.456

3.442 

3.429 

3.415 

3.401 

3.387 

3.373

3.359 

3.345 

3.331 

3.317 

3.303 

3.289

3.275

15' longitude.

Inches. 

5.876 

5.857 

5.838 

5.819 

5.800 

5.781

5.-762 

5.743 

5. 725 

5.704 

5.684 

5.665

5.646 

5.626 

5.606 

5:587 

5.567 

5.547

5.528 

5.507 

5.488 

5.468 

5.448 

5.428

5.408 

5.388 

5.367 

5.347 

5,327 

5.307

5.287 

5.266 

5.246 

5.225 

5.205 

5.184

5.164 

5.143 

5.122 

5.101 

5.080 

5.060

5.039 

5.018 

4.997 

4.976 

4. 955 

4.934

4. 913

20' longitude.

Inches. 

7.835 

7.810 

7.784 

7.769 

7.733 

7.708

7.682 

7.657 

7.631 

7.605 

7.579 

7.553

7.527 

7.501 

7.475 

7.449 

7.422 

7.396

7.370 

7.343 

7.317 

7.290 

7.264 

7.237

7.210 

7.184 

7.156 

7.130 

7,103 

7.076

7.049 

7.022 

6.994 

6.967 

6.940 

6.912

6.885 

6.857 

6.830 

6.802 

6.774 

6.746

6.719 

6.691 

6.663 

6.635 

6.607 

6.579

6.551

25' longitude.

Inches. 

9.794 

9.762 

9.730 

9.699 

9.667 

9.635

9.603 

9.571 

9.539 

9.507 

9.474 

9.442

9.409 

9.376 

9.344 

9.311 

9.278 

9.245

9.212 

9.179 

9.146 

9.113 

9.080 

9.046

9.013 

8. 980 

8.946 

8. 912 

8.878 

8.844

8.811 

8.777 

8.742 

8.708 

8.674 

8.640

8.606 

8.572 

8.537 

8.502 

8.468 

8.433

8.398 

8. 364 

8.328 

8. 294 

8.258 

8.224

8.188

30' longitude.

Inches. 

11.752 

11. 714 

11. 677 

11. 638 

11. 600 

11.562

11. 523 

11.485 

11. 446 

11.408 

11. 369 

11. 330

11. 291 

11.251 

11. 212 

11. 173 

11. 134 

11.094

11. 055 

11.015 

10. 975 

10. 936 

10. 895 

10. 855

10. 816 

10. 775 

10. 734 

10. 694 

10. 654 

10. 613

10. 573 

10. 532 

10. 491 

10. 450 

10. 409 

10.368

10. 327 

10. 286 

10.244 

10. 202 

10. 161 

10. 120

10.078 

10. 036 

9.994 

9. 952 

9.910 

9.868

9.826

Ordinates of developed 

parallel.

Longitude interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

48°

Inches. 

0.001 

.004 

.010 

.017 

.026 

.038

50°

0.001 

.004 

.009 

.017 

.026 

.038

52°

0.001 

.004 

.009 

.017 

.026 

.037

54°

0.001 

.004 

.009 

.016 

.025 

.036

56°

0.001 

.004 

.009 

. 016 

.025 

.036

49°

Inches. 

0.001 

.004 

.010 

.017 

.026 

.038

51°

0.001 

.004 

.009 

.017 

.026 

.037

53° '

0.001 

.004 

.009

.as

.026 

.037

55°

0.001 

.004 

.009 

.016 

.025 

.036
GEOGRAPHIC TABLES AND FORMULAS. 55

TABLE 7. Coordinates for projection of maps (scale js-sWu)- Continued. 

[Prom Smithsonian Geographical Tables.]

Latitude of 

parallel.

O 1

66 00 

10 

20 

30 

40 

50

57 00 

10 

20 

30 

40 

50

58 00 

10 20 

30 

40 

50

69 CO 

10 

20 

30 

40 

50

60 00 

10 

20 

30 

40 

50

61 00 

10 

20 

30 

40 

50

62 00 

10 

20 

30 

40 

50

63 00 

10 

20 

30 

40 

50

64 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.

5.845 

11. 690 

17.535 

23.380 

29. 224

5.846 

11. 692 

17. 537 

23. 383 

29.229

5.847 

11.694 

17. 540 

23. 387 

29.234

5.848 

11. 695 

17.543 

23. 391 

29. 238

5. 849 

11.697 

17.546 

23. 394 

29. 243

5. 850 

11.699 

17. 549 

23.398 

29. 248

5.850 

11.701 

17. 551 

23. 402 

29. 252

5/851 

11.702 

17.554 

23. 405 

29. 256

Abscissas of developed parallel.

5' longitude.

Inches. 

1.638 

1.631 

1.624 

.1.616 

1.609 

1.602

1.595 

1.588 

1.581 

1.574 

1.566 

1.559"

1.552 

1.545 

1.538 

1.530 

1.523 

1.516

1.509 

1.501 

1.494 

1.487 

1.479 

1.472

1.465 

1.457 

1.450 

1. 442 

1.435 

1.428

1.320 

1.313 

1.405 

1.398 

1.390 

1.383

1. 375 

1.368 

1.360 

1.353 

1.345 

1.338

1.330 

1.322 

1.315 

1.307 

1.300 

1.292

1.284

10' longitude.

Inches. 

3.275 

3.261 

3.247 

3.233 

3.219 

3.204

3.190 

3. 176 

3.162 

3.147 

3.133 

3.119

3. 104 

3.090 

3.075 

3. 061. 

3. 046 

3.032

3.017 

3. 003 

2. 988 

2.973 

2. 959 

2. 944

2.929 

2.914 

2. 900 

2.885 

2.870 

2. 855

2.840 

2. 825 

2. 810 

2. 795 

2. 781 

2.766

2. 751 

2.736 

2. 720 

2.705 

2. 690 

2. 675

2.660 

2.645 

2.630 

2.614 

2. 599 

2.584

2. 569

15' longitude.

Inches. 

4.913 

4.892 

4.870 

4.849 

4.828 

4.807

4.785 

4.764 

4.742 

4.721 

4.699 

4.678

4. 656 

4.634 

4.613 

4. 591 

4.569 

4.547

4.526 

4.504 

4.482 

4.460 

4.438 

4.416

4.394 

4.372 

4.349 

4.327 

4.305 

4.283

4. 261 

4.238 

4.216 

4.193 

4.171 

4.148

4.126 

4.103 

4.081 

4.058 

4.035 

4.013

3.990 

3.967 

3.944 

3. 921 

3.899 

3.876

3.853

20' longitude.

Inches. 

6.551 

6. 522 

6.494 

6.466 

6.437 

6.409

6.380 

6. 352 

6.323 

6.294 

6.266 

6.237

6.208 

6.179 

6.150 

6.122 

6. 092 

' 6.003

6.034 

6. 005 

5. 976 

5. 946 

5.917 

5.888

5. 858 

5. 829 

5. 799 

5.770 

5. 740 

5.710

5. 681 

5. 651 

5. 621 

5.591 

5.561 

5. 631

5. 501 

5.471 

5. 441 

5.410 

5. 380 

5.350

5. 320 

5.290 

5. 259 

5. 228 

5.198 

5. 168

5.137

25' longitude. .

Inches. 

8.188 

8. 153 

8. 118 

8.082 

8.046 

8.011

7.976 

7.940 

7. 904 

7.868 

7.832 

7.796

7.760 

7.724 

7.C88 

7. ?52 

7.616 

7.579

7.543 

7. 506 

7.470 

7. 433 

7. 396 

7.360

7.323 

7.286 

7.249 

7.212 

7. 176 

7.138

7.101 

7.064 

7. 026 

6. 988 

6. 952 

6.914

6. 877 

6.839 

6. 8H1 

6. 763 

6.726 

6.688

6.650 

6.612 

6.574 

6.536 

6. 498 

6.460

6.422

30' longitude. 

Inches. 

9. 826 

9.784 

9.741- 

 9.698 

9.656 

9.613

9.571 

9. 527 

9.485 

9.442 

9.398 

9.356

9.313 

9. 269 

9.226 

9. 182 

9. 139 

9.095

9. 052 

9. 008 

8.963 

8.920 

8.876 

8. 831

8.788 

8. 743 

8.699 

8.654 

8. 610 

8.566

8. 521 

8. 476 

8.431 

8.380 

8. 342 

8. 297

8. 252 

8.207 

8.161 

8.116 

8. 071. 

8. 026

7.980 

7.934 

7.889 

7.843 

7.797 

7.751

7.706

Ordinates of developed 

parallel.

Longitude 

interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

66°

Inches. 

0.001 

.004 

.009 

.016 

.025 

.036

58°

0.001 

.004 

.009 

.015 

.024 

' .034

' 60°

0.001 

.004 

.008 

.015 

.023 

.033

. 62°

0. 001 

.004 

.008 

.014 

.022 

.032

64°

0. 001 .00;,

.008 

.013 

.021 

.030

( 57°

 Indies. 

0.001 

 .004 

.009 

.016 

.024 

.035

' 59°

0.001 

. .004 

.008 

.015 

. .024 

.034

01°

0.001 

.004 

. .008 

. . 0.14 

. . 023 ' 

.033

' 63°

0.001 

.003 

.008 

.014 

.022 

 . . 031
56 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 7 . -Coordinates for 'projection of maps (scale TTSTHMJ) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

0 /

64 00 

10 

20 

30 

40 

50

65 00 

 10 

20 

30 

40 

50

66 00 

10 

20 

30 

40 

50

67 00 

10 

20 

30 

40 

50

68 00 

10 

20 

30 

40 

50

69 00 

10 

20 

30 

40 

50

70 00 

10 

20 

30 

40 

50

71 00 

10 

20 

30 

40 

50

72 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.

5\852 

11.704 

17.556 

23.408 

29.260

5.853 

11.706 

17.558 

23. 411 

 29.264

5.854 

11. 707 

17.561 

23. 414 

29.268

5.854 

11. 709 

17.563 

23. 418 

29.272

' 5.855 

11.710 

17. 565 

23.420 

29.276

6.856 

11.712 

17.567 

>23.423 ' 29.279

5.856 

11. 713 

17.570 

23. 426 

29. 282

5.857 

11. 714 

17. 672 

23.429 

29.286

Abscissas of developed parallel.

5' longitude.

Inches. 

1.284 

1. 277 

1.269 

1.261 

1.254 

1.246

1.238 

1.231 

1.223 

1.215 

1.207. 

1.200

1.192 

1.184 

1.176 

1.168 

 1.161 

1. 153

1. 145 

1.137 

1.129 

1.121 

1.113- 

1.106

1.098 

1.090 

1.082 

1.074 

1.066 

1.058

1.050 

1.042 

1.034 

1.026 

1.018 

1.010

1,002 

.994 

.986 

.978 

.970 

.962

.954 

.946 

.938 

.930 

.922 

.914

.906

10' longitude.

Inches. 

' 2.569 

2. 553 

2.538 

2.523 

2.507 

2.492

2.477 

2.461 

2.446 

2.430 

2.415 

2.399

2.384 

2.368 

2.352 

2.337 

2.321 

2.305

2.290 

2.274 

2.258 

2.243 

2.227 

2.211

2.195 

2.180 

2.164 

2. 148 

2. 132 

2.116

2.100 

2.084 

2.068 

2.052 

2.037 

2.021

 2.005 

1.989 

1.972 

1.956 

1.940 

1.924

1.908 

1.892 

1.876 

1:860 

1.844 

1.828

1.811

15' longitude.

Inches. 

3.853 

3.830 

3.807 

3.784 

3.761 

3.738

3. 715 

3.692 

3.668 

3.645 

3.622 

3.599

3.575 

3.552 

3.529 

3.505 

3.482 

3.458

3.435 

3.411 

3.388 

3.364 

3.340 

3.317

3.293 

3.269 

3.246 

3.222 

3.198 

3.174

3.151 

3.127 

3. 103 

3.079 

3.055 

3.031

3.007 

2.983 

2.959 

2.935 

2.911 

2. 886

2.862 

2.838 

2.814 

2.790 

2.765 

2.741

2. 717

20' longitude.

Inches. 

5.137 

5.106 

5.076 

5.045 

5.014 

4.984

4.953 

4.922 

4.891 

4.860 

4.829 

4.798

4.767 

4.736 

4.705 

4.673 

4.642 

4.611

 4.580 

4.548 

4.517 

4.485 

4.454 

4.422

4.391 

4.359 

4. 328 

4.296 

4.264 

4.232

4.201 

4.169 

4.137 

4.105 

4.073 

4.041

4.009' 

3.977 

3.945 

3.913 

3.881 

3.848

3.816 

3.784 

3.752 

3.720 

3.687 

3.655

3.623

25' longitude.

Inches. 

6.422 

6.383 

6. 345 

6.307 

6.268 

6.230

6.192 

6.153 

6.114 

6.075 

6.037 

5.998

5.959 

5. 920 

5.881 

5.842 

5.803 

5.764

5.725 

5.685 

5. 646 

5.607 

5. 5C7 

5.528

5.489 

5. 449 

5.410 

5.370 

5.330 

5.291

5.251 

5. 211 

5.171 

5.131 

5.092 

5.052

5.012 

4. 972 

4.931 

4.891 

4.851 

4. 811

4.771 

4.730 

4.690 

4.650 

4. 609 

4.569

4. 529

30' longitude.

Inches. 

7.706 

7.660 

7.614 

7.568 

7.522 

7.476

7.430 

7.384 

7.337 

7.290 

. 7.244 

7.198

7.151 

7.104 

7.057 

7.010 

6.963 

6.916

6.869 

6.822 

6.775 

6.728 

6.680 

6.634

6.586 

6.539 

6.491 

6.443 

6. 396 

6.349

6.301 

6.253 

6.205 

6.157 

6.110 

6.062

6.014 

5. 966 

5.917 

5. 869 

5.821 

5.773

5.725 

5.676 

5.628 

5. 579 

5.531 

5.483

5. 434

Ordinates of developed 

parallel.

Longitude interval.

' 5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

'

5 

10 

15 

20 

25 

30

64°

Indies. 

0.001 

.003 

.008 

.013 

.021 

.030

66°

0.001 

.003 

.007 

.013 

.020 

.029

68°

' 0.001 

.003 

.007 

.012 

.019 

. .027

70°

0.001 

.003 

.006 

.011 

.017 

.024

72°

0.001 

.003 

.006 

.010 

.016 

.023

65°

Inches. 

0.001 

.003 

.007 

.013 

.020 

.029

67°.

0.001 

.003 

.007 

.012 

.019 

.028

69°

0.001 

.003 

.006 

.011 

.018 

.026

71° °

0.001 

.003 

.006 

.010 

.016 

.024
GEOGRAPHIC TABLES A&D FORMULAS. 57

TABLE 7-. Coordinates for projection of maps (scale

 

[From Smithsonian Geographical Tables.]

 Continued.

Latitude of 

parallel.

o / 

72 00 

10 

20 

30 

40 

50

73 00 

10 

20 

30 

40 

50

74 00 

,10 

20 

30 

40 

50

-75 00 

10 

20 

30 

40 

50

76 00 

10 

20 

30 

40 

50

77 00 

10 

20 

30 

40 

50,

78 00 

10 

20 

30 

40 

50

79 00 

10 

20 

30 

40 

50'

80 00

Meridia- n's,! distances 

from 

even 

degree 

parallels.

Inches.

5.858 

11.716 

17. 573 

23. 431 

29. 289

5.858 

11. 717 

17.575 

23.434 

29.292

5.859 

11.718 

17. 577 

23. 436 

29. 295

5.860 

11.719 

17.578 

23. 438 

29. 298

5.860 

11. 720 

17. 580 

23.440 

29. 300

5.860 

11. 721 

17.582 

23. 442 

29.302

5.861 

11. 722 

17.583 

23. 444 

29.304

5.861 

11.723 

17.584 

23. 445 

29. 306

Abscissas of developed parallel.

5' longitude.

Inches. 

.906 

.898 

.889 

.881 

.873 

. .865

.857 

.849 

 .841 

.832 

.824

.816

.808 

.800 

.791 

.783

.775 

.767

.759 

.750 

 .742 

.734 

.726 

.717

.709 

.701 

.692 

. .684 

. .676 

.668

.659 

.651 

.643 

.634 

.626 

.618

.609 

.601 

.593

.584 

.576 

.568

.659 

.551 

.542 

.534 

.526 

.517

.569

10' longitude.

Inches. 

1. 811 

1.795 

1.779 

1.763 

1.746 

1.730

1.714 

1.697 

1.681 

1.665 

1.648 

1.632

- 1. 616 

1.599 

1.583 

1.566 

1.550 

1.534

1.517 

1.501 

1.484 

1.468 

1.451 

1.435

1.418 

1. 402 

1.385 

1.368 

1.352 

' 1. 336

1.319 

1.302 

1.285 

1.269 

1.252 

1.235

1.219 

1.202 

1.185 

1.169 

1.152 

1. 135

1.119 

1.102 

1.085 

1. 068 

1.052 

1.035

1.018

15' longitude.

Inches. 

2.717 

2.693 

2.668 

2.644 

2.620 

2.595

2.571 

2. 546 

2.522 

2. 497 

2.473 

2.448

2.424 

2. 399 

2.374 

2. 350 

2.325 

2.300

2.276 

2.251 

2.226 

2.201 

2.177 

2.152

2.127 

2.102 

2.078 

2.053 

2.028 

2.003

1.978 

1.953 

1.928 

1.903 

1.878 

1.853

1.828 

1.803 

1.778 

1.753 

1.728 

1.703

1.678 

1.653 

1.628 

1.602 

1.577 

1.552

1.527

20' longitude.

Inches. 

\ 623 

3.590 

3.558 

3.525 

3.493 

3.46.0

3.428 

3.395 

3. 362 

3.330 

3.297 

3.264

3.232 

3.199 

3.160 

3.133 

3.300 

3.067

3.034 

3.002 

2.968 

2.935 

2. 902 

2.870

2.836 

2.803 

2.770 

2.737 

2.704 

2.671

2.638 

2.604 

2.571 

2.538 

2.504 

2.471

2.438 

2.404 

2.371 

2.338 

2. 304 

2.270

2. 237 

2. 204 

2.170 

2. 136 

2. 103 

2.070

2.036

25' longitude.

Inches. 

4.529 

4.488 

4.447 

4.407 

4.366 

4.325

4.285 

4.244 

4.203 

4.162 

4.121 

4.081

4.040 

3.999 

3.957 

3.916 

3.875 

3.834

3.793 

3.752 

3.711 

3.669 

3.628 

3.587

3.546 

3.504 

3.463 

3.421 

3.380 

3.339

3.297 

3. 256 

3.214 

3.172 

3.131 

3.089

3.047 

3.005 

2. 964 

2. 922 

2.880 

2.838

2.797 

2.755 

2.713 

2.671 

2.629 

2.587

2. S45

30' longitude.

Inches. 

5.434 

5.386 

5.336 

6.288 

5. 239 

5. 190

6.141 

5. 092 

5.044 

4. 994 

4.945 

4.897

4.847 

4.798 

4.748 

4.699 

4.650 

4.601

4.552 

4.502 

4.453 

4.403 

4.354 

4.304

4.255 

4.205 

4.155 

4.105 

4.056 

4.006

3.956 

3.907 

3.856 

3.806 

3.757 

3.706

3.656 

3.606 

3.556 

3.506 

3.456 

3.406

3.356 

3.305 

3.255 

3.205 

3.155 

3.104

3.054

Ordinates of developed 

 parallel.

Longitude interval.

5 

10 

15 

20 

26 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

72°

Indies. 

0.001 

.003 

.006 

.010 

. 016 

.023

74°

0.001 

.002 

.005 

.009 

.014 

.020

76°

0.001 

.002 

.005 

.008 

.013 

.018

78°

0.000 

.002 

.004 

.007 

.011 

.016

73°

Inches. 

0. 001 

.002 

.005 

.010 

.015 

.021

75°

0.001 

.002 

.005 

.009 

.013 

.019

77°

0.000 

.002 

.004 

.007 

.012 

.017

79°

0.000 

.002 

.004 

.006 

.010 

.014
58 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 8. Coordinates for projection of maps (scale SS

o 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

o / 

0 00

10 

20 

30 

40 

50.

1 00

10 

20 

30 

40 

50

2 00

10 

20 

30 

40 

60

3 00

10 

20 

30 

40 

50

4 00

10 

20 

30 

40 

50

5 00

10 '20 

30 

40 

50

6 00

10 

20 

30 

40 

50

7 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.

11. 451 

22.901 

34.352 

45. 803 

57.254

68. 704

11. 451 

22.901 

34.352 

45.803 

57.254

08. 704

11. 451

22.902 

34.353 

45. 804 

57. 254

'68.705

11. 451 

22. 902 

34. 353 

45. 804 

57.255

68. 706

11.451 

22. 903 

34.354 

45. 805 

57. 256

68. 708

11. 452 

22. 903 

34.855 

45. 806 

57.258

68. 710

11.452 

22. 904 

31.356 

45. 808 

57. 260

68.712

Abscissas of developed parallel.

5' longitude.

Inches. 

5.764

5.764 

5.764 

5.764 

5.764 

5.764

5.764

5.763 

5.763 

5.762 

5.762 

5.761

5.761

5.760 

5.759 

5.759

5.758 

5.757

5.756

5.756 

5.754 

5.753 

5.752 

5.751

5.750

5.749 

5.748 

5.746 

5.745 

5.744

5.743

5.741 

5.739 

5.738 

5.736 

5.735

5.733

5. 731 

5.729 

5.727 

5.726 

5.724

5.722

10' longitude.

Inches. 

11.529

11.528 

11.528 

11.528 

11.528 

11. 527

11.527

11.526 

11. 525 

11.524 

11. 524 

11. 523

11.522

11.520 

11.519 

11. 517 

11. 516 

11. 514

11.513

11. 511 

11.509 

11.507 

11.505 

11.503

11.501

11. 498 

11.496 

11.493 

11.490 

11.488

11.485

11. 482 

11.479 

11. 476 

11. 472 

11.469

11.466

11.462 

11. 458- 

11.455 

11.451 

11. 447

11.443

15' longitude.

Inches. 

17. 293

17. 293 

17.292 

17. 292 

17. 291 

17. 291

17.291

17. 289 

17. 288 

17.287 

17. 285 

17. 284

17.283

17. 281 

- 17. 278 

17. 276 

17. 274 

17. 272

17. 270

17.267 

17. 264 

17.260 

17. 257 

17.254

17.251

17.247 

17. 243 

17. 240 

17. 236 

17. 232

17.228

17. 223 

17. 218 

17.213 

17. 209 

17. 204

17.199

17. 193 

17. 188 

17. 182 

17. 177 

17. 171

17. 165

20' longitude.

Inches. 

23.058

23.057 

23.056 

23. 056 

23.055 

23. 054

23.054

23. 052 

23.050 

23. 049 

23.047 

23. 045

23.044

23. 041 

23. 038 

23.035 

23. 032 

23. 029

23. 026

23. 022 

23. 018 

23. 014 

23. 010 

23.006

23. 002

22. 996 

22. 991 

22. 986 

22. 981 

22. 976

22.970

22. 964 

22. 958 

22. 951 

22. 945 

22:938

22. 932

22. 924 

22.917 

22. 910 

22. 902 

22. 894

22. 887

25' longitude.

Inches. 

28. 822

28. 821 

28.821 

28. 820 

28. 819 

28. 818

28.818

28.816 

28. 813 

28.811 

28.809 

28.807

28.805

28. 801 

28. 797 

28. 794 

28.790 

28. 786

28. 783

28. 778 

28. 773 

28. 767 

28. 762 

28. 757

28. 752

28. 746 

28. 739 

28. 733 

28. 726 

28. 720

28. 713

28. 705 

28. 697 

28. 689 

28. 681 

28. 673

28.665

28.656 

28.646 

28.637 

28. 628 

28. 618

28.609

30' longitude.

Inches. 

34.686

34.585 

34.585 

34. 583 

34.583 

34. 582

34.581

34.579 

34.576 

34. 573 

34.571 

34.568

34.565

34. 561 

34.556 

34.552 

34.548 

34.543

34. 539

34. 533 

34. 527 

34.520 

34. 514 

34. 508

34.502

34.495 

34. 487 

34. 479 

34.471 

34. 463

34.456

34.446 

34.436 

34.427 

34.417 

34. 408

34. 398

34. 387 

34. 375 

34. 364 

34. 353 

34.342

34.330

Ordinates of developed 

parallel.

Longitude 

interval.

/ 

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

0°

Inch. 

0.000 

.000 

.000 

.000 

.000 

.000

2°

0.000 

.001 

.001 

.002 

.004 

.005

4°

0.000 

.001 

.003 

.005 

.007 

.011

6°

0.000 

.002 

.004 

.007 

.011 

.016

1°

Inch. 

0.000 

.000 

.001 

.001 

.002 

.003

3°

0.000 

.001 

.002 

.003 

.005 

.008

5°

0.000 

.001 

.003 

.006 

.009 

.013

7°

0.000 

.002 

.005 

.008 

.013 

.018
GEOGEAPHIC TABLES AND FORMULAS. 59

TABLE 8. Coordinates for projection of maps (scale siri^) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

O '

7 00

10 

20 

30 

40 

50

8 00

10 

20 

30 

40 

50

9 00

10 

20 

30 

40 

60

10 00

10 

20 

30 

40 

50

11 00

10 

20 

30 

40 

50

12 00

10 

20 

30 

40 

50

13 00

10 

20 

30 

40 

50

14 00

Meridional distances 

from 

even 

degree 

parallels.

Inches. 

08. 712

11.452 

22. 905 

34.358 

45. 810 

67. 262

68. 715

11.453 

22. 906

34.359

45.812 

57. 265

68.718

11.454 

22. 907 

33. 361 

45. 814 

57. 268

68. 722

11.454 

22. 909 

34.263 

45.817 

57. 272

68. 726

11. 455 

22. 910 

34. 365 

45. 820 

67. 275

68.730

11.456 

22. 912 

34.367 

45. 823 

57. 279

68. 735

11.457 

22.913 

34.370 

45. 827 

57. 284

68. 740

Abscissas of developed parallel.

5' longitude.

Inches. 

5.722

5.720 

5.717 

5.715 

5.713 

5.711

5.709

5.706 

5.704 

5.701 

5.699 

5.690

5.694

5.691 

5.688 

5.686 

5.683 

5.680

5.677

5.674 

5.671 

5.668 

5.665 

5.662

5.659

5.656 

5.652 

6. 649 

5.646 

5.642

5.639

5.636 

5.632 

5.628 

6.625 

5. 621

5.618

5.614 

6.610 

5.606 

6.602 

5.598

5.594

10' longitude.

Inches. 

11.443

11.439 

11.435 

11.430 

11.426 

11. 422

11. 417

11.412 

11.407 

11.403 

11.398 

11. 393

11.388

11.382 

11. 377 

11. 371 

11. 366 

11.360

11. 355

11.349 

11. 343 

11. 337 

11. 331 

11.324

11. 318

11.312 

11.305 

11.298 

11. 292 

11.285

11. 278

11.271 

11. 264 

11.257 

11.250 

11.242

11. 235

11. 227 

11.220 

11. 212 

11.204 

11. 196

11.188

15' longitude.

Inches. 

17. 165

17.159 

17. 152 

17. 146 

17.139 

17. 132

17. 126

17.119 

17.111 

17.104 

17.096 

17.089

17.082

17. 073 

17.065 

17.057 

17. 049 

17.040

17. 032

17.023 

17. 014 

17.005 

16. 996 

16.987

16. 978

16. 968 

16. 958 

16. 948 

16.938 

16.928

16. 918

16. 907 

16. 896 

16.885 

36.874 

.16. 864

16. 853

16.841 

16. 829 

16. 818 

16. 806 

16. 794

16. 783

20' longitude.

Inches. 

22.887

22. 878 

22. 869 

22.861 

22. 852 

22. 843

22.834

22.825 

 22.815 

22.805 

22.795 

22. 780

22.776

22.764 

22.754 

22. 742 

22.732 

22. 720

22. 710

22. 698 

22.685 

22. 673 

22. 661 

22. 649

22. 637

22. 624 

22. 610 

22. 697 

22.584 

22.570

22. 557

22.642 

22.528 

22. 514 

22. 499 

22.485

22. 470

22.455 

22.439 

22. 424 

22. 408 

22. 392

22. 377

25' longitude.

Inches. 

28.609

28. 598 

28. 587 

28. 576 

28. 565 

28.554

28.643

28.531 

28.519 

28.507 

28.494 

28.482

28.470

28. 456 

28. 442 

28.428 

28.415 

28. 401

28. 387

28. 372 

28. 357 

28.342 

28.327 

28. 311

28.296

28. 280 

28. 263 

28. 246 

28. 230 

28. 213

28. 196

28. 178 

28. 160 

28.142 

28. 124 

28. 106

28.088

28.069 

28. 049 

28. 030 

28. 010 

27. 991

27. 971

30' longitude.

Inches. 

34.330

34. 317 

34.304 

34.291 

34.278 

34. 265

34. 252

34.237 

34. 222 

34.208 

34.193 

34.178

34. 163

34.147 

34.] 30 

34. 114 

34. 097 

34.081

34. 064

34. 046 

34.028 

34.010 

33.992 

33. 973

33. 955

33. 935 

33. 915 

33. 895 

33.875 

33.855

33. 835

33. 814 

33. 792 

33. 770 

33. 749 

33. 727

33. 706

33.682 

33. 659 

33. 635 

33. 612 

33.589

33. 565

Ordinates of developed 

parallel.

Longitude interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

70

Inch. 

0.000 

.002 

005 

.008 

.013 

.018

9°

0.001 

.003 

.006 

.010 

.016 

.023

11°

0.001 

.003 

.007 

.013 

,020 

.028

13°

0.001 

.004 

.008 

.015 

.023 

.033

8°

Inch. 

0.001 

.002 

.005 

.009 

.014 

.021

10°

0.001 

.003 

.006 

.011 

.018 

.026

12°

0.001 

.003 

.008 

.014 

.021 

.031

14°

0.001 

.004 

.009 

.016 

.025 

.035
GO GEOGRAPHIC TABLES AND FORMULAS.

TABLE 8. Coordinates for projection of maps (scale ssimr) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of. 

parallel.

0 1

14 00

10 

20 

30 

40 

50

15 00

10' 

20 

30 

40 

50

1C 00

10 

20 

30 

40 

50

17 00'

10 

20 

30 

40 

50

18 00

10 

20 

30 40' 

50

19. 00.

10' 

20 

30 

40 

50

20 00

10 

.20 

30 

40 

50.

21 00 :

Meridional distances 

from 

even 

degree 

parallels.

Inches. 

68. 740

11. 458 

..22. 915 

34. 373 

45.830 

57.288

68. 746

11.459 

22. 917 

34.376 

45. 834 

57. 293

68. 752

11.460 

22. 919 

34. 379 

45.838 

57. 298

68.758

11. 461 

22. 921 

34. 382 

45. 843 

57.304

68. 764

11.462 

22.924 

34. 386 

45. 848 

57. 310

68. 771

11. 463

22. 926 

34. 390 

45.853 

.. 57.316

68. 779

11. 464 

22. 929 

34. 394 

45.858 

57. 322

68.787

Abscissas of developed parallel.

5' longitude.

Inches. 

5.594

5.590 

5.586 

5. 582 

5.578 

5.573

5.569

5.565 

5.560 

5.556 

5.551 

5.547

5.542

5.538 

5.533 

5.528 

5.524 

5.519

5.514

5.509 

5.504 

5.499 

5.494 

5.489

5.484

5.479 

5.473 

5.468 

5.463 

5.458

5.452

 5.447 

5.441 

5.436 

5.430

< 5. 424

5.419

5.413 

5.407 

5.401 

5.396 

5.390

5.384

10'longi- 

. tude.

Inches. 

11. 188

11. 180 

11.172 

11. 163 

11. 155 

11. 147

11. 138

11. 130 

11. 121 

11. 112 

11. 103 

11.094

11. 085

11.076 

11.066 

11. 057 

11. 047 

11. 038

11.028

11. 018 

11. 008 

10. 998 

10. 988 

10. 978

 30.968

10. 957 

10. 947 

10. 936 

10. 926 

10. 915

10.905

10. 893 

10.882 

10.871 

10. 860 

10.849

10.838

10.826 

10. 814 

10.803 

10.79'1 

10. 779

10.768

15'longitude.

Inches. 

16. 783

16. 770 

16. 758 

16.745 

16. 733 

16. 720

16.708

16. 694 

16. 681 

16. 667 

16.654 

16. 641

16. 628

16. 613 

16. 599 

16. 585 

16. 571 

16. 556

16.542

16. 527 

16.512 

16. 497 

16. 482 

16. 467

16. 452

16. 436 

16. 420 

16. 404 

16. 389 

16. 373

16.357

16. 340 

16. 324 

16. 307 

16.290 

16. 274

16.257

16. 239 

16. 222 

16. 204 

- 16. 187 

16. 169

16. 151

20' longitude.

Inches. 

22. 377

22.360 

22. 344 

22. 327 

22. 310 

22. 294

22.277

22.259 

22. 241 

22. 223 

22. 206 

22.188

22. 170

22. 151 

22. 132 

22.113 

22. 094 

22. 075

22. 056

22. 036 

22. 016 

21. 996 

21. 976 

21.956

21.936

21.915 

21.894 

21. 872 

21.852 

21. 830

21.809

21. 787 

21. 765 

21. 742 

21. 720 

21. 698

21. 676

21.652 

21. 629 

21.605 

21. 582 

21. 558

21.535

25' longitude.

Inches. 

27. 971

27.950 

27. 930 

27. 909 

27. 888 

a. 867

27.846

27. 824 

27. 802 

27. 779 

27. 757 

27. 735

 27. 713

27. 689 

27. 665 

27. 642 

27. 618 

27. 594

27. 571

27.546 

27.521 

27. 495 

27.470 

27.445

27.420

27. 394 

27. 367 

27. 341 

27. 315 

27.288

27.262

27. 234 

27. 206 

27. 178 

27.150 

27.-123

27.095

27.065 

27. 036 

27.007 

26. 978 

26. 948

26. 919

30' longitude.

Inches. 

33. 565

33. 540 

33.515 

33. 490 

33. 465 

33.440

33.415

33. 389 

33. 362 

33. 335 

33.308 

33. 282

33.255

33. 227 

33. 198 

33. 170 

33.142 

33. 113

33.085

33.055 

33.025 

32. 994 

32. 964 

32. 934

32.904

32.872 

32. 840 

32. 809 

32. 777 

32. 746

32.714

32. 680 

32. 647 

32. 614 

32.580 

32. 547

32. 513

32. 478 

32. 443 

32. 408 

32. 373 

32. 338

32. 303

Ordinates of developed 

parallel.

Longitude interval.

' 5. 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

14°

Inches. 

0.001 

.004 

.009 

.016 

.025 

.035

16°

0.001 

.004 

.010 

.018 

.028 

.040

18°

0.001 

.005. 

.011 

.020 

.031 

. .044

20°

0.001 

.005 

.012 

.022 

.034 

.049

15°

Inches. 

0.001 

.004 

.009 

.017 

.026 

.038

17°

0.001 

.005 

.011 

.019 

.029 

.042

19°

0.001 

.005 

.012 

.021 

.032 

.046

21°

0.001 

.006 

.013 

.022 

.035 

.051
GEOQKAPHIC TABLES AND FOKMULAS.

TABLE 8. Coordinates for projection of maps (scale g-g-g-^) Continued. 

[From Smithsonian Geographical Tables.]

61

Latitude of 

parallel.

0 /

21 00

10 

20 

30 

40 

50

22 00

10 

20 

30 

40 

50

23 00

10 

20 

30 

40 

50

24 00

10 

20 

30 

40 

50

25 00

10 

20 

30 

40 

50

26 00

10 

20 

30 

40 

50

27 00

10 

20 

30 

40 

50

28 00

Meridional distances 

from 

even 

degree 

parallels.

Inches. 

68. 787

11.466 

22. 932 

34.397 

45.863 

57. 329

68. 795

11.467 

22.934 

34. 401 

45. 868 

57. 336

68. 803

11.469 

22. 937 

34.406 

45. 874 

57.343

68. 812

11.470 

22. 940 

34.410 

45. 880 

57. 350

68. 821

11.472 

22. 943 

34.415 

45. 886 

57. 358

, 68.830

11.473 

22. 946 

34.419 

45. 892 

57. 365

68. 838

11. 475 

22. 950 

34. 424 

46. 899 

. 57. 374

68.849

Abscissas of developed parallel.

5' longitude.

Inches. 

5.384

5.378 

5.372 

5.366 

5.359 

5.353

5.347

5.341 

5.334 

5.328 

5.322 

5.315

' 5.309

5.-302 

5.296 

5.289 

5.282 

5.276

'5. 269

5.263 

5.256 

5.249 

5.242 

5.235

5.227

5.220 

5. 213 

5.206 

5. 199 

5.191

5. 184

5.177 

5.169 

5.162 

5,154 

5.147

5.140

5.132 

5.124 

5.116 

5.109 

5.101

5.093

10' longitude.

Inches. 

10. 768

10.755 

10. 743 

10. 731 

10. 719 

10. 707

10. 694

10. 682 

10.669 

10. 656 

10. 643 

10. 631

10.618

10. 604 

10.591 

10. 578 

10. 565 

10.551

10. 538

10. 526 

10. 512 

10. 498 

10. 483 

10. 469

10. 455

10. 441 

10. 426 

10.412 

10. 397 

10.383

10. 369

10.354 

10. 339 

10. 324 

10. 309 

10.294

10.279

10. 264 

10. 248 

10. 233 

10. 218 

10.202

10. 187

15' longitude.

Inches. 

16. 151

16.133 

16.115 

16. 097 

16. 078 

16. 060

16. 042

16.022 

16.003 

15.984 

15. 965 

15. 946

15. 927

15. 907 

15.887 

15. 867 

15. 847 

15.827

15. 807

15. 789 

15. 767 

15. 746 

15. 725 

15. 704

15. 682

15. 661 

15. 639 

15.618 

15.596 

15.575

15.553

15. 531 

15.508 

"15.486 

15. 463 

15. 441

15. 419

 15.396 

15.373 

15: 349 

15. 326 

15. 303

15.280

20' longitude.

Inches. 

21. 535

21. 511 

21. 486 

21. 462 

21. 438 

21. 413

21.-389

21.363 

21.338 

21. 312 

21.287 

21.261

21. 236

21.209 

21. 182 

21. 156 

21.129 

21. 102

21." 076

21. 052 '21. 023 ' 

20. 995 

20. 967 

20. 938

20. 910

20.881 

20. 852 

20. 824 

20. 795 

20.766

20.. 737

20:708 

20. 678 

'20. 648 

20. 618 

20: 588

20. 558

20. 528 

20. 497 

20. 466 

20. 435 

20. 404

20. 374

25' longitude.

Inches. 

26. 919

26. 889 

26. 858 

26.828 

26. 797 

26. 767

26. 736

26. 704 

26.672 

26. 641 

26. 609 

26. 577

26. 545

26.511 

26. 478 

26. 445 

26.412 

26. 378

26. 345

26. 315 

26. 279 

26. 244 

26. 209 

26. 173

26, 137

26. 101 

26. 065 

26. 029 

25. 993 

25. 958

25. 922

25. 884 

25.847 

25. 810 

25. 772 

- 25.735

25. 698

25. 659 

25. 621 

25. 582 

25.544 

25. 505

25. 467

30' longitude.

Inches. 

32. 303

32/J66 

32. 230 

32. 193 

32. 156 

32. 120

32. 083

32. 045 

32.006 

31.969 

31.930 

31.892

31.853

31.813 

31.774 

31. 733 

31.694 

31.654

31. 614

31. 577 

31. 535 

31. 493 

31. 450 

31.408

31. 365

31 . 322 

31.279 

31.235 

31.192 

31. 149

31.106

31.061 

31.01.7 

30. 972 

30. 927 

30. 882

30.838

30. 791 

30. 745 

30. 699 

30. 653 

30. 607

30. 560

Ordinates of developed 

parallel.

Longitude 

interval.

5 

10 

15, 

20 

25. 

30

5 

10 

15 

20 

' 25 

30

5 

10 

15 

20 

25 

' ; '30

5 

10 

15 

20 

25 

30

21°

Inches. 

0.001 

.006 

.013 

.022 

.035 

.051

23°

0. 001. 

.006 

.014 

.024 

.038 

.054

25°

0.002 

.006 

.014 

. 026 

.040 

.058

27°

0. 002 

.007 

.015 

.027 

.042 

.061

. 22°

Inches. 

0. 001 

.006 

.013 

.023 

.036 

.052

24°

0.002 

.006 

.014 

.025 

.039 

.056

26°

0. C02 

.007 

.015 

. 026 

.011 

.059

28°

0.002 

.007 

.016 

.028 

.043 

.063
62 GEOGRAPHIC TABLES AND FORMULAS.

TABLK 8. Coordinates for projection of maps (scale

[Prom Smithsonian Geographical Tables.]

Continued.

Latitude of 

parallel.

0 /

28 00

10 

20 

30 

40 

50

29 00

10

20 

30 

40 

50

30 00

 10 

20 

30 

40 

50

31 00

10 

20 

30 

40 

50

32 00

10 

20 

30 

40 

50

33 00

10 

20 

30 

40 

50

34' 00

10 

20 

30 

40 

50

35 00

Meridional distances 

from 

even 

degree 

parallels.

Inches. 

68. 849

11. 476 

22. 953 

34. 430 

45. 906 

57. 383

68.859

11.478 

22. 957 

34. 435 

45. 913 

57. 391

68. 870

11.480 

22. 960 

34.440 

45. 920 

57. 400

68.880

11.482 

22. 964 

34.446 

45. 927 

57. 409

68.891

11. 484 

22. 967 

34. 451 

45. 934 

57. 418

68.902

11. 485 

22. 971 

34. 456 

45.942 

57. 427

68. 913

11. 487 

22. 975 

34. 462 

45. 949 

57. 437

68. 924

Abscissas of developed parallel.

5' longitude.

Inches. 

5.093

5.085 

5.077 

5.069 

5.061 

5.054

5.046

5.037 

5.029 

5.021 

5.013 

5.004

4.996

4.988 

4.979 

4.971 

4. 962 

4.954

4.945

4.937 

4.928 

4.919 

4.910 

4.902

4.893

4.884 

4.875 

4.866 

4.857 

4.848

4.839

4.830 

4.821 

4.812 

4.802 

4.793

.4.784

4.774 

4.765 

4.755 

4.746 

4.737

4.727

10' longitude.

Inches. 

10.187

10. 171 

10. 165 

10. 139 

10. 123 

10. 107

10. 091

10.075 

10.058 

10. 042 

10. 025 

10.009

9.993

9. 976 

9.959 

9.942 

9.925 

9.908

9.891

9.873 

9.856 

9.838 

9.821 

9.804

9.786

9.768 

9.750 

0. 732 

9.714 

9.696

9.679

9.660 

9.642 

9.623 

9.605 

9.586

9.568

9.549 

9.530 

9.511 

9.492 

9.473

9.454

15' longitude.

Inches: 

15. 280

15. 256 

15. 232 

15. 208 

15. 185 

16. 161

15. 137

15.112 

15. 087 

15. 063 

15.038 

15. 013

14. 989

14. 963 

14. 938 

14. 912 

14.887 

14. 862

14. 836

14.810' 

14. 784 

14. 758 

14. 731 

14. 705

14. 679

14. 652 

14. 625 

14. 598 

14.572 

14. 545

14.518

14. 490 

14. 462 

14. 435 

14. 407 

14. 379

14. 352

14. 323 

14.295 

14. 267 

14. 238 

14. 210

14. 181

20' longitude.

Indies. 

20. 374

20. 342 

20.310 

20. 278 

20. 246 

20. 214

20. 182

20. 150 

20. 117 

20.084 

20. 051 

20. 018

19. 985

19. 951 

19. 917 

19. 883 

19. 849 

19. 815

19. 782

19. 747 

19. 712 

19. 677 

19.642 

19. 607

19. 572

19. 536 

19. 500 

19. 465 

19. 429 

19. 393

19.357

19. 320 

19.283 

19.246 

19.210 

19. 173

19. 136

19. 098 

19. 060 

19.022 

18. 984 

18.946

18. 908

25' longitude.

Inches. 

25.467

25. 427 

25. 387 

25. 347 

25. 308

25.268

25.228

25. 187 

25.146 

25. 105 

25. 064 

25.022

24. 981

24. 939 

24. 896 

24. 854 

24. 812 

24. 769

24. 727

24. 683 

24. 640 

24. 596 

24. 552 

24. 509

24.465

24. 420 

24. 376 

24. 331 

24. 286 

24. 241

24.190

24. 150 

24. 104 

24. 058 

24.012 

23. 966

23. 920

23. 872 

23.825 

23. 778 

23. 730 

23. 683

23.636

30' longitude.

Inches. 

30.560

30. 513 

30.465 

30. 417 

30. 369 

30. 321

30. 274

30. 224 

30. 175 

30. 126 

30.076 

30. 027

29.978

29.927 

29.876 

29. 825- 

29. 774 

29.723

29. 672

29. 620 

29. 568 

29. 515 

29. 463 

29. 411

29.358

29. 305 

29. 251 

29. 197 

29.143 

29. 089

29.036

28. 980 

28. 925 

28.870 

28.814 

28. 759

28.704

28. 647 

28. 590 

28. 533 

28. 476 

28. 420

28. 363

Ordir.ates of developed 

parallel.

Longitude interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

28°

Inches. 

0.002 

.007 

.016 

.028 

.043 

.063

30°

0.002 

.007 

.016 

.029 

.045 

.065

32°

0.002 

.007 

.017 

.030 

.047 

.068,

34°

0.002 

.008 

.017 

.031 

.049 

.070

29°

Inches. 

0.002 

.007 

.016 

.028 

.044 

.064

31°

0.002 

.007 

.017 

.030 

.046 

.067

33°

0.002 

.008 

.017 

.031 

.048 

.069

35°

0.002 

.008 

.018 

.031 

.049 

.071
GEOGRAPHIC TABLES AND FORMULAS. 63

TABLE 8. Coordinates for projection of maps (scale sarjnr) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

o / 

35 00

10 

20 

30 

 4.0 

50

36. 00

10 

20 '30 

40 

50

37 00

10 

20 

30 

40 

50

38 00

10 

20 

30 

40 

50

39 00

10 

20 

30 

40 

50

40 00

10 

20 

30 

40 

50

41 00

10 

20 

30 

40 

50

42 00

Meridional distances 

from 

even 

degree ' 

parallels.

Inches. 

68. 924

11. 489 

. 22.978 

34. 468 

45. 957 

67. 446

68. 935

11.491 

22. 983 

34.474

45.965 

57. 457;

68.948

11. 493 

22. 986 

34. 480 

45. 973 

57. 466

68.959

11. 495 

22.990 

34.485 

45. 980 

57.475

68.970

11.497 

22. 994 

34.491 

45. 988 

57.485

68. 982

11. 499 

22. 998 

34. 497 

45. 996 

57. 495

68. 994

11.501 

23. 002 

34. 503 

46. 004 

57.506

69.007

Abscissas of developed parallel.

5' longitude.

Inches. 

4.727

4.717 

4.708 

4.698 

4.688 

..4.679

4.669

4.659 

4.649 

4.639 

4.629 

4.619

4. 609

4. 599 

4.589 

4.579 

4.568 

4.558

4.548

4.538 

4. 527 

4.517 

4.506 

4.496

4.486

4.475 

4.464 

4.454 

4.443 

4.433

4.422

4.411 

4.400 

4.389 

4.378 

4.368

4.357

4.346 

4.335 

4.324 

4.312 

4.301

4.290

10' longitude.

Inches. 

9.454

9.435 

9. 415 

9.396 

9.377 

9.357

9.338

9.318 

9.298 

9.278 

9.258 

9.238

9.219

9.198 

9. 178 

9.157 

9.137 

9.117

9.096

9.076 

9.055 

9.034 

9.013 

8.992

8.971

8.950 

8.929 

8.908 

8.886 

8.865

8.844

8.822 

8.800 

8.779 

8.757 

8.735

8:713

8.691 

8.669 

8.647 

8.625 

8.603

8.581

15' longitude.

Inches. 

14. 181

14. 152 

14. 123 

14.094 

" 14. 065 

14. 036

14. 007

13. 977 

13.947 

13.917 

13.887 

13. 858

1Q QOC JLo. oZO

13. 797 

13. 767 

13.736 

13. 706 

13. 675

13. 645

13. 613 

13. 582 

13.551 

13.520 

13.488

13.457

13.425 

13.393 

13.361 

13. 330 

13. 298

13. 266

13.233 

13. 201. 

13.168 

13. 135 

13. 103

13. 070

13. 037 

13. 004 

12. 971' 

12. 937 

12. 904

12. 871

20' longitude.

Inches. 

18. 908

18. 870 

18. 831 

18. 792 

18.753 

18. 714

18. 676

18. 636 

18.596 

18.550 

18. 517 

18. 477

18.437

18. 396 

18.356 

18.315 

18.274 

18. 234

18. 193

18. 151 

18. 109 

18. 068 

18. 026 

17. 984

17. 943

17. 900 

17. 858 

17. 815 

17. 773 

17. 730

.17. 688

17. 644 

17. 601 

17.557 

17. 514 

17. 470

17.427

17. 383 

17. 338 

17. 294 

17. 250 

17.205

17. 161

25' longitude.

Inches. 

23. 636

23.587 

23. 539 

23.490 

23. 442 

23. 393

23.345

23. 295 

23.245 

23.195 

23.146 

23. 096

23.046

22. 995 

22. 944 

22. 894 

22. 843 

22. 792

22. 741

22.689 

22. 637 

22.585 

22. 533 

22.481

22. 429

22. 375 

22. 322 

22. 269 

22. 216 

22. 163

22.110

22. 055 

22. 001 

21.947 

21. 892 

21.838

21. 784

21. 728 

2L.673 

21. 618 

21. 562 

21.507

21. 451

30' longitude.

Inches. 

28.363

28. 305 

28. 246 

28.188 

28. 130 

28.072

28. 014

27. 954 

27.894 

27.835 

27. 775 

27. 715

27. 656

27. 594 

27. 533 

27. 472 

27. 41.1 

27. 350

27.289

27.227 

27.164 

27.102 

27. 039 

26. 977

26. 914

26.851 

26. 787 

26. 723 

26. 659 

26. 595

26. 532

26.466 

26. 401 

26. 336 

26.271 

26. 206

26. 140

26. 074 

26. 007 

25.941 

25. 875 

25.808

25. 742

Ordinates of developed 

parallel.

Longitude interval.

5 

10 

15 

20 

25 

30

5 

10 

- 15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

35°

Inches. 

0.002 

.008 

.018 

.031 

.049 

.071

37°

0.002 

.'008 

.018 

. 032 

.050 

.073

39°

0.002 

°.008 

.018 

.033 

.051. 

.074

41°

0.002 

.008 

.019 

.033 

.052 

.075

36°

Indies. 

0.002 

.008 

.018 

.032 

.050 

.072

38°

0.002 

.008 

.018 

.033 

.051 

.073

40°

0.002 

.008 

.019 

.033 

.052 

.074

42°

0.002 

.008 

.019 

.033 

.052 

.075
64

TABLE 8. Coordinates for projection of maps (scale ^3-3-5-7) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

o / 

42 00

10 

20 

30 

40 

50

43 00

10 

20 

30 

40 

50

44 00

10 

20 

30 

40 

50

45 00

10 

20 

30 

40 

50

46 00

10 

20 

. 30 

40 

50

47 00

10 

20 

30 

40 

50

48 00

10 

20 

30 

40 

50

49 00

Meridional distances 

from 

even 

degree 

parallels.

Indies. 

69. 007

11.503 

23.006 

34.510 

46. 013 

57.516

69.019

11. 505 

23. 010 

34. 515 

46. 020 

57.525

69. 030

11. 507 

23. 014 

34. 522 

46. 029 

57.536

69. 043

11.509 

23. 018 

34.528 

46.037 

57.546

69.055

11.° 511 

23. 023 

34. 534 

46. 045 

57.557

G9. 068

11.513 

23.027 

34.540 

46. 053 

57. 567

69. 080

11.516 

23.031 

34. 546 

46. 062

57.577

69. 093

Abscissas of developed parallel.

5' longitude.

Inches. . 4.290

4.279 

4.268 

4.256 

4.245 

4. 234

4.222

4.211 

4.199 

4.188 

4.176 

4.165

4.153

4.142 

4.130 

4.118 

4.106 

9.095

4.083

4.071 

4.059 

4.047 

4.035 

4.023

4. Oil

3.999 

3.987 

3.975 

3.963 

3.951

3.938

3.926 

3.914 

3.901 

3.889 

3.877

3.864

3.852 

3.839 

3.827 

3.814 

3.802

3.789

10' longitude.

Inches. 

8.581

8.558 

8.535 

8.513 

8.490 

8.467

8.445

8.422 

8.399 

 8.376 

8.353 

8.330

8.307

8.283 

8. 260 

8.236 

8.213 

8.189

8.166

8.142 

8.118 

8.094 

8.070 

8.046

8.023

7.998 

7.974 

7. 950 

7. 925 

7.901

7. 877

7.852 

7.827 

7.803 

7.778 

7.753

7. 729

7.704 

7.679 

7.653 

7.628 

7.603

7.578

15' longitude.

Inches. 

12. 871

12. 837 

12. 803 

12.769 

12. 735 

12. 701

12.667

12.633 

12. 598 

12.564 

12. 529 

12. 494

12. 460

12. 425 

12. 390 

32.354 

12. 319 

12. 284

12. 249

12.213 

12.177 

12. 141 

12. 105 

12. 070

12. 034

11. 997 

11.961 

11. 925

11.. 888 

11. 852

11.815

11. 778 

11.741 

11. 704 

11. 667 

11. 630

11.593

11.555 

11.518 

11.480 

11.442 

11. 405

11. 367

20' longitude.

Inches. 

17. 161

17. 116 

17. 071 

17.025 

16.980 

16. 935

16. 890

16.844 

16. 798 

16. 751 

16.705 

16. 659

16. 613

16. 566 

16.519 

16. 473 

16. 426 

16. 379

16. 332

16. 284 

16. 236 

16. 188 

16. 141 

16. 093

16. 045

15. 997 

15. 948 

15. 899 

15.851 

15. 802

15. 754

15. 704 

15.655 

15. 606 

15. 556 

15. 507

15. 457

15.40? 

15. 357 

15. 307 

15.257 

15.206

15. 156

25' longitude.

Inches. 

21.451

21. 395 

21.338 

21.282 

21. 225 

21. 169

21. 112

21. 054 

20. 997 

20. 939 

20.882 

20. 824

20. 767

20. 708 

20. 649 

20. 591 

20. 532 

20. 473

20. 415

20. 355 

20. 295 

20. 236 

20.176 

20. 116

20. 056

19. 996 

19. 935 

19. 874 

19.813 

19. 753

19.692

19. 630 

19.569 

19. 507 

19.445 

19. 383

19. 322

19. 259 

19. 196 

19. 134 

19.071 

19.008

18. 945

30' longitude.

Inches. 

25. 742

25.674 

25. 606 

25.538 

25.470 

25. 402

25. 334

25.265 

25. 196 

25. 127 

25. 058 

24. 989

24. 920

24.849 

24. 779' 

24. 709 

24. 638 

24. 568

24.498

24. 426 

24. 354 

24. 283 

24.211 

24. 139

24.068

23. 995 

23. 922 

23. 849 

23. 776 

23. 703

23. 630

23. 556 

23.482 

23. 408 

23. 334 

23. 260

23. 186

23.111 

23.035 

22. 960 

22. 885 

22. 810

22. 734

Ordinates of developed 

parallel.

Longitude 

interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

42°

Inches. 

0.002 

.008 

.019 

.033 

.052 

.075

44°

0.002 

.008 

.019 

.034 

.052 

.075

46°

0.002 

.008 

.019 

.034 

.053 

.076

48°

0.002 

.008 

.019 

.033 

.052 

.075

43°

Inches. 

0. 002 

.008 

.019 

.033 

.052 

.075

45°

0.002 

.008 

.019 

.034 

.053 

.076

47°

0.002 

.008 

.019 

.034 

.052 

.075

49°

0.002 

.008 

.019 

.033 

.052 

.075
GEOGEAEHIC TABLES AND FOEMULAS. 65

TABLE 8. Coordinates for projection of maps (scale ^yj-^r) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

0 /

49 00

10 

20 

30 

40 

50

50 00

10 

20 

30 

40 

5C

51 00

10 

20 

30 

40 

50

52 00

10 

20 

30 

40 

50

53 00 '10

20 

30 

 40 

.50

54 00

10 

20 

30 

40 

50

55 00

10 

20 

30 

40 

50

56 00

Meridional distances 

from 

even 

degree 

parallels.

Inches. 

69. 093

11.517 

23. 035 

34.552 

46. 070

57.587

69. 105

11.520 

23.039

34. 558 

46. 078 

57. 598

69. 117

11.521 

23.043 

34. 564 

46. 086 

57. 607

69. 128

11. 523 

23. 047 

34.570 

46. 094 

57. 617

69. 140

11. 625 

23. 051 

34. 576 

46. 102 

57. 627

69. 152

11.527 

23. 055 

. 34.582 

46. 109 

57. 636

69. 164

11.529 

23. 059 

34. 588 

46. 117 

57. 646

69. 176

Abscissas of developed parallel.

5' longitude.

Inches. 

3.789

3.776 

3. 761 

3.751 

3.738 

3.725

3.713

3.700 

3.687 

3.674 

3.661 

3.648

3.635

3.622 

3.609 

3.596 

3. 583 

3.570

3.656

3.543 

3.530 

3.516 

3. 503 

3.490

3.477

3.463 

3.450 

3.436 

3.423 

3.409

3.396

3.382 

3.368 

3.355 

3.341 

3.327

3.314

3.300 

3.286 

 3.272 

3.258 

3.245

3.231

10' longitude.

Inches.

7.578

7.553 

7.527 

7.502 

7.476 

7.451

7.425

7.399 

7.374 

7.348 

7.322 

7.296

7.270

7.244 

7.218 

7.191 

7. 165 

7.139

7.113

7.086 

7.060 

7.033 

7. 006 

6.980

6.953

6.926 

6.899 

6.872 

6.845 

6.818

6.791

6.764 

6.737 

6.709 

6.682 

6.655

6.628

6.600 

6.572 

6.545 

6. 517 

6.489

6.462

15' longitude.

Inches. 

11. 367

11. 329 

11. 291 

11. 253 

11. 214 

11. 176

11. 138

11.099 

11.060 

11. 021 

10. 983 

10. 944

10. 905

10.866- 

10. 827 

10. 787 

10. 748 

10. 709

10. 669

10. 629 

10. 589 

10. 650 

10. 510 

10.470

10.430

10. 389 

10.349 

10. 309 

10. 268 

10. 228

10. 187

10. 146 

10. 105 

10. 064 

10. 023 

9.982

9.941

9.900 

9.859 

9.817 

9.776 

9.734

9.693

20' longitude.

Inches. 

15. 156

15. 105 

15. 054 

15. 003 

14. 952 

14. 901

14. 850

14. 799 

14.747 

14. 695 

14. 644 

14. 592

14. MO

14. 488 

14.436 

14. 383 

14. 330 

14. 278

14. 226

14. 172 

14.119 

14. 066 

14. 013 

13. 960

13. 906

13.852 

13. 798 

13. 746 

13.691 

13. 637

13. 583

13. 528 

13. 474 

13.419 

13. 364 

13. 310

13. 255

13. 200 

13. 145 

13. 089 

13. 034 

12. 979

12.924

25' longitude.

Inches. 

18. 945

18.882 

18. 818 

18. 754 

18. 690 

18. 627

18. 563

18.499 

18.434 

18. 369 

18. 305 

18. 240

18. 176

18. 110 

18. 045 

17. 979 

17. 913 

17. 848

17. 782

17.71C 

17. 649 

17. 583 

17. 516 

17. 450

17.383

17. 316 

17. 248 

17. 181 

17. 114 

17. 046

16. 979

16. 910 

16. 842 

16. 774 

16. 706 

. 16. 637

16. 569

16. 500 

16. 431 

36.362 

16. 293 

16. 224

16. 155

30' longitude.

Inches. 

22. 734

22. 658 

22. 581 

22. 605 

22. 429 

22. 352

22. 276

22. 198 

22.121 

22.043 

21. 965 

21. 888

21. 811

21. 732 

21. 653 

21. 574 

21. 496 

21. 417

21.338

21. 259 

21. 179 

21. 099 

21.019 

20. 939

20.860

20. 779 

20. 698 

20. 617 

20. 536 

20. 455

20. 374

20. 292 

20. 210 

20. 128 

20. 047 

19. 964

19. 883

19. 800 

19. 717 

19. 634 

19.551 

19. 468

19. 385

Ordinates of developed 

parallel.

Longitude 

interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15- 

20 

. 25 

30

5 

10 

15 

20 

25 

30

49°

Inches. 

0.002 

.008 

.019 

.033 

.052 

.075

51°

0.002 

.008 

.019 

.033 

.051 

.074

53°

0.002 

.008 

.018 

.032 

.050 

.073

55°

0.002 

.008 

.018 

.032 

.049 

.071

50°

Inches. 

0.002 

.008 

.019 

.033 

.052 

.075

52°

0.002 

.008 

.018 

.033 

.051 

.073

54°

0.002 

.008 

.018 

.032 

.050 

.072

56°

0.002 

.008 

.018 

.031 

.049 

.070

41623° 16-
66 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 8. Coordinate* for projection of maps (scale ^3-5-^) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

0 /

56 00

10 

20 

30 

40 

50

57 00

10 

20 

30 

40 

50

58 00

10 

20 

30 

40 

50

59 00

. 10 

20 

30 

40 

50

60 00

10 

20 

30 

40 

50

61 00

10 

20 

30 

40 

50

62 00

10 

20 

30 

40 

50

63 00

Meridional distances 

from 

even 

degree 

parallels.

Indies, 

69. 176

11.531 

23.063 

34. 594 

46. 125 

57. 656

69. 188

11. 533 

23.066 

34. 599 

46. 132

57. 666

69. 199

11. 535 

23. 070 

34. 605 

46. 140 

57. 675

69. 210

11. 537 

23. 074 

34. 610 

46. 147 

57. 684

69. 221

11. 539 

23. 077 

34. 616 

46. 154 

57.693

69. 232

11.540 

23.081 

34. 621 

46. 162

57. 702

69. 242

11.542 

23.084 

34. 626 

46. 168 

57. 710

69.253

Abscissas of developed parallel.

5' longitude.

Inches. 

3.231

3.217 

3.203 

3.189 

3.175 

3.161

3.147

3.133 

3.119 

3.104 

3.090 

3.076

3.062

3.048 

3.034 

3.019 

3.005 

2.991

2.976

2.962 

2.947 

2.933 

2.918 

2.904

2.890

2.875 

2.860 

2.846 

2.831 

2.816

2.802

2.787 

2.772 

2.758 

2.743 

2.728

2. 713

2.699 

2.684 

2.669 

2.654 

2.639

2.624

10' longitude.

Inches. 

6.462

6.434 

6.406 

6.378 

6.350 

6.322

6.294

6.266 

6.237 

6.209 

6.181 

6.152

6.124

6.096 

6.067 

6.038 

6.010

5.981

5. 953

5.924 

5.895 

5.866 

5.837 

5.808

5.779

5.750 

5.721 

6.691 

5.662 

5.633

5.604

5.574 

5.545 

5.115 

5.486 

5.456

5.427

5.397 

5.367 

5.337 

5.308 

5.278

5.248

15' longi- 

 tude.

Inches. 

9.693

9.651 

9.609 

9.567 

9.525 

9.483

9.441

9.398 

9.356 

9.314 

9.271 

9.229

9.186

9.143 

9.101 

9.058 

9.015 

8.972

8.929

8.885 

8.842 

8.799 

8.755 

8.712

8.669

8.625 

8.681 

8.537 

 8.493 

8.450

8.406

8.361 

8.317 

8.273 

8.229 

8.184

8.140

8.096 

8.051 

8.006 

7.961 

7.917

7.872

20' longitude.

Inches. 

12. 924

12.868 

12. 812 

12. 756 

12. 700 

12.644

12.588

12. 531 

12. 475 

12. 418 

12. 362 

12. 305

12. 248

12. 191 

12. 134 

12. 077 

12. 020 

11.962

11. 905

11. 847 

11. 790 

11. 732 

11. 674 

11. 616

11.558

11. 500 

11.441 

11.383 

11. 324 

11.266

11. 208

11.148 

11.090 

11.030 

10. 972 

10. 912

10.854

10. 794 

10. 734 

10. 675 

10. 615 

10.556

10.496

25' longitude.

Inches. 

16. 155

16. 085 

16.015 

15. 945 

15. 875 

15. 805

15. 735

15. 664 

15. 594 

15. 523 

15. 452 

15.381

15. 311

15.239 

15. 168 

15. 096 

15. 025 

14. 953

14. 882

14. 809 

14. 737 

14.665 

1 14. 592 

14. 520

14.448

14. 375 

14. 302 

14.229 

14. 156 

14.083

14. 010

13. 936 

13. 862 

13. 788 

13. 715 

13. 641

13.567

13. 493 

13. 418 

13.344 

13. 269 

13.195

13. 120

30' longitude.

Inches. 

19. 385

19. 301 

19.217 

19. 134 

19. 050 

18.966

18.882

18. 797 

18. 712 

' 18. 627 

18.542 

18.457

18. 373

18.287 

18. 201 

18. 115 

18. 029 

17.944

17. 858

17. 771 

17. 684 

17.597 

17.510 

17. 424

17. 337

17. 249 

17. 162 

17.074 

16. 987 

16.899

16. 811

16. 723 

16.634 

16. 546 

16.457 

16.369

16. 280

16.191 

16. 102 

16.012 

15. 923 

15.833

15. 744

Ordinates of developed 

parallel.

Longitude interval.

/ 

5 

10 

15 

20 

25. 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20

25

30

5 

10 

15 

20 

25 

30

56° 

Inches. 

0.002 

.008 

.018 

.031 

.049 

.070

58°

0.002 

.008 

.017 

.030 

.047 

.068

60°

0.002 

.007 

.016 

.029 

.045 

.065

62°

0.002 

.007 

.016 

.028 

.044 

.063

57°

Inches. 

0.002 

.008 

.017 

.031 

.048 

.069

59°

0.002 

.007 

.017 

.030 

.046 

.067

61°

0.002 

.007 

.016 

.029 

.045 

.064

63°

0.002 

.007 

.015 

.027 

.043 

.061
GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 8. Coordinates for projection of maps (scale ^si-g-ff) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

O 1

63 00

Iv.

20 

30 

40 

50

64 00

. 10 

20 

30 '40 

50

65 00

10 

20 

30 

40 

60

66 00

10 

20 

30 

40 

50

67 00

10 

20 

30 

40 

50

68 00

10 

20 

30 

40 

50

69 00

10 

20 

30 

40 

50

70 00

Meridional distances 

from 

even 

degree 

parallels.

Inches. 

69. 253

11.544 

23. 087 

34. 631 

46.175 

67.718

69. 262

11.545 

23.091 

34. 636 

46. 182 

57. 727

69.272

11.547 

23.094 

34.641 

46. 188 

57. 735

69.282

11.548 

23. 097 

34. 646 

46. 194 

57. 742

69. 291

11. 550 

23. 100 

34.650 

46. 200

57. 750

69. 300

11.552 

23. 103 

34. 654 

46. 206 

57. 758

69. 309

11. 553 

23. 106 

34. 659 

46. 212

57. 764

69. 317

Abscissas of developed parallel.

5' longitude.

Inches. 

2.624

2.609 

2.594 

2.579 

2.564 

2.549

2.534

2.519 

' 2.504 

2.488 

2.473

2.458

2.443

2.428 

2.412 

2.397 

2.382 

2.366

2.351

2.336 

2.320 

2.305 

2.290 

2.274

2.259

2.243 

2.228 

2.212 

2.197 

2.181

2.166

2.150 

2.134 

2.119 

2.103 

2.088

2.072

2.056 

2.040 

2.025 

2.009 

1.993

1.977

10' longitude.

Inches. 

5.248

5.218 

5.188 

6.158 

5.128 

5.098

5.068

5.037 

5.007 

4.977 

4.947 

4.916

4.886

4.855 

4.825 

4.794 

4.764 

4.733

4.702

4.672 

4.641 

4.610 

4.579 

4.548

4.518

4.487 

4.456 

4.424 

4.393 

4.362

4.331

4.300 

4.269 

4.237 

4.206 

4.175

4.144

4.112 

4.081 

4..049 

4.018 

3.986

3.955

15' longitude.

Inches.

7.872

7. 827 

7.782 

7.737 

7.692 

7.647

7.602

7. 556 

7.511 

7.465 

7.420

7.374

7.329

7.283 

7.237 

7.191 

7.145 

7.100

7.054

' 7. 007 

6.961 

6.915 

6.869 

6.823

6.776

6. 730 

6.683 

6.637 

6.590 

6.543

6.497

 6. 450 

6.403 

6.356 

6.309 

6.263

6.216

6.169 

6.121 

6.074 

6.027 

5.980

5.932

20' longitude.

Inches. 

10. 496

10. 436 

10. 376 

10. 316 

10. 256 

10. 196

10. 136

10.075 

10.014 

. 9. 954 

9.893 

9.832

9.772

9.711 

9. 650 

. 9. 588 

9.527 

9.466

9. 405

9.343 

9.282 

9.220 

9.158 

9.097

9.035

8.973 

 8.911 

8.849 

8.787 

8.724

8.662

8.600 

8.538 

8.475 

8.412 

8.350

8.288

8.225 

8.162 

8.099 

8.036 

7.973

7.910

25' longitude.

Inches. 

13. 120

13. 045 

12. 970 

12. 895 

12.820 

12. 745

12. 670

12.594 

12.518 

12. 442 

12. 367 

12. 291

12.215

12. 139 

12. 062 

11.986 

11. 909 

11.833

11. 756

11. 679 

11. 602 

11.525 

11. 448 

11. 371

11. 294

11.217 

11. 139 

11.061 

10. 984 

10. 906

10. 828

10. 750 

10. 672 

10. 594 

10. 516 

10.438

10.360

10.281 

10. 202 10.124' 

10. 045 

9.966

9.888

30' longitude.

Inches. 

15. 744

15. 654 

15. 564 

15. 473 

15. 383 

15. 293

15. 203

15.112 

15.022 

14. 930 

14. 840 

14. 749

14.658

14. 566 

14. 474 

14.383 

14. 291 

14. 199

14. 107

14. 015 

13. 922 

13.830 

13.738 

13.645

13.553

13. 460 

13. 366 

13. 273 

13.180 

13. 087

12. 994

12. 900 

12.806 

12. 712 

12. 619 

12. 525

12.431

12. 337 

12. 242 

12. 148 

12.054 

11. 959

11.865

Ordinates of developed 

parallel.

Longitude inter-* 

val.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

. 20 

25 

30

63°

Inches. 

0.002 

.007 

.015 

.027 

.043 

.061

65°

0. 002 

.000 

.014 

.026 

.040 

.058

67°

0.001 

.006 

.014 

.024 

.038 

.054

69°

0.001 

.006 

.013 

.022 

.035 

.051

64°

Inches. 

0.002 

.007 

.015 

.026 

.041 

.060

66°

0.002 

.006 

.014 

.025 

.039 

.056

68°

0.001 

.006 

.013 

.023 

.036 

.053

70°

0.001 

.005 

.012 

.022 

.034 

.049
68 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 8. Coordinates for projection of maps (scale -S-STSTS) Continued. 

. [From Smithsonian Geographical Tables.]

Latitude of 

parallel.

O 1

70 00

10 

20 

30 

40 

50

71 00

10 

20 

30 

40 

50

72 00

10 

20 

30 

40 

50

. 73 00

10 

20 

30 

40 

50

74 00

10 

20 

30 

40 

50

75 00

10 

20 

30 

40 

50

76 00

10 

20 

30 

40 

50

77 00

Meridional distances 

from 

even 

degree 

parallels.

Inches. 

69. 317

11. 554 

23.109 

34. 663 

46. 217

57. 772

69. 326

11. 556 

23. Ill 

34. 667 

46. 222 

57. 778

69. 334

11.557 

23. 114 

34. 670 

46. 227 

57.784

69. 341

11. 558 

23. 116 

34. 674 

46. 232 

57. 790

69. 348

11. 559 

23. 118 

34. 677 

46. 236 

57.796

69. 355

11. 560 

23. 120 

34. 681 

46. 241 

57.801

. 69.361

11. 561 

23. 122 

34. 683 

46. 244 

57. 806

69. 367

Abscissas of developed parallel.

5' longitude.

Indies. 

1.977

1.962 

1.946 

1.930 

1.914 

1.898

1.882

1.866 

1.850 

1.835 

1.819 

1.803

1.787

1.771 

1. 755 

1.739 

1. 723 

1. 707

1.691

1.674 

1.658 

1.642 

1.626 

1.610

1.594

1.578 

1.562 

1.545 

1.529 

1.513

1.497

1.480 

1.464 

1.448 

1.432 

1.415

1.399

1.383 

1.366 

1.350 

1.334 

1.317

1.301

10' longitude.

Inches. 

3.955

3.923 

3.892 

3.860 

3.828 

3.796

3.765

3.733 

3.701 

3.669 

3.637 

3.605

3.574

3.542 

3.509 

3.477 

3.445 

3.413

3.381

3.349 

3.317 

3.284 

3.252 

3.220

3.188

3.155 

3.123 

3.091 

3.058 

3.026

2.993

2. 961 

2.928 

2.896 

2. 863 

2.831

2.798

2.765 

2.733 

2.700 

2.667 

2. 634

2.602

15' longitude.

Inches. 

5.932

5.885 

5.837 

5.790 

5.742 

5.695

5.647

5.600 

5.552 

5.504 

5.456 

5.408

5.360

5.312 

5.264 

5.216 

5.168 

5.120

5.072

5.024 

4.975 

4.927 

4.878 

4.830

4.782

4.733 

4.685 

4.636 

4.587 

4,539

4.490

4.441 

4.392 

4.344 

4.295 

4.246

4.197

4.148 

4.099 

4.050 

4.001 

3.952

3.903

20' longitude.

Inches. 

7.910

7.846 

7.783 

7.720 

7.656 

7.593

7.530

7.466 

7.402 

7.338 

7.275 

7.211

7. 147

7.083 

7.019 

6.955 

6.891 

6.826

6.762

6.698 

6.634 

6. 569 

6.504 

6.440

6.376

6.311 

6.246 

6.181 

6.116 

6.052

5.987

5.922 

5.856 

5.792 

5.726 

5.661

5.596

5.530 

5.465 

5.400 

5.334 

5.269

5.204

25' longitude.

Inches. 

9.888

9.808 

9.729 

9.650 

9.571 

9.491

9.412

9.333 

9.253 

9.173 

9.094 

9.014

8.934

8.854 

8.774 

8.694 

8.614 

8.533

8.453

8.373 

8.292 

8.211 

8.131 

8.050

7.970

7.889 

7.808 

7.727 

7.645 

7.565

7.484

7.402 

7.321 

7. 240 

7.158 

7.077

6.995

6.913 

6.832 

6.750 

6.668 

6.586

6.505

30' longitude.

Inches. 

11.865

11. 770 

11. 675 

11. 579 

11.485 

11. 389

11.294

11.199 

11. 103 

11.008 

10. 912 

10. 816

10. 721

10. 625 

10.528 

10. 432 

10. 336 

10. 240

10. 144

10. 047 

9.950 

9.853 

' 9.757 

9.660

. 9. 563

9.466 

9.369 

9. 272 

9. 175 

9.077

8.980

8.882 

8.785 

8.687 

8.590 

8.492

8.394

8.296 

8:198 

8.099 

8.002 

7.903

7.805

Ordinates of developed 

parallel.

Longi 

tude interval.

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

70°

Inches. 

0.001 

.005 

.012 

.022 

.034 

.049

72°

0.001 

.005 

.011 

.020 

.031 

.044

74°

0.001 

.004 

.010 

.018 

.028 

.040

76°

0.001 

.004 

.009 

.016 

.025 

.036

71°

Inches. 

0.001 

.005 

.012 

.021 

.032 

.047

73°

0.001 

.005 

.011 

.019 

.029 

.042

75°

0.001 

.004 

.009 

.017 

.026 

.038

77°

0.001 

.004 

.008 

.015 

.023 

.033
GEOGRAPHIC TABLES AND FORMULAS. 69

TABLE 8. Coordinates for projection of maps (scale 7-3-3-^)' Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

0 /

77 00

10 

20 

30 

40 

50

78 00

. 10 

20 

30 

40 

50

79 00

10 

20 

30 

40 

50

80 00

Meridional distances 

from 

even 

degree 

parallels.

Inches. 

69. 367

11. 502 

23. 124 

34. 686 

46. 248 

57. 810

69. 373

11.503 

23. 120 

34.689 

46. 252 

57. 814

69. 377

11. 564 

23. 127 

34. 691 

46. 255 

57. 818

69. 382

Abscissas of developed parallel.

5' longitude.

Inches. 

1.301

1.284 

1.268 

1. 252 

1.235 

1.219

1.202

1.180 

1.169 

1.153 

1.136 

1.120

1. 104

1.087 

1.070 

1.054 

1.037 

1.021

1.004

10' longitude.

Inches. 

2.602

2.569 

2.536 

2.503 

2.470 

2.438

 2.405

2.372 

2.339 

2.306 

2. 273 

2. 240

2. 207

2. 174

2. 147 

2.308 

2.075 

2. 042

2.009

15' longitude.

Indies. 

3.903

3.854 

3.804 

3.755 

3.706 

3. 656

3.607

3.558 

31508 

3.459 

3.410 

3.360

3.311

3.261 

3.211 

3.162 

3.112 

3.062

3.013

20' longitude.

Inches. 

5.204

5.138 

5.072 

5.006 

4. 941 

4.875

4.810

4.744 

4.G78

4. 612 

4.546 

4.480

4.414

4.348 

4.282 

4.216 

4.150 

4.083

4.017

25' longitude.

Inches. 

6.505

»

6.423 

6.341 

6.258 

6.176 

6.094

6. 012

5.930 

5.847 

5. 765 

5.683 

5.600

5.518

5.435 

5. 352 

5.270 

5.187 

5. 104

5.022

30' longitude.

Inches. 

7.805

7.707 

7.609 

7.510 

7. 411 

7. 313

7. 214

7. 115 

7.010 

6.918 

6.819 

6.720

6.621

6.522 

6.422 

6.323 

6.224 

6.125

6.026

Ordinates of developed 

parallel.

Longitude interval.

/ 

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

77°

Inches. 

0.001 

.004 

.008 

.015 

.023 

.033

79°

0.001 

.003 

.007 

.013 

.020 

.028

78°

Inches. 

0. 001 

.003 

.008 

.014 

.021 

.031

80°

0.001 

.003 

.006 

.011 

.018 

.026
70 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 9. Coordinates for projection of maps (scale ^l

Latitude of 

parallel.

0 /

25 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

26 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

27 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

28 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

29 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.

5.815 

11. 629 

17.444 

23.259 

29.074 

34.888

5.816 

11. 631 

17.447 

23. 262 

29. 078 

34. 893

5.816 

11. 633 

17. 449 

23. 265 

29. 082 

34.898

5.817 

11. 634 

17. 451 

23.268 

29.085 

34. 903

Abscissas of developed parallel.

2i' longitude.

Inches. 

2.650 

2.648 

2.646 

. 2. 644 

2.642 

2.641 

2.639 

2. 637 ' 

2.635 

2.633 

2.631 

2.630

2.628 

2.626 

2.624 

2.622 

2.620 

2.618 

2.617 

2.615 

2.613 

2. 611 

2.609 

2.607

2. 605 

2.603 

2.601 

2.599 

2.597 

2.595 

2.593 

2.591 

2.590 

2.588 

2.586 

2.584

2.582 

2.580 

2.578 

2.576 

2.574 

2. 572 

2.570 

2.568 

2.566 

2.564 

2.562 

2.560

2.558

5' longitude.

Inches. 

5.299 

5.296 

5.292 

5.288 

5.285 

5.281 

5. 277 

5.274 

5.270 

5.266 

5.263 

5.259

5.256 

5.252 

5. 248 

5.244 

5.241 

5.237 

5.233 

5.229 

5.225 

5.222 

5.218 

5.214

5.210 

5.207 

5.203 

5.199 

5.195 

5.191 

5.187 

5.183 

5.179 

5.175 

5.171 

5.167

5.163 

5.159 

5.155 

5.151 

5.147 

5.143 

5. 139 

5.135 

5.131 

5. 327 

5.123 

5.119

5.115

71' longitude.

Inches. 

7.949 

7.944 

7.938 

7.933 

0 7.927 

7.922 

7.916 

7.911 

7.905 

7.900 

7.894 

7.889

7.883 

7.878 

7.872 

7.866 

7.861 

7.855 

7.849 

7.844 

7.838 

7.833 

7.827 

7.821

7.816 

7.810 

7.804. 

7.798 

7.792 

7.786 

7.780 

7.774 

7.769 

7.763 

7.757 

7.751

7.745 

7.739 

7.733 

7.727 

7.721 

7.715 

7.709 

7.703 

7.697 

7.691 

7. 685 

7.679

7.673

10' longitude.

Inches. 

10. 599 

10. 591 

10. 584 

10. 577 

10. 569 

10. 562 

10.555 

10.548 

10. 540 

10.533 

10. 526 

10. 518

10.511 

10. 504 

10.496 

10. 489 

10.481 

10. 473 

10.466 

10. 458 

10. 451 

10.443 

10. 436 

10.428

10. 421 

10. 413 

10. 405 

10. 397 

10. 389 

10. 382 

10. 374 

10. 366 

10.358 

10.350 

10. 342 

10.335

10.327 

10. 319 

10. 311 

10. 303 

10.294 

10. 286 

10. 278 

10. 270 

10.262 

10.254 

10. 246 

10.238

10. 230

121' longitude.

Inches. 

13. 248 

13. 239 

13. 230 

13. 221 

13. 212 

13. 203 

13. 194 

13. 184 

13. 175 

13.166 

13. 157 

13. 148

13. 139 

13. 129 

13. 120 

13. Ill 

13. 101 

13.092 

13. 082 

13. 073 

13.064 

13.054 

13.045 

13. 035

13. 026 

13. 016 

13. 006 

12. 997 

12. 987 

12. 977 

12. 967 

12. 957 

12. 948 

12.938 

12. 928 

12.918

12. 908 

12.898 

12.888 

12.878 

12.868 

12.858. 

12.848 

12. 838 

12.828 

12. 818 

12. 808 

12. 798

12. 788

15' longitude.

Inches. 

15.898 

15,887 

15. 876 

15.865 

15.854 

15. 843 

15.832 

15. 821 

15.810 

15. 799 

15. 788 

15. 777

15. 766 

15. 755 

15.744 

15. 733 

16. 721 

15. 710 

15. 699 

15.688 

15.676 

15. 665 

15.654 

15. 642

15. 631 

15. 620 

15.608 

15. 596 

15. 584 

15. 572 

15. 561 

15. 549 

15. 537 

15. 525 

15. 514 

15.502

15. 490 

15. 478 

15. 466 

15.454 

15.442 

15. 430 

15. 418 

15. 405 

15.393 

15. 381 

15. 369 

15.357

15. 345

Ordinates of developed 

parallel.

Longitude interval.

2* 

5

10 

121 

15

25°

Inches. 

0.000 

.002 

.004 

.007 

. .010 

.015

26°

Inches. 

0.000 

.002 

.004 

.007 

.010 

.015

/

21 

5 

71 

10 

12* 

15

27°

Inches. 

0.000 

.002 

.004 

-.007 

.011 

.015

-

21 

6 

71 

10 

121 

15

27°

Inches. 

0.000 

.002 

.004 

.007 

.011 

.015

28°

Inches. 

0.000 

.002 

.004 

.007 

.011 

.016

21 

5 

71 

10 

121 

15

29°

Inches. 

0.000 

.002 

.004 

.007 

.011 

.016
GEOGRAPHIC TABLES AND FORMULAS. . 71

TABLE 9. Coordinates for projection of maps (scale ^ST^TF) Continued.

Latitude of 

parallel.

o / 

29 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

30 00' 

05 

10 

15 

20 

25 

' 30 

35 

40 

45 

50 

55

31 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

60 

55

32 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

33 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.

5.818 

11. 636 

17. 454 

23. 272 

29. 090 

34. 908

5.819. 

1F.G38 

17. 457 

23. 276 

29.095 

34. 913

5. 820 

11. 640 

17. 460 

23.280 

29. 100 

34. 919

5.821 

11. 642 

17. 462 

23.283 

29. 104 

34. 925

Abscissas of developed parallel.

2-J-' longitude.

Inches. 

2.558 

2.555 

2.553 

2.551 

2. 549 

2.547 

2.545 

2. 543 

2.541 

2. 539 

2.537 

2.535

2.533 

2.530 

2.628 

2.526 

2.524 

2. 522 

2. 520 

2. 518 

2.515 

2.513 

2. 511 

2.509

2.507 

2.505 

2.502 

2.500 

2.498 

2.496 

2. 494 

2. 491 

2.489 

2.487 

2; 485 

2.482

2.480 

2.478 

2.476 

2.473 

2.471 

2.409 

2. 467 

2.464 

2. 462 

2.460 

2.458 

2.455

2.453

5' longitude.

Inches. 

5.115 

5.111 

5.107 

5.103 

5.098 

6.094 

6.090 

5.086 

5.082 

5. 078 

5.073 

5.069

5.065 

5.0G1 

5.057 

5. 052 

5.048 

5.044 

5.039 

5.035 

5.031 

5.026. 

5. 022 

5.018

5.014 

5.009 

5.005 

5.000 

4.996 

4.991 

4.987 

4.983 

4.978 

4.974 

4.969 

4.965

4.960 

4.956 

4.951 

4.947 

4. 942 

4.938 

4.933 

4.929 

4.924 

4.920 

4. 915 

4.910

4.906

74' longitude.

Inches. 

7.673 

7.666 

7.660 

7.654 

7.648 

7.641 

7.635 

7. 629 

7.623 

7. 616 

7.610 

7.604

7.598 

7.591 

7.585

7.578 

7.572 

7.565 

7.559 

7.552 

7.546 

7.540 

7.533 

7.527

7.520 

7. 514 

7.507 

7.500 

7.494 

7.487 

7.480 

7.474 

7. 467 

7.460 

7.454 

7.447

7.441 

7.434 

7.427 

7.420 

7.413 

7.407 

7.400 

7.393 

7.386 

7.379 

7.372 

7. 366

7.359

10' longitude.

Inches. 

10. 230 

10. 222 

10. 213 

10. 205 

10. 197 

10. 188 

10. 180 

10.172 

10.164 

10. 155 

10. 147 

10. 138

10. 130 

10. 122 

10.113 

10. 104 

10. 006 

10. 087 

10.079 

10.070 

10. 001 

10.053 

10. 044 

10. 036

10.027 

10.018 

10. 009 

10.000 

9. 992 

9.983 

9.974 

9.965 

9.956 

9.947 

9.938 

9.930

9.921 

9. 912 

9.903 

9.894 

9.884 

9.875 

9. 866 

9.857 

9.848 

9.839 

9.831 

9.821

9.812

12-4' longitude.

Inches. 

12. 788 

12. 777 

12. 767 

12. 756 

12. 746 

12. 735 

12. 725 

12. 715 

12. 704 

12. 694 

12. 684 

12. 673

12.663 

12. 652 

12.641 

12. 630 

12. 620 

12.609 

12. 598 

12. 587 

12. 577 

12.566 

12.555 

12. 544

12. 534 

12. 523 

12. 512 

12. 500 

12. 489 

12.478 

12. 467 

12. 456 

12. 445 

12. 434 

12. 423 

12.412

12. 401 

12. 390 

12. 378 

12. 367 

12.356 

12. 344 

12.333 

12. 322 

12. 310 

12. 299 

12. 287 

12. 276

12. 265

15' longitude.

Inches. 

15. 345 

15. 333 

15. 320 

15. 308 

15. 295 

15. 283 

15. 270 

15. 258 

15. 245 

15. 233 

15.220 

15.208

15. 195 

15. 182 

15.169 

15. 157 

15. 144 

15.131 

15. 118 

15. 105 

15. 092 

15. 079 

15. 066 

15. 053

15. 040 

15. 027 

15. 014 

15. 000 

14. 987 

14. 974 

14. 961 

14.948 

14.934 

14. 921 

14. 908 

14. 894

14.881 

14. 868 

14. 854 

14.840 

14. 827 

14.813 

14. 800 

14. 786 

14. 772 

14. 759 

14.745 

14. 731

14. 718

Ordinates of developed 

parallel.

Longitude interval.

24 

6 

74 

10 

124 

15

24 

5 

74 

10 

124 

15

29°

Inches. 

0.000 

.002 

.004 

.007 

.011 

.016

31°

0.000 

.002 

.004 

.008 

.012 

.017

30°

Inches. 

0.000 

.002 

.004 

.007 

.012 

.017

Longitude interval.

24 

5 

74 

10 

124 

15

24 

5 

74 

10 

124 

15

31°

Inches. 

0.000 

.002 

.004 

.008 

.012 

.017

33°

0.000 

.002 

.004 

.008 

.012 

.017

32°

Inches. 

0.000 

.002 

.004 

.008 

.012 

'.017
T2 GEOGEAPHIO TABLES AND FOEMULAS.

TABLE 9. Coordinates for projection of maps (scale ^T^IF) Continued. 

[From Smithsonian Geographical Tables.]

Latitude of 

parallel.

o / 

33 00 

05 

10 

15 

20 

25 

30 

35 

40 

- 45 

50 

55

34 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

35 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

36 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

37 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.

5.822 

11. 643 

17. 465 

23. 287 

29. 109 

34. 930

5. 823 

11. 645 

17. 468 

23. 291 

29. 113 

34.936

5.824 

11. 647 

17. 471 

23. 294 

29. 118 

34. 942

5.824 

11. 649 

17.473 

23. 297 

29. 122 

34. 946

Abscissas of developed parallel.

2-J-' longitude.

Inches. 

2. 453 

2.451 

2.448 

2.446 

2.444 

2.441 

2.439 

2.437 

2.434 

2.432 

2.430 

2.427

2.425 

2.423 

2. 420 

2.418 

2.415 

2.413 

2.411 

2.408 

2.406 

2.403 

2.401 

2.399

2.396 

2.394 

2.391 

2.389 

2.380 

2.384 

2.381 

2.379 

2.976 

2.374 

2.372 

2.369

2.367 

2.364 

2.362 

2.359 

2.357 

2.354 

2.352 

2.349 

2.346 

2.344 

2.341 

2.339

2. 336

5' longitude.

Inches. 

4.906 

4.901 

4.897 

4.892 

4.887 

4.882 

4.878 

4.873 

.4. 868 

4.864 

4.859 

4.854

4.850 

4.845 

4.840 

4.835 

4.831 

4.826 

. 4.821 

4.816 

4. 811 

4.807 

4.802 

4.797

4.792 

4.787 

4.782 

4.777 

4.773 

4.768 

4.763 

4.758 

4.753 

4.748 

4.743 

4.738

4. 733 

4. 728 

4.723 

4.718 

4.713 

4.708 

4.703 

4.698 

4.693 

4.688 

4.683 

4.678

4.673

7^' longitude.

Inches. 

7.359 

7.352 

7.345 

7.338 

7.331 

7.324 

7. 317 

7.310 

7.303 

7.296 

7.289 

7.282

7.275 

7.267 

7.260 

7.253 

7.246 

7.239 

7.231 

7. 224 

7.217 

7.210 

7.203 

7.195

7.188 

7.181 

7.174 

7.166 

7.159 

7.151 

7.144 

7.137 

7.129 

7.122 

7.115 

7.107

7.100 

7.092 

7.085 

7.077 

7.070 

7.062 

7.055 

7.047 

7.039 

7.032 

7. 024 

7.017

7.009

10' longitude.

Inches. 

9.812 

9.802 

9.793 

9.784 

9.774 

9.765 

9.756 

9.746 

9.737 

9.728 

9.718 

9.709

9.700 

9.690 

9.680 

9.671 

9. 661 

9.652 

9. 642 

9.632 

9.623 

9.613 

9.604 

9.594

9.584 

9.574 

9.565 

9.555 

9.545 

9.535 

9.525 

9.516 

9.506 

9.496 

9.486 

9.476

9.466 

9.456 

9.446 

9.436 

9.42G 

9.416 

9.406 

9.396 

9.380 

9.376 

9.366 

9.356

9.345

121' longitude.

Inches. 

12. 265 

12.253 

12. 241 

12.230 

12. 218 

12. 206 

12. 195 

12. 183 

12. 171 

12. 160 

12.148 

12. 136

12. 124 

12. 112 

12. 100 

12.088 

12. 076 

12. 064 

12. 052 

1'2. 040 

12. 028 

12. 010 

12. 004 

11. 992

11. 980 

11. 968 

11. 956 

11. 944 

11. 931 

11.919 

11. 907 

11. 895 

11.882 

11.870 

11. 858 

11.845

11. 833 

11.820 

11.808 

11. 795 

11. 783 

11. 770 

11. 758 

11. 745 

11. 732 

11. 720 

11. 707 

11. 694

11. 682

15' longitude.

Inches. 

14. 718 

14. 704 

14. 690 

14. 676 

14. 662 

14.648 

14. 633 

14. 619 

14. 605 

14. 591 

14.577 

14. 563

14.549 

14. 535 

14. 520 

14. 506 

14. 492 

14. 477 

14. 463 

14.448 

14. 434 

14. 420 

14.405 

14. 391

14. 376 

14. 362 

14. 347 

14. 332 

14.318 

14. 303 

14. 288 

14. 273 

14. 259 

14. 244 

14. 229 

14. 214

14.200 

14. 185 

14.169 

14. 154 

14. 139 

14. 124 

14. 109 

14. 094 

14. 079 

14. 064 

14. 048 

14. 033

14.018

Ordinates of developed 

parallel.

Longitude interval.

/ 

21 

5 

71 

10

121

15

21 

5 

71 

10 

121 

15

33°

Inches. 

0.000 

.002 

.004 

.008 

.012 

.017

35°

Inches. 

0.000 

.002 

.004 

.008 

.012 

.018

34°

Inches. 

0.000 

.002 

.004 

.008 

.012 

' .018

Longitude 

interval.

/

21 

5 

71 

10 

121 

15

/ 

 21 

5 

71 

10 

121 

15

35°

Inches. 

0.000 

.002 

.004 

.008 

.012 

.018

37°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.018

36°

Inches 

0.001 

.002 

.005 

.008 

.013 

.018
GEOGEAPHIO TABLES AND FOEMULAS.

TABLE 9. Coordinates for projection of maps (scale -g-^^) Continued. 

[From Smithsoniaii Geographical Tables.]

Latitude of 

parallel.

o / 

37 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

65

38 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

39 00 

05 

10 

15 

20 

» 25 

30 

35 

40 

45 

50 

55

40 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

60 

55

41 00"

Meridional distances 

from 

even 

degree 

parallels.

Inches.

5. 826 

11. 651 

17. 477 

23.302 

29. 128 

34. 954

5. 827 

11. 653 

17.480 

23. 306 

29. 133 

34. 960

5.828 

11.655 

17. 483 

23. 310 

29. 138 

34. 966

5.829 

11. 657 

17. 486 

23.314 

29. 143 

34. 972

Abscissas of developed parallel.

2J' longitude.

Inches. 

2.336 

2. 334 

2.331 

2. 329 

2.326 

2.323 

2.321 

2.318 

2. 316 

2. 313 

2.311 

2.308

2.305 

2.303 

2.300 

2.298 

. 2. 295 

2.292 

2. 290 

2.287. 

2.284 

2.382 

2.279 

2.276

2.274 

2.271 

2.268 

2.266 

2. 263 

2.260 

2.258 

2. 255 

2. 252 

2.250 

2.247 

2.244

2.241 

2.239 

2.236 

2.233 

2.230 

2.228 

2.225 

2.222 

2.219 

2.217 

2.214 

2.211

2. 208

5' longitude.

Inches. 

4.673 

4.667 

4.662 

4.657 

4.652 

4. 047 

4.642 

4.637 

4.631 

4.626 

4.621 

4.616

4. 611 

4.606 

4.600 

4.595 

4.590 

4.584 

4.579 

4.574 

4.569 

4.563 

4.558 

4.553

4.547 

4.542 

4.537 

4.531 

4. 526 

4.521 

4.515 

4.510 

4.504 

4.499 

4.494 

4.488

4.483 

4.477 

4.472 

4.466 

4.461 

4.455 

4.450 

4.444 

4.439 

4.433 

4.428 

4.422

4. 417

7£' longitude.

Indies. 

7.0Q9 

7.001 

6.994 

6.986 

6.978 

6.970 

6.963 

6.955 

6.947 

6.939 

6.932 

6.924

6.916 

6.908 

0.900 

6.892 

6.885 

6.877 

6.869 

6.861 

6.853 

6.845 

6.837 

6.829

6.821 

6.813 

6.805 

6.797 

6.789 

6.781 

6.773 

6.765 

6.757 

6.748 

6.740 

6.732

6.724 

6.716 

6.708 

6.699 

6.691 

6.683 

6.675 

6.666 

6.658 

6.650 

6.642 

6.633

6. 625

10' longitude.

Inches. 

9.345 

9.335 

9. 325 

9.314 

9.304 

9.294 

9.283 

9.273 

9.263 

9.253 

9. 242 

9.232

9.222 

9.211 

9.201 

9.190 

9.179 

9.169 

9.158 

9.148 

9.137 

9.127 

9. 116 

9.106

9.095 

9.084 

9.073 

9.063 

9.052 

9! 041 

9.030 

9.020 

9.009 

8.998 

8.987 

8.976

8.966 

8.955 

8.944 

8.933 

8.922 

8.911 

8.899 

8.888 

8.877 

8.866 

8.855 

8.844

8.833

12£' longitude.

Inches. 

11. 682 

11. 669 

11. 656 

11. 643 

11. 630 

11.617 

11.604 

11.591 

11. 578 

11. 566 

11. 553 

11.540

11.527 

11. 514 

11. 501 

11.488 

11.474 

11. 461 

11.448 

11.435 

11.422 

11. 408 

11. 395 

11. 382

11. 369 

11. 355 

11. 342 

11. 328 

11. 315 

11. 301 

11. 288 

11. 274 

11.261 

11. 247 

11. 234 

11.221

11.207 

11. 193 

11.180 

11. 166 

11. 152 

11.138 

11. 124 

11. Ill 

11. 097 

11. 083 

11. 069 

11. 056

11.042

15' longitude.

Inches. 

14. 018 

14. 003 

13. 987 

13. 972 

13. 956 

13.941 

13. 925 

13. 910 

13.894 

13. 879 

13. 863 

13. 848

13.832 

13. 817 

13. 801 

13.785 

' 13.769 

13. 753 

13.737 

13. 722 

13. 706 

13. 690 

13. 674 

13. 658

13. 642 

13. 626 

13. 610 

13. 594 

13. 578 

13. 562 

13. 545 

13. 529 

13. 513 

13. 497 

13.481 

13.465

13.448 

13.432 

13.415 

13. 399 

13.382 

13.366 

13. 349 

13. 333 

13. 316 

13. 300 ' 

13.283 

13. 267

13. 250

Ordinates of developed 

parallel.

Longitude interval.

/ '2i 

5 

U 

10 

12J 

15

2i 

5 

U 

10

m

15

Longitude interval.

2i 

5 

U 

10 

12i 

15

2* 

5 

7i 

10 

12£ 

15

37°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.018

39°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

39°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

41°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

38°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

40°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019
74 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 9. Coordinates for projection of maps (scale 5-^77) Continued. 

[From Smithsonian Geographical Tables.] '

Lati- 

 tude of 

parallel.

o / 

41 00 

05 

10 

. 15 

2C 

25 

30 

.35 

40 

45 

50 

55

42 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

43 00 

05 

10 

15 

20 

25 

 30 

35 

40 

45 

50 

55

44 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

45 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.

5.830 

11.659 

17. 489 

23. 319 

29. 149 

34. 978

5.831 

11. 661 

17. 492 

23. 323 

29. 154 

34. 984

5. 832 

11.663 

17. 495 

23. 327 

29. 159 

34. 990

5.833 

11.666 

17. 498 

23. 331 

29. 164 

34. 997

Abscissas of developed parallel.

2 4' longitude.

Inches. 

2.208 

2.206 

2.203 

2.200 

2. 197 

2. 194 

2.192 

2. 189 

2. 186 

2.183 

2.180 

2.178

2.175 

2. 172 

2.169 

2.166 

2.163 

2.160 

2. 158 

2.155 

2. 152 

2.149 

2.146 

2. 143

2.140 

2. 137 

2.134 

2.132 

2.129 

2. 126 

2.123 

2.120 

2.117 

2.114 

2.111 

2.108

2. 105 

2.102 

2.099 

2.096 

2.093 

2.090 

2.087 

2. 084 

2.081 

2.078 

2.076 

2.073

2.070

5' longitude.

Inches. 

4.417 

4.411 

4.406 

4.400 

4.394 

4. 389 

4.383 

4.377 

4.372 

4. 366 

4.361 

4.355

4.349 

4.344 

4.338 

4.332 

4.326 

4.321 

4.315 

4. 309 

4.304 

4.298 

4.292 

4.280

4.281 

4.275 

4. 269 

4.263 

4.257 

4.251 

4.246 

 4.240 

4.234 

4.228 

4.222 

4.216

4.210 

4.205 

4.199 

4.193 

4.187 

4.181 

4.175 

4.169 

4.163 

4.157 

4.151 

4.145

4.139

74' longitude.

Inches. 

6.625 

6.617 

6.608 

6.600 

6.591 

6. 583 

6.575 

6.566 

6.558 

6.549 

6.541 

6.533

6. 524 

6.515 

6.507 

6.498 

6.490 

6.481 

6.472 

6.464 

6.455 

6.447 

6.438 

6.429

6.421 

6.412 

6.403 

6.395 

6. 386 

6.377 

6.368 

6.359 

6.351 

6.342 

6.333 

6.324

6. 316 

6.307 

6.298 

6.289 

6.280 

6.271 

6.262 

6.253 

6.244 

6.235 

6.227 

6.218

6. 209

10' longitude.

Inches. 

8.833 

8.822 

8.811 

8.800 

8. 789 

8. 777 

8. 766 

8.755 

8.744 

8.732 

8. 721 

8.710

8. 699 

8.687 

8.676 

8.664 

8:653 

8.641 

8.630 

8.618 

8.607 

8.596 

8.584 

8. 573

8.561 

8.550 

8.538 

8.526 

8.514 

8.503 

8.491 

8.479 

8.468 

0.456 

8.444 

8. 432

8.421 

8.409 

8.397 

8.385 

8.373 

8.361 

8.350 

8.338 

8.326 

8.314 

8.302 

8.290

8.278

124' longitude.

Inches. 

 11.042 

11. 028 

11.014 

11. 000 

10. 986 

10. 972 

10. 958 

10. 944 

10.930 

10.916 

10. 902 

10. 888

10. 873 

10. 859 

10.845 

10. 830 

10. 816 

10. 802 

10. 787 

10. 773 

10. 759 

10. 744 

10. 730 

10. 716

10. 701 

10. 687 

10. 672 

10. 658 

10. 643 

10. 628 

10.614 

10. 599 

10. 585 

10. 570 

10. 555 

10.541

10.526 

10.511 

10. 496 

10. 482 

10. 467 

10. 452 

10. 437 

10. 422 

10. 407 

10. 392 

10. 377 

10. 363

10. 348

15' longitude.

Inches. 

13. 250 

13. 233 

13. 216 

13. 200 

13. 183 

13. 166 

13. 149 

13.132 

13.115 

13. 099 

13.082 

13. 065

13.048 

13.031 

13. 014 

12. 996 

12. 979 

12.962 

12. 945 

12. 928' 

12. 910 

12. 893 

12. 876 

12. 859

12. 842 

12. 824 

12. 807 

12. 789 

12. 772 

12. 754 

12. 736 

12. 719 

12. 701 

12. 684 

12. 666 

12. 649

12. 631 

12.613 

12.596 

12. 578 

12. 560 

12. 542 

12. 524 

12.506 

12. 489 

12.471 

12. 453 

12.435

12. 417

Ordinates of .developed 

parallel..

Longitude interval.

24 

5 

74 

10 

124 

15

21 6" 

74 

10 

124 

15

Longitude interval.

24 

5 

74 

10 

124 

15

24 

5 

74 

10 

124 

15

41°

Indies. 

0.001 

.002 

.005 

.008 

.013 

.019

43°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

43°

Inches. 

0.001 

.002 

.005 

.008 

.013 

. .019

45°

Inches. 

0.001 

.002 

.005 

.009 

.013 

.019

42°

Inches. 

0.001 

.002 

.005. 

.008 

.013 

.019

44°

Inches. 

0.001 .002' 

.005 

.009 

.013 

.019
GEOGBAPHIC TABLES AND FOKMDLAS. 75

TABLE 9. Coordinates for projection of maps (scale Tnrlbff) Continued. 

[From Sinithsonian Geographical Tables.]

Latitude of 

parallel.

o / 

45 00 

05 

10 15' 

' 20 

25 

30 

35 

40 

45 

50 

55

46 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

47 00 

05 

10 

' 15 

20 

25 

30 

35 

40 

45 

50 

55

48 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

49 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

50 00

Meridional distances 

from 

even 

degree 

parallels.

Inches.

5.834 

11. 668 

17.501 

23. 335 

29. 169 

 35. 003

5.835 

11. 670 

17. 504 

23. 339 

29. 174 

35.009

5.836 

11. 672 

 17.508 

23. 344 

29.180 

35.015

5.837 

11. 674 

17. 511 

23. 318 

29. 185 

35. 021

5.838 

11.676 

17.514 

23.352 

29. 190 

35.027

Abscissas of developed parallel.

24' longitude.

Inches. 

2.070 

2.067 

2.064 

2.061 

2.058 

2.054 

2.051 

2.048 

2.045 

2. 042 

2.039 

2.036

2.033 

2.030 

2.027 

2.024 

2. 021 

2.018 

2.015 

2.012 

2.009 

2.006 

2.003 

1.999

1.996 

1.993 

1.990 

1.987 

1.984 

1.981 

1.977 

1.974 

1.971 

1.968 

1.965 

1.962

1.959 

1.956 

1.952 

1.949 

1.946 

1.943 

1.940 

1.937 

1.933 

1.930 

1.927 

1.924

1.921 

1.917 

1.914 

1.911 

1.908 

1.905 

1.901 

1.898 

1.895 

1.892 

1.888 

1.885

1.882

5' longitude.

Inches. 

4.139 

4.133 

4.127 

4.121 

4.115 

4.109 

4.103 

4.097 

4.091 

4.085 

4.079 

4.073

4.067 

4.060 

4.054 

4.048 

4.042 

4.036 

4.030 

4.023 

4.017 

4.011 

4.005 

3.999

3.993 

3.986 

3.980 

3.974 

3.968 

3.961 

3.955 

3.949 

3.943 

3.936 

3.930 

3.924

3.917 

3. 911 

3.905 

3.898 

3.892 

3.886 

3.879 

3.873 

3.867 

3.860 

3.854 

3.848

3.841 

3.835 

3.828 

3.822 

3.815 

3.809 

3. 802 

3.796 

3.790 

3.783 

3.777 

3.770

3.764

74' longitude.

Inches. 

6.209 

6.200 

6.191 

6.181 

6. 172 

6. 163 

6.154 

6.145 

6.136 

6. 127 

6.118 

C.109

0.100 

6.091 

6.081 

6.072 

6. 063 

6.054 

6.044 

6. 035 

6.026 

6.017 

6.008 

5.998

6.989 

5.980 

5.970 

5.961 

5.951 

5. 942 

5.933 

5.923 

5.914 

5.904 

5.895 

5.886

5.876 

5.867 

5.857 

5.848 

5. 838 

5. 829 

5.819 

5.810 

5.800 

5. 790 

5.781 

5.771

5.762 

5. 752 

5.742 

5.733 

5.723 

5.713 

5.704 

5.694 

5.684 

5. 675 

5.665 

5.655

5.646

10' longitude.

Inches. 

8.278 

8. 200 

8. 254 

8. 242 

8.230 

8. 218 

8. 200 

8.194 

8.181 

8.169 

8.157 

 8. 145

8.133 

8. 121 

8.108 

8.096 

8. 084 

8.072 

8. 059 

8.047 

8.035 

8.022 

8.010 

7.998

7.985 

7.973 

7.960 

. 7. 948 

7. 935 

7.923 

7.910 

7.898 

7.885 

7.872 

7.860 

7.848

7.835 

7.822 

7.810 

7.797 

7.784 

7.771 

7.759 

7.746 

7.733 

7.721 

7.708 

7.695

7.682 

7.670 

7.657 

7.644 

7.631 

7.618 

7.605 

7.592 

7.579 

7. 566 

7.553 

7.540

7.528

12i' longitude.

' Inches. 

10. 348 

10.333 

10. 318 

10. 302 

10.287 

10. 272 

10. 257 

10. 242 

10. 227 

10.212 

10. 197 

10. 182

10.166 

10. 151 

10. 130 

10. 120 

10.105 

10. 090 

10.074 

10. 059 

10. 043 

10. 028 

10.013 

9. 997

9.982 

9.966 

9.950 

9.935 

9.919 

9.903 

9.888 

9.872 

9.856 

9.841 

9.825 

9.809

9.794 

9.778 

9.703 

9.740 

9.730 

9.7.14 

9. 698 

9.683 

9.067 

9. 051 

9. 035 

9. 619

9.603 

9.587 

9.571 

9.555 

9.538 

9.522 

9.506 

9.490 

9.474 

9.458 

9.442 

9.426

9.409

15' longitude.

Inches. 

12. 417 

12. 399 

12. 381 

12.363 

12. 345 

12. 327 

12. 308 

12.290 

12. 272 

12. 254 

1.2. 236 

12.218

12.200 

12.181. 

12. 163 

.12. 144 

12.126 

12. 107 

12.089 

12. 070 

12.052 

12. 033 

12.015 

1.1. 996

11.978 

11.959 

11.940 

11.922 

11. 903 

11.884 

 11.865 

11.846 

11.828 

11.809 

11. 790 

11. 771

11.752 

11.733 

11.714 

11.695 

11.676 

11.657 

11.638 

11 619 

11. 600 

11.581 

11.562 

11. 543

11/524 

11. 504 

11.485 

11. 466 

11.446 

11. 427 

11.407 

11. 388 

11. 369 

11.349 

11.330 

.11.311

11. 291

Ordinates of developed 

parallel.

Longitude 

interval.

24 

5 

74 

10 

124 

15

25- 

5 

74 

10 

124 

15

Longitude interval.

/

24 

5 

74 

10 

124 

15

2J 

5 

74 

10 

124 

15

24 

5 

74 

10 

124 

15

45°

Inches. 

0.001 

.002 

.005 

.009 

.013 

.019

47°

Inches. 

0.001 

. .002 

.005 

.008 

.013 

.019

47°

Inches. 

0. 001 

.002 

.005 

.008 

.013 

.019

49°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

49°

Inches. 

0.001 

.002 

.005 

.008 

' .013 

.019

46°

Inches. 

0.001 

.002 

.005 

.009 

.013 

.019

48°

Indies. 

0.001 

.002 

. .005 .008' 

.013 

.019

50°

Inches. 

0.001 .002 ' 

.005 

.008 

.013 

.019
76 GEOGRAPHIC TA.BLES AND FORMULAS.

TABLE 10. Coordinates for projection of maps (scale 

[Prepared by S. S..Gannett.]

Latitude 

of 

parallel.

25 00 

05 

07i 

10 

15

20 

22* 

25 

30

35 

37J 

40 

45

50 

52£ 

55 

60

26 00 

05 

07J 

1.0 

15

20 

22i 

25 

30

35 

37$ 

40 

45

50 

52i 

55 

60

27 00 

05 

07| 

10 

15

20

m

25 

30

35 

371 

40 

45

50 

52J 

55 

60

Abscissas of developed parallel.

Longitude interval.

21'

Inches. 

3.450 

.448 

.446 

.445 

.443

3.441 

.440 

.438 

.436

3.434 

.433 

.431 

.429

3.426 

.425 .424' 

.422

3.422 

.419 

.418 

.417 

.414

3.412 

.410 

.409 

.407

3.405 

.403 

.402 

.400

3. 397 

.396 

.394 

..392

3.392 

.390 

.388 

.387 

.385

3.382 

.380 

.379 

.377

3.374 

.373 . 

.371 

.369

3.367 

.365 

.364 

.361

5'

Inches. 

6.900 

.895 

.893 

.890 

.886

6.881 

.879 

.876 

.872

6.867 

.865 

.862 

.858

6.852 

.850 

.848 

.843

6. 843 

.838 

.836 

.833

.828

6.824 

.821 

.819 

.814

6.809 

.806 

.804 

.799

6.794 

.792 

.789 

.784

6.784 

.779

.777 

.774 

.769

' 6.764 

.761 

.759 

.754

6.749 

.746 

.743 

.738

6.733 

.730 

.728 

.723

71'

Inches. 

10.350 

.343 

.339 

.336 

.329

10. 322 

.318. 

.314 

.307

10. 300 

.297 

.293 

.280

10. 279 

.276 

.272 

.264

10. 264 

.257 

.253 

.250 

.243

10. 236 

.232 

.238 

.221

10. 214 

.210 

.206 

.198

10. 191 

.188 

.184 

.176

10. 177 

.169 

.165 

.161 

.153

10. 146 

.142 

.138 

.131

10. 124 

!l20 

.116 

.108

10. 100 

.095 

.092 

.084

10'

Inches. 

13. 800 

.790 

.786 

.781 

.772

13. 772 

.758 

.753 

.744

13. 734 

.730 

.725 

.715

13. 705 

.700 

.696 

.686

13. 68C 

.677 

.672 

.666 

.657

13. 647 

.642 

.638 

.628

13. 618 

.612 

.608 

.598

13.588 

.583 

.578 

.569

13. 569 

.559 

.554 

.548 

.538

13. 528 

.523 

.518 

.508

13. 498 

.492

.487 

.477

13. 467 

.461 

.456 

.446

15'

Inches. 

20. 700 

.685 

.678 

.671 

.657

20. 643 

.636 

.029 

.615

20. 601 

.594 

.587 

.573

20. 558 

.551 

.544 

.529

20.529 

.514 

.506 

.499 

.485

20. 471 

.464 

.457 

.442

20.427 

.419 

.412 

.397

20. 382 

.375 

.367 

.353

20.353 

.338 

.330 

.322 

.307

20. 292 

.284 

.277 

.262

20. 247 

.239 

.231 

.215

20. 200 

.191 

.184 

.169

Ordinates of developed parallel.

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Longitude 

interval.

5 

71 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Longitude 

interval.

5 

7i 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Inch.

0.002 

.005 

.008 

.019

Meridional 

distance.

Inches. 

1.514 

3.028 

4.542 

6.057 

. 7.571 

9.085 

10. 599 

12. 114 

13. 628 

15. 142

Inch.

0.002 

.005 

.009 

.020

Meridional 

distance.

Inches. 

1.915 

3.029 

4.544 

6.058 

7.573 

9. 087 

10.602 

12. 115 

13.631 

15. 145

Inch.

0.002 

.005 

.009 

.020

Meridional 

distance.

Inches. 

1.515 

3.029 

4. 514 

6.058 

7.574 

9.087 

10. 003 

12. 117 

13. 632 

15. 147

a This table can be used for even multiples or divisions of the TOA5C scale, as indicated in the two following cases. Scale 55^ : For a given latitude the meridional distance for a certain latitude interval and the abscissas and ordinates for a certain longitude interval are double the values given in the 

table. Scale ^m,: For a given latitude the meridional distance for a certain latitude interval and 

the abscissas and ordinates for a certain longitude interval are half the values given in the table.
GEOGBAPHIC TABLES AND FORMULAS. 77

TABLE 10. Coordinates for projection of maps (scale j^^nr) Continued.

Latitude 

of 

parallel.

28 00 

05 

07$ 

10 

15

20 

22J 

25 30 '

35 

374 

40 

45

50 

524 

55 

60

29 00 

054 

07 

10 

15

20 

22J 

25 

30

35 

374 

40 

45

50 

524 

55 

60

30 00 

05 

074 

10 

15

20 

22J 

25 

30

35 

.374 

40 

45

50 

524 

55 

60

Abscissas of developed parallel.

Longitude interval.

24'

Inches. 

3.361 

.359 

.357 

.356 

.354

3.352 

.350 

.349 

.346

3.343 

.342 

.340 

.338

3.336 

.334 

.333 

.330

3.330 

.328 

.326 

.325 

.322

3.319 

.318 

.317 

.314

3.311 

.310 

.309 

.305

3.303 

.302 

.300 

.298

3.298 

.295 

.294 

.292 

.289

3.286 

.285 

.284 

.281

3.278 

.277 

.275 

.273

3.270 

.268 

.267 

.264

5'

Inches. 

6. 723 . 

.718 

.715 

.713 

.708

6.703 

.700 

.698 

.692

6.687 

.684 

.681 

.676

6.671 

.668 

.666 

.660

6.660 

.655 

.652 

.649 

.644

6.638 ' 

.636 

.633 

.628

6.622 

.620 

.617 

.611

6.605 

.603 

.600 

.595

0.595 

.590 

.587 

.584 

.578

6.572 

.570 

.567 

.562

6.556 

.553 

.550 

.545

6.540 

.537 

.534 

.528

74'

Inches. 

10. 084 

.077 

.072 

.069 

.061

10. 054 

.050 

.046 

.038

10.030 

.026 

.022 

.014

10. 006 

.002 

9.998 

.990

9.990 

.982 

.978 

.974 

.966

9.958 

.954 

.950 

.942

9.934 

.930 

.925 

.916

9.908 

.904 

.900 

.892

9.892 

.884 

.880 

.876 

.867

9.858 

.855 

.850 

.842

9.824 

.830 

.826 

.818

9.810 

.805 

.801 

.792

10'

Inches. 

13. 446 

.436 

.430 

.425 

.415

13. 405 

.400 

.395 

.384

13. 373 

.368 

.363 

.352

13.342 

.336 

.331 

.320

13. 320 

.310 

.304 

.299 

.288

13. 277 

.271 

.266 

.255

13.245 

.239 

.234 

.222

13. 211 

.206 

.200 

.190

13. 190 

.179 

.173 

.168 

.156

13. 145 

.140 

.134 

.123

13. 112 

.106 

.101 

.090

13.080 

.074 

.068 

.056

15'

Inches. 

20. 169 

.154 

.145 

.138 

.123

20. 108 

.100 

.092 

.076

20.060 

.052 

.044 

.028

20.013 

.005 

19. 997 

.981

19. 980 

.964 

.956 

.948 

.932

19. 915 

.907 

.899 

.883

19.867 

.859 

.850 

.833

19 816 

.808 

.800 

.785

19. 785 

.768 

.760 

.751 

.734

19. 717 

.710 

.701 

.685

19.668 

.659 

.65L 

.635

19.619 

.611 

.602 

.584

Ordi nates of developed parallel.

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1 

2

"4 3 

5 

6

7 

8 

9 

10

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1

2 

3 

4 

5 

6 

7 

8 

9 

10

Inch.

0.002 

.005 

.009 

.021

Meridional 

distance.

Inches. 1.515 ' 

3.030 

4.545 

6.060 

7.575 

9.090 

10. 605 

12. 120 

13.635 

15.150

Inch.

0.002 

.005 

.009 

.021

Meridional 

distance.

Inches. 

1.515 

3.030 

4.545 

6.060 

7.575 

9.090 

10.605 

12. 122 

13.637 

15. 152

Inch.

0.002 

.005 

.009 

.021

Meridional 

distance.

Inches. 

1.515 

3.030 

4.545 

6.061 

7.576 

9.092 

10.608 

12. 123 

13.638 

15. 154
78 GEOGRAPHIC TABLES AND FOEMULAS.

TABLE 10. Coordinates for projection of maps (scale ^-g^^) Continued.

Latitude 

of 

parallel.

0 /

31 00 

05 

074. 

10 

15

20 

224. 

25 

30

35 

374. 

40 

45

50 

52J 

55 

60

32 00 

05 

07* 10" 

15

20 

224. 

25 

30

35 

374, 

40 

45

50 

52* 

55 

60

33 00 

05 

074. 

10 

15

20 

224 25" 

30

35 

374. 

40 

45

50 

52£ 

55 

60

Abscissas of developed parallel.

Longitude interval.

2£'

Inches. 

3.264 

.261 

.259 

.258 

.256

3.253 

.251 

.250 

.247

3.244 

.243 

.241 

.239

3.236 

.234 

.233 

.230

3.230 

.227 

.225 

.223 

.220

3.218 

.216 

.214 

.212

3.208 

.207 

.205 

.202

3.200

.198

.197 

.194

3.194 

.191 

.190 

.188 

.185

3.182 

.180 

.178 

.176

3.172 

.171 

.169 

.166

3.163 

.162 

.160 

.157

5'

Inches. 

6.528 

.522 

.519 

.517 

.511

6.505 

.502 

.499 

.494

6.488 

.485 

.482 

.477

6.471 

.468 

.465 

.459

6.459 

.453 

.450 

.447 

.441

6.435 

.432 

.429 

.423

6.417 

.414 

.411 

.405

6.400 

.396 

.393 

.387

6.387 

.382 

.379 

.376 

.370

6.364 

.360 

.357 

.351

6.345 

.342 

.339 

.333

6.327 

.324 

.320 

.314

74'

Inches. 

9.792 

.783 

.779 

.775 

.766

9.757 

.753 

.749 

.741

9.732 

.728 

.723 

.715

9.707 

.702 

.697 

.688

9.688 

.680 

.675 

.670 

.661

9.652 

.648 

.644 

.635

9.625 

.621 

.617 

.608

9.600 

.595 

.590 

.581

9.581 

.572 

.568 

.563 

.554

9.545 

.540 

.536 

.527

9.' 517 

.513 

 .508 

.499

9.490 

.485 

.481 

.472

10'

Inches. 

13. 056 

.044 

.039 

.033 

.022

13. 010 

.004 

12. 999 

.988

12. 976 

.970 

.964 

.953

12. 942 

.936 

.930 

.918

12. 918 

.906 

.900 

.894 

.882

12. 870 

.864 .858' 

.846

12.834 

.828 

..822 

.811

12. 799 

 .793 

.787 

.775

12. 775 

.763 

.757 

.751 

.739

12. 727 .720" 

.714 

.702

12. 690 

.684 

.678 

.665

12.653 

.647 

.641 

.629

15'

Inches. 

19. 584 

.567 

.558. 

.550 

.533

19. 515 

.506 

.498 

.481

19. 464 

.455 

,447 

.430

19. 413 

.404 

.395 

.377

19. 377 

.359 

.350 

.341 

.323

19. 305 

.296 

.287 

.269

19. 251 

.242 

.233 

.216

19. 199 

.189 

.180 

.162

19. 162 

.145 

.136 

.127 

.109

19. 090 

.080 

.071 

.053

19. 035 

.026 

.017 

18. 998

18. 980 

.971 

.961 

.943

Ordinates of developed parallel.

Longitude 

interval.

5 

. 74. 

10 

15

Latitude, 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Longitude, 

interval.

5

n

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 7 ' 

8 

9

10

Longitude 

interval.

5 

74. 

10 

15

Latitude 

interval.

 1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Inch.

0.002 

.005 

.010 

.022

Meridional 

distance.

Inches. 

1.515 

3.031 

4.545 

6.062 

7.578 

9.093 

10. 609 

12. 124 

13. 640 

15. 156

Inch.

0.002 

.006 

.010 

.022

Meridional 

distance.

Inches. 

1.516 

3.032 

4.547 

6.063 

7.579 

9.095 

10. 611 

12. 127 

13. 643 

15. 159

Inch.

0.003 

.006 

.010 

.023

Meridional 

distance.

Inches. 

1.516 

3.032 

4.548 

6.065 

7.580 

9.097 

10.613 

12. 129 

13.645 

15. 161
GEOGRAPHIC TABLES AND FORMULAS 79

TABLE 10. Coordinates for projection of maps (scale Continued.

Latitude 

of 

parallel.

34 00 

05 

07£ 

10 

15

20 

22* 25" 

30

35 

37* 40' 

45

50 

52* 55" 

60

35 00 

05 

07* 10" 

15

20 

' 22* 25" 

30

35 

37fc 

40 

45

50 

52J 

55 

60

36 00 

05 

07J 

10 . 

15

20 

25' 22* 

30

35 

37 

40 

45

50 

52 55' 

60

Abscissas of developed parallel.

Longitude interval.

2*'

Inches. 

3.157 

.154 

.152 

.151 

.148

3.145 

.143 

.142 

.139

3.135 

.134 

.132 

.129

3.126 

.124 

.123 

.120

3.120 

.117 

.115 

.114 

.110

3.107 

.105 

.104 

.100

3.097 

.090 

.094 

. 091

3.088 

.086 

.084 

.082

3.082 

.078 

.070 

.075 

.072

3. 068 

.067 

.065 

.062

3.058 

.057 

.055 

.052

3.048 

.047 

.045 

.042

5'

Inches. 

6.314 

.309 

.305 

.302 

.296

6.290 

.286 

.283

.277

6.271 

.208 

.264 

.258

6.252 

.249 

.246 

.240

6.240 

.233 

.230 

.227 

.220

6.214 

.211 

.208 

.201

6.195 

.192 

.188 

.182

 -6.176 

.172 

.169 

.163

6. 163 

.156 

.153 

.150 

.144

6.137 

.134 

.130 

.124

6.117 

.114 

.110 

.104

6.097 

.094 

.091 

.084

7i'

Inches. 

9.472 

.462 

.457 

.453 

.444

9.434 

.430 

.425 

.416

9.406 

.402 

.396 

.387

9.378 

.374 

.369 

.360

9.360 

.350 

.345 

.340 

.330

9.321 

.317 

.312 

.302

9.292 

.288 

.283 

.273

9.263 

.258 

.254 

.244

9.244 

.234 

230 

.225 

.215

9.205 

.200 

.195 

.185

9.176 

.171 

.166 

.156

9.146 

.141 

.136 

.126

10'

Inches. 

12. 629 

.617 

.610 

.604 

.592

12. 579 

.572 

.567 

.554

12. 542 

.535 

.529 

.517

12. 504 

.498 

.492 

.479

12. 479 

.406 

.460 

.454 

.441 '

12. 428 

.422 

.415 

.402

12.390 

.384 

.377 

.364

12. 351 

.345 

.338 

.326

12. 326 

.313 

.306 

.300

.287

12.274 

.268 

.260 

.247

12. 234 

.228 

.221 

.208

12. 194 

.188 

.182 

..169

15'

Inches. 

18. 943 

.925 

.915 

.906 

.888

'18.869 

.859 

.850 

.831

18.813 

.803 

.793 

.775

18. 756 

.747 

.738 

.719

18. 719 

.699 

.690 

.681 

.661

18. 642 

.633 

.623 

.604

IS. 585 

.576 

.565 

.546

18. 527 

.517 

.508 

.489

18. 489 

.469 

.459 

.450 

.431

18. 411 

.401 

.390 

.371

18. 351 

.342 

.332 

.312

18. 292 

.282 

.272 

.253

Ordinates of developed parallel.

Longitude 

interval.

5 

7* 

10 

15

Latitude 

interval.

1 

2

4 

5 

6 

7 

8 

9 

10

Longitude 

interval.

5

10" n

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Longitude 

interval.

5 

. 7* 

10 15 '

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Inch.

0.003 

.006 

.010 

.023

Meridional 

distance.

Inches. 

1.510 

3.032 

4. 548 

6.065 

7.581 

9.096 

10. 613 

12. 130 

13. 646 

15. 162

Inch.

0. 003 

.006 

.010 

.023

Meridional 

distance.

Inches. 

1.516 

3.033 

4.549 

6. 067 

7.583 

9.100 

10. 616 

12. 133 

13. 648 

15. 164

Inch.

0.003 

.006 

.010 

.024

Meridional 

distance.

Inches. 

1.517 

3.034 

4.551 

6.067 

7.584 

9.102 

10.619 

12. 135 

13.652 

15. 169
80 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 10. Coordinates for projection of maps (scale 25-^3-) Continued.

Latitude 

of 

parallel.

37 00 

05 

07£ 

10 

15

20 

22J 

25 

30

35 

37J 

40 

45

50 

52£ 

55 

60

38 00 

05 

07J 

10 

15

20 

22J 

25 

30

35 

37J 

40 

45

50 

52£ 

55 

60

39 -00 

05 

07§ 

10 

15

20 

22§ 

25 

30

35 

37J 

40 

45

50 

52§ 

55 

60

Abscissas of developed parallel.

Longitude interval.

21'.

Inches. 

3.042 

.038 

.037 

.035 

.032

3.028 

.027 

.024 

.022

3.019 

.017 

.015 

.012

3.009 

.006 

.005 

.001

3.001 

2.998 

.997 

.995 

.991

2.988 

.987 

.984 

.981

2.978 

.976 

.974 

.971

2.968 

.966 

.964 

.960

2.960 

.957 

.955 

.954 

.950

2.946 

.945 

.943 

.940

2.936 

.934 

.933 

.929

2.926 

.924 

.922 

.919

5'

Inc hes. 

6.084 

.077 

.074 

.070 

.064

6.057 

.053 

.049 

.044

6.037 

.034 

.030 

.024

6.017 

.013 

.010 

.003

6.003 

5.996 

.993 

.990 

.983

5.976 

.973 

.969 

.962

5.955 

.952 

.949 

.942

5.935 

.932 

.928 

.921

5.921 

.914 

.910 

.907 

.900

5.893 

.890 

.886 

.879

5.872 

-.868 

.865 

.858

5.851 

.848 

.844 

.837

7J'

Inches. 

9.126 

.116 

.111 

.106 

.096

' 9.086 

.081 

.076 

.066

9.056 

.051 

.045 

.035

9.025 

.020 

.015 

.004

9.004 

8.994 

.989 

.984 

.974

8.964 

.959 

.954 

.944

8.933 

.927 

.923 

.913

8.902 

.897 

.892 

.882

8.882 

.871 

.865 

.860 

.850

8.840 

.835 

.829 

.819

8.808 

.802 

.798 

.787

8.777 

.772 

.766 

.755

10'

Inches. 

12. 1C9 

.155 

.148 

.141 

.128

12. 114 

.107 

.101 

.088

12.074 

.068 

.061 

.048

12.034 

.027 

.020 

.006

12. 006 

11. 993 

.986 

.980 

.966

11. 952 

.946 

.939 

.925

11. 911 

.904 

.898 

.884

11.870 

.863 

.856 

.842

11. 842 

.828 

.821 

.814 

.800

11. 786 

.779 

.772 

.758

11. 744 

.737 

.730 

.716

11. 702 

.695 

.688 

.674

15'

Inches. 

18. 253 

.232 

.222 

.212 

.192

18. 172 

.162 

.152 

.132

18. 112 

.102 

.091 

.071

18.050 

.040 

.030 

.009

18.009 

17. 989 

.979 

.969 

.949

17.929 

.919 

.908

.887

17. 867 

.856 

.846 

.826

17.805 

.795 

.784 

.763

17. 763 

.742 

.731 

.721 

.700

17.679 

.669 

.658 

.637

17.616 

.605 

.595 

.574

17. 553 

.543 

.532 

.511

Ordinates of developed parallel.

Longitude 

interval.

5 

7i 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Longitude 

interval.

5 7J10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9

10

Longitude 

interval.

/ 

5 

7J 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Inch.

0.003 

.006 

.010 

.024

Meridional 

distance.

Inches. 

1.517 

3.034 

4.551 

6.068 

7.585 

9.102 

10. 619 

12. 136 

13.653 

15. 170

Inch.

0.003 

.006 

.010 

.024

Meridional 

distance.

Inches. 

1.517 

3.034 

4.551 

6.069 

7.586 

9.103 

10. 620 

12. 138 

13. 655 

15. 172

Inch.

0.003 

.006 

.011 

.024

Meridional 

distance.

Inches. 

1.517 

3.035 

4.552 

6.070 

7.587 

9.105 

10. 622 

12. 140 

13.658 

15. 175
GEOGBAPHIC TABLES AND FORMULAS.

TABLE 10. Coordinates for projection of maps (scale j-gihre) Continued.

8.1

Latitude 

of 

parallel.

40 00 

05 

07J 

10 

15

 20 

22 J 

25 

30

 35 

37£ 

' 40 

45

50 

52£ 

55 

60

41 00 

05 

07i 

10. 

. 15

20 

22J 

25 

30

35 

37J 

40 

45

50 

52J 

55 

60

42 00 

05 

07J 

10 15'

20 

22$ 

25 

30

35 

37£ 

40 

45

50 

521 

55 

60

Abscissas of developed parallel.

Longitude interval.

2$'

2.919 

.915 

.913 

.912 

.908

2.904 

.902 

.900 

.897

2.894 

.892 

.890 

.886

2.883 

 .881 

.879 

.875

2.875 

.872 

.870 

.868 

.864

2.861 

.859 

.857 

.854

2.850 

.848 

.846 

.843

2.839 

.837 

.835 

.831

2.831 

.827 

.826 

.824 

.820

2.817 

.815 

.813 

.809

2.805 

.804 

.802 

.798

2.794 

.793 

.791

.787

5'

5.837 

.830 

.826 

.823 

.816

5.808 

.804 '.'801 

.794

5.787 

.784 

.780 

.772

5.765 

.762 

.758 

.750

5.750 

.743 

.740 

.736 

.729

5.722 

.718 

.714 

.707

5.700 

.696 

.692 

.685

5. 678 

.674 

.670 

.663

5.663 

.655 

.652 

.648 

. 6.41

. 5.634 

.630 

.626 

.618

5.611 

.608 

.604 

.597

5.589 

.585 

.582 

.574

IV

8.755 

.745 

.740 

.734 

.723

8.712 

.706 

.702 

.691

8.680 

.675 

.670 

.650

8.648 

.642 

.636 

.625

8.625 

.614 

.609 

.604 

.594

8.582 

.577 

.572 

.561

8.550 

.544 

.539 

.528

8. 517 

.510 

.505 

.494

8.494 

.483 

.478 

.472 

.462

8.450 

.444 

.439 

.428

8.417 

.412 

.406 

.395

8.384 

.378 

.372 

.361

10'

11. 674 

.660 

.653 

.646 

.631

11. 616 

.609 

.602

.588

11. 574 

.567 

.560 

.545

11.530 

.523 

.516 

.501

11.501 

.486 

.479 

.472 

.458

11.443 

.436

.428 

.414

11. 399 

.392 .385' 

.370

11. 355 

.347 

.340 

.326

11. 326 

.311 

.304 

.296 

.282

11. 267 

.259 

.252 

.237

U. 222 

.215 

.208 

.192

11. 178 

.170 - 

.163 

.148

15'

17. 511 

.490 

.479 

.469

.447

17. 424 

.413 

.403 

.382

17. 361 

.351 

.340 

.317

17.295 

.285 

.273 

.251

17.251 

.229 

 .219 

.208 

.187

17. 165 

.154 

.143 

.121

17.099 

.088 

.077 

.055

17. 033 

.021 

.011 

16. 989

16. 989 

.966 

.956 

.944 

.923

16. 901

.889 

.878 

.855

16. 833 

.823 

.812 

.790

16. 767 

 .755 

.745 

.722

Ordinates of developed parallel.

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Longitude 

interval.

5 

7J 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Inch.

0.003 

.006 

.011 

.024

Meridional 

distance.

Inches. 

1.518 

3. 035 

' 4. 557 

6.070 

7. 588 

9.106

10. 624 

12. 143 

13. 660 

15. 178

Inch.

0. 003 

.006 

. .011 

.025

Meridional 

distance.

Inches. 

1. 518 

3.036 

4.554 

6.072 

7.590 

9.108 

10. 626 

12. 145 

13. 663 

15. 181

Inch.

0.003 

 .006 

.011 

.025

Meridional 

distance.

Inches. 

1.518 

3.036 

4.554 

6.073 

7. 591 

9. 109 

10. 627 

12.147 

13. 666 

15.184

41623° 16 6
82 GEOGEAPHIC TABLES AND FOEMULAS.

TABEE 10. Coordinates for projection of maps (scale Continued.

Latitude 

of 

parallel.

43 00 

05 

07J 

10 

15

20 

22J 

25 

30

35 

37£ 

40 

45

50 

52i 

55 

60

44 00 

05 

07J 

10 

15

20 

22J 

25 

30

35 

37fc 

40 

45

50 

52£ 

55 

.60

45 00 

05 

07J 

10 

15

20 

22J 

25 

30

35 

37J 

40 

45

50 

52£ 

55 

60

Abscissas of developed parallel.

Longitude interval.

2i'

Inches. 

2.787 

.783 

.781 

.779 

.776

2.772 

.770 

.768 

.764

2.760 

.758 

.756 

.752

2.749 

.747 

.745 

.741

2.741 

.737 

.735 

.733 

.730

2.726 

.723 

.722 

.718

2.714 

.712 

.710 

.706

2.702 

.700 

.698 

.695

2.695 

.691 

.689 

.687 

.683

2.679 

.677 

.675 

.671

2.667 

.665 

.663 

.660

2.655 

.654 

.652 

.648

5'

Inches. 

5.574 

.566 

.562 

.558 

.551

5.543 

.539 

.535 

.528

5.520 

.516 

.512 

.505

5.498 

.494 

.490 

.482

5.482 

.474 

.470 

.467 

.459

5.451 

.447 

.444 

.436

5.428 

.424 

.420 

.413

5.405 

.401 

.397 

.390

5.390 

.382 

.378 

.374 

.366

5.358 

.354 

.350 

.342

5.334 

.330 

.326 

.319

5.311 

.307 

.303 

.295

75'

Inches. 

8.361 

.349 

.343 

.338 

.326

8.314 

.308 

.303 

.292

8.280 

.274 

.268 

.257

8.246 

.240 

.235 

.223

8.223 

.212 

.206 

.200 

.188

8.177 

.171 

.166 

.154

8.142 

.136 

.130 

.119

8.108 

.102 

.096 

.084

8.084 

.073 

.067 

.061 

.049

8.038 

.032 

.026 

.014

8.002 

7.996 

.990 

.978

J 7.966 

.960 

.954 

.942

W

Inches.' 

11.148 

.132 

.124 

.117 

.102

11.086 

.078 

.070 

.055

11.040 

.032 

.025 

.010

10.995 

.987 

.980 

.964

10.964 

.949 

.941 

.934 

.918

10.902 

.894 

.887 

.872

10. 856 

.848 

.840 

.825

10.810 

.802 

.794 

.779

10. 779 

.764 

.756 

.748 

.732

10.717 

.708 

.701 

.685

10. 669 

.661 

.653 

.638

10. 622 

.614 

.606 

.590

15'

Inches. 

16.722 

.698 

.686 

.675 

.653

16.629 

.617 

.606 

.583

16.560 

.548 

.537 

.515

16. 493 

.481 

.470 

.446

16. 446 

.423 

.411 

.400 

.377

16. 354 

.341 

.331 

.308

16.284 

.272 

.261 

.238

16.215 

.203 

.192 

.169

16. 169 

.146 

.134 

.122 

.098

16.075 

.063 

.051 

.027

16.003 

15.991 

.980 

.957

15.933 

.921 

.909

.885

Ordinates of developed parallel.

Longitude 

interval.

5 

7i 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Longitude 

interval.

5 

7J 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Longitude 

interval.

5

n

10 

15

Latitude 

interval.

1

2 

3

4 

5 

6 

7 

8 

9 

10

Inch.

0.003 

.006 

.011 

.025

Meridional 

distance.

Inches. 

1.519 

3.038 

4.557 

6.075 

7.594 

9.113 

10.631 

12. 149 

13.668 

15. 187

Inch.

0.003 

.006 

.011 

.025

Meridional 

distance.

Inches. 

1.519 

3.038 

4.557 

6.076 

7.595 

9.114 

10. 633 

12. 152 

13.671 

15.190

Inch.

0.003 

.006 

.011 

. .025

Meridional 

distance.

Inches. 

1.519 

3.038 

4.557 

6.077 

7.596 

9.115 

10.635 

12. 154 

13.673 

15. 192
GEOGKAPHIC TABLES AND FOEMTJLAS. 83

TABLE 10. Coordinates for projection of maps (scale 55-^^) Continued.

Latitude 

of 

parallel.

46 00 

05 

07J 

10 

15

20 

22$ 

25 

30

35 

374 

40 

45

50 

52J 

55 

CO

47 00 

05 

074 

10 

15

20 

22 

25 

30

35 

37J 

40 

45

50 

524 

55 

60

48 00 

05 

074 

10 

15

20 

22J 

25 

30

35 

37J 

40 

45

50 

52J 

55 

60

Abscissas of developed parallel.

Longitude interval.

24'

Inches. 

2.648 

.644 

.640 

.639 

.635

2.631 

.630 

.627 

.623

2.619 

.617 

.615 

.011

2.607 

.605 

.603 

.599

2.599 

.595 

.593 

.591 

.587

2.583 

.581 

.579 

.575

2.570 

.568 

.567 

.563

2.559 

.557 

.555 

.550

2.550 

.546 

.544 

.542 

.538

2.534 

.532 

.530 

.526

' 2.522 

.520 

.517 

.513

2.509 

.507 

.505 

.501

5'

Inches. 

5.295 

.287 

.281 

.279 

.271

5.203 

.259 

.255 

.247

5.239 

.235 

.230 

.223

5.214 

.210 

.206 

.198

5.198 

.190 

.186 

.182 

.174

5.166 

.162 

.158 

.150

5.141 

.137 

.133 

.125

5.117 

.113 

.109 

.100

5.100 

.092 

.088 

.084 

.076

5.068 

.064 

.060 

.051

5.043 

.039 

.034 

.026

5.018 

.014 

.010 

.002

74'

Inches. 

7.942 

.930 

.922 

.918 

.906

7.894 

.888 

.882 

.870

7.858 

.852 

.840 

.834

7.822 

.816 

.810 

.798

7.798 

.786 

.780 

.774 

.761

7.749 

.743 

'.737 

.724

7.712 

.706 

.700 

.088

7.676 

.670 

.663 

.650

7.650 

.638 

.632 

.626 

.614

7.602 

.596 

.590

.577

7.564 

.558 

.552 

.539

7.527 

 .521 

.515 

.502

10'

Inches. 

10. 590 

.574 

.562 

.558 

.542

10. 526 

.518 

.510 

.494

10. 478 

.470 

.461 

.445

10. 429 

.421 

.413 

.397

10. 397 

.381 

.373 

.365 

.348

10. 332 

.324 

.316 

.299

10. 282 

.274 

.206 

.250

10. 234 

.226 

.218 

.201

10.201 

.185 

.177 

.168 

.152

10. 136 

.128 

.119 

.102

10. 086 

.078 

.069 

.052

10. 036 

.028 

.020 

.003

15'

Inches. 

15. 885 

.861 

.844 

.837 

.813

15. 789 

.777 

.765 

.741

15. 717 

.705 

.692 

.667

15. 643 

.631 

.619 

.595

15. 595 

.571 

.559 

.547 

.522

15. 498 

.486 

.474 

.449

15. 423 

.411 

.399 

.375

15. 351 

.339 

.326 

.307

15. 301 

.277 

.205 

.252 

.228

15. 204 

.192 

.179 

.154

15. 129 

.116 

.103 

.078

15. 054 

 .042 

.030 

.005

Ordinates of developed parallel.

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

0 

7 

8 

9 

10

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

0 

7 

8 

9 

10

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10

Inch.

0.003 

.006 

.011 

.025

Meridional 

distance.

Inches. 

1.520 

3.039 

4.559 

6. 078 

7.598 

9.117 

10. 637 

12. 157 

13.677 

15. 196

Inch.

0.003 

.006 

.011 

.025

Meridional 

distance.

Inches. 

1.520 

3.039 

4. 559 

6. 079 

7.599 

9.119 

10. 638 

12. 158 

13. 678 

15. 197

Inch.

0.003 

.006 

.011 

.025

Meridional 

distance.

Inches. 

1. 520 

3. 0<10 

4.560 

6.080 

7.600 

9.120 

10. 640 

12. 100 

13.680 

15. 200
84 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 10. Coordinates for the projection of maps (scale ¥8 % 00 ) Continued.

Latitude 

of 

parallel.

49 00 

05 

07$ 

10 

15

20 

22$ 

25 

30

35 

37£ 

40 

45

50 

52£ 

55 

CO

50 00 

05 

07£ 

10 

.15

20 

22-i 

25 

30

35 

37fc 

40 

. 45

* 50 

52J 

55 

60

51 00 

05 

.07J 

10 

15

20 

22£ 

25 

30

35 

37* 40" 

45

50 

52£ 

55 

60

Abscissas of developed parallel.

Longitude interval.

21'

Inches. 

2.501 

.496 

.494 

.492 

.488

2.484 

.482 

.480 

.476

2.472 

.470 

.467 

.463

2.459 

.457 

.455 

.450

2.450 

.446 

.444 

.442 

.438

2.434 

.432 

.429 

.425

2. 420 . 

.418 

.416 

.412

2.408 

.406 

.404 

.399

2.399 

.395 

.392 

.390 

.386

2.382 

.380 

.377 

.373

2.369 

.366 

.364 

.360

2.356 

.354 

.351 

.347

5'

Inches. 

5.002 

4.993 

.989 

.985 

.976

4.968 

.964 

.960 

.952

4.943 

.939 

.934 

.926

4.918 

.914 

.910 

.901

4.901 

.892

.888 

.884 

.875

4.867 

.862 

.858 

.850

4.841 

.837 

.833 

.824

4.815 

.811 

.807 

.798

4.798 

.789

.785 

.781 

.772

4.764 

.760 

.755

.747

4.738 

.734 

.729 

.720

4.711 

.707 

.703 

.694

7J'

Inches. 

7.502 

.490 

.484 

.477 

.464

7.452 

.446 

.440 

.428

7.415 

.408 

.402 

.389

7.377 

.371 

.364 

.352

7.351 

.338 

.332 

.326 

.313

7.300 

.294 

.287 

.274

7.261 

.255 

1 .249 

.236

7.223 

.216 

.210 

.197

7.197 

.184 

.178 

.172 

.159

7.146 

.140 

.133 

.120

7.107 

.100 

.094 

.081

7.068 

.062 

.055 

.042

10'

Inches. 

10. 003 * 

9.986 

 .978 

.970 

.952

9.936 

.928 

.920 

.903

9.886 

.878 

.869 

.852

9.836 

.828 

.819 

.802

9.802

.785 

.777 

.768 

.751

9.734 

.725 

.716 

.699

9.682 

.674 

.665 

.648

9.631 

.622 

.614 

.597

9.597 

.580 

.571 

.562 

.545

9.528 

.519 

.510 

.493

9.476 

.467 

.458 

.441

9.424 

.415 

.406 

.389

15'

Inches. 

15.005 

14. 980 

.967 

.955 

.929

14.904 

.892 

.880 

.855

14.829 

.816 

.803 

.778

14.754 

.742 

.729 

.703

14.702 

.677 

.664 

.651 

.626

14.600

.588 

.575 

.549

14. 523 

.510 

.498 

.472

14.446 

.434 

.421 

.395

14.395 

.369 

.356 

.343 

.317

14.291 

.278 

.266 

.240

14.214 

.200 

.187 

' .161

14.135 

.122 

.109 

.083

Ordinates of developed parallel.

Longitude 

interval.

5

74 

 10 

15

Latitude 

interval.

1

2 

3 

4 

5 

6 

7 

8 

9 

10

Longitude 

interval.

5 

71 

10 

15

Latitude 

interval.

1 

2. 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Inch.

0.003 

.006 

.011 

.025

Meridional 

distance.

Inches. 

1.520 

3.040 

4.560 

6.081 

7.601 

9.121 

10.641 

12. 162 

13. 682 

15.202

Inch.

0.003 

.006 

.011 

.025

Meridional 

distance.

Inches. 

1.521 

3.041 

4.562 

6.082 

7.603 

9. 123 

10. 644 

12.164 

13.685 

15. 206 

22. 809

Inch.

0.003 

.006 

.011 

.024

Meridional 

distance.

Inches. 

1.521 

3.042 

4.562 

6.083 

7.604 

9.125 

10. 646 

12. 167 

13. 687 

15. 208 

22. 813
GEOGRAPHIC TABLES AND FORMULAS. 85 

TABLE 10. Coordinates for the projection of maps (scale 48 fl 00 ) Continued.

Latitude 

of 

parallel.

52 00 

05 

074 

10 

15

2Q 

22* 

25 

30

35

374 

40 

45

50 

524 

55 

60

53 00 

05 

07J 

10 

15

20 

224 

25 

30

35' 

374 

40 

45

50 

524 

55 

60

54 00 

05 

07J 

10 

15

20 

224 

25 

30

35 

374 

40 

45

50 

524 

55 

60

Abscissas of developed parallel.

Longitude interval.

24'

Inches. 

2.347 

.343 

.340 

.338 

.334

2.330 

.328 

.325 

.321

2.317 

.314 

.312 

.308

2.304 

.302 

.299 

.295

2.295 

.290 

.288 

.286 

.281

2.277 

.274 

.272 

.268

2.264 

.262 

.259 

.255

2.250 

.248 

.246 

.241

2.241 

.237 

.234 

.232 

.228

2.223 

.221 

.219 

.214

2.210 

.208 

.205 

.201

2.196 

.194 

.192 

.187

5'

Inches. 

4.694 

.685 

.681 

.677 

.668

4.659 

.655 

.651 

.642

4.633 

.629 

.625 

.616

4.607 

.602 

.598 

.589

4.589 

.580 

.576 

.572 

.563

4.554 

.550 

.545 

.536

4.527 

.522 

.518 

.509

4.500 

.496 

.491 

.482

4.482 

.473 

.468 

.464 

.455

4.446 

.442 

.437 

.428

4.419 

.414 

.410 

.401

4.392 

.388 

.383 

.374

74'

Inches. 

7.042 

.029 

.022 

.015 

.002

6.989 

.982 

.976 

.963

6.950 

.943 

.936 

.923

6.910 

.904 

.897 

.884

6.884 

.871 

.864 

.857 

.844

6.831 

.824 

.817 

.804

6.791 

.784 

.777 

.764

6.751 

.744 

.737 

.724

6.724 

.710 

.704 

.697 

.683

6.670 

.663 

.656 

.643

6.629 

.622 

.616 

.602

6.588 

.582 

.575 

.561

10'

Inches. 

9.389 

.372 

.363 

.354 

.337

9.319 

.310 

.302 

.284

9.266 

.258 

.249 

.231

9.213 

.204 

.196 

.178

9.178 

.160 

.152 

.143 

.125

9.107 

.098 

.090 

.072

9.054 

.045 

.036 

.018

9.000 

8.992 

.983 

.965

8.965 

.947 

.938 

.929 

.911

8.893

.884 

.875 

.857

8. 839 

.830 

.821 

.803

8.785 

.776 

.766

.748

15'

Inches. 

14.083 

.057 

.044 

.031 

.005

13.979 

.966 

.952 

.926

13.900 

.886 

.873 

.846

13.820 

.806 

.793 

.767

13. 767 

.740 

.727 

.714 

.687

13. 661 

.648 

.634 

.608

13. 581 

.568 

.555 

.528

13.501

.488 

.474 

.447

13.447 

.420 

.406 

.493 

.366

13. 339 

.326 

.312 

.285

13. 258 

.244 

.231 

.204

13.177 

.164 

.150 

.123

Ordinates of developed parallel.

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 . 

10 

15

Longitude 

interval.

t

5 

74 

10 

15

Latitude 

interval.

1

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

5 

74 

10 

15

Latitude 

interval.

1

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Inch.

0.003 

.006 

.011 

.024

Meridional 

distance.

Inches. 

1.521 

3.042 

4.563 

6.084 

7.605 

9.126 

10.647 

12. 169 

13.690 

15. 211 

22.817

Inch.

0.003 

.006 

.011 

.024

Meridional 

distance.

Inches. 

1.521 

3.043 

5.564 

6.085 

7.607 

9.128 

10.650 

12. 171 

13. 692 

15. 214 

22.820

Inch.

0.003 

.006 

.011 

.024

Meridional 

distance.

Inches. 

1.522 

3. 043 

4.565 

6.086 

7.608 

9.130 

10. 651 

12. 173 

13. 694 

15. 216 

22. 824
86 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 10. Coordinates for the projection of maps (scale 4B ft 00 ) Continued.

Latitude 

of 

parallel.

0 1

55 00 

05 

07J 

10 

15

20 

22$ 

25 

30

35 

37$ 

40 

45

50 

52$ 

55 

60

56 00 

05 

07$ 

10 

15

20 

22$ 

25 

30

35 

37$ 

40

45

50 

52$ 

55 

60

57 00 

05 

07$ 

10 

15

20 

22$ 

25 

30

35 

37$ 

40 

45

50 

52$ 

55 

60

Abscissas of developed parallel.

Longitude interval.

2i'

Inches. 

2.187 

.183 

.180 

.178 

.174

2.169 

.167 

.165 

.160

2.155 

.153 

.150 

.146

2.141 

.139 

.137 

.132

2.132 

.128 

.126 

.123 

.119 

2.114 

.112 

.110 

.105

2.100 

.098 

.095 

.091

2.086 

.084 

.082 

.077

2.077 

.072 

.070 

.068 

.063

2.058 

.056 

.054 

.049

2.044 

.042 

.040 

.035

2.030 

.028 

.026 

.021

5'

Inches. 

4.374 

.365 

.360 

.356 

.347

4.338 

.334 

.329 

.320

4.310 

.306 

.301 

.292

4.283 

.278 

.274 

.265

4.265 

.256 

.251 

.246 

.237

4.228 

.224 

.219 

.210

4.200 

.196 

.191 

.182

-4.173 

.168 

.163 

.154

4.154 

.145 

.140 

.135 

.126

4.117 

.112 

.107 

.098

4.089 

.084 

.079 

.070

4.061 

.056 

.051 

.042

7$'

Inches. 

6.561 

.548 

.541 

.534 

.521

6.507 

.500 

.494 

.480

6.466 

.459 

.452 

.438

6.424 

.418 

.411 

.397

6.397 

.383 

.376 

.370 

.356

6.342 

.336 

.329 

.315

6.301 

.294 

.287 

.273

6.259 

.252 

.245 

.231

6.231 

.217 

.210 

.203 

.189

6.175 

.168 

.161 

.147

6.133 

.126 

.119 

.105

6.091 

.084 

.077 

.063

10'

Inches. 

8.748 

.730 

.721 

.712 

.694

8.676 

.666 

.657 

.639

8.621 

.612 

.603 

.584

8.566 

.556 

.547 

.529

8.529 

.511 

.502 

.492 

.474

8.456 

.447 

.438 

.420

8. 401 , 

.392 

.383 

.364

8.345 

.336 

.327 

.308

8.308 

.289 

.280 

.271 

.252

8.233 

.224 

.215 

.196

8.177 

.168 

.159 

.140

8.121 

.112 

.103 

.084

15'

Inches. 

13. 123 

.096 

.082 

.068 

.041

13.014 

.000 

12.986 

.959

12. 932 

.918 

.904 

.877

12. 849 

.836 

.822 

.794

12. 794 

.767 

.753 

.740 

.712

12. 684 

.670 

.657 

.629

12.601

.588 

.574 

.546

12. 518 

.504 

.490 

.462

12.462 

.434 

.420 

.406 

.378

12.350 

.336 

.323 

.295

12.267 

.252 

.238 

.210

12. 182 

.168 

.154 

.126

Ordinates of devel- 

. oped parallel.

Longitude 

interval.

5 

7$ 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

Interval.

5 

7$ 

10 

15

Latitude 

interval.

1 

2 

3

- 4 

. 5 

6 

1, 

8 

9 

10 

15

Longitude 

interval.

5 

7$ . 

10 

15

Latitude 

interval.

1 

2 

3

4 

5 

6 

7 

8 

9 

10 

15

Inch.

0.003 

.006 

.010 

.024

Meridional 

distance.

Inches. 

1.522 

3.044 

4.566 

6.088 

7.609 

9.131 

10. 653 

12. 175 

13. 697 

15. 219 

22. 828

Inch.

0.003 

.006 

.010 

.023

Meridional 

distance.

Inches. 

1.522 

3.044 

4.566 

6.088 

7.611 

9.133 

10.655 

12. 177 

13.699 

15. 221 

22. 832

Inch.

0.002 

.006 

.010 

.023

Meridional 

distance.

Inches. 

1.522 

3.045 

4.567 

6.089 

7.612 

9.134 

10.657 

12. 179 

13. 701 

15. 224 

22.836
GEOGRAPHIC TABLES AND FORMULAS. 87 

TABLE 10. Coordinates for the projection of maps (scale 48 ooo) Continued.

Latitude 

of 

parallel.

58 00 

05 

071 

10 

15

20 

22J 

25 

30

35 

37J 

40 

45

50 

521 

55 

60

59 00 

05 

07i 

10 

15

20 

22} 

25 

30

35 

37J 

40 

45

50 

52} 

55 

60

60 00 

05 

07J 

10 

15

20 

22} 

25 

30

35 

37J 

40 

45

50 

521 

55 

60

Abscissas of developed parallel.

Longitude interval.

24'

Inches. 

2.021 

.016 

 .014 

.012 

.007

2.003 

.000 

1.998 

.993

1.988 

.986 

.984 

.979

1.974 

.972 

5 .969 

.964

1.964 

.959 

.957 

.955 

.950

1.945 

.943 

.941 

.936

1.931 

.928 

.926 

.921

1.916 

.914 

.912 

.907

1.907 

.902 

.900 

.898 

.893

1.888 

.886 

.883 

.878

1.873 

.871 

.869 

.864

1.859 

.856 

.854 

.849

5'

Inches. 

4.042 

.033 

.028 

.023 

.014

4.005 

.000 

3.995 

.986

3.976 

.971 

.967 

.957

3.948 

.943 

.938 

.929

3.929 

.919 

.914 

.910 

.900

3.891 

.886 

.881 

.872

3.863 

.858 

.853 

.843

3.833 

.828 

.824 

.814

3.814 

.804 

.800 

.795

.785

3.775 

.770 

.765 

.756

3.747 

.742 

.737 

.728

3.718 

.713 

.708 

.698

7J'

Inches. 

6.003 

.049 

.042 

.035 

.021

6.007 

.000 

5.992 

.978

5.964 

.957 

.950 

.936

5.922 

.915 

.907 

.893

5.893 

.879 

.877 

 .864 

.850

5.836 

.828 

.821 

.807

5.793 

.786 

.778 

.764

5.750 

.742 

.735 

.721

5.721 

.707 

.700 

.692 

.678

5.664 

.656 

.649 

.635

5.620 

.613 

.606 

.591

5.577 

.569 

.562 

.548

10'

Inches. 

8.084 

.065 

.050 

.047 

.028

8.009 

.000 

7.990 

.971

7.952 

.942 

.932 

.913

7.895 

.886 

.876 

.858

7.858 

.839 

.829 

.819 

.800

7.781 

.771 

.762 

.743

7.724 

.714 

.704 

.685

7.666 

 .656 

.647 

.628

7.628 

.609 

.600 

.590 

.571

7. 552 

.542 

.532 

.513

7.494 

.484 

.474 

.455

7.436 

.426 

.416 

.397

15'

Inches. 

12. 120 

.098 

.084 

.069 

.041

12.013 

11.999 

.984 

.956

11.928. 

.914 

.899 

.871

11.843 

.829 

.815

.787

11. 787 

.758 

.743 

.729 

.700

11. 671 

.657 

.643 

.614

11.585 

.571 

.557 

.528

11.499 

.485 

.471 

.442

11.442 

.413 

.399 

.385 

.356

11. 327 

.313 

.299 

.270

11.241 

.226 

.212 

.183

11.154 

.139 

.124 

.095

Ordinates of developed parallel.

Longitude 

interval.

5 

U 10 

15

Latitude 

interval.

1 

2 

3

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

5 

71 

10 

' 15

Latitude 

interval.

1

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

/ 

5 

71 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Inch.

0.002 

.006 

.010 

.022

Meridional 

distance.

Inches. 

1.523 

3.045 

4.568 

6.090 

7.C13 

9.136 

10. 658 

12. 181 

13. 703 

15.226 

22.839

Inch.

0.002 

.006 

.010 

.022

Meridional 

distance.

Inches. 

1.523 

3.046 

4.569 

6.091 

7.614 

9.137 

10.660 

12.183 

13. 706 

15.229 

22.843

Inch.

0.002 

.005 

.010 

.022

Meridional 

distance.

Inches. 

1.523 

3.046 

4.569 

6.092 

7.616 

9.139 

10.662 

12.185 

13. 708 

15. 231 

22.847

-
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 10. Coordinates for the projection of maps (scale -48000) Continued.

Latitude 

of 

parallel.

61 00 

05 

07$ 

10 

15

20 

22$ 

25 

30

3537$

40 

45

50 

52$ 

55 

60

62 00 

05 

07$ 

10 

15

20 

22$ 

25 

30

35 

37$ 

40 

45

50 

52$ 

55 

60

63 00 

05 

07$ 

10 

15

20 

22$ 

25 

30

35 

37$ 

40 

45

50 

52$ 

55 

60

Abscissas of developed parallel.

Longitude interval.

2J'

Inches. 

1.849 

.844 

.842 

.839 

.835

1.830 

.828 

.825 

.820

1.815 

.812 

.810 

.805

1.800 

.798 

.796 

.791

1.791 

.786 

 .784 

.781 

.776

1. 771 

.768 

.766 

.761

1.756 

.754 

.752

.747

1.742 

.740 

.737 

.732

1.732 

.727 

.724 

.722 

.717

1.712 

.710 

.707 

.702

1.697 

.694 

.692 

.687

1.682 

.680 

.677 

.672

5'

Inches. 

3.698 

.689 

.684 

.679 

.669

3.659 

.654 

.649 

.640

3.630 

.625 

.620 

.611

3. 601 

.596 

.591

.582

 3. 582 

.572 

.567 

.562 

.552

3.541 

. .538 

.533 

.523

3.513 

.508 

.503 

.493

3.483

.478 

.474 

' .464

3.464 

.454 

.449 

.444 

.434

3.424 

.419 

.414 

.404

3.394 

.389 

.385 

.375

3. 365 

.360 

.355 

.345

IV

Inches. 

5.548 

.533 

.526 

. 518 

.504

5.489 

.482 

.475 

.460

5.445 

.438 

.431 

.416

5.401 

.394 

.387 

.372

5.372 

.357 

.350 

.343 

.328

5.313 

.306 

.299

.284

5.270 

.262 

.255 

.240

5.225 

.218 

.210 

.195

5.195 

.180 

.173 

.166 

.151

5.136 

.128 

.121 

.106

*>.

5.091 

.084 

.077 

.062

5.047 

.040 

.032 

.017

10'

Inches. 

7.397 

.378 

.368 

.358 

.339

7.319 

.310 

.300 

.280

7.261 

.251 

.241 

.222

7.202 

.192 

.183 

.163

7.163 

.144 

.134 

.124 

.105

7.085 

.076 

.066 

.046

7.026 

.016 

.007 

6.987

6.968 

'.958 

.948 

.928

6.928 

.908 

.898 

.888 

.868

6.848 

.838 

.829 

.809

6.789 

.779 

.769 

.749

6.729 

.720 

.710 

.690

15'

Inches. 

11. 095 

.066 

.052 

.037 

.008

10. 979 

.964 

.949 

,920

10. 891 

.876 

.862 

.833

10. 804 

.789 

.774 

'.745

10. 745 

.716 

.701 

-.686 

.657

10. 627 

.612 

.598 

.568

10.539 

.524 

.509 

.480

10. 450 

..436 

'.421 

.391

10. 391 

.361 

.346 

.331 

.302

10. 272 

.257 

.243 

.213

10.183 

.168 

.153 

.123

10.094 

.079 

.064 

.035

Ordinates of developed parallel.

Longitude 

interval.

5 

7J 

10 

15

Latitude 

interval.

1 

2

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

/ 

5 

7$ 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8

9 

10 

15

Longitude 

interval.

5 

7$ 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Inch.

0.002 

.005 

.009 

.021

Meridional 

distance.

Inches. 

1.523 

3.047 

4.570 

6.093 

7. 617 

9.140 

' 10. 663 

12. 187 

13. 710 

15. 233 

22.850

Inch.

0.002 

.005 

.009 

.021

Meridional 

distance.

Inches. 

1.524 

3.047 

4.571 

6.094 

7.618 

9.141 

10.665 

12. 188 

13. 712 

15. 236 

22.853

Inch.

0.002 

.005 

.009 

.020

Meridional 

distance.

Inches. 

1.524 3.047 - 

4.571 

6.095 

7.619 

9.142 

10. 666 

12. 190 

13. 713 

15.237 

22.856
GEOGRAPHIC TABLES AND FORMULAS. 89 

TABLE 10. Coordinates for the projection of maps (scale 43000) Continued.

Latitude 

of

parallel.

0 ,

64 00

05

07J

10

1 fi J.U

20

22J

25

30

35

37i

40

45

50

52fe

55

60

Abscissas of developed parallel.

Longitude interval.

2}'

Inches.

1.672

.667

.664

.662

.657

1.652

.650

.647

.642

1.637

.634

.632

.627

1.622

.620

.617

.612

5'

Inches.

3.345

.335

.330

.325 

. 111 Oil)

3

OAE

. OUO

.300

.295

.285

3.275

.270

.265

.255

3.245

.240

.235

.225

74'

Inches.

5.017

.002

4.994

.987

Q79 u i£t

4.957

.950

.942

.927

4.912

.905

.897

.882

4.867

.860

.852

.837

10'

Inches.

6.690

.670

.660

.650

.630

6.610

.600

.590

.570

6.550

.540

.530

.509

6.489

.479

.469

.449

15'

Inches.

10. 035

.005

9.990

.975

Q4^ . t/T J

9 Q1fi . yiu 

.900

.885

.855

9.825

.810

.794

.764

9.734

.719

.704

.674

Ordinates of developed parallel.

Longitude 

interval.

,

5

71

10

15

Latitude

interval.

' .

1

2

3

4

5

6

7

8

9

10

15

Inch.

0.002

° .005

.009

.020

Meridional

distance.

Inches.

1.524

3.048

4.572

6.096

7.620

9.144

10. 668

12. 192

13. 716

15. 240

22.860
90 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 11. Coordinates for the projection of maps (scale 24 % 00 ).

Latitude of 

parallel.

000 

05 

07£ 

10 

15

20 

22J 

25 

30

35 

37J 

40 

45

50 

52J 

55 

60

1 00 

05 

07J 

10 

15

20 

22£ 

25 

30

35 

37£ 

40 

45

50 

52} 

55 

60

2 00 

05 

07} 

10 

15

20 

25" 22* 

30

35 

37£ 

40 

4.5

50 

52J 

55 

60

Abscissas of developed parallel.

Longitude interval.

1'

Inches. 

3.043 

.043 

.043 

.043 

'.043

3.043 

.043 

.043 

.043

3.043 

.043 

.043 

.043

3.043 

.043 

.043 

.043

3.043 

.043 

.043 

.043 

.043

3.043 

.043 

.043 

.042

3.042 

.042 

.042 

.042

3.042 

.042 

.042 

.042

3.042 

.041 

.041 

.041 

.041

3.041 

.041 

.041 

.041

3.041 

.041 

.040 

.040

3.040 

.039 

.039 

.039

2'

Inches. 

6.087 

.087 

.087 

.087 

.087

6.087 

.087 

.087 

.087

6.087 

.087 

.087 

.087

6.087 

.087 

.087 

.087

6.087 

.086 

.086 

.086 

.086

6.086 

.085 

.085 

.085

6.084 

.084 

.084 

.084

6.084 

.084 

.084 

.083

6.083 

.083 

.083 

.083 

.082

6.082 

.082 

.082 

.081

6.081 

.080 

.080 

.080

6.080 

.079 

.079 

.079

3'

Inches. 

9.130 

.130 

.130 

.130 

.130

9.130 

.130 

.130 

.130

9.130 

.130 

.130 

.130

9.130 

.130 

.130 

.130

9.130 

.129 

.129 

.129 

.129

9.129 

.128 

.128 

.127

9.127 

.127 

.127 

.127

9.126 

.126 

.126 

.125

9.125 

.124 

.124 

.124 

.124

9.123 

.123 

.123 

.122

9.121 

.121 

.121 

.120

9.119 

.119 

.119 

.118

4'

Inches. 

12. 175 

.175 

.175 

.175 

.175

12. 175 

.175 

.175 

.175

12.174 

.174 

.174 

.173

12. 173 

.173 

.173 

.173

12. 173 

.172 

.172 

.172 

.171

12. 171 

.171 

.170 

.170

12. 170 

.169 

.169 

.169

12. 168 

.168 

. 168 

.167

12. 167 

.166 

.166 

.166 

.165

12. 164 

.164 

.163 

.163

12. 162 

.162 

.161 

.160

12. 159 

.159 

.159 

.158

5'

Inches. 

15. 218 

.218 

.218 

.218 

.218

15.218 

.217 

.217 

.217

15.217 

.217 

.217 

.217

15.216 

.216 

.216 

.216

15. 216 

.215 

.215 

.215 

.214

15. 214 

.213 

.213 

.213

15.212 

.212 

.212 

.211

15. 210 

.210 

.210 

.209

15. 209 

.208 

.208 

.207 

.206

15.205 

.205 

.205 

.204

15. 203 

.202 

.202 

.201

15.200 

.199 

.198 

.197

10'

Inches. 

30.435 

.435 

.435 

.435 

.435

30.435 

.435 

.435 

.435

30.434 

.434 

.434 

.433

30.433 

.432 

.432 

.432

30.432 

.431 

.430 

.429 

.428

30.427 

.426 

.426 

.425

30.424 

.424 

.423 

.422

30.421 

.4-20 

.419 

.417

30.417 

.416 

.415 

.414 

412

30.411 

.410 

.409 

.407

30.405 

.404 

.403 

.400

30. 398 

.397 

.396 

.394

15'

Inches. 

45.653 

.653 

.653 

.653 

.653

45. 653 

.652 

.652 

.652

45.651 

.651 

.651 

.650

45.649 

.649 

.648 

.648

45.648 

.646 

.645 

.644 

.643

45.641 

.640 

.639 

.638

45.637 

.636 

.635 

.633

45.631 

.630 

.629 

.626

45. 626 

.624 

.623 

.621 

.619

45.616 

.615 

.614 

.611

45.608 

.606 

.604 

.601

45. 598 

.596 

.594 

.591

Ordinates of developed 

parallel.

Longitude 

interval.

5 

7* 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

". 5 

7} 

10 

15

Latitude 

interval.

1

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

5

71 

10 

15

Latitude 

interval.

/ 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Inch.

0.000 

.000 

.000 

.000

Meridional 

distance.'

Inches. 

3.023 

6.046 

9.069 

12.092 

15.115 

18. 138 

21.161 

24.184 

27. 207 

30. 230 

45. 345

Inch.

0.000 

.000 

.001 

.002

Meridional 

distance.

Inches. 

3.023 

6.046 

9.069 

12.092 

15. 115 

18.138 

21.161 

24.184 

27. 207 

30. 230 - 

45. 345

Inch.

0.000 

.001 

.001 

.003

Meridional 

distance.

Inches. 

3.023 

6.046 

9.069 

12. 092 

15. 115 

18i. 138 

21.161 

24.184 

27. 207 

30.230 

45. 345
GEOGRAPHIC TABLES AND FORMULAS. 91 

TABLE 11. Coordinates for the projection of maps (scale 3-4 ooo) Continued.

Latitude of 

parallel.

3 00 

05 

07} 

10 

15

20 

22} 

25 

30

35 

37} 

40 

45

50 

52} 

55 

CO

4 00 

05 

07} 

10 

15

20 

22} 

25 

30

35 

37$ 

40 

45

50 

52} 

55 

60

5 00 

05 

07} 

10 

15

20 

22} 

25 

30

35 

37} 

40 

45

50

 ^ 55

60

Abscissas of developed parallel.

Longitude interval.

1'

Inches. 

3.039 

.039 

.039 

.039 

.039

3.039 

.038 

.038 

.038

3.038 

.037 

.037 

.037

3.037 

.037 

.036 

.036

3.036 

.036 

.036 

.035 

.035

3.035 

.035 

.034 

.034

3.034 

.034 

.033 

.033

3.033 

.032 

.032 

.032

3.032 

.031 

.031 

.031 

.031

3.031 

.031 

.030 

.030

3.029 

.029 

.029 

.028

3.028 

.028 

.027 

.027

2'

Inches. 

6.079 

.078 

.078 

.078 

.077

6.077 

.076 

.076 

.076

6.076 

.075 

.075 

.074

6.074 

.073 

.073 

.073

6.073 

.072 

.072 

.071 

.071

6.070 

.070 

.070 

.069

6.068 

.068 

.067 

.066

6.065 

.064 

.064 

.064

6.064 

.063 

.063 

.062 

.062

6.061 

.000 

.060 

.059

6.058 

.058 

.058 

.057

6. 056 

.056 

.055 

.054

3'

Inches. 

9.118 

.117 

.117 

.117 

.116

9.115 

.115 

.115 

.114

9.113 

.112 

.112 

.111

9.110 

.100 

.109 

.108

9.108 

.107 

.107 

.107 

.106

9.105 

.104 

.104 

.103

9.102 

.102 

.101 

.100

9.099 

.098 

.097 

.096

9.096 

.095 

.094 

.094 

.093

9.092 

.091 

.090 

.089

9.088 

.087 

.086 

.085

9.084 

.083 

.082 

.081

4'

Inches. 

12. 158 

.157 

.156 

.156 

.155

12. 154 

.153 

.153 

.152

12. 151 

.150 

.149 

.148

12. 147 

.147 

.146 

.145

12. 145 

.144 

.143 

.142 

.141

12. 140 

.139 

.138 

.137

12. 136 

.135 

.134 

.133

12. 131 

.130 

.129 

.128

12. 128 

.127 

.126 

.125 

.124

12. 123 

.122 

.121 

.119

12. 117 

.116 

.115 

.114

12. 112 

.111 

.110 

.108

5'

Inches. 

15. 197 

.196 

.196 

.195 

.194

15. 193 

.192 

.191 

.190

15. 189

.188 

.187 

.186

15.185 

.184 

.183 

.181

15. 181 

.179

.178 

.177 

.176

15. 175 

.174 

.173 

.171

15.169 

.168 

.167 

.166

15. 164 

.163 

.162 

.160

15. 160 

.158 

.157 

.156 

.154

15. 152 

.151 

.150 

.148

15. 146 

.145 

.144 

.142

15. 140 

.138 

.137 

. 135

10'

Inches. 

30. 394 

.392 

.390 

.389 

.387

30. 385 

.384 

.382 

.380

30. 378 

.376 

.374 

.371

30. 369 

.367 

.366 

.363

30. 363 

.360 

.358 

.356 

.353

30. 350 

.348 

.346 

.343

30. 340 

.338 

.335 

.332

30. 328 

.326 

.324 

.320

30.320 

.316 

.314 

.312 

.309

30. 305 

.303 

.301 

.297

30. 293 

.290

.288 

.284

30. 279 

.276 

.274 

.269

15'

Inches. 

45.591 

.588 

.586 

.584 

.581

45.577 

.575 

.573 

.569

45. 565 

.563 

.561 

.557

45. 553 

.551 

.548 

.544

45. 544 

.539 

.536 

.534 

.529

45. 524 

.522 

.519 

.514

45. 509 

.506 

.503 

.498

45. 492 

.489 

.486 

.480

45. 480 

.475 

.472 

.469 

.463

45. 457 

.454 

.451 

.445

45. 439 

.435 

.432 

.426

45.419 

.415 

.411 

. 404

Ordinates of developed 

parallel.

Longitude 

interval.

5

10" n

15

Latitude 

interval.

1

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

5 

7} 

10 

15

Latitude 

interval.

1 

2 

3 

4

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

5 

7} 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15 '

Inch.

0.001 

.001 

.002 

.005

Meridional 

distance.

Inches. 

3.023 

6.046 

9.069 

12. 092 

15. 115 

18. 138 

21. 162 

24.185 

27. 208 

30. 231 

45.346

Inch.

0.001 

.002 

.003 

.007

Meridional 

distance.

Inches. 

3.023 

6.046 

9.069 

12.093 

15. 116 

18. 139 

21. 162 

24. 185 

27.208 

30. 231 

45.347

Inch.

0.001 

.002 

.004 

.009

Meridional 

distance.

Inches. 

3.023 

6.046 

9.070 

12. 093 

15. 116 

18. 139 

21. 163 

24. 186 

27. 209 

'30. 232 

45. 348
92 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 11. Coordinates for the projection of maps (scale 2 4ooc) Continued.

Latitude of 

parallel.

0 /

6 00 

05 

074 10" 

15

20 

22*. 

25 

30 '

35 

37* 40" 

45

50 

52J

55 

60

7 00 

05 

07*. 

10 

15

20 22i 

25 

30

35 

37*. 

40 

45

50 

52J 

55 

60

8 00 

05 

07* 10" 

15

20 

22£ 

25 

30

35 

37J 

40 

45

50 

55" 52* 

60

Abscissas of developed parallel.

Longitude interval.

1'

Inches. 

3.027 

.027 

.027 

.026 

.026

3. 025 

.025 

.024 

.024

3.024 

.024 

.023 

.023

3.022 

.022 

.021 

.021

3.021 

.020 

.020 

.020 

.019

3.019 

.019 

.018 

.018

3.017 

.017 

.016 

.016

3.015 

.015 

.015 

.014

3.014 

.013 

.013 

.013 

.012

3.012 

.011 

.011 

.010

3.009 

.009 

.009 

.008

3.008 

.007 

.006 

.006

2'

Inches. 

6.054 

.054 

.053 

.052 

.051

6.050 

.050 

.049 

.048

6.048 

.047 

.046 

.045

6.044 

.044 

.043 

.042

6.042 

.041 

.040 

.040 

.039

6.038 

.037 

.036 

.035

6.034 

.034 

.033 

.032

6.031 

.030 

.029 

.028

6.028 

.027 

.026 

.026 

.025

6.024 

.023 

.022 

.021

6.020 

.019 

.018 

.017

6.016 

.015 

.014 

.013

3'

Inches. 

9.081 

.080 

.079 

.078 

.077

9.076 

.075 

.074 

.072

9.071 

.070 

.069 

.068

9.067 

.066 

.065 

.063

9.063 

.061 

.060 

.059 

.058

9.057 

.056 

.055 

.053

9.051 

.050 

.049 

.048

9.046 

.045 

.044 

.042

9.042 

.041 

.040 

.039 

.037

9.035 

.034 

.033 

.031

9.029 

.028 

.027 

.025

9.023 

.022 

.021 

.019

4'

Inches. 

12. 108 

.107 

.106 

.105 

.103

12. 101 

.100 

.099 

.097

12.095 

.094 

.093 

.091

12. 089 

.088 

.086 

.084

12. 084 

.082 

.081 

.080 

.078

12. 076 

.075 

.073 

.071

12. 068 

.067 

.066 

.064

12.061 

.060 

.059 

.056

12.056 

.054 

.052 

.051 

.049

12. 047 

.045 

.044 

.041

12. 039 

.037 

.036 

.034

12.031 

.030 

.028 

.026

5'

Inches. 

15. 135 

.133 

.132 

.130 

.128

15. 126 

.125 

.123 

.121

15. 119 

.117 

.115 

.113

15.110 

.109 

.107 

.105

15. 105 

.102 

.101 

.099 

.097

15. 095 

.093 

.091 

.089

15. 086 

.084 

.082 

.080

15.077 

.075 

.074 

.071

15.071 

.068 

.066 

.064 

.061

15. 058 

.056 

.055 

.052

15. 049 

.047 

.045 

.042

15.039 

.037 

.035 

.032

10'

Inches. 

30. 269 

.265 

.263 

.261 

.257

30. 252 

.249 

.246 

.241

30. 236 

.234 

.231 

.227

30. 222 

.219 

.216 

.211

30.211 

.205 

.202 

.199 

..194

30. 188 

.186 

.183 

.177

30. 171 

.168 

.165 

.159

30. 153 

.150 

.147 

.141

30. 141 

.135 

.132 

.129 

.123

30.117 

.114 

.110 

.101

30.097 

.094 

.091 

.084

30.077 

.074 

.071 

.064

15'

Inches. 

45. 404 

.398 

.394 

.391 

.385

45.377 

.374 

.370 

.362

45. 355 

.351 

.347 

.340

45.332 

.328 

.324 

.316

45.316 

.308 

.304 

.299 

.291

45.283 

.279 

.274 

.266

45. 257 

.252 

.248 

.239

45.230 

.225 

.221 

.212

45.212 

.203 

.198 

.193 

.184

45.175 

.170 

.165 

.156

45. 146 

.141 

.136 

.126

45. 116 

.111 

.106 

.096

Ordinates of developed 

parallel.

Longitude 

interval.

5 

10" 7* 

15

Latitude 

interval.

1 

2 

3

4 

5 

6 

7 

 8 

9 

10 

15

Longitude 

interval.

/

5 

7i 

10 

15

Latitude 

interval.

1

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

5

n

10 

15

Latitude 

interval.

/

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Inch.

0.001 

.003 

.005 

.010

Meridional 

distance.

Inches. 

3.023 

6.047 

9.070 

12. 093 

15. 117 

18. 140 

21. 164 

24. 187 

27. 210 

30.234 

45. 350

Inch.

0.001 

.003 

.005 

.012

Meridional 

distance.

Inches. 

3.023 

6.047 

9.070 

12.094 

15. 117 

18.141 

21. 164 

24. 187 

27. 211 

30.234 

45. 351

Inch.

0.001 

.003 

.006 

.014

Meridional 

distance.

Inches. 

3.024 

6.047 

9.071 

12.094 

15. 118 

13.141 

21. 165 

24. 189 

27. 212 

' 30.236 

45.354
GEOGRAPHIC TABLES AND FORMULAS. 93 

TABLE 11. Coordinates for the projection of maps (scale 2 4 1 0?) Continued.

Latitude of

parallel.

o 1

9 00

05

 071

10

15

20

252

30

35 

371 

40 

45

50 

521

60

10' 00 

05

10"*

15

20

25"° .

30

35 

371 

40

45

50 

551 

55

Rft OU

11 00

05

071 

10 

15

20 

221

25

Oft OU

35

371

40

45

50

521

55

60

Abscissas of developed parallel.

Longitude interval.

1'

Inches.

3.006

.005

.005

.005

.004

3.004

.003 

.002

.002

3.001 

.001 

.000 

.000

2.999 

.999

.998 

.998

2.998 

.997 

.996 

.996

.995

2.994 

.994

.994

.993

2.992 

.992 

.992

.991

2.990 

.990 

.989

. Voo QQQ

2.988

.987

.986 

.986 

.985

2.984 

.984

.984

QQQ '

2.982

.982

.981

.980

2.980

.979

.979

.978

2'

Inches.

6.013

.012

.011

.010

.009

6.007

.006 

.005

.004

6.003 

.002 

.001 

.000

5.999 

.998

QO7 . yy i 

.995

5.995 

.994 

.993 

.992

.991

5.989 

.988

.987

.986

5.985 

.984 

.983

.981

5.979 

.978 

.977

.976

5.976

.975

.974 

.973 

.971

5.969 

.968

.967

.966

5.964

.963

.962

.960

5.959

.958

.957

.955

3'

Inches.

9. 019

.017

.016

.015

.013

9. Oil

.009 

.008

.006

9.004 

.003 

.002 

.000

8.998 

.997

AQC

. yyo 

.993

8.993 

.991 

.990 

.988

.986

8.984 

.982

.981

.979

8.977 

.976 

.974

.972

8.969 

.968 

.967

.96

8.964

.961

.960 

.959 

.956

8.954 

.952

.951

' Q4Q

8.946

.944

.943

.940

8.938

.936

.935

.933

4'

Inches.

12. 026

.023

.021

.020

.017

12. 015

.013 

.011

.009

12.006 

.004 

.002 

.000

11. 997 

.995

nr\o

. wao

.990

11.990 

.987 

.986 

.984

.981

11. 978 

.976

.975

.972

11.969 

.967 

.965

.962

11. 959 

.957 

.955

QCO

. OVA

11. 952

.949

.947 

.945 

.942

H QOQ  GOO

.936

.934

QQ1

'

11. 928

.926

.924

.921

11.918

.916

.914

..910

5'

Inches .

15. 032

.028

.026

.024

.021

15. 018

.016 

.014

.011

15.007 

.005 

.003 

.000

14.996 

.994

QQ9 . OULt

.988

14.988 

..984 

.982 

.980

.976

14.972 

.970

.968

.964

14. 960 

.958 

.957

.953

14. 949 

.946 

.944

.9

14. 940

.936

.934 

.931 

.927

14. 923 

.920

.918

Ql 4 '

14. 910

.908

.905

.901

14. 896

.894

.892

.887

10'

Inches.

30. 064

.057

.054

.050

.043

30. 036

.032 

.028

.021

30.014 

.010 

.006 

29. 999

29. 991 

.988

!976

29. 976 

.968 

.964 

.961

.953

29. 945 

.942

.938

.930

29. 922 

.918 

.913

.905

29. 897 

.893 

.889

QQ1

. ool

29. 881

.872

.868 

.863 

.854

29. 845 

.841

.837

QOQ * Q£O

29. 819

.815

.811

.802

29. 793

.789

.785

.776

15'

Inches.

45. 096

.085

.080

.075

.064

45.053

.048 

.043

.032

45.021 

.015 

.009 

44.998

44. 987 

.981

. 976 

.964

44. 964 

.952 

.946 

.941

.929

44. 917 

.911

.906

.894

44.880 

.876 

.870

.858

44. 846 

.839 

.833

.821

44. 821

.808

.802 

.795 

.782

44. 769 

.762

.756

' 743

44. 730

.723

.716

.703

44. 690

.683

.676

.663

Ordinates of developed

parallel.

Longitude 

interval.

,

5

71

10

15

Latitude

interval.

1 

2

3

4 

5 

6

7 

8

9

10 

15

Longitude

interval.

05 

071

10 

15

Latitude 

interval.

,

1

2

3 

4 

5

6

7

8

9 

10 

15

Longitude

interval.

,

05 

071

10

15

Latitude

interval.

/

1

2

3

4

5

6

7

8

9

10

15

Inch.

0.002

.004

.005

.015

Meridional

distance.

Inches.

6!047

9.071

12.095 

15. 119 

18. 142 

21. 166 

24. 190

27. 213

30. 237 

45.357 '

Inch.

0.002 

.004

!017

Meridional 

distance.

T .

3.024

6.048

9.072 

12.096 

15. 120 

18. 144

21. 167

24. 191

27. 215 

30. 239 

45. 359

Inch.

0.002 

.005 

nns * Uvo

.019

Meridional

distance.

Inches.

3.024

6.048

9.072

12.097

15. 121

18. 145

21. 169

24. 193

27.217

30. 241

45. 362
94 GEOGEAPHIC TABLES AND FOBMULAS.

TABLE 11. Coordinates for the projection of maps (scale 24000) Continued.

Latitude of 

parallel.

12 00 

05 07-J ' 

10 

15

20 

22$ 

25 

30 .

35 

37$ 

40 

45

50 

52J 

55 

60

13 00 

05 

07J 

10 

15

20 

22$ 

25 

30

35 

37$ 

40 

45

50 

524 

55 

60

14 00 

05 

07$ 

10 

15

20 

22* 

25 

30

35 

37$ 

40 

45

50 

52$ 

55 

60

Abscissas of developed parallel.

Longitude interval.

1'

Inches. 

2.978 

.977 

.976 

.976 

.975

2.974 

.974 

.973 

.972

2.971 

.970 

.970 

.969

2.968 

.968 

.967 

.966

2.966 

.965 

.964 

.964 

.963

2.962 

.962 

.961 

.960

2. 959 

.958 

.958 

.957

2. 956 

.956 

.955 

.954

2.954 

.953 

.952 

.951 

.950

2.949 

.948 

.948 

.947

2.946 

.946 

.945 

.944

2.943 

.942 

.941 

.940

2'

Inches. 

5.955 

.953 

.952 

.951 

.950

5-948 

.947 

.946 

.944

5.942 

.941 

.940 

.938

5.936 

.935 

.934 

.932

5.932 

.930 

.929 

.928 

.926

5.924 

.923 

.922 

.920

5.918 

.917 

.916 

.914

5.912 

.911 

.910 

.908

5.908 

.906 

.904 

.903 

.901

5-899 

.898 

.896 

.894

5.892 

.891 

.890 

.888

5.886 

.884 

.833 

.881

3'

Inches. 

8.933 

. .930 

.928 

.927 

.924

8.921 

.920 

.919 

.916

8.913 

.911 

-.910 

.907

8.904 

.902 

.901 

.898

8.898 

.895 

.894 

.892 

.889

8.886 

.884 

.883 

.880

8.877 

.876 

.874 

.871

8.868 

.866 

.864 

.861

8.861 

.858 

.856 

.854 

.851

8.848 

'.846 

.845 

.842

8.839 

.837 

.835 

.832

8.828 

.826 

.824 

.821

4'

Inches. 

11. 910 

.906 

.904 

.903 

.899

11. 895

.894 

.892 

.888

11.884 

.882 

.880 

.876

11. 872 

.870 

.868 

.864

11. 864 

.860 

.858 

.856 

.853

11.849 

.846 

.844 

.840

11.836 

.834 

.832 

.828

11.824 

.822 

.820 

.815

11.815 

.810 

.808 

.806 

.802

11.798 

.796 

.793 

' .789

11. 785

.782 

.780 

.776

11.771 

.769 

.767 

.762

5'

Inches.

14.887 

.883 

.880 

.878 

.874

14. 869 

.867 

.865 

.860

14. 855 

.852 

.850 

.845

14. 840 

.838 

.835 

.830

14. 830 

.825 

.823 

.821 

.816

14.811 

.808 

.805 

.800

14. 795

.792 

.790 

.785

14. 780

.777 

.774 

.769

14. 769 

.764 

.761 

.758 

.753

14. 747

.744 

.742 

.736

14. 731 

.728 

.725 

.720

14. 714 

.712 

.709 

.703

10'

Inches. 

29-776 

.767 

.762 

.757 

.748

29. 739 

.734 

.729 

.720

29. 710 

.705 

.700 

.690

29. 680 

.676 

.671 

.661

29. 661 

.651 

.646 

.641 

.631

29. 621 

.616 

.610 

.600

29. 590 

.584 

.580 

.569

29. 558 

.554 

.548 

.538

29. 538 

.527 

.522 

.516 

.505

29. 494 

.488 

.483

.472

29. 461 

.456 

.451 

.440

29. 428 

.422 

.417 

.405

15'

Inches . 

44. 663 

.649 

.642 

.635 

.621

44. 607 

.600 

.594 

.580

44.565 

.558 

.550 

.535

44.520 

.513 

.506 

.491

44.491 

.476 

.469 

.462 

.447

44. 431 

.424 

.416 

.400

44.384 

.377 

.369 

.354

44.338 

.330 

.323 

.307

44.307 

.290 

.282 

.274 

.257

44.240 

.232 

.224 

.208

44.192 

.184 

.176 

.159

44. 142 

.134 

.125 

.108

Ordinates of developed 

parallel.

Longitude 

interval.

i 

05 

07$ 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

05 

07$ 

10 

15

Latitude 

interval.

1

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

05 

07$ 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Inch.

0.002 

.005 

.009 

.020

Meridional 

distance.

Inches. 

3.024 

6.049 

9.073 

12.097 

15. 121 

18. 146 

21. 170 

24. 195 

27.220 

- 30. 243 

45. 365

Inch.

0.002 

.005 

.010 

.022

Meridional 

distance.

Inches. 

3.025 

6.049 

9.074 

12.098 

15. 123 

18. 147 

21.172 

24. 196 

27.221 

30. 246 

45. 368

Inch.

0.003 

.006 

.010 

.023

Meridional 

distance.

 Inches. 

3.025 

6.050 

9.074 

12. 099 

15. 124 

18. 149 

21. 174 

24. 199 

27.223 

30.248 

45. 372
GEOGRAPHIC TABLES AND FORMULAS. 95 

TABLE 11. Coordinates for the projection of maps (scale jTJ7n7)-j-Continued.

Latitude of 

parallel.

15 00 

05 

07J 

10 

15

20 

22J 

25 

30

35 

37J 

40 

45

50 

52J 

55 

60

16 00 

05 

07J 

10 

15

20 

22J 

25 

30

35 

374 

40 

45

50 

524 

55 

60

17 00 

05 

074 

10 

15

20 

224 

25 

30

35 

374 

40 

45

50 

52} 

55 

60

Abscissas of developed parallel.

Longitude interval.

1'

Inches. 

2.940 

.939 

.938 

.938 

.937

2.936 

.936 

.935 

.934

2.933 

.932 

.931 

.930

2.929 

'.928 

.927 

.926

2.926 

.925 

.924 

.924 

..923

2.922 

.921 

.920 

.919

2.918 

.917 

.916 

.915

2.914 

.913 

.912 

.911

2.911 

.910 

.909 

.908 

.907

2.906 

.906 

.905 

.904

2.903 

.902 

.901 

.900

2.899 

.898 

.897 

.896

2'

Inches.

5.881 

.879 

.878 

.876 

.874

5.872 

.870 

.869 

.867

5.865 

.864 

.862 

.860

5.858 

.856 

.855 

.853

5.853 

.850 

.849 

.848 

.845

5.843 

.842 

.840 

.838

5.835 

.834 

.833 

.830

5.828 

.826 

.825 

.823

5.823 

.820 

.819 

.818 

.815

5.812 

.811 

.810 

.807

5.804 

.803 

.802 

.799

5.796 

.795 

.794 

.791

3'

Inches. 

8.821 

.818 

.816 

.814 

.811

8.808 

.800 

.804 

.801

8.798 

.796 

.794 

.790

8.786 

.784 

.782 

.779

8.779 

.775 

.774 

.772 

.768

8.764 

.762 

.760 

.757

8.753 

.752 

.750 

.746

8.742 

.740 

.738 

.734

8.734 

.730 

.728 

.726 

.722

8.718 

.716 

.714 

.711

'8.707 

.705 

.703 

.699

8.695 

.693 

.691 

.687

4'

Inches. 

11.762 

.757 

.755 

.753 

.748

11.743 

.741 

.739 

.734

11.729 

.727 

.724 

.720

11.715 

.712 

.710 

.705

11.705 

.700 

..698 

.696 

.691

11.686

.684 

.681 

.676

11.671 

.668 

.666 

.661

11.656 

.654 

.651 

.646

11.646 

.641 

.638 

.635 

.630

11.625 

.622 

.619 

.614

11.609 

.606 

.603 

.598

11.593 

.590

.587 

.582

5'

Inches. 

14. 703 

.697 

.694 

.691 

.686

14.680 

.677 

.674 

.668

14.662 

.659 

.656 

.650

14.644 

.641 

.638 

.632

14.632 

.626 

.623 

.620 

.614

14.608 

.604 

.601 

.595

14. 589 

.586 

.582 

.576

14. 570 

.566 

.563 

.557

14. 557 

.551 

.548 

.544 

.538

14.531 

.528 

.525 

.518

14.511 

.508 

.505 

.498

14.491

.488 

.485 

.478

10'

Inches. 

29.405 

.393 

.388 

.382 

.370

29.359 

.353 

.347 

.336

29.324 

.318 

.312 

.300

29. 288 

.282 

.276 

.264

29.264 

.252 

.246 

.239 

.227

29. 215 

.208 

.202 

.190

29. 177 

.171 

.165 

.152

29. 139 

.133 

.126 

.114

29. 114 

.101 

.094 

.088 

.075

29.062 

.056 

.049 

.036

29. 022 

.016 

.009 

28. 996

28. 982 

.976 

.969 

.955

15'

Inches. 

44. 108 

.091 

.082 

.073 

.056

44.039 

.030 

.021 

.004

43.986 

.977 

.968 

.950

43.932 

.923 

.914 

.896

43.896 

.878 

.868 

.859 

.841

43.822 

.813 

.804 

.785

43. 766 

.756 

.747 

.728

43.709 

.699 

.690 

.671

43.671 

.052 

.6-12 

.032 

.613

43.593 

.584 

.574 

.554

43.534 

.524 

.514 

.494

43.474 

.464 

.454 

.433

Ordinates of developed 

parallel.

Longitude 

interval.

05 

074 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

05 

07^ 

10 

15

Latitude 

interval.

1

2 

3

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

05

074

10 

15

Latitude 

interval.

/ 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Inch.

0.003 

.006 

.011 

' .025

Meridional 

distance.

Inches. 

3.025 

6.050 

9.075 

12.100 

15.125 

18. 150 

. 21.175 

24.200 

27.225 

30. 250 

45.375

Inch.

0.003 

.007 

.012 

.020

Meridional 

distance.

Inches. 

3.025 

6.051 

9.076 

12. 101 

15. 127 

18. 152 

21.177 

24. 202 

27. 228 

30. 253 

45.380

Inch.

0.003 

.007 

.012 

.028

Meridional 

distance.

Inches. 

3.026 

6.051 

9.077 

12. 103 

15. 128 

18. 154 

' 21. 180 

24. 205 

27. 231 

30. 257 

45. 385
96 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 11. ^-Coordinates for the projection of maps (scale ^^nr) Continued.

Latitude of 

parallel.

18 00 

05 

07J 

10 

15

20 

22J 

25 

30

35 

37£ 

40 

45

50 

521 55" 

60

19 00 

05 

07£ 

10 

15

20 

22J 

25 

30

35 

37£ 

40 

45

50 

52J 

55 

60

20 00 

05 

 07J 

10 

15

20 

22£ 

25 

30

35 

37J 

40 

45

50 

52J 

55 

60

Abscissas of developed parallel.

Longitude interval.

1'

'nches. 

2.896 

.894 

.893 

.892 

.891

2.890

.889 

.888 

.887

2.886 

.885 

.884 

.883

2.882 

.881 

.880 

.879

2.879

.878 

.877 

.876 

.875

2.873 

.872 

.871 

.870

2.869 

.868 

.867 

.866

2.865 

.864 

.863 

.861

2.861 

.860 

.859

.858 

.857

2.856 

.854 

.853 

.852

2.851 

.850 

.849 

.847

2.846 

.845 

.844 

.843

2'

'nches. 

5.791

.788 

.787 

.786 

.783

5.780

.779 

.778 

.775

5.772 

.770 

.769 

.766

5.763 

.762 

.761 

.758

5.758 

.755 

.754 

.752 

.749

5.746 

.744 

.743 

.740

5.737 

.736 

.734 

.731

5.728 

.726 

.725 

.722

5.722 

.719 

.718 

.716 

.713

5.710 

.708 

.707 

.704

5.701 

.700 

.698 

.695

5.692 

.690 

.688 

.685

3'

rnchcs. 

8.687 

.683 

.680 

.678 

.674

8.670 

.668 

.666 

.662

8.658 

.656 

.654 

.649

8.645 

.642 

.640 

.636

8.636 

.632 

.630 

.628 

.624

8.619 

.617 

.615 

.610

8.606 

.604 

.601 

.597

8.592 

.590 

.588 

.583

8.583 

.579 

.576 

.574 

.570

'8.565 

.563 

.561 

.556

8.551 

.549 

.547 

.542

8.537 

.535 

.533 

.528

4'

Inches. 

11.582 

.577 

.574 

.571 

.566

11. 560

.558 

.555 

.549

11.543 

.541 

.538 

.532

11.526 

.524 

.521 

.515

11.515

.509 

.506 

.504 

.498

11.492

'.489 

.486 

.480

11. 474 

.472 

.469 

.463

11.457 

.454 

.450 

.444

11.444 

.438 

.436 

.433 

.427

11.421

.418 

.414 

.408

11.402 

.398 

.395 

.389

11.383 

.380 

.377 

.371

5'

Inches. 

14. 478 

.471 

.467 

.464 

.457

14. 450 

.446 

.443 

.436

14. 429 

.426 

.423 

.416

14. 409 

.405 

.401 

.394

14.394 

.387 

.383 

.379 

.372

14.365 

.361 

.357 

.350

14.343 

.339 

.335 

.328

14.321 

.317 

.313 

.306

14. 306 

.298 

.294 

.291 

.283

14.275 

.272 

.268 

.260

14. 252 

.248 

.245 

.237

14. 229 

.225 

.221 

.213

10'

Inches. 

28.955 

.941 

.935 

.928 

.914

28.901 

.894 

.887 

.874

28.860 

.852 

.845 

.831

28.827 

.810 

.802 

.788

28. 788 

.774 

.767 

.760 

.746

28. 731 

.724 

.716 

.701

28. 686 

.679 

.672 

.657

28. 642 

.634 

.626 

.611

28.611 

.596 

.589 

.582 

.567

28. 552 

.544 

.536 

.521

28.505 

.497 

.489 

.473

28. 458 

.450 

.442 

.427

15'

Inches. 

43. 433 

.412 

.402 

.391 

.371

43.350 

.340 

.330 

.310

43. 289 

.278 

.267 

.246

43. 225 

.214 

.203 

.182

43. 182 

.160 

.150 

.139 

.118

43. 096 

.084 

.073 

.051

43. 029 

.018 

.007 

42.985

42. 962 

.950 

.939 

.916

42. 916 

.894 

.883 

.872 

.850

42. 827 

.816 

.804

.781

42. 757 

.745 

.734 

.710

42. 687 

.675 

.663 

.640

Ordinates of developed 

parallel.

Longitude 

interval.

05 

07£ 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

5 

7* 

10 

15

Latitude 

interval.

1

2 

3 

4 

5 

6

7 

8 

9 10 ' 

15

Longitude 

interval.

5 

7J 

10 

15

Latitude 

interval.

1

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Inch.

0.003 

.007 

.013 

.029

Meridional 

distance.

Inches. 

3.026 

6.052 

9.078 

12. 104 

15. 130 

18. 156 

21. 182 

24. 207 

27.233 

30. 259 

45.389

Inch.

0.003 

.008 

.014 

.031

Meridional 

distance.

Inches. 

3.026 

6.053 

9.079 

12. 105 

15. 131 

18. 158 

21. 184 

24. 210 

27. 237 

30. 263 

45.394

Inch.

0.004 

.008 

.014 

.032

Meridional 

distance.

Inches. 

3.027 

6.053 

9.080 

12. 107 

15. 133 

18.160 

21. 186 

24. 213 

27. 240 

30. 266 

45. 399
GEOGRAPHIC TABLES AND FORMULAS. 97 

TABLE 11. Coordinates for the projection of maps (scale ^4^0) Continued.

Latitude of 

parallel.

21 00 

05 

07J 

10 

15

20 

22J 

25 

30

35 

37J 

40 

45

50 

52J 

55 

60

22 00 

05 

07J 

10 

15

20 

' 22J 

25 

30

35 

37J 

40 

45

50 

52§ 

55 

60

23 00 

05 

07J 

10 

15

20 

22J 

25 

30

35 

37J 

40 

45

. . 50 

52J 

55 

60

Abscissas of developed parallel.

Longitude interval.

l'

nches. 

2.843 

.841 

.840 

.839 

.838

2.837 

.836 

.835 

.833

2.831 

.830 

.829 

.828

2.827 

.826 

.825 

.823

2.823 

.821 

.820 

.819 

.818

2.817 

.816 

.815 

.813

2.811 

.810 

.809 

.808

2.807 

.806 

.805 

.803

2.803 

.801 

.800 

.799 

.798

2.797 

.796 

.795 

.793

2.791 

.790 

.789 

.787

2.785 

.784 

.783 

.782

2'

nches. 

5.685 

.682 

.680 

.679 

.676

5.673 

.671 

.669 

.666

5.663 

.662 

.660 

.657

5.654 

.652 

.650 

.647

5.647 

.643 

.642 .640' 

.636

5.633 

.632 

.630 

.627

5.624 

.622 

.620 

.617

5.613 

.612 

.610 

.606

5.606 

.603 

.601 

.599 

.596

5.592 

.590 

.588 

.585

5.582 

.580 

.578 

.575

5.572 

.570 

.568 

.564

3'

nches. 

8.528 

.523 

.521 

.519 

.514

8.509 

.506 

.504 

.499

8.494 

.492 

.490 

.485

8.480 

.478 

.475 

..470

8.470 

.465 

.462 

.460 

.455

8.450 

.448 

.445 

.440

8.435 

.432 

.430 

.425

8.420 

.417 

.414 

.409

8.409 

.404 

.402 

.399 

.394

8.389 

.386 

.383 

.378

8.373 

.370 

.367 

.362

8.357 

.354 

.351 

.346

4'

'nches. 

11.371 

.365 

.362 

.358 

.352

11.345 

.342 

.339 

.332

11.326 

.322 

.319 

.313

11.307 

.304 

.300 

.294

11.294 

.287 

.284 

.280 

.273

11. 266 

.263 

.260 

.253

11. 246 

.243 

.240 

.233

11. 226 

.222 

.219 

.212

11.212 

.205 

.202 

.199 

.192

11. 185 

.182 

.178 

.171

11.164 

.160 

.157 

.150

11. 143 

.139 

.135 

.128

5'

rnches. 

14. 213 

.205 

.202 

.198 

.190

14. 182 

.178 

.174 

.165

14. 157 

.153 

.149 

.141

14. 132 

.129 

.125 

.117

14.117 

.109 

.104 

.100 

.092

14.083 

.079 

.075 

.066

14.058 

.054 

.050 

.041

14.033 

.028 

.024 

.016

14. 016 

.007 

.002 

13.998 

.989

13.980 

.976 

.972 

.963

13.954 

.950 

.946 

.937

13.928 

.924 

.919 

.910

10'

inches. 

28.427 

.411 

.404 

.396 

.380

28.363 

.355 

.347 

.330

2S.314 

..306 

.299 

.283

28.267 

.258 

.250 

.234

28.234 

.217 

.208 

.199 

.182

28.166 

.158 

.149 

.133

28.116 

.108 

.100 

.083

28.065 

.056 

.048 

.030

28.030 

.013 

.005 

27.997 

.980

27. 962 

.954 

.945 

.927

27.909 

.900 

.892 

.874

27.856 

.847 

.838 

.820

15'

rnches. 

42. 640 

.617 

.605 

.593 

.570

42.545 

.533 

.521 

.496

42.472 

.460 

.448 

.424

42.400 

.387 

.375 

.350

42.350 

.325 

.312 

.299 

.274

42.249 

.237 

.225 

.200

42. 175 

.162 

.150 

.124

42.098 

.085 

.072 

.046

42.046 

.020 

.008 

41.995 

.969

41.943 

.930 

.916 

.890

41. 864 

.850 

.837 

.811

41.784 

.770 

.757 

.730

0 rdinates of developed 

parallel.

Longitude 

interval.

5 

7J 

10 

15

Latitude 

interval.

/ 

1 

2 

3 

4 

5

6 

7 

8 

9 

10 

15

Longitude 

interval.

5 

7J 

10 

15

Latitude 

interval.

1

2 

.3 

4 

5 

6 

7 

8 

9 

10 

15

Longitude 

interval.

5 

7J 

10 

15

Latitude 

interval.

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15

Inch.

0.004 

.008 

.015 

.033

Meridional 

distance.

Inches. 

3.027 

6.054 

9.081 

12. 108 

15.135 

18. 162 

21. 189 

 24.216 

27.243 

30. 270 

45. 405

Inch.

0.004 

.009 

.015 

.035

Meridional 

distance.

Inches. 

3.027 

6.055 

9.082 

12.109 

15. 137 

18. 164 

21. 191 

24. 219 

27.246 

30.273 

45. 410

Inch.

0.004 

.009 

.016 

.036

Meridional 

distance.

Inches. 

3.028 

6.056 

9.083 

12. Ill 

15. 139 

18. 166 

21. 194 

24. 222 

27.250 

30. 277 

45. 416

41623° 16 7
f 

98 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 11. Coordinates for the projection of maps (scale Z4 § 00 ) Continued.

Latitude of

parallel.

o ,

24 00

05

07*

10 

15

20

22*

25

30

35

37i

40

45

50

52J

55

60

Abscissas of developed parallel.

Longitude interval.

1'

Inches.

2.782

.781

.780

.779

.777

9 &* 77^i t iO

.774

.773

.771

2.770

.769

.768

.766

2.764

.763

.762

.700

2'

Inches.

5.564

.560

.558

.556 

.553

5.549

'.548

.546

.542

5.538

.536

.535

.531

5.527

.526

.524

.520

3'

Inches.

8.346

.341

.338

.335

oon

 oou

8

0OC

 o«u

.322

.319

.314

8.308

.306

.303

.297

8.291

.288

.286

.280

4'

Incites.

11. 128

.121

.117

.113 infi . 1L/O

n. noo \Jya

.096

.092

.085

11.077

 .074

.070

.062

11.055

.051

.047

.040

5'

Inches.

13.010

.901

.896

.892

OQQ

. OOO

13. 874 .8"0

.865

.856

13.847

.842

.837

.828

13.819

.814

.810

.801

10'

Inches.

27. 820

.802

.793

.784

nod

. /DO

eyj IAQ Zt. /4S

.739

.730

.712

27. 693

.684

.675

.656

27.638

.628

.619

.601

15'

Inches.

41. 730

.703

.690

.676 

.649

41.622

.6^8

.595

.568

41.540

.526

.5i2

.484

41. 456

.442

.429

.401

Ordinates of developed

parallel.

Longitude 

interval.

,

5

7&

10

15

Latitude

interval.

/

1

2

3

4

5

6

7

8

9

10

15

Inch.

0.004

.009

.016

.037

Meridional

distance.

Inches.

3.028

6.056

9.084

12. 112

15. 140

18. 169

21. 197

24.225

27. 253

30. 281

45. 422
GEOGRAPHIC TABLES AND FORMULAS. 99

TABLE 12. Coordinates for the projection of maps (scale 12 & 00 ). 

[Prepared by S. S. Gannett and George T. Hawklns.]

Latitude 

of 

parallel.

25 00 

05 

07$ 

10 

15

20 

22J 

25 

30

35

37$ 

40 

45

50 

52$ 

55 

60

26 00 

05 

07$ 

10 

15

20 

 22$ 

 25 

30

35 

37$ 

i 40

: 45

50 

52$ 

55 

60

27 00 

05 

07$ 

10 

15

20 

22$ 

25 

30

35 

37$ 

40 

45

50 

52$ 

55 

60

Abscissas of developed parallel.

Longitude interval.

1'

Inches. 

5.520 

.516 

.515 

.512 

.509

5.505 

.503 

.501 

.497

5.494 

.492 

.490 

.486

5.482 

.480 

.478 

.475

5.475 

.470 

.469 

.467 

.463

5.459 

.457 

.455 

.451

5.447 

.445 

.443 

.439

5.435 

.433 

.431 

.428

5.428 

.422 

.421 

.420 

.415

5.410 

.409 

.407 

.403

5.399 

.397 

.395 

.391

5.387 

.384 

.382 

.378

2'

Inches. 

11. 040 

.032 

.029 

.025 

.018

11.010 

.006 

.002 

10.995

10.988 

.984 

.980 

.972

10.965 

.961 

.957 

.950

10. 950 

.942 

 .937 

.933 

.925

10. 918 

.914 

.910 

.902

10.894 

.890

.887 

.878

10. 870 

.866 

.863 

.855

10.855 

.848 

.843 

.839 

.831

10. 822 

.818 

.815 

.805

10. 798 

.794 

.790 

.782

10. 774 

.768 

.765 

.758

3'

Inches. 

16. 5GO 

.549 

.544 

.538 

.528

16. 515 

.509 

.503 

.492

16.480 

.476 

.470 

.458

16.448 

.441 

.435 

.424

16.424 

.412 

.406 

.400 

.389

16. 377 

.371 

.365 

.353

16.341 

.335 

.330 

.318

16.306 

.298 

.294 

.282

16.283 

.270 

.264 

.258 

.247

16.233 

.227 

.220 

.210

16. 198 

.191 

.185 

.172

16.160 

.154 

.148 

.135

4'

' Inches. 

22.080 

.065 

.057 

.050 

.035

22. 020 

.012 

.005 

21. 990

21. 975 

.968 

.960 

.945

21.930 

.921 

.915 

.900

21.900

.882 

.875 

.867 

.852

21.835 

.828 

.820 

.805

21. 789 

.780 

.773 

.758

21. 741 

.732 

.725 

.710

21. 710 

.695 

.686 

.678 

.662

21.645 

.636 

.628 

.612

21. 595

.588 

.580 

.562

21. 548 

.538 

.530 

.515

5'

Inches. 

27.600 

.581 

.572 

.562 

.544

27. 525 

.516 

.506 

.487

27. 468 

.459 

.449 

.430

27. 411 

.401 

.392 

.373

27. 373 

.353 

.343 

.333 

.314

27.294 

.284 

.275 

.255

27. 235 

.225 

.216 

.196

27. 176 

.167 

.157 

.138

27. 138 

.118 

.108 

.097 

.077

27.056 

.046 

.035 

.015

26. 995 

.984 

.974 

.953

26. 933 

.922 

.912 

.892

Ordinates of developed parallel.

Longitude 

interval.

1

2 

3 

4 

5

Latitude 

interval.

1

2 

3 

4 

5

Inch.

.000 

.002 

 .003 

.006 

.009

Meridional 

distance.

Inches. 

6.057 

12. 114 

18. 171 

24. 228 

30. 285

Longitude 

interval.

1 

2 

3 

4 

5

Latitude 

interval.

1

2 

3 

4

5

Inch.

.000 

.002 

.003 

.006 

.009

Meridi- 

.onal 

distance.

Inches. 

6.058 

12. 115 

18. 173 

24. 231 

. 30. 289

Longitude 

interval.

1 2 ' 

3

4 

5

Latitude 

interval.

1 

2 

3 

4 

5

Inch.

.000 

.002 

.003 

.006 

.010

Meridional 

distance.

Inches. 

6.058 

12.117 

18. 175 

24.235 

30. 292
100 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 12. Coordinates for the projection of maps (scale r^inr) Continued.

Latitude 

of 

parallel.

o / 

28 00 

05 

07* 

10 

15

20 

22* 

25 

30

35 

37* 

40 

45

50 

52* 

55 

60

29 00 

05 

07* 

10 

15

20

22* 

25 

30

35 

37* 

40 

45

50 

52* 

55 

60

30 00 

05 

07* 

10 

15

20 

22* 

25 

30

35 

37* 

40 

45

50 

52* 

55 

60

Abscissas of developed parallel.

Longitude interval.

1'.

Inches. 

5.378 

.374 

.372 

.370 

.366

5.362 

.360 

.358 

.354

5.349 

.347 

.345 

.341

5.336 

.334 

.332 

.328

5.328 

.324 

.322 

.320 

.315

5.310 

.308 

.306 

.302

5.298 

.295 

.294 

.289

5.284 

.282 

.280 

.275

5.275 

.272 

.269 

.267 

.262

5.258 

.256 

.254 

.249

5.245 

.243 

.240 

.236

6.232 

.229 

.227 

.222

2'.

Inches. 

10. 758 

.749 

.745 

.740 

.732

10.724 

.720

.715 

.708

10. 698 

.694 

.690 

.682

10.673 

.668 

.665 

.657

10. 657 

.648 

.643 

.640 

.630

10.621 

.617 

.612 

.605

10. 596 

.591 

. .587. 

.578

10.569 

.565 

.560 

.552

10.552 

.543 

.538 

.534 

' .525

10.516 

.512 

.507 

.499

10.490 

.485 

.480 

.472

10.463 

.459 

.454 

.445

3'.

Inches. 

16.135 

.122 

.116 

.110 

.098

16.085 

.078 

.072 

.060

16.048 

.041 

.035 

.022

16.010 

.004 

15. 998 

.985

15.985 

.971 

.965 

.958 

.945

15.932 

.925 

.920 

.907

15.894 

.886 .880 ' 

.867

15.853 

.847 

.841 

.828

15.828 

.815 

.808 

.801 

.787

15. 774 

.768 

.760 

.748

15,735

.728 

.721 

.708

15. 695 

.688 

.681 

,667

4'.

Inches. 

21. 515 

 .498 

.488 

.480 

.465

21.448 

.439 

.430 

.415

21. 398 

.388 

.380 

.362

21.348 

.339 

.330 

.312

21. 312 

.295 

.287 

.278 

.260

21.242 

.234 

.225 

.209

21. 192 

.183 

.174 

.156

21. 137 

.130 

.121 

.104

21. 104 

.086 

.077 

.068 

.050

21.032 

.024 

.014 

20.998

20. 980 

.971 

.961 

.944

20.927 

.918 

.908 

.890

5'.

Inches. 

26. 892 

.871 

.861 

.850 

.830

26. 810 

.799 

.789 

.768

26. 746 

.735 

.725 

.703

26.683 

. 672 

.662 

.640

26. 640 

.619 

.608 

.598 

.575

26. 553 

.542 

.532 

.511

26.490 

.478 

.468 

.445

26. 422 

.412 

.401 

.380

26.380 

.358 

.346 

.335 

.312

26.290 

.280 

.268 

.247

26.225 

.213 

.202 

.180

26.159 

.147 

.135 

.112

Ordiiiates of developed parallel.

Longitude 

interval.

1 

2 

3 

4 

5

Latitude 

interval.

/

1 

2 

3 

4 

5

Inch.

.000 

.002 

.003 

.006 

.010

Meridional 

distance.

Inches. 

6.060 

12. 120 

18. 178 

24.238 

30.298

Longitude 

interval.

/

' 1 

2 

3

 4 

5

Latitude 

interval.

/ 

1 

2 

3 

4 

5

Inch.

.000 

.002 

.003 

.006 

.010

Meridional 

distance.

Inches. 

6.060 

12. 121 

18. 182 24.242' 

30. 302

Longitude 

interval.

i 

1

2 

3 

4 

5

Latitude 

interval.

/

1 

2 

3 

4 

5

Inch.

.000 

.002 

.003, 

.006 

.010

Meridional 

distance.

Inches. 

6.061 

12.122 

18.183 

24.245 

30.305
GEOGRAPHIC TABLES AND FORMULAS. 101

TABLE 12. Coordinates for the projection of maps (scale TinhftjO Continued.

Latitude 

of

parallel.

o /

31 00

05

07|

10

15

20

25°

30

35

40* 

45

50

55 

GO

32 00

05

07£

10

15

20 1

25"

30

35

40" 

45

50

55°

60

33 00

0507i

10

15

20

z5

30

35 

37| 

40 

45

50

52&

65

60

Abscissas of developed parallel.

Longitude interval.

1'.

 Inches.

5. 222

.218

.216

.213

.209

5.204 

.202

.200

.195

5.190 

.188 

.186 

.181

5. 177 

.174 

.172 

.167

5.167

.162

.160

.158

.153

5.148 

.146

.143

.139

5.134 

.131 .129 ' 

.124

5.120

.117

.115

.110

5.110

.105

.103

.100

.096

5.091 

.088

.086

.081

6.076 

.074 

.071 

.066

5.061

.059

.056

.052

2'.

Inches.

10. 445

.435

.432

.426

.417

' 10.408 

.404

.400

.390

10. 381 

.376 

.372 

.362

10.353 

.348. 

.344 

.334

10. 334

.325

.320

.315

.305

10. 296 

.291

.286

.277

10. 268 

.263

.258 

.249

10.239

.234

.229

.220

10. 220

.210

.206 '

.201

.191

10. 182 

.176

.171

.162

10. 152 

.147 

.143 

.132

10. 123

.118

.113

.103

3'.

Inches.

15. 667

.654

.647

.640

.626

15. 613 

.605

.598

.585

15.571 

.565 

.557 

.544

15. 530 

.523 

.516 

.502

15.502

.487

.480

.473

.458

15. 444 

.437

.430

.416

15. 401 

.394

.387 

.373

15.359

.352

.344

.330

15. 330

.316

.308

.301

.287

15. 272 

.264

.257

.242

*

15.228 

.220 

.213 

.199

15.184

.177

.169

.155

4'.

Inches.

20 890

.872

.863

.853

.834

20.817 

.807

.798

.780

20. 762 

.753 

.743 

.725

20. 706 

.697 

.688 

.669

20. 669

.650

.640

.630

.611

20. 592

.582

.573

.554

20.535 

.526 

.516 

.498

20. 478

.469

.459

.440

20.440

.421

.411

.402

.382

20. 363 

.352

.342

.323

20. 304 

.294 

.285 

..265

20. 246

.236

.226

.206

5'.

Inches.

26. 112

.089

.079

.066

.043

26. 021 

.009

25. 998

.975

25.952 

.941 

.929 

.906

25.883 

.871 

.860 

.836

25.836

.812

.800

.788

.764

25.740 

.728

.716

.693

25. 669 

.659 

.645 

.622

25.598

.586

.574

.550

25. 550

.526

.514

.502

.478

25.454 

.440

.428

.404

25.380 

.368 

.356 

.331

25. 307

.295

.282

.258

Ordinatesof developed parallel.

Longitude

interval.

' ,

1

2

3

4

5

Latitude 

interval.

/

1

2 

3 

4 

5

Inch.

.000

.002

.003

.006

.010

Meridional 

distance.

Inches.

6.062

12. 124 

18. 187 

24.249 

30. 311

Longitude 

interval.

1

2

3

4

5

Latitude 

interval.

/

1

2 

3 

4 

5

Inch.

.000

.002

.003

.007

.010

Meridional 

distance.

Inches.

6.063

12. 127 

18. 190 

24.254 

30. 317

Longitude

interval.

1

2

3

4

5

Latitude 

interval.

/

1

2 

3 

4 

5

Inch.

.000

.002

.003

.007

.010

Meridional 

distance.

Inches.

6.065

12. 129 

18. 193 

24. 258 

30.322
102 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 12. Coordinates for the projection of maps (scale x^-^^) Continued.

Latitude 

of

parallel.

o /

34 00

05

071

10

15

20

25°

30

35j 

40°

45

50

521 

55 60'

35 00

05

10"

15

20 

221

25

30

35 

371 

40

45

60 

521 

65

60

36 00

05

071

10

15

20 

221

25

30

35 

371 

40 

45

50

521

55

60

Abscissas of developed parallel.

Longitude interval.

1'.

Inches. 

5.052

.047

.044

.042

.037

5.032

.029

.027

.022

5.017 

.014 

' .012

.007

5.002

4.999 

.997 

.992

4.992

.987

.984

.982

.976

4. 971 

.969

.966

.961

4.956 

.953 

.951

.946

4.940 

.938 

.935

.930

4.930

.925

.923

.920

.915

4.910 

.907

.904

.899

4.894 

.891

.888 

.883

4.878

.875

.873

.868

2'.

Inches.

30.103

 .093

.089

.083

.073

10. 063

.058

.053

.043

10.033 

.028 

.023

.013

10. 003

9.998 

.993 

.983

9.983

.973

.968

.963 1

.953

9.942 

.937

.932

.922

9.912 

.907 

.902

.891

9.881 

.876 

.871

.861

9.861

.850

.845

.840

.830

9.819 

.814

.808

.798

9.787 

.782 

.777 

.766

9.756

.750

.745

.735

3'.

Inches.

15. 155

.140

.132

.125

.110

15. 095

.087

.080

.065

15.050 

.042 

.035

.020

15. 005

14.997 

' .9SO 

.975

14. 975

.960

. .952

.945

.929

14. 913 

.906

.898

.883

14.868 

.860 

.853

.837

14. 821 

.814 

.806

.791

14. 791

.776

.768

.760

.745

14.719 

.721

.712

.697

14. 681 

.673 

.665 

.649

14. 633

.626

.618

.603

4'.

Inches.

20. 206

.186

.176

..166

.146

20. 126

.116

.106

.086

20. 066 

.066 

.046

.026

20.006

19. 996 

.986 

.966

19. 966

.947

.936

.926

.906

19. 885

.874

.864

.844

19. 824 

.814 

.805

.783

19. 762 

.752 

.742

.722

19. 722

.701

.690

.680

.660

19. 638 

.628

.617

.596

19. 574 

.564 

.554 

.532

19. 512

.501

.490

.470

5'.

Inches.

25. 258

.233

.220

.208

.183

25.158

.145

.133

.108

25. 083 

.070 

.058

.033

25. 008

24. 995 

.983 

.958

24. 958

.933

.920

.908

.882

24. 856 

.843

.830

.805

24. 780 

.767 

.754

.728

24. 702 

.690 

.677

.652

24. 652

.626

.613

.600

.574

24. 548 

.535

.521

.495

24. 468 

.455 

.442 

.415

24. 389

.376

.363 

.338

Ordinates of developed parallel.

Longitude

interval.

,

1

2

3

4

5

Latitude

interval.

/

1

2 

3 

4

5

Inch.

.000

.002

.003

.007

.010

Meridional

Inches.

6.065

12.130 

18. 198 

24. 262

30. 328

Longi-. 

tude 

interval.

1

2

3

4

5

Latitude 

interval.

/

1

2 

3

4

Inch.

.000

.002

.003

.007

.010

Meridional 

distance.

Inches.

6.067

is! 200

24.266

qfl qoo ou. ooo

Longitude

interval.

1

2

3

4

5

Latitude 

interval.

/

1

2 

3 

4 

5

Inch.

.000

.002

.005

.007

.010

Meridional 

distance.

Inches.

6.067

12. 135 

18. 202 

24.269 

30.336

v
GEOGKAPHIC TABLES AND FOKMULAS. 103

TABLE 12. Coordinates for the projection of maps (scale r^^nr) Continued.

Latitude 

of

parallel.

0 1

37 00

05

074

 10

15

20 

224

25

30

35 

374 

40 

45

50

524 

55

60 '

38 00

05

074

10

15

20 

224

25

30

35 

374 

40 

45

50

524 

55

60

39 00

05

074

10

15

20 

224

25

30

35 

374 

40 

45

50

524

55

60

Abscissas of developed parallel.

Longitude interval.

1'.

Inches.

4.868

.862

.859

.850

.?51

4.840 

.843

.840

.835

4.830 

.827 

..C2t 

.819

4.814

.811 

.808

.802

4. 802

.797

.',91

.792

.786

4.781

.778

.776

.770

4.764 

.762 

.759 

.754

4.748

.745 

.742

.737

4.737

.731

.728

.726

.720

4.714 

.712

.709

.703

4.698 

.695 

.692 

.686

4.681

.678

.675

.669

2'.

Inches.

9. 735

.724

.718

.713

.702

9.691 

.686

.680

.670

9.659 

.664 

.649 

.638

9.627

.622 

.616

.605

9.605

.594

.589

.584

.573

9.562 

.556

.551

.540

9.529 ' 

.524 

.518 

.507

9.496

.490 

.485

.474

9.474

.463

.457

.451

.440

9.429 

.423

.417

.407

9.395 

.389 

.384 

.373

9.362

.356

.350

.339

3'.

Inches.

14. 603

.586

.578

.569

.553

14. 537 

.529

.521

.505

14.489 

.481 

.473 

.457

14. 441

.432 

.424

.407

14.407

.391

.383

.375

.359

14. 343 

.335

.326

.310

14. 293 

.285 

.277 

.261

14. 244

.236 

.227

.211

14.211

.194

.185

. .177

.160

14. 143 

.135

.126

.119

14. 093 

.084 

.076 

.059

' 14.042

.034

.025

.008

4'.

Inches.

19. 470

.448

.437

.426

.404

19. 382 

.372

.362

.340

19.318 

.308 

.298 

.276

19.254

.243 

.232

.209

19. 209

.188

.178

.167

.146

19. 124 

.113

.102

.080

19. 058 

.047 

.036 

.015

18.993

.981 

.970

.948

18. 948

.926

.914

.902

.880

18.858 

.846

.835

.813

18. 790 

.779 

.768 

.746

18. 723

.712

.700

.678

5'.

Inches.

24.338

.310

.296

.282

.255

24. 228 

.215

.202

.175

24.148 

.135 

.122 

.095

24. 068

.054 

.040

.012

24. 012

23. 985

.972

.959

.932

23. 905 

.891

.878

.850

23. 822 

.809 

.795 

.768

23. 740

.720 

.712

.685

23. 685

.657

.642

.628

.600

23. 672

.558

.544

.516

23.488 

.474 

.460 

.432

23. 404

.390

.375

.347

Ordinates of developed parallel.

Longitude

interval.

,

1

2

3

4

5

Latitude 

interval.

/

1

2 

3 

4 

5

Inch.

.000

.002

.005

.007

.010

Meridional 

distance.

Inches.

6.068

12. 136 

18.205 

24. 273 

30. 341

Lorgitude

interval.

1

2

3

4

5

Latitude 

interval.

/

1

2 

3 

4 

5

Inch.

.000

.002

.005

.007

.010

Meridional distance.

Inches.

6.069

12. 138 

18. 207 

24. 277 

30. 345

Longitude

interval.

1

2

3

4

5

Latitude 

interval.

/

1

2 

3 

4 

5

Inch.

.000

.002

.005

.007

.010

Meridional 

distance.

Inches.

6.070

12. 140 

18. 210 

24. 281 

30. 351
104 GEOGRAPHIC TABLES AND FOKMULAS.

TABLE 12. Coordinates for the projection of maps (scale xTjhnr) Continued.

Latitude 

of

parallel.

O 1

40 00

05

07*

10

15

20 

22*

25

30

35

37* 

40 

45

50

52* 

55

60

41 00

05

07*

10

15

20 

22*

25

30

35 

37* 

40 

45

50

52*

55

42 00

05

07*

10

15

20

22* 

25

30

35

37*

40

45

50

52*

55

60

Abscissas of developed parallel.

Longitude interval.

1'.

Inches.

4.669

.664

.661

.658

.652

4.647 

.644

.641

.635

4.630 

.627 

.624 

.618

4.612

.609 

.606

.600

4.600

.595

.592

.589

.583

4. 57.7 

.574

.571

.566

4.560 

.557 

.554 

.548

4.542

.539

.536

4.530

.524

.521

.518

.513

4.507

.504 

.501

.495

4.489

.486

.483

.477

4.471

.468

.465

.459

2'.

Inches.

9.339

.328

.322

.316

.305

9.293 

.288

.282

.271

9.259 

.253 

.248 

.236

9.224

.219 

.213

.201'

9.201

.189

.183

.178

.166

9.154 

.149

.143

.131

9.119 

.114 

.108 

.096

9.084

.078

.072

9.060

.049

.043

..037

.025

9.013

.007 

.002

.990

8.978

.972

.966

.954

8.942

.936

.930

.918

3'.

Inches.

14.008

13.991

.983

.975

.957

13.940 

.931

.923

.906

13.889 

.880 

.871 

.854

13.837

.828 

.819

.801

13.801

.784

.775

.766

'.749

13 /32 

.723

.714

.697

13. 679 

.670 

.661 

.644

13. 626

.617

.608

13. 591

.572

,564

.555

.537

13. 520

.511 

.502

.484

13.467

.458

.449

.431

13.413

.404

.395

.377

4'.

Inches.

18. 678

.655

.644

.632

.610

18. 586 

.575

.564

.542

18.518 

.507 

.495 

.472

18.449

.438 

.426

.402

18.402

.378

.368

.355 .

.332

18. 309 

.298

.286

.262

18. 239 

.227 

.215 

.192

18. 168

.156

.145

18. 122

.098

.086

.073

.050

18. 027

.014 

.003

17. 979

17.956

.944

.932

.908

17.884

.872

.860

.836

5'.

Inches.

23. 347

.319

.305

.291

.262

23. 233 

.219

.205

.177

23. 148 

.134 

.119 

.090

23. 061

.047 

.032

.002

23.002

22.973

.958

.944

.915

22. 886 

.872

.857

.828

22. 798 

.784 

.769 

.740

22.710

.695

.681

22.652

.622

.607

.592

.563

22. 533

.518 

.504

.474

22.445

.430

.415

.385

22.355

.340

.325

.295

Ordinates of developed parallel.

Longitude

interval.

/

1

2

3

4

5

Latitude 

interval.

/

1

2 

3 

4 

5

Inch.

.000

.002

.005

.007

.010

Meridional 

distance.

Inches.

6.072

12.143 

18. 215 

24. 286 

30.358

Longitude

interval.

1 .

2

3

4

5

Latitude 

interval.

>

1

2 

3

4 

5

Inch.

.000

.002 .

.005

.007

.010

Meridional 

distance.

Inches.

6.072

12. 145 

18. 218 

24. 290 

30. 362

Longitude

interval.

1

2

3

4

5

Latitude

interval.

7

1

2

3

4

5

Inch.

.000

.002

.005

.007

.010

Meridional

distance.

Inches.

6.073

12. 148

18.220

24. 294

30. 367
GEOGRAPHIC TABLES AND FORMULAS. 105 

TABLE 12. Coordinates for the projection of maps (scale tifonr) Continued

Latitude 

of 

parallel.

o /

43 00 

05 

074 

10 

15

20 

224 

25 

30

35 

371 

40 

45

50 

52* 

55 

60

44 00 

06 

074 

10 

15

20 

224 

25 

30

35 

874 

40

45

50 

524 

65 

60

45 00 

05 

074 

10 

15

20 

224 

25 

30

35 

374 

40 

45

50 

524 

56 

60

Abscissas of developed parallel.

Longitude interval.

1'.

Inches. 

4.459 

.453 

.450 

.447 

.441

4. 434 

.431 

.428 

.422

4.416 

.413 

.410 

.404

4.398 

.395 

.392 

.386

4.386 

.380 

.376 

.373 

.367

4.361 

.358 

.855 

.349

4.342 

.339 

.336 

.330

4.324 

.321 

'.318 

.312

4.312 

.305 

.302 

.299 

.293

4.287 

.283 

.280 

.274

4.268 

.264 

.261 

.255

4.249 

'.246 

.242 

.236

2'.

Incites. 

8.918 

.906 

.899 

.894 

.882

8.869 

.863 

.856 

.844

8.832 

.826 

.820 

.808

8.796 

.789 

.784 

.772

8.772 

.759 

.763 

.747 

.734

8.722 

.716 

.709 

.697

8.685 

.678 

.672 

.660

8.648 

.642 

.635 

.623

8.623 

.610 

.604 

.598 

.586

8.573 

.567 

.560 

.548

8.535 

.529 

.622 

.510

8.497 

.491 

.485 

.472

3'.

Inches. 

13. 377 

.359 

.349 

.340 

.322

13.303 

.294 

.285 

.266

13.248 

.239 

.230 

.212

13. 194 

.184 

.175 

.157

13. 157 

.139 

.129 

.120 

.102

13. 083 

.074 

.064 

.046

13.027 

.018 

.009 

12.990

12.971 

.963 

.953 

.935

12.935 

.916 

.906 

.897 

.878

12.860 

.849 

.841 

.822

12.803 

.793 

.784 

.765

12. 746 

.737 

.727 

.707

4'.

Inches. 

17.836 

.812 

.799 

.787 

.762

17.738 

.726 

.713 

.688

17.664 

.652 

.640 

.616

17. 592 

.579 

.567 

.643

17.543 

.518 

.506 

.494 

.469

17.444 

.431 

.419 

.394

17.370 

.357 

.345 

.320

17.295 

.283 

.270 

.246

17.246 

.221 

.208 

.196 

.171

17. 146 

.134 

.121 

.096

17.070 

.058 

.045 

.020

16.995 

.982 

.970 

.944

5'.

Inches. 

22.295 

.265 

.249 

.234 

.203

22. 172 

.157 

.141 

.110

22.080 

.065 

.050 

.020

21. 990 

.974 

.959 

' .929

21. 929 

.898 

.882 

.867 

.836

21.805 

.789 

.774 

.743

21.712 

.696 

.681 

.650

21.619 

.604 

.588 

.568

21.558 

.527 

.511 

.495 

.464

21.433 

.417 

.401 

.370

21.338 

.322 

.306 

.276

21.243 

.228 

.212 

.180

Ordinates of developed parallel.

Longitude 

interval.

/

1 

2 

3 

4 

5

Latitude 

interval.

1 

2 

3 

4 

5 

Inch.

.000 

.002 

.005 

.007 

.010

Meridional 

distance.

Inches. 

6.075 

12. 149 

18.223 

24. 298 

30. 372

Longitude 

interval.

/ 

1

2 

3

4 

5

Latitude 

interval.

i 

1 

2 

3 

4 

5

Inch.

.000 

.002 

.005 

.007 

.010

Meridional 

distance.

Inches. 

6.076 

12. 152 

18,228 

24.304 

30.380

Longitude 

interval.

/

1 

2 

3 

4 

5

Latitude 

interval.

/ 

1 

2 

3 

4 

5

Inch.

.000 

*002 

.005 

.007 

.010

Meridional 

distance.

Inches. 

6.077 

12.164 

18.231 

24. 308 

30.386
106 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 12. Coordinates for the projection ^f-}maps (scale T^tr) Continued.

Latitude 

 of 

parallel.

0 '

46 -00 

05 0?i 

10 

15

20 22i 

25 

30

35 

37J 

40 

45

50 521 

55 

60

47 00 

05 07i 

10 

15

20 

22i 

25 

30

3537i 

40 

45

50 521 

55 

60

48 00 

05 

o 07i 

10 

15

20 22i 

25 

30

35 

37J 

40 

45

50 

52£ 

55 

60

Abscissas of developed parallel.

Longitude interval.

1'.

Inches. 

4. 236 

.229 

.226 

.223 

.216

4.210 

.207 

.204 

.198

4.191 

.188 

.184 

.178

4. 172 

.168 

.165 

.159

4.159 

.152 

.149 

.146 

.139

4.133 

.130 

.126 

.120

4. 113

 .110

.106 

.100

4.094 

.090 

.089 

.080

4.080 

.074 

.071 

.067 

.061

4.054 

.051 

.048 

.041

4.034 

.031 

.028 

.021

4.014 

.011 

.008 

.001

2'.

Inches. 

8.472 

.459 

.452 

.446 

.433

8.420 

.414 

.408 

.395

8.382 

.376 

.369 

.356

8.343 

.337 

.330 

.318

8.318 

.305 

.299 

.292 

.279

8.266 

.259 

.252 

.239

8. 226 

.220 

.213 

.200

8.187 

.180 

.174 

.161

8.160 

.148 

.142 

.135 

.122

8.108 

.102 

.095 

.082

8. 069 

.062 

.055 

.042

8.029 

.022 

.016 

.002

3'.

Inches. 

12. 707 

.688 

.679 

.669 

.649

12.630 ' 

.621 

.611 

.593

12.573 

.564 

.553 

.534

12. 515 

.505 

.496 

.476

12. 476 

.457 

.448 

.438 

.418

12. 398 

.389 

.378 

.359

12.339 

.329 

.319 

.300

12.281 

.271 

.261 

.241

12. 241 

.222 

.212 

.202 

.182

12.162 

.153 

.143 

.123

12.103 

.093 

.083 

.063

12.043 

.034 

.024 

.003

4'.

Inches. 

16. 944 

.918 

.905 

.892 

.867

16.840 

.828 

. 815 

;790

16. 764 

.752 

.738 

.712

16. 687 

.674 

.661 

.635

16. 635 

.610 

.597 

.584 

.558

16.531 

.518 

.505 

.478

16. 452 

.439 

.426 

.400

16.375 

.361 

.348 

.322

16. 32] 

.296 

.284 

.270 

.244

16.217 

.204 

.190 

.164

16.138 

.124 

.110 

.084

16. 058 

.045 

.031 

.004

5'.

Inches. 

21. 179 

.147 

.131 

.115 

.082

21.051 

.035 

.019 

20. 988

20. 955 

.939 

.922 

.890

20.858 

.842 

.826 

.794

20. 794 

.762 

.746 

.730 

.697

20.664 

.648 

.631 

.598

20. 565 

.549 

.532 

.500

20.468 

..461 

.435 

.402

20. 401 

.370 

.354 

.337 

. .304

20. 271 

.255

. _oo

.205

20. 172 

.155 

.138 

.105

20. 072 

.056 

.039 

.006

Ordinates of developed parallel.

Longitude 

interval.

1 

2 

3 

4 

5

Latitude 

interval.

1 

2 

3 

4 

5

Inch.

.000 

.002 

.005 

.007 

.010

Meridional 

distance.

Inches. 

6.078 

12. 157 

18.235 

24.313 

30. 391

Longitude 

interval.

1 

2 

3 

4 

5

Latitude 

interval.

1 

2 

3 

4 

5

Inch.

.000 

.002 

.005 

.007 

.010

Meridional 

distance.

Inches. 

6.078 

12.157 

18. 235 

24. 315 

30. 392

Longitude 

interval.

1 

2 

3 

4 

5

Latitude 

interval.

1 

2 

3 

4 

5

Inch.

.000 

.002 

.005 

.007 

.010

Meridional 

distance.

Inches. 

6.080 

12. 160 

18. 240 

24. 320 

30. 400
GEOGRAPHIC TABLES AND FORMULAS. 107

TABLE 12. Coordinates for the projection of maps (scale rsihn?) Continued.

Latitude 

of

parallel.

O 1

49 00

05

07£

10

15

20 

22J 

25

inOv

35

37i

40

45

50

52£

55

60

Abscissas of developed parallel.

Longitude interval.

V.

Inches.

4.001

3.995

.991

.988

.981

3.974 

.971 

.968

.961

3.954

.951

.948

.941

3.934

.931

.928

.921

2'.

Indies.

8.002

7.989

.982

.976

.962

7. 949 

.942 

.936

. 922

7.908

.902

.895

.882

7.8C9

.862

.855

.842

3'.

Inches.

12. 003

11. 984

.974

.964

.943

11 . 923 

.914 

.904

.883

11.863

.853

.843

.823

11.803 .

.793

.783

.762

4'.

Inches.

16.004

15.978

.965

.952

.924

15.898 

.885 

.872

.844

15.817

.804

.790

. 764

15. 738

.724

.710

.683

5'.

Inches.

20. 006

19.973

.956

.939

.905

19.872 

.856 

.840

onp; 

. Owt)

19.771

.755

.738

.705

19.672

.655

.638

.604

Orclinates of developed parallel.

Longitude

interval.

,

1

2

3

4

5 .

Latitude 

interval.

/

1

2

3.

4

5

Inch.

.000

.002

.005

.007

.010

Meridional 

distance.

Inches.

6.081

12. 102

18.243

24. 324

30. 405
108 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 13. Areas of quadrilaterals of earth's surface of 1° extent in latitude and

longitude.

[From Smithsonian Geographical Tables.]

Middle latitude of 

quadrilateral.

0 /

0 00 

0 30 

1 00 

1 30

2 00 

2 30 

3 00 

3 30

4 00 

4 30 

5 00 

5 30

6 00 

6 30 

7 00 

7 30

8 00 

8 30 

9 00 

9 30

10 00 

10 30 

11 00 

11 30

12 00 

12 30 

13 00 

13 30

14 00 

14 30 

15 00 

15 30

16 00 

16 30 

17 00 

17 30

18 00 

18 30 

19 00 

19 30

20 00 

20 30 

21 00 

21 30

Area in 

square miles.

4, 752. 33 

4, 752. 16 

4, 751. 63 

4, 750. 75

4, 749. 52 

4, 747. 93 

4, 746. 00 

4, 743. 71

4, 741. 07 

4, 738. 08 

4, 734. 74 

4, 731. 04

4, 727. 00 

4,722.61 - 

4, 717. 86 

4, 712. 76

4, 707. 32 

4, 701. 52 

4, 695. 38 

4, 688. 89

4, 682. 05 

4, 674. 86 

4, 667. 32 

4, 659. 43

4, 651. 20 

4, 642. 63 

4, 633. 71 

4,624.44

4, 614. 82 

4, 604. 87 

4, 594. 57 

4, 583. 92

4, 572. 94 

4, 561. 61 

4, 549. 94 

4, 537. 93

4, 525. 59 

4, 512. 90 

4, 499. 87 

. 4,486.51

4, 472. 81 

4, 458. 78 

4, 444. 41 

4, 429. 71

Middle latitude of 

quadrilateral.

o- /

22 00 

22 30 

23 00 

23 30

24 00 

24 30 

25 00 

25 30

26 00 

26 30 

27 00 

27 30

28 00 

28 30 

29 00 

29 30

30 00 

30 30 

31 00 

31 30

32 -00 

32 30 

33 00 

33 30

34 00 

34 30 

35 00 

35 30

36 00 36 30 ' 

37 00 

37 30.

38 00 

38 30 

39 00 

39 30

40 00 

40 30 

41 00 

41 30

42 00 

42 30 

43 00 

43 30

Area in 

square miles.

4, 414. 67 

4, 399. 30 

4, 383. 60 

4, 367. 57

4, 351. 21 

4, 334. 52 

4, 317. 51 

4, 300. 17

4, 282. 50 

4, 264. 51 

4, 246. 20 

4, 227. 56

4, 208. 61 

4, 189. 33 

4, 169. 74 

4,149.83

4, 129. 60 

4, 109. 06 

4,088.21 

4, 067. 05

4, 045. 57 

4, 023. 79 

4, 001. 69 

3, 979. 30

3, 956. 59 

3, 933. 59 

3,910.28 

3, 886. 67

3, 862. 76 

3, 838. 56 

3, 814. 06 

3, 789. 26

3, 764. 18 

3, 738. 80 

3, 713. 14 

3, 687. 18

3, 660. 95 

3, 634. 42 

3, 607. 62 

3, 580. 54

3, 553. 17 

3, 525. 54 

3,497.62 

3, 469. 44

Middle latitude of 

quadrilateral.

0 /

44 00 

44 30 

45 00 

45 30

46 00 

46 30 

47 00 

47 30

48' 00 

48 30 

49 00 

49 30

50 00 

50 30 

51 00 

51 30

52 00 

52 30 

53 00 

53 30

54 00 

54 30 

55 00 

55 30

56 00 

56 30 

57 00

57 30

58 00 

58 30 

59 00 

59 30

60 00 

60 30 

61 00 

61 30

62 00 

62 30 

63 00 

63 30

64 00 

64 30 

65 00 

65 30

Area in 

square miles.

3, 440. 98 

3, 412. 26 

3, 383. 27 

3, 354. 01

3,324.49 

3, 294. 71 

3, 264. 68 

3, 234. 39

3,203.84 

3, 173. 04 

3, 141. 99 

3, 110. 69

3, 079. 15 

3, 047. 37 

3, 015. 34 

2, 983. 08

2, 950. 58 

2,917.85 

2, 884. 88 

2, 851. 68

2, 818. 27 

2, 784. 62 

2, 750. 76 

2, 716. 67

2. 682. 37 

2, 647. 85 

2, 613. 13

2, 578. 19

2, 543. 05 

2, 507. 70 

2, 472. 16 

2,436.42

2, 400. 48 

2, 364. 34 

2,328.02 

; 2, 291.51

2,254.82 

2,217.94 

2, 180. 89 

2, 143. 66

2, 106. 26 

2, 068. 68 

2, 030. 94 

1, 993. 04
GEOGRAPHIC TABLES AND FORMULAS. 109

TABLE 13. Areas of quadrilaterals of earth's surface of 1° extent in latitude and

longitude Continued.

[From Sraithsonian Geographical Tables.]

Middle latitude of 

quadrilateral.

o /

66 00 

66 30 

67 00 

67 30

68 00 

68 30 

69 00 

69 30

70 00 

70 30 

71 00 

71 30

72 00 

72 30 

73 00 

73 30

74 00 

74 30 

75 00 

75 30

Area in 

square miles.

1, 954. 97 

1,916.75 

1,878.37 

1, 839. 84

1, 801. 16 

1,762.33 

1, 723. 36 

1, 684. 24

1, 645. 00 

1, 605. 62 

1, 566. 10 

1, 526. 46

1, 486. 70 

1, 446. 81 

1, 406. 81 

1, 366. 69

1,326.46 

1,286.12 

1, 245. 68 

1, 205. 13

Middle latitude of 

quadrilateral.

0 /

76 00 

76 30 

77 00 

77 30

78 00 

78 30 

79 00 

79 30

80 00 

80 30 

81 00 

81 30

82 00 

82 30 

83 00 

83 30

84 00 

84 30 

85 00 

85 30

Area in 

square miles.

1, 164. 49 

1, 123. 75 

1, 082. 91 

1, 041. 99

1, 000. 99 

959. 90 

918. 73 

877. 49

836. 18 

794.79

753. 34 

711. 83

670. 27 

628. 64 

586. 97 

545. 24

503. 47 

461. 66 

419. 81 

377. 93

Middle latitude of 

quadrilateral.

0 /

86 00 

86 30 

. 87 00 

87 30

88 00 

88 30 

89 00 

89 30

90 00

Area in 

square miles.

336. 02 

294. 08 

252. 11 

210. 12

168. 12 

126. 10 

84. 07 

42.04

00.00
110 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 14. Areas of quadrilaterals of earth's surface of 80' extent in latitude and

longitude.

[From Smithsonian Geographical Tables.]

Middle latitude of 

quadrilateral.

0 /

0 00 

0 15 

0 30 

0 45

1 00 

1 15 

1 30 

1 45

2 00 

2 15 

2 30 

2 45

3 00 

3 15 

3 30 

3 45

4 00 

4 15 

4 30 

4 45

5 00 

5 15 

5 30 

5 45

6 00 

6 15 

6 30 

6 45

7 00 

7 15 

7 30 

7 45

8 00 

8 15 

8 30 

8 45

9 00 

9 15 

9 30 

9 45

10 00 

10^15 

10 30 

10 45

Area in 

square miles.

1,188.10 

1,188.08 

1, 188. 05 

1, 188. 00

1,187.92 

1, 187. 82 

1, 187. 70 

1,187.56

1, 187. 39 

1,187.20 

1, 186. 99 

1, J.86. 76

1,186.51 

1, 186. 24 

1, 185. 95 

1, 185. 62

1, 185. 28 

1, 184. 92 

1, 184. 53 

1, 184. 13

1, 183. 70 

1, 183. 24

1, 182. 77 

1,182.28

1, 181. 76 

1,181.22 

1, 180. 66 

1, 180. 08

1, 179. 48 

1, 178. 85 

1, 178. 20 

1, 177. 53

1, 176. 84 

1, 176. 13 

1, 175. 39 

1, 174. 63

1, 173. 86 

1, 173. 06 

1, 172. 23 

1, 171. 39

1, 170. 52 

1, 169. 63 

1, 168. 73 

1, 167. 80

Middle latitude of 

quadrilateral.

o /

11 00 

11 15 

11 30 

11 45

12 00 

12 15 

12 30 

12 45

13 00 

13 15 

13 30 

13 45

14 00 

14 15 

14 30 

14 45

15 00 

15 15 

15 30 

15 45

16 00 

16 15 

16 30 

16 45

17 00 

17 15 

17 30

17 45

18 00 

18 15 

18 30 

18 45

19 00 

19 15 

19 30 

19 45

20 00 

20 15 

20 30 

20 45

21 00 

21 15 

21 30 

21 45

Area in 

square miles.

1, 166. 84 

1, 165. 86 

1, 164. 86 

1, 163. 85

1, 162. 81 

1, 161. 75 

1, 160. 67 

1, 159. 56

1, 158. 44 

1, 157. 29 

1, 156. 12 

1, 154. 93

1, 153. 72 

1, 152. 48 

1, 151. 23 

1,149.95

1, 148. 65 

1, 147. 33 

1, 145. 99 

1,144.63

1, 143. 25 

1,141.84 

1, 140. 41 

1, 138. 96

1, 137. 50 

1,136.00 

1,1G4.49 

1, 132. 96

1,131.41 

1, 129. 83 

1, 128. 24 

1, 126. 62

1, 124. 98 

1, 123. 32 

1, 121. 64 

1, 119. 93

1, 118. 21 

1, 116. 47 

1, 114. 71 

1, 112. 92

1,111.11 

1, 109. 28 

1, 107. 44 

1,105.57

Middle latitude of 

quadrilateral.

0 /

22 00 

22 15 

22 30

22 45

23 00 

23 15 

23 30 

23 45

24 00 

24 15 

24 30 

24 45

25 00 

25 15 

25 30 

25 45

26 00 

26 15 

26 30 

26 45

27 00 

27 15 

27 30 

27 45

28 00 

28 15

98 on 40 OU

28 45

29 00 

29 15 

29 30 

29 45

30 00 

30 15 

30 30 

30 45

31 00 

31 15 

31 30 

31 45

32 00 

32 15 

32 30

32 45

Area in 

square miles.

1,103.68 

1, 101. 77 

1,099.84 

1, 097. 88

1,095.91 

1,093.92 

1, 091. 90 

1, 089. 87

1, 087. 81 

1,085.74 

1, 083. 64 

1, 081. 52

1, 079. 39 

1, 077. 23 

1, 075. 05 

1,072.85

1, 070. 64 

1, 068. 40 

1, 066. 14 

1,063.86

1,061.56 

1, 059. 24 

1, 056. 90 

1, 054. 54

1, 052. 16 

1,049:76

1,047.34

1,044.90

1,042.44 

1, 039. 97 

1, 037. 47 

1,034.95

1,032.41 

1,029.85 

1,027.27 

1,024.68

1,022.06 

1,019.43 

1,016.77 

1, 014. 10

1,011.40 

1, 008. 69 

1,005.96 

1,003.20
GEOGRAPHIC TABLES AND FORMULAS. Ill

TABLE 14. Areas of quadrilaterals of earth's surface of S0f extent in latitude and longitude Continued.

[From Smithsonian Geographical Tables.]

Middle latitude of 

quadrilateral.

0 /

33 00 

33 15 . 

33 30 

33 45

34 00 

34 15 

34 30 

34 45

35 00 

35 15 

35 30 

35 45.

36 00 

36 15 

36 30 

36 45

37 00 

37 15 

37 30 

37 45

38 00 

38 15 

38 30 

38 45

39 00 

39 15 

39 30 

39 45

40 00 

40 15 

40 30 

40 .45

41 00 

41 15 

41 30 

41 45

42 00 

42 15 

42 30 

42 45

43 00 

43 15 

43 30 

43 45

Area in 

square miles.

1, 000. 43 

997. 64 

994. 83 

992.00

989. 16 

986. 29 

983. 41 

980. 50

977. 58 

974.64

971. 68 

968. 70

965. 70 

962. 68 

959. 65 

956. 60

953. 52 

950. 43 

947. 32 

944. 21

: 941. 05 

937. 88 

934. 71 

931. 51

928. 29 

925..06 

921. 80 

918. 53

915. 25 

911. 94 

908. 61 

905. 27

901. 91 

898. 54 

895. 14 

. 891. 73

888. 30 

884. 85 

881. 39 

* 877.91

874. 41 

870. 90 

867. 37 

863. 82

Middle latitude of 

quadrilateral.

0 /

44 00 

44 15 

44 30 

44. 45

45 00 

45 15 

45 30 

45 45

46 00 

46 15 

46 30 

46 45

47 00 

47 15 

47 30 

47 45

48 00 

48 15 

48 30 

48 45

49 00 

49 15 

49 30 

49 45

50. 00 

50 15 

50 30 

50. 45

51 00 

51 15 

51 30 

51 45

52 00 

52 15 

52 30 

52 45

53 00 

53 15 

53 30 

53 45

54 00 

54 15 

54 30 

54 45

Area in 

square miles.

860. 25 

856. 67 

853. 07 

849. 46

845. 82 

842. 18 

838. 51 

834. 83

831. 13

827.42

823. 68 

819. 94

81.6. 18 

812. 40 

808. 60 

804. 79

800. 97 

797. 13 

793. 27 

789. 39

785. 50 

781.60

777. 68 

77.3. 74

769. 79 

765. 83 

761. 85 

757. 85

753. 84 

749. 82 

745. 78 

741. 72

737. 65 

733. 57 

729. 47 

725. 36

721. 23 

717. 08 

712. 93 

708. 76

704. 57 

700. 38 

696. 16 

691. 94

Middle latitude of 

quadrilateral.

0 '/

55 00 

55 15 

55 30 

55 45

56 00 

56 15 

56 30 

56 45

57 00 

57 15 

57 30 

57 45

58 00 

 58 15 

58 30 

58 45

59 00 

59 15 

59 30 

59 45

60 00 

60 15 

60 30 

60 45

61 00 

1 61 15 

61 30

61 45

62 00 

62 15 

62 30 

62 45

63 00 

63 15 

63 30 

63 45

64 00 

64 15 

64 30 

64 45

65 00 

65 15 

65 30 

65 45

Area in 

square miles.

687. 70 

683. 44 

679. 17 

674. 89

670. 60 

666. 29 

661. 97 

657.64

653. 29 

648.93 

644.55 

640. 17

635. 77 

631. 36 

626. 93 

622. 49

618. 05 

613. 59 

609. 11 

604. 62

600. 13 

595. 62 

591. 09 

586. 56

582. 01 

577. 45 

572. 88 

568. 30

563.71 

559. 11 

554. 49 

549. 86

545. 23 

540. 58 

535. 92 

531. 25

526. 57 

521. 88 

517. 17 

512. 46

507. 74 

503. 01 

498. 26 

493. 51
112 GEOGEAPHIC TABLES AND FORMULAS.

TABLE 14. Areas of quadrilaterals of earth's surface of 30/ extent in latitude and longi'

tude Continued.

[From Smlthsonian Geographical Tables.]

Middle latitude 

of quadrilateral.

0 /

66 00 

66 15 

66 30 

66 45

67 00 

67 15 

67 30 

67 45

68 00 

68 15 

68 30 

68 45

69 00 

69 15 

69 30 

69 45

70 00 

70 15 

70 30 

70 45

71 00 

71 15 

71 30 

71 45

72 00 

72 15 

72 30 

72 45

73 00 

73 15 

73 30 

73 45

Area in square 

miles.

488. 75 

483. 97 

479. 19 

474. 40

469. 60 

464. 78 

459. 96 

455. 13

450. 29 

445. 45 

. 440. 59 

435.72

430.84 

425. 96 

421.06 

416. 16

411.25 

406. 34 

401. 41 

396.47

391. 53 

386. 58 

381. 62 

376. 65

371. 68 

366. 70 

361. 71 

356.71

351. 71 

346.69 

341.68 

336. 65

Middle latitude 

of quadrilateral.

'. ° ' 

74 00 

74 15 

74 30 

74 45

75 00 

75 15 

75 30 

75 45

76 00 

76 15 

76 30 

76 45

77 00 

77 15 

77 30 

77 45

78 00 

78 15 

78 30 

78 45

79 00 

79 15 

79 30 

79 45

80 00

80 15 

80 30 

80 45

81 00 

81 15 

81 30 

81 45

Area in square 

miles.

331. 62 

326. 58 

321. 53 

316.48

311. 42 

306. 36 

301. 28 

296. 21

291. 12 

286. 04 

280. 94 

275.84

270. 73 

265. 62 

260. 50 

255. 38

250. 25 

245.12 

239. 98 

234. 83

229. 68 

224. 53 

219. 37 

214. 21

209. 05 

203. 88 

198. 70 

193.52

188. 34 

183. 15 

177. 96 

172. 77

Middle latitude 

of quadrilateral.

! 

0 /

82 00 

82 15 

82 30 

82 45

83 00 

83 15 

83 30 

83 45

84 00 

84 15 

84 30 

84 45

85 00 

85 15 

85 30 

85 45

86 00 

86 15 

86 30 

86 45

87 00 

87 15 

87 30 

87 45

88 00 

88 15 

88 30

88 45

89 00 

89 15 

89 30 

89 45

Area in square 

miles.

167. 57 

 162. 37 

157. 16 

151. 95

146. 74 

141.53 . 

136. 31 

131. 09

125.87 

120. 64 

115. 42 

. 110.18

104. 95 

99.72 

94.48 

89.25

84.01 

78.76 

73.52 

68.27

63.03 

57.78 

52.53 

47.28

42.03 

36.78 

31.53 

26.27

21.02 

15.76 

10.51 

5.26
GEOGRAPHIC TABLES AND FORMULAS. 113

TABLE 15. Areas of quadrilaterals of earth's surface of 15' extent in latitude and

longitude.

[From Smithsonian Geographical Tables.]

Middle latitude 

of quadrilateral.

0 / //

0 07 30 

0 15 00 

0 22 30 

0 30 00

0 37 30 

0 45 00 

0 52. 30 

1 00 00

1 07 30 

1 15 00 

1 22 30 

1 30 00

1 37 30 

1 45 00 

1 52 30 

2 00 00

2 07 30 

2 15 00 

2 22 30 

 2 30 00

2 37 30 

2 45 00 

2 52 30 

3 00 00

3 07 30' 

3 15 00 

3 22 30 

3 30 00

3 37 30 

3 45 00 

3 52 30 

4 00 00.

4 07 30 

4 15 00 

4 22 30 

4 30 00

4 37 30 

4 45 00 

4 52 30 

5 00 00

5 07 30 

5 15 00 

5 22 30 

5 30 00

Area in 

square miles.

297. 02 

297. 02 

297. 02 

297. 01

297. 01 

297. 00 

296. 99 

296. 98

296. 97 

296. 96 

296. 94 

296. 93

296. 91 

296. 89 

296. 87 

296. 85 

296. 82 

296. 80 

296. 77 

296. 75

296. 72 

296. 69 

296. 66 

296. 63

296. 60 

296. 56 

296. 53 

296. 49

296. 45 

296. 41 

296. 36 

296. 32

296. 28 

296. 23 

296. 18 

296. 13

296. 08 

296. 03 

295. 98 

295. 93

295. 87 

295. 81 

295. 75 

295. 69

Middle latitude 

of quadrilateral.

0 / //

5 37 30 

5 45 00 

5 52 30 

6 00 00

6 07 30 

6 15 00 

6 22 30 

6 30 00

6 37 30 

6 45 00 

6 52 30 

7 00 00

7 07 30 

7 15 00 

7 22 30 

7 30 00

7 37 30 

7 45 00 

7 52 30 

8 00 00

8 07 30 

8 15 00 

8 22 30 

8 30 00

' 8 37 30 

8 45 00 

8 52 30 

9 00 00

9 07 30 

9 15 00 

9 22 30 

9 30 00

9 37 30 

9 45 00 

9 52 30 

10 00 00

10 07 30 

10 15 00 

10 22 30 

10 30 00

10 37 30 

10 45 00 

10 52 30 

11 00 00

Area in 

squaremiles.

295. 63 

295. 57 

295. 51 

295. 44

295. 37 

 295.31 

295. 24 

295.17

295. 09 

295. 02 

294. 95 

294. 87

294. 79 

294. 71 

294. 63 

294. 55

294. 47 

294. 39 

294. 30 

294. 21

294. 12 

294. 03 

293. 94 

293. 85

293. 75 

293. 66 

293. 56 

293. 47

293. 37 

293. 27 

293. 16 

293. 06

292. 95 

292. 85 

292. 74 

292. 63

292. 52 

292. 41 

292. 30 

292. 19

292. 07 

291.95 

291.83 

291. 71

Middle latitude 

of quadrilateral.

0 / //

11 07 30 

11 15 00 

11 22 30 

11 30 00

11 37 30 

11 45 00 

11 52 30 

12 00 00

12 07 30 

12 15 00 

12 22 30 

12 30 00

12 37 30 

12 45 00 

12 52 30 

13 00 00

13 07 30 

13 15 00 

13 22 30 

13 30 00

13 37 30 

13 45 00 

13 52 30 

14 00 00

14 07 30 

14 15 00 

14 22 30 

14 30 00

14 37 30 

14 45 00 

14 52 30 

15 00 00

15. 07 30 

15 15 00 

15 22 30 

15 30 00

15 37 30 

15 45 00 

15 52 30 

16 00 00

16 07 30 

16 15 00 

16 22 30 

16 30 00

Area in 

squaremiles.

291. 59 

291. 47 

291. 34 

291. 22

291.09 

290. 96 

290. 83 

290. 70

290. 57 

290. 44 

290.30 

290. 17

290. 03 

289. 89 

289. 75 

289. 61

289. 47 

289. 33 

289. 18 

289. 03

288. 88 

288. 73 

288. 58 

288. 43

288. 28 

288. 12 

287. 96 

287. 81

287. 65 

287. 49 

287. 33 

287. 17

287. 00 

286. 83 

286. 67 

286. 50

286. 33 

286. 16 

285. 99 

285. 82

285. 64 

285. 46 

285. 28 

285. 10

41623° 16-
114 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 15. Areas of quadrilaterals of earth's surface of 15' extent in latitude and longitude Continued.

[From Smithsonian Geographical Tables.]

Middle latitude 

of quadrilateral.

0 / //

16 37 30 

16 45 00 

16 52 30 

17 00 00

17 07 30 

17 15 00 

17 22 30 

17 30 00

17 37 30 

17 45 00 

17 52 30 

18 .00 00

18 07 30 

18 15 00 

18 .22 30 

.18 30. 00

18 37 30 

18 45. 00 

18 52 30 

19 00 00

19 07 30 

19 15 00 

19 22 30 

19 30 00

19 37 30 

19 45 00 

19 52 30 

20 00 00

20 07 30 

20 15 00 

20 22 30 

20 30 00

20 37 30 

20 45 00 

20 52 30 

21 00 00

21 07 30 

21 15 00 

21 22 30 

21 30 00

21 37 30 

21 45 00 

21 52 30 

22 00 00

Area in 

square miles.

284. 92 

284. 74 

284. 56 

284. 38

284. 19 

284.00 

283. 81 

283.62

283. 43 

283. 24 

283. 05 

282. 86

282. 66 

282. 46 

282. 26 

282. 06

281. 86 

281. 66 

281. 45 

281. 25

281. 04 

280. 83 

280. 62 

280. 41

280. 20 

279. 99 

279. 77 

279. 55

279. 34 

279. 12 

278. 90 

278. 68

278. 46 

278. 23 

278. 00 

277. 78

277. 55 

277. 32 

277. 09 

276. 86

276. 63 

276. 39 

276. 16 

275. 92

Middle latitude 

of quadrilateral.

Of//

22 07 30 

22 15 00 

22 22 30 

22 30 00

22 37 30 

22 45 -00 

22 52 30 

23 00 00

23 07 30 

23 15 00 

23 22 30 

23 30 00

23 37 30 

23 45 00 

23 52 30 

24 00 00

24 07 30 

24 15 00 

24 22 30 

24 30 00

24 37 30 

24 45 00 

24 52 30 

25 00 00

25 07 30 

25 15 00 

25 22 30 

25 30 00

25 37 30 

25 45 00 

25 52 30 

26 00 00

26 07 30 

26 15 00 

26 22 30 

26 30 00

26 37 30 

26 45 00 

26 52 30 

27 00 00'

27 07 30 

27 15 00 

27 22 30 

27 30 00

Area in 

square miles.

275. 68 

275. 44 

275. 20 

274. 96

274. 72 

274. 47 

274. 22 

273. 98

273. 73 

273. 48 

273. 23 

272. 98

272. 72 

272. 47 

272. 21 

271. 95

371.69 

271.44 

271. 17 

270. 91

270. 65 

270. 38 

270. 11 

269. 85

269. 58 ' 

269. 31 

269. 04 

268. 76

268. 49 

268. 21 

267. 94 

267. 66

267. 38 

267. 10 

266. 82 

266. 54

266. 25 

265. 97 

265. 68 

265. 39

265. 10 

264. 81 

264. 52 

264. 23

Middle latitude 

of quadrilateral.

0 / //

27 37 30 

27 45 00 

27 52 30 

28 00 00

28 07 30 

28 15 00 

28 22 30 

28 .30. 00

28 37 30 

28 45 00 

28 52 30 

29 00 00

29 07 30 

29 15 00 

29 22 30 

29 30 00

29 37 30 

29 45 00 

29 52 30 

30 00 00

30 07 30 

30 15 00 

30 22 30 

30 30 00

30 37 30- 

30 45 00 

30 52 30 

31 00 00

31 07 30 

31 15 00 

31 22 30 

31 30 00

31 37 30 

31 45 00 

31 52 30 

32 00 00

32 07 30 

32 15 00 

32 22 30 

32 30 00

32 37 30 

32 45 00 

32 52 30 

33 00 00

Area in 

square miles.

263. 93 

263. 64 

263. 34 

263. 04

262. 74 

262. 44 

262. 14 

261. 84

261. 53 

261. 23 

260. 92 

260. 61

260. 30 

259. 99 

259. 68 ° 

259. 37

259. 05 

258. 74 

258. 42 

258. 10

257. 78 

257.46 

-57. 14 

256. 82

256. 49 

256. 17 

255. 84 

255. 52

255. 19 

254. 86 

254. 53 

254. 19

253. 86 

253. 53 

253. 19 

252. 85

252. 51 

252.17 

251. 83 

251. 49

251. 15 

250. 80 

250. 45 

250. 11
GEOGRAPHIC TABLES AND FORMULAS. 115

TABLE 15. Areas of quadrilaterals of earth's surface of 15' extent in latitude and longitude Continued.

[From Smithsonian Geographical Tables.]

Middle latitude 

of quadrilateral.

o / //

33 07 30 

33 15 00 

33 22 30 

33 30 00

33 37 30 

33 45 00 

33 52 30 

34 00 00

34 07 30 

34 15 00 

34 22 30 

34 30 00

34 37 30 

34 45 00 

34 52 30 

35 00 00

35 07 30 

35 15 00 

35 22 30 

35 30 00

35 37 30 

35 45 00 

35 52 30 

36 00 00

36 07 30 

36 15 00 

36 22 30 

36 30 00

36 37 30 

36 45 00 

36 52 30 

37 00- 00

37 07 30 

37 15 00 

37 22 30 

37 30 00

37 37 30 

37 45 00 

37 52 30 

38 00 00

38 07 30 

38 15 00 

38 22 30 

38 30 00

Area in 

squaremiles.

249. 76 

249. 41 

249. 06 

248. 71

248. 36 

248. 00 

247. 65 

247. 29

246. 93 

246. 57 

246. 21 

245. 85

245. 49 

245. 13 

244. 76 

244. 40

244. 03 

243. 66 

243. 29 

242. 92

242. 55 

242. 18 

241. 80 

241. 43

241. 05 

240. 67 

240. 29 

239. 9]

239- 53 

239. 15 

238. 77 

238. 38

237. 99 

237. 61 

237.22 

236. 83'

236. 44 

236. 05 

235. 66 

235. 26

234. 87 

234. 47 

234. 07 

233. 68

Middle latitude 

of quadrilateral.

0 / //

38 37 30 

38 45 00 

38 52 30 

39 00 00

39 07 30 

39 15 00 

39 22 30 

39 30 00

39 37 30 

39 45 00 

39 52 30 

40 00 00

40 07 30 

40 15 00 

40 22 30 

40 30 00

40 37 30 

40 45 00 

40 52 30 

41 00 00

41 07 30 

 41 15 00 

41 22 30 

41 30 00

41 37 30 

41 45 00 

41 52 30 

42 00 00

42 07 30 

42 15 00 

42 22 30 

42 30 00

42 37 30 

42 45 00 

42 52 30 

43 00 00

43 07 30 

43 15 00 

43 22 30 

43 30 00

43 37 30 

43 45 00 

43 52 30 

44 00 00

Area in 

squaremiles.

233. 28 

232. 88 

232. 48 

232. 07

231.67 ' 

231. 27 

230. 86 

230! 45

230. 04 

229. 63 

229. 22 

228. 81

228. 40 

227. 99 

227. 57 

227. 15

226. 73 

226. 32 

225. 90 

225. 48

225. 06 

224. 64 

224. 21 

223. 79

223. 36 

222. 93 

222. 50 

222. 08

221. 65 

221. 21 

220. 78 

220. 35

219. 91 

219. 48 

219. 04 

218.60

218. 16 

217. 73 

217. 28 

216. 84

216. 40 

215. 96 

215.51 

215. 06

Middle latitude 

of quadrilateral.

0 / //

44 07 30 

44 15 00 ' 

44 22 30 

44 30 00

44 37 30 

44 45 00 

44 52 30 

45 00 00

45 07 30 

45 15 00 

45 22 30 

45 30 00

45 37 30 

45 45 00 

45 52 30 

46 00 00

46 07 30 

46 15 00 

46 22- 30 

46 30 00

46 37 30 

46 45 00 

46 52 30 

47 00 00

47 07 30 

47 15 00 

47 22 30 

47 30 00

47 37 30 

47 45 00 

47 52 30 

48 00 00

48 07 30 

48 15 00 

48 22 30 

48 30 00

48 37 30 

48 45 00 

48 52 30 

49 00 00

49 07 30 

49 15 00 

49 22 30 

49 30 00

Area in 

squaremiles.

214. 61 

214. 17 

213. 72 

213. 27

212. 82 

212. 37 

211. 91 

211.46

211. 00 

210. 55 

210. 09 

209. 63

209. 17 

208. 71 

208. 25 

207. 78

207. 32 

206. 86 

206. 39 

205. 92

205.45 

204. 99 

204. 52 

204. 05

203. 57 

203. 10 

202. 63 

202.15

201. 67 

201. 20 

200. 72 

200. 24

199. 76 

199. 28 

198. 80 

198. 32

197. 83 

197. 35 

196. 86 

196. 38

195. 89 

195. 40 

194. 91 

194. 42
116 GEOGEAPHIC TABLES AND FORMULAS.

TABLE 15. Areas of quadrilaterals of earth's surface of 15' extent in latitude and longi'

tude Continued.

[From Smithsonian Geographical Tables.]

Middle latitude 

of quadrilateral.

0 / //

49 37 30 

49 45 00 

49 52 30 

50 00 00

50 07 30 

50 15 00 

50 22 30 

50 30 00

50 37 30 

50 45 00 

50 52 30 

51 00 00

51 07 30 

51 15 00 

51 22 30 

51 30 00

51 37 30 

51 45 00 

51 52 30 

52 00 00

52 07 30 

52 15 00 

52 22 30 

52 30 00

52 37 30 

52 45 00 

52 52 30 

53 00 00

53 07 30 

53 15 00 

53 22 30 

53 30 00

53 37 30 

53 45 00 

53 52 30 

54 00 00

54 07 30 

54 15 00 

54 22 30 

54 30 00

54 37 30 

54 45 00 

54 52 30 

55 00 00

Area in 

square miles.

193. 93 

193.44 

192. 94 

192. 45

191. 95 

191. 46 

190. 96 

190. 46

189. 96 

189. 46 

188. 96 

188. 46

187. 96 

187. 46 

186. 95 

186. 45

185. 94 

185. 43 

184. 92 

184. 41

183. 90 

183. 39 

. 182.88 

182. 37

181. 85 

181. 34 

180. 82 

180. 31

179. 79 

179. 27 

178. 75 

178. 23

177.71 

177. 19 

176. 67 

176. 14

175. 62 

175. 10 

174. 57 

174. 04

173. 51 

172. 99 

172. 46 

171. 93

Middle latitude 

of quadrilateral.

0 / //

55 07 30 

55 15 00 

55 22 30 

55 30 00

' 55 37 30 

55 45 00 

55 52 30' 

56 00 00

56 07 30 

56 15 00 

56 22 30 

56 30 00

56 37 30 

56 45 00 

56 52 30 

57 00 00

57 07 30 

57 15 00 

57 22 30 

57 30 00

57 37 30 

57 45 00 

57 52 30 

58 00 00

58 07 30 

58 15 .00 

58 22 30 

58 30 00

58 37 30 

58 45 00 

58 52 30 

59 00 00

59 07 30 

59 15 00 

59 22 30 

59 30 00

59 37 30 

59 45 00 

59 52 30 

60 00 00

60 07 30 

60 15 00 

60 22 30 

60 30 00

Area in 

square miles.

171. 39 

170. 86 

170. 33 

169. 79

169. 26 

168. 72 

168. 19 

167. 65

167. 11 

166. 57 

166. 03 

165. 49

164. 95 

164. 41 

163. 87 

163. 32

162. 78 

162. 23 

161.68 

161.14

160. 59 

160. 04 

159. 49 

158. 94

158. 39 

157. 84 

157. 29 

156. 73

156. 18 

155. 62 

155. 07 

154. 51

153. 96 

153. 40 

152. 84 

152. 28

151. 72 

151. 16 

150. 60 

150. 03

149. 47 

148. 91 

148. 34 

147. 77

Middle latitude 

of quadrilateral.

0 / //

60 37 30 

60 45 00 

60 52 30 

61 00 00

61 07 30 

61 15 00 

61 22 30 

61 30 00

61 37 30 

61 45 00 

61 52 30 

62 00 00

62 07 30 

62 15 00 

62 22 30 

62 30 00

62 37 30 

62 45 00 

62 52 30 

63 00 00

63 07 30 

63 15 00 

63 22 30 

63 30 00

63 37 30 

63 45 00 

63 52 30 

64 00 00

64 07 30 

64 15 00 

64 22 30 

64 30 00

64 37 30 

64 45 00 

64 52 30 

65 00 00

65 07 30 

65 15 00 

65 22 30 

65 30 00

65 37 30 

65 45 00 

65 52 30 

66 00 00

' Area in 

square miles.

147. 21 

146. 64 

146. 07 

145. 50

144. 93 

144. 36 

143. 79 

143. 22

142.65 

142. 08 

141. 50 

140. 93

140. 35 

139. 78 

139. 20 

138. 62

138. 04 

137. 47 

136. 89 

136. 31

135.73 

135. 15 

134. 56 

133. 98

133. 40 

132. 81 

132. 23 

131.64

131.06 

130. 47 

129. 88 

129. 29

128. 70 

128. 12 

127. 53 

126. 94

126. 34 

125. 75 

125. 16 

124. 57

123. 97 

123.38 

122. 78 

122. 19
GEOGRAPHIC TABLES AND FORMULAS. 117

TABLE 15. Areas of quadrilaterals of earth's surface of 15' extent in latitude and longitude Continued.

[Prom Smithsonian Geographical Tables.]

Middle latitude 

of quadrilateral.

0 / //

66 07 30 

66 15 00 

66 22 30 

66 30 00

66 37 30 

66 45 00 

66 52 30 

67 00 00

67 07 30 

67 15 00 

67 22 30 

67 30 00

67 37 30 

67 45 00 

67 52 30 

68 00 00

68 07 30 

68 15 00 

68 22 30 

68 30 00

68 37 30 

68 45 00 

68 52 30 

69 00 '00

69 07 30 

69 15 00 

69 22 30 

69 30 00

69 37 30 

69 45 00 

69 52 30 

70 00 00

70 07 30 

70 15 00 

70 22 30 

70 30 00

70 37 30 

70 45 00 

70 52 30 

71 00 00

71 07 30 

71 15 00 

71 22 30 

71 30 00

Area in 

square miles.

121.59 

120. 99 

120. 40 

119. 80

119. 20 

118.60 

118.00 

117. 40

116. 80 

116. 20 

115. 59 

114. 99

114. 39 

113. 78 

113. 18 

112. 57

111.97 

111. 36 

110. 76 

110. 15

109. 54 

108. 93 

108. 32 

107. 71

107. 10 

106. 49 

105. 88 

105. 27

104.65 

104. 04 

103. 43 

102. 81

102. 20 

101.59 

100. 97 

100. 35

99.74 

99.12 

98.50 

97.88

97.26 

96.65 

96.03 

95.41

Middle latitude 

of quadrilateral.

0 / //

71 37 30 

71 45 00 

71 52 30 

72 00 00

72 07 30 

72 15 00 

72 22 30 

72 30 00

72 37 30 

72 45 00 

72 52 30 

73 00 00

73 07 30 

73 15 00 

73 22 30 

73 30 00

73 37 30 

73 45 00 

73 52 30 

74 00 00

74 07 30 

74 15 00 

74 22 30 

74 30 00

74 37 30 

74 45 00 

74 52 30 

75 00 00

75 07 30 

75 15 00 

75 22 30 

75 30 00

75 37 30 

75 45 00 

75 52 30 

76 00 00

76 07 30 

76 15 00 

76 22 30 

76 30 00

 76 37 30 

76 45 00 

76 52 30 

77 00 00

Area in 

square miles.

94.78 

94.16 

93.54 

92.92

92.30 

91.68 

91.05 

90.43

89.80 

89.18 

88. 55 

87.93

87. 30 

86.67 

86.05 

85.42

84.79 

84.16 

83.53 

82.91

82.28 

81.65 

81.01 

80.38

79.75 

79.12 

78.49 

77.86

77.22 

76.59 

75.95 

75.32

74.69 

74.05 

73.42

72.78

72.14 

71.51 

70.87 

70.24

69.60 

68.96 

68.32 

67.68

Middle latitude 

of quadrilateral.

o / //

77 07 30 

77 15 00 

77 22 30 

77 30 00

77 37 30 

77 45 00 

77 52 30 

78 00 00

78 .07 30 

78 15 00 

78 22 30 

78 30 00

78 37 30 

78 45 00 

78 52 30 

79 00 00

79 07 30 

79 15 00 

79 22 30 

79 30 00

79 37 30 

79 45 00 

79 52 30 

80 00 00

80 07 30 

80 15 00 

80 22 30 

80 30 00

80 37 30 

80 45 00 

80 52 30 

81 00 00

81 07 30 

81 15 00 

81 22 30 

81 30 00

81 37 30 

81 45 00 

81 52 30 

82 00 00

82 07 30 

82 15 00 

82 22 30 

82 30 00

Area in 

square miles.

67.04 

66.41 

65.77 

65.13

64.49 

63.85 

63.20 

62.56

61.92 

61.28 

60.64 

60.00

59.35 

. 58.71 

58.06 

57.42

56.78 

56.13 

55.49 

54.84

54.20 

53.55 

52.91 

52.26

51.62 

50.97 

50.32 

49.68

49.03 

48.38 

47.73 

47.08

46.44 

45.79 

45.14 

44.49

43.84 

43.19 

42.54 

41.89

41.24 

40.59 

39.94 

39.29
118 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 15. Areas of quadrilaterals of earth's surface of 15' extent in latitude and longitude Continued.

[From Smithsonian Geographical Tables.]

Middle latitude 

of quadrilateral.

o / //

82 37 30 

82 45 00 

82 52 30 

83 00 00

83 07 30 

83 15 00 

83 22 30 

83 30 00

83 37 30 

83 45 00 

83 52 30 

84 00 00

84 07 30 

84 15 00 

84 22 30 

84 30 00

84 37 30 

84 45 00 

84 52 30 

85 00 00

Area in 

square miles.

38.64 

37.99 

37.34 

36.69

36.03 

35.38 

34.73 

34.08

33.42 

32.77 

32.12 

31.47

30.81 

30.16 

29.51 

28.86

28.20 

27.54 

26.89 

26.24

Middle latitude 

of quadrilateral.

0 / //

85 07 30

85 15 00 

85 22 30 

85 30 00

85 37 30 

85 45 00 

85 52 30 

86 00 00

86 07 30 

86 15 00 

86 22 30 

86 30 00

86 37 30 

86 45 00 

86 52 30 

87 00 00

87 07 30 

87 15 00 

87 22 30 

87 30 00

Area in 

square miles.

25.58 

24.93 

24.27 

23.62

22.97 

22. 31 

21.66 

21.00

20.35 

19.69 

19.04 

18.38

17.72 

17.07 

16.41 

15.76

15. 10 . 

14.44 

13.79 

13.13

Middle latitude 

of quadrilateral.

0 / //

87 37 30 

87 45 00 

87 52 30 

88 00 00

88 07 30 

88 15 00 

88 22 30 

88 30 00

88 37 30 

88 45 00 

88 52 30 

89 00 00

89 07 30 

89 15 00 

89 22 30 

89 30 00

89 37 30 

89 45 00 

89 52 30

Area in 

square miles.

12.48 

11.82 

11.16 

10.51

9.85 

9.20 

8.54 

7.88

7.22 

6.57 

5.91 

5.26

4.60 

3.94 

3.28 

2.63

1.97 

1.31 

0.66
GEOGRAPHIC TABLES AND FORMULAS. 119

TABLE 16. Areas of quadrilaterals of earth's surface of W extent in latitude and

longitude.

[From Smithsonian Geographical Tables.]

Middle latitude of 

quadrilateral.

0 /

0 05 

0 15 

0 25 

0 35

0 45 

0 55 

1 05 

1 15

1 25 

1 35 

1 45 

1 55

2 05 

2 15 

2 25 

2 35

2 45 

2 55 

3 05 

3 15

3 25 3 35 ;

3 45 

3 55

4 05 

4 15 

4 25 

4 35

4 45 

4 55 

5 05 

5 15

5 25 

5 35 

5 45 

5 55

6 05 

6 15 

6 25 

6 35

6 45 

6 55

7 05 

7 15

Area in square 

miles.

132. 01 

132. 01 

132. 01 

132. 00

132. 00 

131. 99 

131.99 

131. 98

131. 97 

131. 96 

131.95 

131. 94

131. 93 

131.91 

131.90 

. 131. 88

131. 86 

131.84 

131. 82 

131.80

131. 78 

131. 76 

131. 74 . 

131.71

131. 68 

131. 66 

131. 63 

131.60

131.57 

131. 54 

131.50 

131. 47

131. 44 

131. 40 

131. 36 

131. 33

131. 29 

131. 25 

131. 21 

131. 16

131. 12 

131. 07 

131. 03 

130. 98

Middle latitude of 

quadrilateral.

0 /

7 25 

7 35 

7 45 

7 55

8 05 

8 15 

8 25 

8 35

8 45 

8 55 

9 05 

9 15

9 25 

9 35 

9 45 

9 55

10 05 

10 15 

10 25 

10 35

10 45 

10 55 

11 05 

11 15

11 25 

11 35 

11 45 

11 55

12 05 

12 15 

12 25 

12 35

12 45 

12 55 

13 05 

13 15

13 25 

13 35 

13 45 

13 55

14 05 

14 15 

14 25 

14 35

Area in square 

miles.

130. 93 

130. 88 

130. 84 

130. 79

130. 73 

130. 68 

130. 63 

130.57

130. 51 

130. 46 

130. 40 

' 130.34

130. 28 

130. 22 

130. 15 

130. 09

130. 02 

129. 96 

129. 89 

129. 82

129. 76 

129. 68 

129. 61 

129. 54

129. 47 

129. 39 

129. 32 

129. 24

129. 16 

129. 08 

129. 00 

128. 92

128. 84 

128. 76 

128. 67 

128. 59

128. 50 

128. 41 

128. 33 

128. 24

128. 14 

128. 05 

127. 96 

127. 87

Middle latitude of 

quadrilateral.

0 /

14 45 

14 55 

15 05 

15 15

15 25 

15 35 

15 45 

15 55

16 05 

16 15 

16 25 

16 35

16 45 

16 55 

17 05 

17 15

17 25 

17 35 

17 45 

17 55 

18 05 '. 

18 15 

18 25 

18 35

18 45 

18 55 

19 05 

19 15

19 25 

19 35 

19 45 

19 55

20 05 

20 15 

20 25 

20 35

20 45 

20 55 

21 05 

21 15

21 25 

21 35 

21 45 

21 55

Area in square 

miles.

127. 77 

127. 67 

127. 58 

127.48

127. 38 

127. 28 

127. 18 

127. 08

126. 98 

126. 87 

126. 77 

126.66

126. 55 

126. 44 

126.33 

126. 22

126. 11 

126. 00 

125. 88 

125. 77

125. 65 

125. 54 

125.42 ! 

125.30 <

125. 18 

125. 06 

124. 94 

124. 81

124. 69 

124. 56 

' 124. 44 

124. 31

124. 18 

124. 05 

123. 92 

123. 79

123. 66 

123. 52 

123. 39 

123. 25

123. 12 

122. 98 

122. 84 

122. 70
120 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 16. Areas of quadrilaterals of earth's surface of 10' extent in latitude and longitude Continued.

[From Smithsonian Geographical Tables.]

Middle latitude of 

quadrilateral.

o /

22 05 

22 15 

22 25 

22 35

22 45 

22 55 

23 05 

23 15

23 25 

23 35 

23 45 

23 55

24 05 

24 15 

24 25 

24 35

24 45 

24 55 

25 05 

25 15

25 25 

25 35 

25 45 

25 55

26 05 

26 15 

26 25 

26 35

26 45 

26 55 

27 05 

27 15

27 25 

27 35 

27 45 

27 55

28 05 

28 15 

28 25 

28 35

28 45 

28 55 

29 05 

29 15

Area in square 

miles.

122. 56 

122. 42 

122. 28 

122. 13

121. 99 

121. 84 

121. 69 

121. 55

121. 40 

121. 25 

121. 10 

120. 94

120. 79 

120. 64 

120.48 

120. 33

120. 17 

120. 01 

119. 85 

119. 69

119. 53 

119. 37 

119. 21 

119. 04

118. 87 

118. 71 

118. 54 

118. 37

118. 21 

118. 04 

. 117.87 

117. 69

117.52 

117. 35 

117.17 

116. 99

116. 82 

116.64 

116. 46 

116. 28

116. 10 

115.92 

115. 73 

115. 55

Middle latitude of 

quadrilateral.

o /

29 25 

29 35 

29 45 

29 55

30 05 

30 15 

30 25 

30 35

30 45 

30 55 

31 05 

31 15

31 25 

31 35 

31 45 

31 55

32 05 

32 15 

32 25 

32 35

32 45 

32 55 

33 05 

33 15

33 25 

33 35 

33 45 

33 55

34 05 

34 15 

34 25 

34 35

34 45 

34 55 

35 05 

35 15

35 25 

35 35 

35 45 

35 55

36 05 

36 15 

. 36 25 

36 35

Area in square 

miles.

115. 37 

115. 18 

114. 99 

114. 81

114. 62 

114. 43 

114. 24 

114. 04

113. 85 

113. 66 

113. 47 

113. 27

113. 07 

112. 88 

112. 68 

112. 48

112. 28 

112. 08 

111.87 

111.67

111.47 

111. 26 

111. 06 

110. 85

110.64 

110.43 

110. 22 

110. 01

. 109. 80 

109. 59 

109. 37 

109. 16

108. 94 

108. 73 

108. 51 

108. 29

108. 07 

107. 85 

107. 63 

107. 41

107. 19 

106. 96 

106. 74 

106. 51

Middle latitude of 

quadrilateral.

0 /

36 45 

36 55 

37 05 

37 15

37 25 

37 35 

37 45 

37 55

38 05 

38 15 

38 25 

38 35

38 45 

38 55 

39 05 

39 15

39 25 

39 35 

39 45 

39 55

40 05 

40 15 

40 25 

40 35

40 45 

40 55 

41 05 

41 15

41 25 

41 35 

41 45 

41 55

42 05 

42 15 

42 25 

42 35

42 45 

42 55 

43 05 

43 15

43 25 

43 35 

43 45 

43 55

Area in square 

miles.

106. 29 

106. 06 

105. 83 

105. 60

105. 37 

105. 14 

104. 91 

104. 68

104.44 

104. 21 

103. 97 

103. 74

103. 50 

103. 26 

103.02 

102. 78

102. 54 

102. 30 

102. 06 

101. 82

101. 57 

101. 33 

101. 08 

100. 83

100. 59 

100. 34 

100. 09 

99.84

99.59 

99.33 

99.08 

98.83

98. 57 

98.32 

98.06 

97. 80

97.55 

97.29 

97. 03 

96.77

96.50 

96.24 

95.98 

95.71
GEOGRAPHIC TABLES AND FORMULAS. 121

TABLE 16. Areas of quadrilaterals of earth's surface of 10' extent in latitude and longitude Continued.

[From Smithsonian Geographical Tables.]

Middle latitude of 

quadrilateral.

0 /

44 05 

44 15 

44 25 

44 35

44 45 

44 55 

45 05 

45 15

45 25 

45 35 

45 45 

45 55

46 05 

46 15 

46 25 

46 35

46 45 

46 55 

47 05 

47 15

47 25 

47 35 

47 45 

47 55

48 05 

48 15 

48 25 

48 35

48 45 

48 55 

49 05 

49 15

49 25 

49 35 

49 45 

49 55

50 05 

50 15 

50 25 

50 35

Area in square 

miles.

95.45 

95.19 

94.92 

94.65

94.38 

94.11 

93.84 

93.58

93.30 

93.03 

92.76 

92.48

92.21 

91.94 

91.66 

91.38

91.10 

90.82 

90.55 

90.27

89.99 

89.70 

89.42 

89.14

88.85 

88.57 

88.28 

88.00

87.71 

87.42 

87.13 

86. 84

86.55 

86.26 

85.97 

85.68

85.39 

85.09 

84.80 

84.50

Middle latitude of 

quadrilateral.

0 /

50 45 

50 55 

51 05 

51 15

51 25 

51 35 

51 45 

51 55

52 05 

52 15 

52 25 

52 35

52 45 

52 55 

53 05 

53 15

53 25 

53 35 

53 45 

53 55

54 05 

54 15 

54 25 

54 35

54 45 

54 55 

55 05 

55 15

55 25 

55 35 

55 45 

55 55

56 05 

56 15 

56 25 

56 35

56 45 

56 55 

57 05 

57 15

Area in square 

miles.

84.21 

83.91 

83.61 

83.31

83.01 

82, 71 

82.41 

82.11

81.81 

81.51 

81.20 

80.90

80.60 

80.29 

79.98 

79.68

79.37 

79.06

78.75 

78.44

78.13 

77.82 

77.51 

77.19

76.88 

76.57 

76.25 

75.94

75.62 

75.30 

74.99 

74. 67 

74.35 

74.03 

73.71 

73.39

73.07 

72.75 

72.43 

72.10

Middle latitude of 

quadrilateral.

0 /

57 25 

57 35 

57 45 

57 55

58 05 

58 15 

58 25 

58 35

58 45 

58 55 

59 05 

59 15

59 25 

59 35 

59 45 

59 55

60 05 

60 15 

60 25 

60 35

60 45 

60 55 

61 05 

61 15

61 25 

61 35 

61 45 

61 55

62 05 

62 15 

62 25 

62 35

62 45 

62 55 

63 05 

63 15

63 25 

63 35 

63 45 

63 55

Area in square 

miles.

71.78 

71.46 

71.13 

70.80

70.48 

70.15 

69.82 

69.49

69.17 

68.84 

68.51 

68.18

67.84 

67.51 

67.18 

66.85

66. 51 

66.18 

65.84 

65.51

65.17 

64.84 

64.50 

64.16

63.82 

63.48 

63.14 

62.80

62.46 

62.12 

61.78 

61.44

61.10 

60.75 

60.41 

60.06

59. 72 

59.37 

59.03 

58.68
122 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 16. Areas of quadrilaterals of earth's surface of W extent in latitude and longitude Continued.

[From Smithsonian Geographical Tables.]

Middle latitude of 

quadrilateral.

0 /

64 05 

64 15 

64 25 

64 35

64 45 ' 

64 55 

65 05 

65 15

65 25 

65 35 

65 45 

65 55

66 05 

66 15 

66 25 

66 35

66 45 

66 55 

67 05 

. 67 15

67 25 

67 35 

67 45 

67 55

68 05 

68 15 

68 25 

68 35

68 45 

68 55 

69 05 

69 15

69 25 

69 35 

69 45 

69 55

70 05 

70 15 

70 25 

70 35

Area in square 

miles.

58.33 

57.99 

57.64 

57.29

56.94 

56. 59 

56.24 

' 55. 89

55.54 

55.19 

54.83 

54.48

54.13 

53.78 

53.42 

53.06

52.71 

52.35 

52.00 

51.64

51.28 

50.93 

50.57 

50.21

49.85 

49.49 

49.13

48.77

48.41 

48. 05 

47.69 

47.33

46.97 

46.60 

46.24 

45.88

45.51 

45.15 

44.78 

44.42

Middle latitude of 

quadrilateral.

o /

70 45 

70 55 

71 05 

71 15

71 25 

71 35 

71 45 

71 55.

72 05

72 15 

72 25 

72 35

72 45 

72 55 

73 05 

73 15

73 25 

73" 35 

1 73 45 

73 55

74 05 ; 

74 15 ' 

74 25 

74 35

74 45 

74 55 

75 05 

75 15

75 25 

75 35 

75 45 

75 55

76 05 

76 15 

76 25 

76 35

76 45 

76 55

77 05 

77 15

Area in square 

miles.

44.05 

43.69 

43.32 

42.95

42. 58 

42.22 

41.85 

41.48

41.11 

40. 74 

40.37 

40.00

39.63 

39.26 

38.89 

38.52

38.15 

37.78 

37.41 

37.03

36.66 

36.29 

35.91 

35.54

35.17 

34.79 

34.42 

34.04

33.66 

33.29 

32.91 

32.53

32.16 

31.78 

31.40 

31.03

30.65 

30.27 

29.89 

29.51

Middle lati- 

.tude of 

quadrilateral.

0 /

77 25 

77 35 

77 45 

77 55

78 05 

78 15 

 78 25 

78 35

78 45 

-78 55 

79 05 

79 15

79 25 

79 35 

79 45 

79 55

80 05 

80 15 

80 25 

80 35

80 45 

80 55 

81 05 

81 15

81 25 

81 35 

81 45 

81 55

82 05 

82 15 

82 25 

82 35

82 45 

82 55 

83 05 

83 15

83 25 

83 35 

83 45 

83 55

Area in square 

miles.

29.13

28.76 

28.37 

27.99

27. 62 

27.24 

26.85 

26.47

26.09 

25.71 

25.33 

24.95

24.57 

24.18 

23.80 

23.42

23.04 

22.65 

22.27 

21.89

21.50 

21.12 

20.73 

20. 35

19.97 

19.58 . 

19. 20 ! 

18.81 ;

18.43 . 

18.04 

17.65 

17.27

16.88 

16.50 

16.11 

15.73

15.34 

14.95 

14.57 

14.18
GEOGRAPHIC TABLES AND FORMULAS. 123

TABLE 16. Areas of quadrilaterals of earth's surface of W extent in latitude and longitude Continued.

[From Smithsonian Geographical Tables.]

Middle latitude of 

quadrilateral.

0 /

84 05

84 15

84 25

84 35

84 45

84 55

85 05

85 15

85 25

85 35

85 45

85 55

Area in square 

miles.

13.79

13.40

13.02

12. 63

12.24

11.86

11.47

11.08

10.69

10.30

9.92

9.53

Middle latitude of 

quadrilateral.

o /

86 05

86 15

86 25

86 35

86 45

86 55

87 05

87 15

87 25

87 35

87 45

87 55

Area in square 

miles.

9.14

8.75

8.36

7.97

7.59

7.20

6.81

6.42

6.03

5.64

5.25

4.86

Middle latitude of 

quadrilateral.

0 /

88 05

88 15

88 25

88 35

88 45

88 55

89 05

89 15

89 25

89 35

89 45

89 55

Area in square 

miles.

4.47

4.09

3.70

3.31

2.92

2.53

2.14

1.75

1.36

0.97

0.58

0.19
124 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 17. For conversion of arc into time.

o

0

1 

2 

3 

4 

5 

6 

7 

8 

9

10

11 

12 

13 

14 

15 

16 

17 

18 

19

20

21 

22 

23 

24 

25 

26 

27 

28 

29

30

31 

32 

33 

34 

35 

36 

37 

38 

39

40

41 

42 

43 

44 

45 

46 

47 

48 

49

50

51 

52 

53 

54 

55 

56 

57 

68 

59

60

h. m.

0 0 

0 4 

0 8 

0 12 

0 16 

020 

0 24 

028 

0 32 

0 36

0 40

044 

048 

0 52 

0 56 

1 0 

1 4 

1 8 

1 12 

1 16

1 20

1 24 

1 28 

1 32 

1 36 

1 40 

1 44 

1 48 

1 52 

1 56

2 0

2 4 

2 8 

2 12 

2 16 

2 20 

2 24 

2 28 

2 32 

2 36

2 40

2 44 

2 48 

262 

2 56 

3 0 

3 4 

3 8 

3 12 

3 16

3 20

3 24 

3 28 

3 32 

3 36 

3 40 

3 44 

348 

3 52 

356

4 0

o

60

61 

62 

63 

64 

65 

66 

67 

68 

69

70

71 

72 

73 

74 

75 

76 

77 

78 

79

80

81 

82 

83 

84 

85 

86 

87 

88 

89

90

91 

92 

93 

94 

95 

96 

97 

98 

99

100

101 

102 

103 

104 

105 

106 

107 

108 

109

110

111 

112 

113 

114 

115 

116 

117 

118 

119

120

h. m.

4 0 

4 4 

4 8 

4 12 

4 16 

4 20 

4 24 

4 28 

4 32 

436

440

4 44 

448 

4 52 

4 56 

5 0 

5 4 

5 8 

5 12 

516

5 20

524 

528 

532 

536 

5 40 

544 

5 48 

5 52 

566

6 0

6 4 

6 8 

6 12 

6 16 

6 20 

6 24 

6 28 

6 32 

6 36

6 40

6 44 

6 48 

652 

656 

7 0 

7 4 

7 8 

7 12 

7 16

7 20

7 24 

7 28 

7 32 

7 36 

7 40 

7 44 7 48" 

7 52 

7 56

8 0

o

120

121 

122 

123 

124 

125 

126 

127 

128 

129

130

131 

132 

133 

134 

135 

136 

137 

138 

139

140

141 

142 

143 

144 

145 

146 

147 

148 

149

150

151 

152 

153 

154 

155 

156 

157 

158 

159

160

161 

162 

163 

164 

165 

166 

167 

168 

169

170

171 

172 

173 

174 

175 

176 

177 178' 

179

180

h. m.

8 0 

8 4 

8 8 

8 12 

8 16 

8 20 

824 

828 

8 32 

8 36

8 40

8 44 

8 48 

852 

8 56 

9 0 

9 4 

9 8 

9 12 

9 16

9 20

9 24 

9 28 

9 32 

9 36 

9 40 

9 44 

9 48 

9 52 

956

10 0

10 4 

10 8 

1012 

1016 

1020 

10 24 

10 28 

10 32 

10 36

10 40

10 44 

10 48 

1052 

1066 

11 0 

11 4 

11 8 

11 12 

11 16

11 20

11 24 

11 28 

11 32 

11 36 

1140 

11 44 

11 48 

11 52 

11 56

12 0

o

180

181 

182 

183 

184 

185 

186 

187 

188 

189

190

191 

192 

193 

194 

195 

196 

197 

198 

199

|200

201 

202 

203 

204 

205 

206 

207 

208 

209

210

211 

212 

213 

214 

216 

216 

217 

218 

219

220

221 

222 

223 

224 

225 

226 

227 

228 

229

230

231 

232 

233 

234 

235 

236 

237 

238 

239

240

h. m.

12 0 

12 4 

12 8 

12 12 

12 16 

12 20 

12 24 

1228 

12 32 

12 36

12 40

12 44 

12 48 

12 52 

12 56 

13 0 

13 4 

13 8 

13 12 

13 16

13 20

13 24 

13 28 

13 32 

13 36 

13 40 

1344 

13 48 

13 52 

13 56

14 0

14 4 

14 8 

1412 

14 16 

14 20 

1424 

14 28 

14 32 

1436

14 40

14 44 

14 48 

1452 

14 56 

35 0 

15 4 

15 8 

15 12 

15 16

1520

1524 

15 28 

15 32 

15 36 

15 40 

15 44 

1548 

1552 

15 56

16 0

o

240

241 

242 

243 

244 

245 

246 

247 

248 

249

250

251 

252 

253 

254 

255 

256 

257 

258 

259

260

261 

262 

263 

264 

265 

266 

267 

268 

269

270

271 

272 

273 

274 

275 

276 

277 

278 

279

280

281 

282 

283 

284 

285 

286 

287 

288 

289

290

291 

292 

293 

294 

296 

296 

297 

298 

299

300

h. m.

16 0 

16 4 

16 8 

16 '12 

16 16 

16 20 

16 24 

1628 

16 32 

16 36

1640

16 44 

16 48 

16 52 

16 56 

17 0 

17 4 

17 8 

17 12 

17 16

17 20

17 24 

17 28 

17 32 

17 36 

17 40 

17 44 

17 48 

17 62 

17 56

18 0

18 4 

18 8 

1812 

18 16 

18 20 

18 24 

18 28 

18 32 

18 36

18 40

1844 

18 48 

18 52 

1856 

19 0 

19 4 

19 8 

19 12 

19 16

19 20

19 24 

1928 

19 32 

19 36 

1940 

1944 

19 48 

1952 

19 56

20 0

o

300

301 

302 

303 

304 

305 

306 

307 

308 

309

310

311 

312 

313 

314 

315 

316 

317 

318 

319

320

321 

322 

323 

324 

325 

326 

327 

328 

329

330

331 

332 

333 

334 

335 

336 

337 

338 

339

340

341 

342 

343 

344 

345 

346 

347 

348 

349

350

351 

352 

.353 

354 

355 

356 

357 

358 

359

360

h. m.

20 0 

20 4 

20 8 

20 12 

20 16 

20 20 

20 24 

20 28 

20 32 

20 36

2040

20 44 

20 48 

20 52 

20 56 

21 0 

21 4 

21 8 

21 12 

21 16

21 20

21 24 

21 28 

21 32 

21 36 

21 40 

21 44 

21 48 

21 52 

21 56

22 0

22 4 

22 8 

22 12 

22 16 

2220 

22 24 

22 28 

22 32 

22 36

22 40

22 44 

22 48 

22 52 

2256 

23 0 

23 4 

23 8 

23 12 

23 16

2320

23 24 

2328 

23 32 

23 36 

23 40 

23 44 

23 48 

23 52 

2356

24 0

'

0

1 

2 

3 

4 

5 

6 

7 

8 

9

10

11 

12 

13 

14 

15 

16 

17 

18 

19

20

21 

22 

23 

24 

26 

26 

27 

28 

29

30

31 

32 

33 

34 

35 

36 

37 

38 

39

40

41 

42 

43 

44 

45 

46 

47 

48 

49

50

51 

52 

53 

54 

55 

56 

57 

58 

69

60

m. s.

0 0 

0 4 

0 8 

012 

0 16 

0 20 

0 24 

0 28 

0 32 

0 36

0 40

0 44 

0 48 

0 52 

0 56 

1 0 

1 4 

1 8 

i 12 

1 16

1 20

1 24 

1 28 

1 32 

1 36 

1 40 

1 44 

1 48 

1 52 

1 56

2 0

2 4 

2 8 

2 12 

2 16 

2 20 

2 24 

2 28 

2 32 

2 36

2 40

244 

2 48 

2 52 

256 

3 0 

3 4 

3 8 

3 12 

3 16

320

324 

3 28 

3 32 

336 

3 40 

3 44 

3 48 

3 52 

3 56

4 0

ii

0

1 

2 

3 

4 

5 

6 

7 

8 

9

10

11 

12 

13 

14 

15 

16 

17 

18 

19

20

21 

22 

23 

24 

25 

26 

27 

28 

29

30

31 

32 

33 

34 

35 

36 

37 

38 

39

40

41 

42 

43 

44 

46 

46 

47 

48 

49

50

51 

62 

63 

54 

55 

56 

57 

58 

59

60

s.

0.000 

0.067 

.0.133 

0.200 

0.267 

0.333 

0.400 

0.467 

0.533 

0.600

0.667

0.733 

0.800 

0.867 

0.933 

1.000 

1.067 

1.133 

1.200 

1.267

1.333

1.400 

1.467 

1.533 

1.600 

1.667 

1.733 

1.800 

1.867 

1.933

2.000

2.067 

2.133 

2 200 

2.267 

2.333 

2.400 

2.467 

2.533 

2.600

2.667

2.733 

2.800 

2.867 

2.933 

3.000 

3.067 

3.133 

3.200 

3.267

3.333

3.400 

3.467 

3.533 

3.600 

3.667 

3.733 

3.800 

3.867 

3.933

4.000
GEOGEAPHIO TABLES AND FOEMULAS.

TABLE 18. For conversion of time into arc.

125-

Hours of time into arc.

Time.

hrs.

1

2

3

4

Arc.

o

15

.30

45

60

Time.

hrs.

5

6

7

8

Arc.

o

75

90

105

120

Time.

hrs.

9

10

11

12

Arc.

0

135

150

165

180

Minutes of time into arc.

m.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

o /

0 15

030

0 45

1 0

1 15

1 30

1 45

2 0

2 15

2 30

2 45

3 0

3 15

3 30

3 45

4 0

4 15

4 30

4 45

5 0

m.

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

O 1

5 15

530

5 45

6 0

6 15

6 30

6 45

7 0

7 15

7 30

7 45

8 0

8 15

8 30

8 45

9 0

9 15

9 30

9 45

10 0

in

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

o /

10 15

1030

10 45

11 0

11 15

11 30

11 45

12 0

12 15

12 30

12 45

13 0

13 15

13 30

13 45

14 0

14 15

14 30

14 45

15 0

Time.

hrs.

13

14

15

16

Arc.

O

195

210

225

240

Time.

hrs.

17

18

19

20

Arc.

o

255

270

285

300

Time.

hrs.

21

22

23

24

Arc.

0

315

330

345

360

Seconds of time into arc.

s.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

0 15

030

0 45

1 0

1 15

1 30

1 45

2 0

2 15

2 30

2 45

3 0

3 15

3 30

3 45

4 0

4 15

4 30

4 45

5 0

s.

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

5 15

5 30

5 45

6 0

6 15

6 30

6 45

7 0

7 15

7 30

7 45

8 0

 8 15

8 30

8 45

9 0

9 15

9 30

9 45

10 0

s.

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

/ n

10 15

10 30

10 45

11 0

11 15

11 30

11 45

12 0

12 15

12 30

12 45

13 0

13 15

13 30

13 45

14 0

14 15

14 30

14 45

15 0

Hundredths of a second of time into arc.

Hundredths

of a second

of time.

g

0.00

.10

.20

.30

.40

0.50

.60

.70

.80

.90

.00

0.00

1.50

3.00

4.50

6.00

7.50

9.00

10.50

12.00

13.50

.01

0.15

1.65

3.15

4.65

6.15

7.65

9.15

10.65

12.15

13.65

.02

n

0.30

1.80

3.30

4.80

6.30

7.80

9.30

10.80

12.30

13.80

.03

0.45

1.95

3.45

4.95

6.45

7.95

9.45

10.95 

12.45

13.95

.04

n

0.60

2.10

3.60

5.10

6.60

8.10

9.60

LI. 10

12.60

L4.10

.05 .06

// //

0.75 0.90

2.25 2.40

3.75 3.90

5.25 5.40

6.75 6.90

8.25 8.40

9.75 9.90

11.25 11.40

12.75 12.90

14.25 14.40

.07

n

1.05 °2".55

4.05

5.55

7.05

8.55

10.05

11.55

13.05

14.55

.08

n

1.20

2.70

4.20

5.70

7.20

8.70

10.20

11.70

13.20

14.70

.09

n

1.35

2.85

4.35

5.85

7.35

8.85

10.35

11.85

13.35

14.85
126 GEOGRAPHIC TABLES AND FOEMULAS.

TABLE 19. For conversion of mean time into sidereal time.

a

0

i

2 

3 

4 

5

6

7 

8 

9

10

11 

12 

13 

14 

15 

16 

17 

18 

19

20

21 

22 

23 

24 

25 

26 

27 

28 

29

30

31 

32 

33 

34 

35 

36 

37 

38 

39

40

41 

42 

43 

44 

45 

46 

47 

48 

49

50

51 

52 

53 

54 

55 

56 

57 

58 

59

60

m 

0

h m s 

000

065 

0 12 10 

0 18 16 

0 24 21 

0 30 26 

0 36 31 

0 42 37 

0 48 42 

0 54 47

1 0 52

1 6 58 

1 13 3 

1 19 8 

1 25 13 

1 31 19 

1 37 24 

1 43 29 

1 49 34 

1 55 40

2 1 45

2 7 50 

2 13 55 

2 20 1 

2 26 6 

2 32 11 

2 38 16 

2 44 22 

2 50 27 

2 56 32

3 2 37

3 8 43 

3 14 48 

3 20 53 

3 26 58 

3 33 3 

3 39 9 

3 45 14 

3 51 19 

3 57 24

4 3 30

4 9 35 

4 15 40 

4 21 45 

4 27 51 

4 33 56 

4 40 1 

4 46 6 

4 52 12 

4 58 17

5 4 22

5 10 27 

5 16 33 

5 22 38 

5 28 43 

5 34 48 

5 40 54 

5 46 59 

5 53 4 

5 59 9

6 5 15

m 

1

h m s 

6 5 15

6 11 20' 

6 17 25 

6 23 30 

6 29 36 

6 35 41 

6 41 46 

6 47 51 

6 53 56 

702

767

7 12 12 

7 18 17 

7 24 23 

7 30 28 

7 36 33 

7 42 38 

7 48 44 

7 54 49 

8 0 54

8 6 59

8 13 5 

8 19 10 

8 25 15 

8 31 20 

8=37 26 

8 43 31 

8 49 36 

8 55 41 

9 1 47

9 7 52

9 13 57 

9 20 2 

9 26 8 

9 32 13 

9 38 18 

9 44 23 

9 50 28 

9 56 34 

10 2 39

10 8 44

10 14 49 

10 20 55 

10 27 0 

10 33 5 

10 39 10 

10 45 16 

10 51 21 

10 57 26 

11 3 31

11 9 37

11 15 42 

11 21 47 

11 27 52 

11 33 58 

11 40 3 

11 46 8 

11 52 13 

11 58 19 

12 4 24

12 10 .29

m 

2

h m s 

12 10 29

12 16 34 

12 22 40 

12 28 45 

12 34 50 

12 40 55 

12 47 1 

12 53 6 

12 59 11 

13 5 16

13 11 21

13 17 27 

13 23 32 

13 29 37 

13 35 42 

13 41 48 

13 47 53 

13 53 58 

14 0 3 

14 6 9

14 12 14

14 18 19 

14 24 24 

14 30 30 

14 36 35 

14 42 40 

14 48 45 

14 54 51 

15 0 56 

15 7 1

15 13 6

15 19 12 

15 25 17 

15 31 22 

15 37 27 

15 43 33 

15 49 38 

15 55 43 

16 1 48. 

16 7 54

16 13 59

16 20 4 

16 26 9 

16 32 14 

16 38 20 

16 44 25 

16 50 30 

16 56 35 

17 2 41 

17 8 46

17 14 51

17 20 56 

17 27 2 

17 33 7 

17 39 12 

17 45 17 

17 51 23 

17 57 28 

18 3 33 

18 9 38

18 15 44

m 

3

h m s 

18 15 44

18 21 49 

18 27 54 

18 33 59 

18 40 5 

18 46 10 

18 52 15 

18 58 20 

19 4 26 

19 10 31

19 16 36

19 22 41 

19 28 47 

19 34 52 

19 40 57 

19 47 2 

19 53 7 

19 59 13 

20 5 18 

20 11 23

20 17 28

20 23 34 

20 29 39 

20 35 44 

20 41 49 

20 47 55 

20 54 0 

21 0 5 

21 6 10 

21 12 16

21 18 21

21 24 26 

21 30 31 

21 36 37. 

21 42 42 

21 48 47 

21 54 52 

22 0 58 

22 7 3 

22 13 8

22 19 13

22 25 19 

22 31 24 

22 37 29 

22 43 34 

22 49 39 

22 55 45 

23 1 50 

23 7 55 

23 14 0

23 20 6

 23 26 11 

23 32 16 

23 38 21 

23 44 27 

23 50 32 

23 56 37 

24 2 42 

24 8 48 

24 14 53

24 20 58

s 

0.00

0.01 

0.02 

0.03 

0.04 

0.05 

0.06 

0.07 

0.08 

0.09

0.10

0.11 

0.12 

0.13 

0.14 

0.15 

0.16 

0.17 

0.18 

0.19

0.20

0.21 

0.22 

0.23 

0.24 

0.25 

0.26 

0.27 

0.28 

0.29

0.30

0.31 

0.32 

0.33 

0.34 

0.35 

0.36 

0.37 

0.38 

0.39

0.40

0.41 

0.42 

0.43 

0.44 

0.45 

0.46 

0.47 

0.48 

0.49

0.50

m s 

0 0

0 4 

0 7 

0 11 

0 15 

0 18 

0 22 

0 26 

0 29 

0 33

0 37

0 40 

0 44 

0 47 

0 51 

0 55 

0 58 

1 2 

1 6 

1 9

1 13

1 17 

1 20 

1 24 

1 28 

1 31 

1 35 

1 39 

1 42 

1 46

1 50

1 53 

1 57 

2 1 

2 4 

2 8 

2 11 

2 15 

2 19 

2 22

2 26

2 30 

2 33 

2 37 

2 41 

2 44 

2 48 

2 52 

2 55 

2 59

3 3

s 

0.50

0.51 

0.52 

0.63 

0.54 

0.55 

0.56 

0.57 

0.58 

0.59

0.60

0.61 

0.62 

0.63 

0.64 

0.65 

0.66 

0.67 

0.68 

0.69

0.70

0.71 

0.72 

0.73 

0.74 

0.75 

0.76 

0.77 

0.78 

0.79

0.80

0.81 

0.82 

0.83 

0.84 

0.85 

0.86 

0.87 

0.88 

0.89

0.90

0.91 

0.92 

0.93 

0.94 

0.95 

0.96 

0.97 

0.98 

0.99

1.00

m s 

3 3

3 6 

 3 10 

3 14 

3 17 

3 21 

3 25 

3 28 

3 32 . 

3 35

3 39

3 43 

3 46 

3 50 

3 54 

3 57 

4 1 

4 5 

4 8 

4 12

4 16

4 19 

4 23 

4 27 

4 30 

4 34 

4 38 

4 41 

4 45 

4 49

4 52

4 56 

4 59 

5 3 

5 7 

5 10 

5 14 

5 18 

5 21 

5 25

5 29

5 32 

5 36 

5 40 

5 43 

5 47 

5 51 

5 54 

5 58 

6 2

6 5

Example: Let the given mean 

time be 14>> 57°> 32 ».56. 

The table gives 

first for 14h 54m 51 2"> 27 » 

then for 2 41.56 0.44

The sum 14»57">32<>.56+2m 

is the required

2 27. 

27 ». 44-1

sidereal

44

ShQmO'

time.
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 20. For conversion of sidereal lime into mean lime.

127

s

0

1

2 

3 

4 

5 

6 

7 

8 

0

10

11 

12 

13 

14 

15 

16 

17 

18 

19

20

21

22 

23 

24 

25 

26 

27 

28 

29

30

31 

32 

33 

34 

35 

36 

37 

38 

39

40

41 

42 

43 

44 

45 

46 

47 

48 

49

60

51

52 

53 

64 

55 

56 

57 

58 

59

60

m 

0

h m s 

000

0 6 ,- 6 

0 12 12 

0 18 19 

 0 24 25 

0 30 31 

0 36 37 

0 42 44 

0 48 50 ' 

0 64 56

112

179 

1 13 15 

1 19 21 

1 25 27 

1 31 34 

1 37 40 

1 43 46 

1 49 52 

1 55 59

225

2 8 11 

2 14 17 

2 20 24 

2 26 30 

2 32 36 

2 38 42 

2 44 49 

2 50 55 

2 57 1

337

3 9 14 

3 15 20 

3 21 26 

3 27 32 

3 33 38 

3 39 45 

3 45 51 

3 51 57 

3 58 3

4 4 10

4 10 16 

4 16 22 

4 22 28 

4 28 35 

4 34 41 

4 40 47 

4 46 53 

4 53 0 

4 59 6

5 5 12

5 11 18 

5 17 25 

5 23 31 

5 29 37 

5 35 43 

6 41 50 

5 47 56 

5 54 2 

608

6 6 15

m 

1

h m s 

6 6 15

6 12 21 

6 18 27 

6 24 33 

6 30 40 

6 36 46 

6 42 52 

' 6 48 58 

6 55 4 

7 1 11

7 7 17

7 13 23 

7 19 29 

7 25 36 

7 31 42 

7 37 48 

7 43 54 

7 50 1 

7 66 7 

8 2 13

8 8 19

8 14 26 

8 20 32 

8 26 ;*8 

8 32 44 

8 38 51 

8 44 57 

8 51 3 

8 57 9 

9 3. 16

9 9 22

9 15 28 

9 21 34 

9 27 41 

9 33 47 

9 39 53 

9 45 59 

9 52 5 

9 58 12 

10 4 18

10 10 24

10 16 30 

10 22 37 

10 28 43 

10 34 49 

10 40 55 

10 47 2 

10 53 8 

10 59 14 

11 5 20

11 11 27

11 17 33 

11 23 39 

11 29 45 

11 35 62 

11 41 58 

11 48 4 

11 54 10 

12 0 17 

12 6 23

12 12 29

m

2 .

h m s 

12 12 29

12 18 35 

12 24 42 

12 30 48 

12 36 54 

12 43 0 

12 49 7 

12 55 13 

13 1 19 

13 '7 25

13 13 31

13 19 38 

13 25 44 

13 31 50 

13 37 56 

13 44 3 

13 50 9 

13 56 15 

14 2 21 

14 8 28

14 14 34

14 20 40 

14 26 46 

14 32 53 

14 38 59 

14 45 5 

14 51 11 

14 57 18 

16 3 24 

15 9 30

15 15 36

15 21 43 

15 27 49 

15 33 55 

15 40 1 

15 46 8 

15 52 14 

15 58 20 

16 4 26 

16 10 33

16 16 39

16 22 45 

16 28 51 

16 34 57 

16 41 4 

16 47 10 

16 53 16 

16 59 22 

17 5 29 

17 11 35

17 17 41

17 23 47 

17 29 54 

17 36 0 

17 42 6 

17 48 12 

17 54 19 

18 0 25 

18 6 31 

18 12 37

18 18 44

m 

3

h m s 

18 18 44

18 24 60 

18 30 56 

18 37 2 

18 43 9 

18 49 15 

18 55 21 

19 1 27 

19 7 34 

19 13 40

19 19 46

19 25 52 

19 31 59 

19 38 5 

19 44 11 

19 50 17 

19 56 23 

20 2 30 

20 8 36 

20 14 42

20 20 48

20 26 55 

20 33 1 

20 39 7 

20 45 13 

20 51 20 

20 57 26 

21 3 32 

21 9 38 

21 15 45

21 21 51

21 27 57 

21 34 3 

21 40 10 

21 46 16 

21 52 22 

21 58 28 

22 4 35 

22 10 41 

22 16 47

22 22 53

22 29 0 

22 35 6 

22 41 12 

22 47 18 

22 53 24 

22 59 31 

23 5 37 

23 11 43 

23 17 49

23 23 56

 23 30 2 

23 36 8 

23 42 14 

23 48 21 

23 54 27 

24 0 33 

24 6 39 

24 12 46 

24 18 52

24 24 58

s 

0.00

0.01 

0.02 

0.03 

0.04 

0.05 

0.06 

0.07 

0.08 

0.09

0.10

0.11 

0.12 

0.13 

0.14 

0.15 

0.16 

0.17 

0.18 

0.19

0.20

0.21 

0.22 

0.23 

,0. 24 

0.25 

0.26. 

0.27 

0.28 

0.29

0.30

0.31 

0.32 

0.33 

0.34 

0.35 

0.36 

0.37 

0.38 

0.39

0.40

0.41 

0.42 

0.43 

0.44 

0.45 

0.46 

0.47 

0.48 

0.49

0.50

m s 

0 0

0 4 

0 7 

0 11 

0 15 

0 18 

0 22 

0 26 

0 29 

0 33

0 37

0 40 

0 44 

0 43 

0 51 

0 55 

0 59 

1 2 

1 6 

1 10

1 13

1 17 

1 21 

1 24 

l'28 

1 32 

1 35 

1 39 

1 43 

1 46

1 50

1 54 

1 57 

2 1 

2 5 

2 8 

2 12 

2 16 

2 19 

2 23

2 .26

2 30 

2 34 

2 37 

2 41 

2 45 

2 48 

2 52 

2 56 

2 59

3 3

s 

0.50

0.51 

0.52 

0.53 

0.54 

0.55 

0.66 

0.57 

0.58 

0.59

0.60

0.61 

0.62 

0.63 

0.64 

0.65 

0.66 

0.67 0.68 ' 

0.69

0.70

0.71 

0.72 

0.73 

0.74 0.75 ' 

0.76 

0.77 

0.78 

0.79

0.80

0.81 

0.82 

0.83 

0.84 

0.85 

0.86 

0.87 

0.88 

0.89

0.90

0.91 

0.92 

0.93 

0.94 

0.95 

0.96 

0.97 

0.98 

0.99

1.00

m s 

3 3

3 7 

3 10 

3 14 

3 18 

3 21 

3 25 

3 29 

3 32 

3 36

3 40

3 43 

3 47 

3 51 

3 64 

3 58 

4 2 

4 5 

4- 9 

4 13

4 16

4 20 

4 24 

4 27 

4 31 

4 35 

4 38 

4 42 

4 46 

4 49

4 63

4 57 

5 0 

5 4 

5 8 

5 11 

5 15 

5 19 

5 22 

5 26

5 30

5 33 

5 37 

5 41 

5 44 

5 48 

5 52 

5 55 

5 59 

6 3

6 6

Example: Given 15h 0 0». 

The table gives 

 first for 14h 57m 18' 2 27" 

then for 2 42 0.44

15 0 0 2 27.44 

The difference 

15i.0m Os _ 2m 27M4 = 14" 57 32°.56

is the required mean time.
128 GEOGEAPHIO TABLES AND FORMULAS.

TABLE 21. For inlercohversion of feet and decimals of a mile.

Feet.

53

106

158

211

264

317

370

422

475

528

581

634

686

739

792

845

898

950

1003

1056

1109

1162

1214

1267

1320

Miles.

.01

.02

.03

.04

.05

.06

.07

.08

.09

.10

.11

.12

.13

.14

.15

.16

.17

.18

.19

.20

.21

.22

.23

.24

.25

Feet.

1373

1426.

1478

1531

1584

1637

1690

1742

1795

1848

1901

1954

2006

2059

2112

2165

2218

2270

2323

2376

2429

2482

2534

2587

2640

Miles.

.26

.27

.28

.29

.30

.31

.32

.33

.34

.35

.36

.37

.38

.39

.40

.41

.42

.43

.44

.45

.46

.47

.48

.49

.50

Feet.

2693

2746

2798

2851

2904

2957

3010

3062

3115

3168

3221

3274

3326

3379

3432

3485

3538

3590

3643

3696

3749

3802

3854

3907

3960

Miles.

.51

.52

.53

.54

.55

.56

.57

.58

.59

.60

.61

.62

.63

.64

.65

.66

.67

.68

.69

.70

.71

.72

.73

.74

.75

Feet.

4013

4066

4118

4171

4224

4277

4330

4382

4435

4488

4541

4594

4646

4699

4752

4805

4858

4910

4963

5016

5069

5122

5174

5227

5280

Miles.

.76

.77

.78

.79

.80

.81

.82

.83

' .84

.85

.86

.87

.88

.89

.90

.91

.92

.93

.94

.95

.96

.97

.98

.99

1.00
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 22. For conversion of chains into feet.

129

0

10

20

30

40

50

60

70

80

90

0

Feet. 0

660

1,320

1,980

2,640

3,300

3,960

4,620

5,280

5,940

1

Feet.

66

726

1,386

2,046

2,706

3,366

4,026

4,686

5,346

6,006

2

Feet.

132

792

1,452

2,112

2, 772

3,432

4,092

4,752

5,412

6,072

3

Feet.

198

858

1,518

2,178

2,838

3,498

4,158

4,818

5,478

6,138

4

Feet.

264

924

1,584

2,244

2,904

3,564

4,224

4,884

5, 544 '

6,204

5

Feet.

330

990

1,650

2,310

2,970

3,630

4,290

4,950

5,610

6,270

6

Feet.

396

1,056

1,716

2,376

3,036

3,696

4,356

5,016

5,676

6,336

7

Feet.

462

1,122

1,782

2,442

3,102

3,762

4,422

5,082

5,742

6,402

8

Feet.

528

1,188

1,848

2,508

3,168

3,828

4,488

5,148

5,808

6,468

9

Feet.

594

1,254

1,914

2,574

3,234

3,894

4,554

5,214

5,874

6,534

The feet for each whole number of chains up to 99 are given; and 

as links are hundredths they can also be read off (by pointing off 

two places) and added to the chains. Example: Convert 16 chains 

27 links to feet. From the table 16 chains is read as 1,056 feet, and 27 

links (read 27 chains and point off two places) as 17.82 feet. The 

sum, 1,073.83 feet, is obtained by mental addition.

TABLE 23. For conversion of feet into chains.

Feet.

000

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

00

Chains.

0.00

1.52

3.03

4.55

6.06

7.58

9.09

10.61

12.12

13.64

15.15

16.67

18.18

10

Chains.

0.15

1.67

3.18

4.70

6.21

7.73

9.24

10.76

12.27

13.79

15.30

16.82

18.33

20

Chains.

0.30

1.82

3.33

4.85

6.36

7.88

9.39

10.91

12.42

13.94

15.46

16.97

18.48

30

Chains.

0.46

1.97

3.48

5.00

6.53

8.03

9.55

11.06

12.58

14.09

15.61

17.12

18.64

40

Chains.

0.61

2.12

3.64

5.15

6.67

8.18

9.70

11.21

12.73

14.24

15.76

17.27

18.79

50

Chains.

0.76

2.27

3.79

5.30

6.82

8.33

9.85

11.36

12.88

14.40

15.91

17.42

18.94

60

Chains.

0.91

2.42

3.94

5.46

6.97

8.48

10.00

11.52

13.03

14.55

16.06

17.58

19.09

70

Chains.

1.06

2.58

4.09

5.61

7.12

8.64

10.15

11.67

13.18

14.70

16.21

17.73

19.24

80

Chains.

1.21

2.73

4.24

5.76

7.27

8.79

10.30

11.82

13.33

14.85

16.36

17.88

19.39

90

Chains.

1.36

2.88

4.39

5.91

7.42

8.94

10.46

11.97

13.49

15.00

16.52

18.03

19.55

Example: Convert 457 feet into chains 450 feet (line 400, column 

50) equals 6.82 chains; 7 feet (line 000, column 70; 1.06 divided by 

10) equals 0.106 chain; therefore, 457 feet equals 6.93 chains.

41623° 16 9
130 GEOGKAPHIC TABLES AND FOEMULAS.

TABLE 24. Converting wheel revolutions into hundredths of a mile,

[Prepared by J. H. Jennings.] 

[Scale divisions outside; revolutions inside.] 

CIRCUMFERENCE OF WHEEL, 9.5 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

6

61

117

172

228

283

339

394

450

506

2

11

67

122

178

233

289

344

400

455

511

3 

17

72

128

183

239

294

350

405

461

516

4

22

78

133

189

244

300

355

411

466

522

5

28

83

139

194

250

305

361

416

472

528

6

33

89

144

200

255

311

366

422

478

533

7

39

94

150

205

261

316

372

428

483

539

8

44

100

155

211

266

322

378

433

489

544

9

50

105

161

216

272

328

383

439

494

550

10

56

111

167

222

278

333

389

444

500

555

CIRCUMFERENCE OF WHEEL, 9.6 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

5

60

116

171

225

281

336

391

446

501

2

11

66

121

177

231

286

341

396

451

506

3

16

72

126

182

236

292

347

402

457

512

4

22

77

132

188

242

297

352

407

462

517

5

27

82

137

193

247

303

358

413

468

523

(i

33

88

143

199

253

308

363

418

473

528

7

38

93

148

204

258

314

369

424

479

534

8

44

99

154

209

264

319

374

429

484

539

9

50

105

159

215

270

325

380

435

490

544

10

55

110

165

220

275

330

385

440

495

550

CIRCUMFERENCE OF WHEEL, 9.7 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

5

60

114

169

223

277

331

386

441

495

2

11

65

120

174

228

283

337

392

446

500

3

16

71

125

179

234

288

342

397

451

506

4

22

76

131

185

239

294

348

403

457

511

5

27

81

136

190

245

299

353

408

462

517

6

33

87

142

196

250

305

359

414

468

522

7

38

92

147

201

256

 310

364

419

473

528

8

44

98

152

206

261

316

370

424

479

533

9

49

103

158

212

267

321

376

429

484

539

10

54

109

163

218

272

326

381

435

490

544
GEOGRAPHIC TABLES AND FORMULAS. 131

TABLE 24. Converting wheel revolutions into hundredths of a mile Continued. 

CIRCUMFERENCE OP WHEEL, 9.8 FEET.

0

0

10

L'O

30

40

50

60

70

80

90

1

5

59

113

167

221

275

329

383

437

490

2

11

65

119

172

 226

280

334

388

442

496

3

16

70

124

178

231

286

339

394

447

501

4

22

. 75

129

183

237

291

345

400

453

506

5

27

81

135

189

242

296

350

405

458

512

6

- 32

86

140

194

248

302

356

410

464

517

7

38

91

145

199

253

307

361

415

469

522

8

43

97

151

205

259

313

366

421

474

528

9

49 'l02

156

.211

265

318

372

426

480

533

10

54

108

162

216

270

324

377

431

485

539

CIRCUMFERENCE OF WHEEL, 9.9 FEET.

0

0

10

20

30

40

50

60

70

80

00

1

5

59

112

165

 219

272

325

378

432

485

2

11

64

117

170

224

277

330

384

437

490

3

16

69

122

176

229

282

336

389

442

496

4

21

75

128

181

235

288

341

394

448

501

5

27

80

133

186

240

293

346

400

453

506

6

32

85

138

192

245

298

352

405

458

512

7

37

91

144

197

251

304

357

410

464

517

8

43

96

149

203

256

309

362

416

469

522

»

48

101

155

208

261

314

368

421

474

528

10

53

107

160

213

267

320

373

426

480

533

CIRCUMFERENCE OF WHEEL, 10 FEET.

0

0

10

20

80

40

50

60

70

80

90

1

5

58

111

.164

217

269

322

375

428

481

2

11

63

116

169

222

275

327

380

433

486

3

16

69

121

174

227

280

333

385

438

491

4

21

75

127

180

232

285

338

391

444

496

5

26

80

132

185

238

290

343

396

449

502

6

32

85

137

190

243

296

349

401

454

507

7

37

90

143

195

248

301

354

406

459

512

8

42

96

148

201

253

306

359

412

465

517

9

48

101

153

206

259

311

364

417

470

523

10

53

106

158

211

264

317

370

422

475

528
132 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 24. Converting wheel revolutions into hundredths of a mile Continued. 

CIRCUMFERENCE OF WHEEL, mi FEET.

0

0

10

20

30

40

50

60

70

80

90

1

5

58

110

162

214

267

319

371

424

476

2

10

63

115

167

220

272

324

376

429

481

3

16

68

121

173

226

277

329

381

434

486

4

21

73

126

178

231

282

334

386

439

492

5

26

79

131

183

236

288

340

392

445

497

6

31

84

136

188

241

293

345

397

450

502

7

36

89

142

193

247

298

350

402

455

507

8

41

94

147

199

252-

303

355

408

460

513

9

47

100

152

204

257

308

361-

413

466

518

10

52

105

157

209

262

314

366

418.

471

523

CIRCUMFERENCE OF WHEEL, 10.2 FEET.

0

0

10

20

30

40

50

60

70

80

90

i

5

57

-109

161

212

264

316

368

419

471

2

10

62

114

166

218

269

321

373

425

476

3

16

67

119

171

224

275

326

378

430

481

4

21

73

124

176

229

280

332

383

435

487

5

26

78

130

181

234

285

337

388

440

492

6

31

83

135

186

239

290

342

394

446

497

7

36

88

140

191

244

295

347

399

451

503

8

41

93

145

197

249

300

352

404

456

508

9

47

98

150

202

254

306

357

409

461.

513

10

52

104

155

207

259

311

363

414

466

518

CIRCUMFERENCE OF WHEEL, 10.3 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

5

56

108

159

209

262

313

364

416

467

2

10

62

113

164

214

.267

318

369

421

472

3

15

67

118

169

219

272

323

374

426

477

4

20

72

123

174

224

277

328

380

431

482

5

26

77

128

180

230

282

333

385

436

487

6

31

82

133

185.

235

287

338

390

441

492

7

36

87

138

190

240

292

344

395

446

498

8

41

92

144

195

245

297

349

400

451

503

9

46

97

149

200

250

303

354

405

457

508

10

51

103

154

204

256

308

359

410

462

513
GEOGRAPHIC TABLES AND FOBMULAS. 133

TABLE 24. Converting wheel revolutions into hundredths of a ?ra7e Continued.

CIRCUMFERENCE OF WHEEL, 10.4 FEET. 

0

0

10

20

30

40

50

GO

70

80

90

1

5

56

107

157

208

259

310

361

411

462

2

10

61

112

163

213

264

315

366

. 416

467

3

15

66

117

168

218

269

320

371

421

472

4

20

71

122

173

223

274

325

376

426

.478

5

25

76

127

178

228

279

330

381

432

483

6

30

81

132

183

233

284

335

386

437

488

7

36

86

137

188

238

289

340

391

442

493

8

41

91

142

193

244

295

345

396

447

498

9

46

97

147

198

249

300

350

401

452

503

10

51

102

152

203

254

305

356

406

457

508

CIRCUMFERENCE OF WHEEL, 10.5 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

5

55

106

156

206

257

307

357

407

458

2

10

60.

Ill

161

211

262

312

362

412

463

3

15

65

116

166

216

267

317

367

417

468

4

20

70

121

171

221

' 272

322

372

422

473

5

25

75

126

176

226

277

327

377

428

478

6

30

80

131

181

231

282

332

382.

433

483

7

35

85

136

186

. 236

287

337

387

438

488

8

40

90

141

191

241

292

342

392

443

493

9

45

95

146

196

246

297

347

397

448

498

10

50

101

151

201

251

302

352

402

453

503

CIRCUMFERENCE OF WHEEL, 10.C FEET.

0

0

10

20

30

40

50

GO

70

80

90

1

5

55

105

154

204

254

304

354

403

453

t>

10

60

110

159

209

259

309

359

408

458

3

15

65

115

164

214

264

314

364

413

463

4

20

70

120

169

219

269

319

369

418

468

5

25

75

125

174

224

274

324

374

423

473

G

30

80

130

179

229

279

329

379.

428

478

7

35

85

135

184

234

284

334

384

433

483

8

40

90

140

189

239

289

339

389

438

488

9

45

95

144

194

244

294

344

393

 443

493

10

50

100

149

199

249

299

349

398

448

498
134 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 24. Converting wheel revolutions into hundredths of a mile Continued. 

CIRCUMFERENCE OF WHEEL, 10.7 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

5

54

104

153

203

252

301

351

400

450

2

10

59

109

158

207

257

306

356

405

454

3

15

64

114'

163

212

262

311

361

410

459

4

20

69

119

168

217

'267

316

366

415

464

5

25

74

123

173

222

272

321

371

420

469

6

30

79

128

178

227

277

326

375

425

474

7

35

84

133

183

232

282

331

380

430

479

8

40

89

138

188

237

287

336

385

435

484

9

44

94

143

193

242

291

341

390

440

489

10

49

99

148

198

247

296

346

395

445

494

CIRCUMFERENCE OF WHEEL, 10.8 FEET.

0

0

10

20

30

40

50

60

70

80

90

i

5

54

103

152

200

249

298

346

396

445

2

10

59

108

156

205

254

303

351

401

450

3

15

64

113

161

210

259

308

356

406

455

4

20

68

118

166

215

264

313

361

411

460

5

24

73

122

171

220

269

318

366

416

464

6

29

' 78

127

176

225

274

323

371

421

469

7

34

83

132

181

230

279

328

376

425

474

8

39

88

137

186

235

283

332

381

430

479

9

44

93

142

191

240

288

337

386

435

484

10

49

98

147

196

244

293

341

391

440

489

CIRCUMFERENCE OF WHEEL, 10.9 FEET.

0

0

10

20

30

40

50

60

70

80

80

1

5

53

102

150

197

247

295

344

392

.440

2

10

58

107

155

202

252

300

349

397

445

3

15

63

111

160

207

257

305

353

402

450

4

19

68

116

165

212

261

310

358

407

455

5

24

73

121

170

217

266

315

363

411

460

6

29

78

126

175

222

271

319

368

416

465

7

34

82

131

179

227

276

324

373

421

469

8

39

87

136

184

232

281

329

378

426

474

9

44

92

141

189

237

286

334

383

431

479

10

48

97

145

193

242

290

339

387

436

484
GEOGEAPHIC TABLES AND FOEMULAS. 135

TABLE 24. Converting wheel revolutions into hundredlhs of a mile Continued. 

CIRCUMFERENCE OP WHEEL, 11.0 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

5

53

101

149

197

245

293

341

389

437

2

10

57

106

154

202

250

298

346

394

442

3

14

62

110

158

206

254

302

350

398

446

4

19

67

115

163

211

259

307

355

403

451

5

24

72

119

168

216

263

312

360

408

456

6

29

76

124

173

221

268

317

365

413

461

7

33

81

129

178

225

273

321

369

417

465

8

38

86

134

182

230

278

326

374

422

470

9

43

91

139

187

235

283

331

379

427

475

10

48

96

144

192

240

288

336

384

432

480

CIRCUMFERENCE OF WHEEL, 11.1 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

5

52

100

147

195

243

290

338

386

433

2

10

57

104

152

200

248

295

343

390

438

3

14

62

109

157

205

252

300

347

395

443

4

19

66

114

161

209

257

305

352

400

447

5

24

71

119

166

214

262

309

357

405

452

G

29

76

124

171

219

267

314

362.

409

457

7

33

81

129

176

224

271

319

367

414

462

8

38

85

133

180

229

276

324

371

419

466

9

43

90

138

185

233

281

328

376

424

471

10

48

95

143

190

238

286

333

381

428

476

CIRCUMFERENCE OF WHEEL, 11.2 FEET.

0

0

10

20

30

40

50

60

70

SO

90

1

5

52

99

146

193

240

287

334

382

429

2

9

57

104

151

198

245

292

339

386

434

3

14

62

108

155

203

250

297

344

391

438

4

19

66

113

160

207

255

302

348

396

443

5

24

71

117

165

212

259

307

353

400

447

0

28

. 76

122

169

217

264

312

358

405

452

7

33

80

127

174

222

269

316

363

410

456

8

38

84

' 132

179

226

274

321

367

. 415

461

9

42

89

137

184

231

278

326

372

419

466

10

47

94

141

188

236

283

330

377

424

471
136 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 24. Converting wheel revolutions into hundredths of a mile Continued.

CIRCUMFERENCE OF WHEEL, 11.3 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

5

51

98

145

191

238

285

332

378

425

. 2

9

56

103

150

196

243

290

336

383

430

3

14

61

108

154

200

248

294

341

387

434

4

19

65

112

159

205

252

299

346

392

439

5

23

70

117

164

210

.257

304

350

397

444

6

28

74

122

168

215

261

308

355

402

448.

7

33

79

126

173

220

266

313

360

406

453

8

37

83

131

178

224

271

318

364

411

458

9

42

88'

135

183

229

276

322

370

416

462

10

47

93

140

187

234

280

327

374

420

467

CIRCUMFERENCE OF WHEEL, 11.4 FEET.

0

0

10

20

30

40

50

60

70

80

90

l

5

50

97

143

190

236

282

329

375

421

2

9

56

102

148

195

241

287

333

380

426

3

14

60

107

152

199

245

291

338

384

431

4

18

65

111

157

204

250

296

343

389

435

5

23

69

116

162

208

255

301

347

394

440

6

28

74

120

167

213

259

306

352

398

445

7

32

79

125

171

217

264

310

357

403

449

8

37

83

129

176

222

269

315

361

407

454

9

42

88

134

180

227

273

319

366

412

458

10

46

93

139

185

231

278

324

370

417

463

CIRCUMFERENCE OF WHEEL, 11.5 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

5

50

96

142

188

234

280

326

372

418

2

9

55

101

147

193

239

285

331

377

422

3

14

59

105

151

197

243

289

335

381

427

4

18

63

110

156

202

248

294

340

386

432

5

23

68

114

161

207

252

298

344

390

436

6

28

72

119

165

211

257

303

349

395

441

7

32

77

124

170

216

262

308

353

399

445

8

37

82

128

174

220

266

312

358

404

450

9

41

'87

133

179.

225

271

317

363

409

454

10

46

92

138

184

229

275

321

367

413

459
GEOGRAPHIC TABLES AND FORMULAS. 137

TABLE 24. Comerting wheel revolutions into hundredths of a mile Continued.

CIRCUMFERENCE OF WHEEL, 11.6 FEET.

0

0

10

20

30

40

50

GO

70

80

90

1

5

50

96

141

187

232

. 278

323

369

414

2

9

55

100

146

191

237

282

328

373

419

3

14

59

104

150

196

241

287

332

378

423

4

18

64

109

155

200

246

291

337

382

428

5 

23

68

114

159

205

250

296

341

387

. 432

6

27

73

118

164

209

255

300

346

391

437

7

32

77

123

168

214

259

305

350

396

441

8

36

82

127

173

218

264

309

355

400

446

9

41

87

132

178

223

269

314

360

405

450

10

46

91

136

182

227

273

318

364

410

455

CIRCUMFERENCE OF WHEEL, 11.7 FEET.

0

0

10

20

30

40

50

GO

70

80

90

1

5

50

95

140

185

230

275

320

365

410

2

9

54

99

144

189

235

280

325

370

415

3

13

59

104

149

194

239

284

329

374

419

4

18

63

108

153

198

244

289

334

379

424

5

23

68

113

158

203

248

293

338

383

428

6

27

72

117

162

207

253

298

343

. 388

433

7

32

77

122

167

212

257

302

347

392

437

8

36

81

126

171

217

262

307

352

397

442

9

41

86

131

176

221

266

311

356

401

446

10

45

90

135

180

225

271

316

361

406

451

CIRCUMFERENCE OF WHEEL, 11.8 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

4

49

94

139

183

228

273

317

362

407

o

9

53

 98

143

187

. 232

277

321

367

411

3

13

58

103

148

192

237

282

326

372

416

4

18

62

107

152

197

241

286

330

376

420

5

22

67

112

157

201

246

291

335

380

425

G

27

72

116

161

206

250

295

339

385

429

7

32

76

121

165

210

255

300

344

389

434

'8

36

80

125

170

215

259

304

348

393

438

9

40

85

130

174

219

264

309

353

398

443

10

45

89

134

179

223

268

313

358

402

447
138 GEOGRAPHIC TABLES AtfD FORMULAS.

TABLE 24. Converting wheel revolutions into hundredths of a mile Continued.

CIRCUMFERENCE OF WHEEL, 11.9 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

4

49

93

138

182

226

271

315

360

404

2

9

53

98

142

187

231

275

320

364

409

3

13

58

102

146

191

235

280

324

369

413

4

18

62

107

151

195

240

284

329

373

417

5

22

67

111

155

200

244

289

333

377

422

6

27

71

115

160

204

249

293

338

382

426

7

31

76

120

164

209

253

298

342

386

431

8

35

80

124

169

213

258

302

346

391

435

9

40

84

129

173

218

262

306

350

395

440

10

44

89

133

178

222

266

311

355

399

444

CIRCUMFERENCE OF WHEEL, 12 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

4

48

91

136

180

224

268

312

356

400

2

9

53

96

141

185

229

273

317

361

405

3

13

57

100

145

189

233

277

321

365

409

4

18

62

104

150

194

238

281

326

370

414

5

22

66

109

154

198

242

286

330

374

418

6

26

70

113

158

202

246

290

334

378

422

7

31

75

118

163

207

251

295

339

383

427

8

35

79

122

168

211

255

299

343

388

431

9

40.

84

128 .

172

216

260

304

348

392

436

10

44

88

132

176

220

264

308

352

396

440

CIRCUMFERENCE OF WHEEL, 12.1 FEET.

0

0

10

20

30

40

50

60

70

80

90

1

4

48

91

135

178

222

266

310

353

397

2

9

53

96

139

183

227

270

314

358

401

3

13

57

100

144

187

231

275

318

362

405

4

17

61

105

148

192

235

279

323

366

410

5

22

66

109

153

196

240

283

327

370

414

6

26

70

113

157

201

244

288

331

375

419

7

31

75

118

161

205

249

292

336

379

423

8

35

79

122

165

209

253

296

340

384

427

9

39

83

 126

170

214

257

301

344

388

432

10

44

87

131

174

218

262

305

349

392

436
GEOGRAPHIC TABLES AND FORMULAS. 139

TABLE 24. Converting wheel revolutions into hundredths of a mile Continued. 

CIRCUMFERENCE OP WHEEL, 12.2 FEET.

0

0

10

20

30

40

50

60

70

80

iiO

1

4

48

91

134

178

221

264

307

351

395

2

9

52

95

138

182

225

268

312

356

399

3

13

56

100

143

186

230

273

316

359

404

4

17

61

104

147

191

234

277

320

364

408

5

 22

65

108

151

195

238

281

325

368

412

G

26

69

113

156

199

243

7

30

74

117

160

204

247

286

329

372

417

290

333

377

421

8

35

78

121

165

208

251

294

338

381

425

9

39

82

126

169

212

256

299

342

385

429

10

43

87

130

173

216

260

303

346

390

433

After measuring wheel use nearest tenth for size of wheel.
140 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 25. Five-place logarithms of natural numbers.

[Fractional change in a number corresponding to a change in its logarithm.]

Computed from the formula,

AN A log N 

N ~ 'ju '

y/u=rnodulus of common logarithms = 0.43429448.

For 

A log N 

= 1 unit in

Fifth place ...........

Sixth place ...........

Seventh place. ........

6.N

N

*?v?

¥¥??? 

¥¥?V?¥

For 

A log N 

= 4 units in

Fifth place ...........

Sixth place ...........

Seventh place .........

AJV 

N 

(in round 

numbers)
GEOGRAPHIC TABLES AND FORMULAS.

 TABLE 25. Five-place logarithms of natural numbers Continued.

141

N.

0

1 

2 

3

4 

5 

6

7 

8 

9

10

11 

12 

13

14

15

16

17 

18 

19

20

21 

22 

23

24 

25 

26

27 

28 

29

30

31 

32 

33

34 

35 

36

37 

38 

39

.40

41

42 

43

44 

45 

46

47 

48 

49

60

N.

L. 0 12 3 4

00 000 30 103 47 712 60 206

00 000 04 139 07 918 11 394 14 613 

30 103 32 222 34 242 36 173 38 021 

47 712 49 136 50 515 51 851 53 148

60 206 61 278 62 325 63 347 64 345 

69 897 70 757 71 600 72 428 73 239 

77 815 78 533 79 239 79 934 80 618

84 510 85 126 85 733 86 332 86 923 

90 309 90 849 91 381 91 908 92 428 

95 424 95 904 96 379 96 848 97 313

00 000 00 432 00 860 01 284 01 703

04 139 04 532 04 922 05 308 05 690 

07 918 08 279 08 636 08 991 09 342 

11 394 11 727 12 057 12 385 12 710

14 613 14 922 15 229 15 534 15 836 

17 609 17 898 18 184 18 469 18 752 

20 412 20 683 20 952 21 219 21 484

23 045 23 300 23 553 23 805 24 055 

25 527 25 768 26 007 26 245 26 482 

27 875 28 103 28 330 28 556 28 780

30 103 30 320 30 535 30 750 30 963

32 222 32 428 32 634 32 838 33 041 

34 242 34 439 34 635 34 830 35 025 

36 173 36 361 36 549 36 736 36 922

38 021 38 202 38 382 38 561 38 739 

39 794 39 967 40 140 40 312 40 483 

41 497 41 664 41 830 41 996 42 160

43 136 43 297 43 457 43 616 43 775 

44 716 44 871 46 025 45 179 45 332 

46 240 46 389 46 538 46 687 46 835

47 712 47 857 48 001 48 144 48 287

49 136- 49 276 49 415 49 654 49 693 

50 515 50 651 50 786 50 920 61 055 

51 851 51 983 52 114 52 244 52 375

53 148 53 275 53 403 53 529 53 656 

54 407 54 531 54 654 54 777 54 900 

55 630 65 751 55 871 55 991 56 110

56 820 56 937 57 054 57 171 57 287 

57 978 58 092 58 206 58 320 58 433 

59 106 69 218 59 329 59 439 59 550

60 206 60 314 60 423 60 531 60 638

61 278 61 384 61 490 61 595 61 700 

62 325 62 428 62 531 62 634 62 737 

63 347 63 448 63 548 63 649 63 749

64 345 64 444 64 642 64 640 64 738 

65 321 65 418 65 514 65 610 65 706 

66 276 66 370 66 464 66 658 66 652

67 210 67 302 67 394 67 486 67 578 

68 124 68 215 68 305 68 395 68 485 

69 020 69 108 69 197 69 285 69 373

69 897 69 984 70 070 70 157 70 243

L. 0 1 2 3 4

56789

69 897 77 815 84 510 90 309 95 424

17 609 20 412 23 045 25 627 27 875 

39 794 41 497 43 136 44 716 46 240 

54 407 55 630 56 820 67 978 59 106

65 321 66 276 67 210 68 124 69 020 

74 036 74 819 75 587 76 343 77 085 

81 291 81 954 82 607 83 251 83 885

87 606 88 081 88 649 89 209 89 763 

92 942 93 450 93 952 94 448 94 939 

97 772 98 227 98 677 99 123 99 564

02 119 02 631 02 938 03 342 03 743

06 070 06 446 06 819 07 188 07 555 

09 691 10 037 10 380 10 721 11 059 

13 033 13 354 13 672 13 988 14 301

16 137 16 435 16 732 17 026 17 319 

19 033 19 312 19 590 19 866 20 140 

21 748 22 Oil 22 272 22 531 22 789

24 304 24 651 24 797 26 042 25 285 

26 717 26 951 27 184 27 416 27 646 

29 003 29 226 29 447 29 667 29 885

31 175 31 387 31 597 31 806 32 015

33 244 33 445 33 646 33 846 34 044 

35 218 35 411 35 603 35 793 35 984 

37 107 37 291 37 475 37 658 37 840

38 917 39 094 39 270 39 445 39 620 

40 654 40 824 40 993 41 162 41 330 

42 325 42 488 42 651 42 813 42 975

43 933 44 091 44 248 44 404 44 560 

45 484 45 637 45 788 45 939 46 090 

460 982 47 129 47 276 47 422 47 567

48 430 48 572 48 714 48 855 48 996

49 831 49 969 60 106 50 243 50 379 

51 188 51 322 51 455 51 587 51 720 

52 504 -52 634 52 763 62 892 63 020

53 782 53 908 54 033 54 158 54 283 

65 023 55 145 65 267 55 388 55 509 

56 229 56 348 56 467 56 685 56 703

57 403 57 519 57 634 57 749 57 864 

58 546 58 659 58 771 58 883 58 995 

59 660 59 770 59 879 59 988 60 097

60 746 60 853 60 969 61 066 61 172

61 805 61 909 62 014 62 118 62 221 

62 839 62 941 63 043 63 144 63 246 

63 849 63 949 64 048 64 147 64 246

64 836 64 933 65 031 65 128 65 225 

65 801 65 896 65 992 66 087 66 181 

66 745 66 839 66 932 67 025 67 117

67 669 67 761 67 852 67 943 68 034 

68 574 68 664 68 753 68 842 68 931 

69 461 69 548 69 636 69 723 69 810

70 329 70 415 70 501 70 586 70 672

5 6 7 8-9

0° 1'= 60" S. 4. 68 557 T. 4. 68 557 0° 5' =300" S. 4. 68 557 T. 4. 68 558 

0 2 =120 4. 68 657 4. 68 557 0 6 =360 4. 68 557 4. 68 558 

0 3 =180 4. 68 557 4. 68 557 0 7 =420 4. 68 557 4. 68 558 

0 4 = 240 4. 68 657 4. 68 558 08= 480 4. 68 557 4. 68 558
142 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

50

51 

52 

53

54 

55 

56

57 

58 

59

60

61 

62 

63

64 

65 

66

67 

68 

69

70

71

72 

73

74 

75 

76

77 

78 

79

80

81 

82 

83

84 

85 

86

87 

' 88 

89

90

91 

92 

93

94 

95 

96

97 

98 

99

100

N.

L. 0 1 2 3 4

69 897 69 984 70 070 70 157 70 243

70 757 70 842 70 927 71 012 71 096 

71 600 71 684 71 767 71 850 71 933 

72 428 72 509 72 591 72 673 72 754

73 239 73 320 73 400 73 480 73 560 

74 036 74 115 74 194 74 273 74 351 

74 819 74 896 74 974 75 051 75 128

75 587 75 664 75 740 75 815 75 891 

76 343 76 418 76 492 76 567 76 641 

77 085 77 159 77 232 77 305 77 379

77 815 77 887 77 960 78 032 78 104

78 633 78 604 78 675 78 746 78 817 

79 239 79 309 79 379 79 449 79 518 

79 934 80 003 80 072 80 140 80 209

80 618 80 686 80 754 80 821 80 889 

81 291 81 358 81 425 81 491 81 558 

81 954 82 020 82 086 82 151 82 217

82 607 82 672 82 737 82 802 82 866 

83 251 83 315 83 378 83 442 83 506 

83 885 83 948 84 Oil 84 073 84 136

84 510 84 572 84 634 84 696 84 757

85 126 85 187 85 248 85 309 85 370 

85' 733 85 794 85 854 85 914 85 974 

86 332 86 392 86 451 86 510 86 570

86 923 86 982 87 040 87 099 87 157 

87 506 87 564 87 622 87 679 87 737 

88 081 88 138 88 195 88 252 88 309

88 649 88 705 88 762 88 818 88 874 

89 209 89 265 89 321 89 376 89 432 

89 763 89 818 89 873 89 927 89 982

90 309 90 363 90 417 90 472 90 526

90 849 90 902 90 956 91 009 91 062 

91 381 91 434 91 487 91 540 91 593 

91 908 91 960 92 012 92 065 92 117

92 428 92 480 92 531 92 583 92 634 

92 942 92 993 93 044 93 095 93 146 

93 450 93 500 93 551 93 601 93 651

93 952 94 002 94 052 94 101 94 151 

94 448 94 498 94 547 94 596 94 645 

94 939 94 988 95 036 95 085 95 134

95 424 95 472 95 521 95 569 95 617

95 904 95 952 95 999 96 047 96 095 

96 379 96 426 % 473 96 520 96 567 

96 848 96 895 96 942 96 988 97 035

97 313 97 359 97 405 97 451 97 497 

97 772 97 818 97 864 97 909 97 955 

98 227 98 272 98 318 98 363 98 408

98 677 98 722 98 767 98 811 98 856 

99 123 99 167 99 211 99 255 99 300 

99 564 99 607 99 651 99 695 99 739

00 000 00 043 00 087 00 130 00 173

L. 0 1 2 3 4

56789

70 329 70 415 70 501 70 586 70 672

71 181 71 265 71 349 71 433 71 517 

72 016 72 099 72 181 72 263 72 346 

72 835 72 916 72 997 73 078 73 159

73 640 73 719 73 799 73 878 73 957 

74 429 74 507 74 586 74 663 74 741 

75 205 75 282 75 358 75 435 75 511

75 967 76 042 76 118 76 193 76 268 

76 716 76 790 76 864 76 938 77 012 

77 452 77 525 77 597 77 670 77 743

78 176 78 247 78 319 78 390 78 462

78 888 78 958 79 029 79 099 79 169 

79 588 79 657 79 727 79 796 79 865 

80 277 80 346 80 414 80 482 80 550

80 956 81 023 81 090 81 158 81 224 

81 624 81 690 81 757 81 823 81 889 

82 282 82 347 82 413 82 478 82 543

82 930 82 995 83 059 83 123 83 187 

83 569 83 632 83 696 83 759 83 822 

84 198 84 261 84 323 84 386 84 448

84 819 84 880 84 942 85 003 85 065

85 431 85 491 85 552 85 612 85 673 

86 034 86 094 86 153 86 213 86 273 

86 629 86 688 86 747 86 806 86 864

87 216 87 274 87 332 87 390 87 448 

87 795 87 852 87 910 87 967 88 024 

88 366 88 423 88 480 88 536 88 593

88 930 88 986 89 042 89 098 89 154 

89 487 89 542 89 597 89 653 89 708 

90 037 90 091 90 146 90 200 90 255

90 580 90 634 90 687 90 741 90 795

91 116 91 169 91 222 91 275 91 328 

91 645 91 698 91 751 91 803 91 855 

92 169 92 221 92 273 92 324 92 376

92 686 92 737 92 788 92 840 92 891 

93 197 93 247 93 298 93 349 93 399 

93 702 93 752 93 802 93 852 93 902

94 201 94 250 94 300 94 349 94 399 

94 694 94 743 94 792 94 841 94 890 

95 182 95 231 95 279 95 328 95 376

95 665 95 713 95 761 95 809 95 856

96 142 96 190 96 237 96 284 96 332 

96 614 96 661 96 708 96 755 96 802 

97 081 97 128 97 174 97 220 97 267

97 543 97 589 97 635 97 681 97 727 

98 000 98 046 98 091 98 137 98 182 

98 453 98 498 98 543 98 588 98 632

98 900 98 945 98 989 99 034 99 078 

99 344 99 388 99 432 99 476 99 520 

99 782 99 826 99 870 99 913 99 957

00 217 00 260 00 303 00 346 00 389

56789

0° 9' = 540" S. 4. 68 557 T. 4. 68 558 0° 13' = 780" S. 4. 68 557 T. 4. 68 558 

0 10 = 600 4. 68 557 4. 68 558 0 14 = 840 4. 68 557 4. 68 558 

0 11 = 660 4. 68 557 4. 68 558 0 15 = 900 4. 68 557 4. 68 558 

0 12 =720 4. 68 557 4. 68 558 0 16 =960 4. 68 557 4. 68 558
GEOGRAPHIC TABLES AND FORMULAS. 143

TABLE 25. Five-place logarithms of natural numbers Continued.'

N,

100

101

102

103

104 

105 

106

107 

108 

109

110

111

112

113

114 

115 

116

117 

118 

119

120

121

122

123

124 

125 

126

127 

128 

129

130

131

132 

133

134 

135 

136

137 

138 

139

140

141

142

143

144 

145 

146

147 

148 

149

150

N:

L. 0 1 2 3 4

00 000 043 087 130 173

432 475 518 5G1 604

860 903 945 988 #030

01 284 326 368 410 452

703 745 787 828 870 

02 119 160 202 243 284 

531 672 612 653 694

938 979 #019 #060 #100 

03 342 383 423 463 503 

743 782 822 862 902

04 139 179 218 258 297

532 571 610 650 .689

922 961 . 999 #038 #077

05 308 346 385 423 461

690 729 767 805 843 

06 070 108 145 183 221 

446 483 521 658 595'

819 856 893 930 967 

07 188 225 262 298 335 

555 591 628 664 700

918 954 990 #027 #063

08 279 314 350 386 422

636 672 707 743 778

991 #026 #061 #096 #132

09 342 377 412 447 482 

691 726 760 795 830 

10 037 072 106 140 175

380 415 449 483 517 

721 765 789 823 857 

11 059 093 ]26 160 193

394 428 461 494 528

727 760 793 826 860

12 057 090 123 156 189 

385 418 450 483 616

710 743 775 808 840 

13 033 066 098 130 162 

354 386 418 450 481

672 704 735 767 799 

988 #019 #051 #082 #114 

14 301 333 364 395 426

613 644 675 706 737

922 953 983 #014 #045

15 229 259 290 320 351

534 564 594 625 655

836 866 897 927 957 

16 137 167 197 227 256 

435 465 495 624 554

732 761 791 820 850 

17 026 056 085 114 143 

319 348 377 406 435

609 638 667 696 725

L. 0 1 2 3 4

56789

217 260 303 346 389

647 689 732 775 817

#072 #115 #157 #199 #242

494 536 578 620 662

912 953 995 #036 #078 

325 366 407 449 490 

735 776 816 857 898

#141 #181 #222 #262 #302 

543 683 623 663 703 

941 981 #021 #060 #100

336 376 415 454 493

727 766 805 844 883

#115 #154 #192 #231 #269

500 538 576 614 652

881 918 956 994 #032 

258 296 333 371 408 

633 670 707 744 781

#004 #041 #078 #115 #151 

372 408 445 482 518 

737 773 809 846 882

,099 #135 #171 #207 #243

458 493 529 565 600

814 849 884 920 955

#167 #202 #237 #272 #307

517 552 587 621 656 

864 899 934 968 #003 

209 243 278 312 346

551 585 619 653 687 

890 924 958 992 #025 

227 261 294 327 361

561 594 628 661 694

893 926 959 992 #024

222 254 287 320 352 

548 581 613 646 678

872 905 937 969 #001 

194 226 258 290 322 

513 645 577 609 640

830 862 893 925 956 

#145 #176 #208 #239 #270 

457 489 520 551 582

768 799 829 860 891

#076 #106 #137 #168 #198

381 41? 442 473 503

685 715 746 776 806

987 #017 #047 #077 #107 

286 316 346 376 406 

584 613 643 673 702

879 909 938 967 997 

173 202 231 260 289 

464 493 522 551 580

754 782 811 840 869

56789

P. P.

44 43 42

2

3 

4 

5 

6

7 

8 

9

8,8 8,6 8,4

13,2 12,9 12,6 

17,6 17,2 16,8 

22,0 21,5 21,0 

26,4 25,8 25,2

30,8 30,1 29,4 

35,2 34,4 33,6 

39,6 38,7 37,8

41 40 30

1

2

3 

4 

5 

6

7 

8 

9

4,1 4,0 3,9

 8,2 8,0 7,8

12,3 12,0 11,7 

16,4 16,0 15,6 

20,5 20,0 19,5 

24,6 24,0 23,4

28,7 28,0 27,3 

32,8 32,0 31,2 

36,9 36,0 35,1

38 37 36

1

2

3 

4 

5 

6

7 

8 

9

3,8 3,7 3,6

7,6 7,4 7,2

11,4 11,1 10,8 

15,2 -14,8 14,4 

19,0 18,5 18,0 

22,8 22,2 21,6

26,6 25,9 25,2 

30,4 29,6 28,8 

34,2 33,3 32,4

35 34 33

1 

2

3 

4 

5 

6

7 

8 

9

3,6 3,4 3,3 

7,0 6,8 6,6

10,5 10,2 9,9 

14,0 13,6 13,2 

17,5 17,0 16,5 

21,0 20,4 19,8

24,5 23,8 23,1 

28,0 27,2 26,4 

31,5 30,6 29,7

32 31 30

1

2

0

4 

5 

6

7 

8 

9

3,2 3,1 3,0

6,4 6,2 6,0

n e no nn

12,8 12,4 12,0

16,0 15,5 15,0 

19,2 18,6 18,0

22,4 21,7 21,0 

25,6 24,8 24,0 

28,8 27,9 27,0

P. P.

0° 16' = 960" S. 4. 68 557 T. 4. 68 558 0° 21' = 1260" S. 4. 68 557 T. 4. 68 558

0 17 = 1020 4. 68 557 4. 68 558 0 22 = 1320 4. 68 557 4. 68 558

0 18 = 1080 4. 68 557 4. 68 558 0 23 = 1380 4. 68 557 4. 68 558

0 19 = 1140 4. 68 557 4. 68 558 0 24 = 1440 4. 68 557 4. 68 558

0 20 = 1200 4. 68 557 4. 68 558 0 25 = 1500 4. 68 557 4. 68 568
144 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

150

151 

152 

153

154 

155 

156

157 

. 158 

159

160

161 

162 

163

164 

165 

166

167 

168 

169

170

171 

172 

173

174

176 

176

177 

178 

179

180

181 

182 

183

184 

185 

186

187 

188 

189.

190

191 

192 

193

194 

195 

196

197 

198 

199

.200

N.

L. 0 1 2 3 4

17 609 638 667 696 725

898 926 955 984 *013 

18 184 213 241 270 298 

469 498 526 554 583

752 780 808 837 865 

19 033 061 089 117 145 

312 340 368 396 424

590 618 645 673 700 

866 893 921 948 976 

20 140 ' 167 194 222 249

412 439 466 493 520

683 710 737 763 790 

952 978 *005 *032 *059 

21 219 245 272 299 325

484 511 537 564 590 

748 775 801 827 854 

22 Oil 037 063 089 115

272 298 324 350 376 

531 557 583 608 634 

789 814 840 866 891

23 045 070 096 121 147

300 325 350 376 401 

553 578 603 629 654 

805 830 855 880 905

24055 080 105 130 155 

304 329 353 378 403 

651 576 601 625 650

797 822 846 871 895 

25 042 066 091 115 139 

285 310 334 358 3S2

527 551 575 600 624

768 792 816 840 864 

26 007 031 055 079 102 

245 269 293 316 340

482 505 529 553 576 

717 741 764 788 811 

961 975 998 *021 *045

27 184 207 231 264 277 

416 439 462 48§ 508 

646 669 692 715 738

875 898 921 944 967

28 103 126 149 171 194 

330 353 375 398 421 

556 578 601 623 646

780 803 825 847 870 

29 003 026 048 070 092 

226 248 270 292 314

447 469 491 513 535 

667 688 710 732 754 

885 907 929 951 973

30 103 125 146 168 190

L. 0 1 2 3 4

5 6 7 89

754 782 811 840 869

*041 *070 *099 *127 *156 

327 355 384 412 441 

611 639 667 696 724

893 921 949 977 $005 

173 201 229 257 285 

451 479 507 535 562

728 756 783 811 838 

*003 *030 *058 #085 *112 

276 303 330 358 385

548 575 602 629 656

817 844 871 898 925 

*085 *112 *139 *165 *192 

352 378 405 431 458

617 643 669 696 722 

880 906 932 958 985 

141 167 194 220 246

401 427 453 479 505 

660 686 712 737 763 

917 943 968 994 *019

172 198 223 249 274

426 452 477 502 528 

679 704 729 754 779 

930 955 980 *005 *030

180 204 229 254 279 

428 452 477 502 527 

674 699 724 748 773

920 944 969 993 *018 

164 188 212 237 261 

406 431 455 479 503

648 672 696 720 744

888 912 935 959 983 

126 150 174 198 221 

364 387 411 435 458

600 623 647 670 694 

834 858 881 905 928 

*068 *091 *114 438 *161

300 323 346 370 393

531 554 577 600 623 

761 784 807 830 852

989 *012 *035 *058 *081

217 240 262 285 307 

443 466 488 511 533 

668 691 713 735 758

892 914 937 959 981 

115 137 159 181 203 

336 358 380 403 425

557 579 601 623 645 

776 798 820 842 863 

994 *016 *038 #060 *081

211 233 255 276 298

56789

P. P.

1 

2 

3 

4 

5 

6 

7 

8 

9

1

2 

3 

4 

5 

6 

7 

8 

9

1 

2 

3 

4 

5 

6 

7 

8 

9

1 

2 

3 

4 

5 

6 

7 

8 

9

29 28

2,9 2,8 

5,8 5,6 

8,7 8,4 

11,6 11,2 

14,5 14,0 

17,4 16,8 

20,3 19,6 

23,2 22,4 

26,1 25,2

27 26

2,7 2,6 

5,4 5,2 

8,1 7,8 

10,8 10,4 

13,5 13,0 

16,2 15,6 

18,9 18,2 

21,6 20,8 

24,3 23,4

25

1 2,5 

2 5,0 

3 7,5 . 

4 10,0 

5 12,5 

6 15,0 

7 17,5 

8 20,0 

9 22,5

24 28

2,4 2,3 

4,8 4,6 

7,2 6,9 

9,6 9,2 

12,0 11,5 

14,4 13,8 ' 

16,8 16,1 

19,2 18,4 

21,6 20,7

22 21

2,2 2,1 

4,4 4,2 

6,6 6,3 

8,8 8,4 

11,0 10,5 

13,2 12,6 

15,4 14,7 ' 

17,6 16,8 

19,8 18,9

P. P.

0° 25' = 1500" S. 4. 68 657 T. 4. 68 558 0° 30' = 1800" S. 4. 68 557 T. 4. 68 559 

0 26 = 1560 4. 68 557 4. 68 558 0 31 = 1860 4. 68 557 4. 68 559 

0 27 = 1620 4. 68 557 4. 68 558 0 32 = 1920 4. 68 557 4. 68 559 

0 28 = 1680 4. 68 557 4. 68 558 0 33 = 1980 4. 68 557 4. 68 559 

0 29 = 1740 4. 68 557 4. 68 558 0 34 = 2040 4. 68 657 4. 68 559
GEOGRAPHIC TABLES AND FORMULAS. 145 

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

200

201

202

203

204 

205 

206

207 

208 

209

210

211

212

213

214

215

216

217 

218

219

220

221

222

223

224

226

226

227

228

229

230

231

232

233

234 

235

236

237

238

239

240

241

242

243

244

245

246

247 

248

249

260

.N.

L. 0 1 2 3 4

30 103 125 146 168 190

320 341 363 384 406

535 557 578 600 621

750 771 792 814 835

963 984 *006 *027 *048 

31 175 197 218 239 260 

.387 408 429 450 471

597 618 639 660 681 

806 827 848 869 890 

32 015 035 056 077 098

222 243 263 284 305

428 449 469 490 510

634 654 675 695 715

838 858 879 899 919

33 041 062 082 102 122

244 264 284 304 325

445 465 486 506 526

646 666 686 706 726 

846 866 885 905 925

34 044 064 084 104 124

242 262 282 301 321

439 459 479 498 518

635 655 674 694 713

' 830 850 869 889 908

35 025 044 064 083 102

218 238 257 276 295

411 430 449 468 488

603 622 641 660 679

793 813 832 851 870

984 *003 *021 ,,,040 *059

36 173 192 211 229 248

361 380 399 418 436

549 568 586 605 624

736 754 773 791 810

922 940 959 977 996 

37 107 125 144 162 181

291 310 328 346 365

475 493 511 530 548

658 676 694 712 731

840 858 876 894 912

38 021 039 057 075 093

202 220 238 256 274

382 399 417 435 453

561 578 596 614 632

739 757 775 792 810

917 934 952 970 987

39 094 111 129 146 164

270 287 305 322 340 

445 463 480 498 515

620 637 655 672 690

794 811 829 846 863

L. 0 1 2 3 4

5

211

428

643

856

*069 

281 

492

702 

911 

118

326

531

736

940

143

345

546

746 

945

143

341

537

733

928

122

315

507

698

889

6789

233 255 276 298

449 47} 492 514

664 685 707 728

878 899 920 942

,091- ,112 *133 *154 

302 323 345 366 

613 534 555 576

723 744 765 785 

931 952 973 994 

139 160 181 201

346 366 387 408

552 572 593 613

756 777 797 818

960 980 *001 *021

163 183 203 224

365 385 405 425

566 586 606 626

766 786 806 826 

965 985 *005 *025

163 183 203 223

361 380 400 420

557 577 596 616

753 772 792 811

947 967 986 »005

141 160 180 199

334 353 372 392

526 545 564 583

717 736 755 774

908 927 946 965

*078 *097 *116 *135' *154

267

455

642

829

286 305 324 342

474 493 511 530

661 680 698 717

847 866 884 903

*014 *033 *051 *070 *088 

199 218 236 254 273

383

566

749

931

112

292

471

650

828

401 420 438 457

585 603 621 639

767 785 803 822

949 967 985 *003

130 148 166 184

310 328 346 364

489 507 525 543

668 686 703 721

846 863 881 899

*005 *023 *041 #058 *076

182

358 

533

707

881

5

0° 33' = 1980" S. 4. 68 557 T. 4. 68 559

0 34 =2040 4. 68 557 4. 68 569

0 35 =2100 4. 68 557 4. 68 659

0 36 = 2160 4.. 68 557 4. 68 559

0 37 = 2220 4. 68 557 4. 68 559

199 217 235 252

375 393 410 428 

550 668 585 602

724 742 759 777

898 915 933 950

6789

P. P.

22 21

1 2,2 2,1

2 4,4 4,2

3 6,6 6,3 

. 4 8,8 8,4 

5 11,0 10,5 

6 13,2 12,6

7 15,4 14,7 

8 17,6 16,8 

9 19,8 18,9

20

J O A

2

3 

4

co

6

7 

8

g

4/0

6,0

mo

12,0

14,0 

16,0

1S.A *"'"

19

1 1 °

2

3

4

5

6

7

3,8

6,7 

7,6

11/4

13,3 

15,2

IT 1 i "i

18

1 i.s

2

3 

4 

5

6

7

g

3,6

5,4 

7,2 

9/0

10,8

12,6 

14,4

lfi.9.

17

1 1-7

2

3 

4

5

6

7 

8 

g

3,4

5,1 

6,8

8,5

10,2

11,9 

13,6 

15.3

P. P.

0° 38' = 2280" S. 4. 68 557 T. 4. 68 659

0 39 = 2340 4. 68 557 4. 68 559

0 40 = 2400 4. 68 557 4. 68 559

0 41 = 2460 4. 68 556 4. 68 560

0 42 = 2520 4. 68 656 4. 68 660

41623° 16 10
146 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

250

251 

252 

253

254 

255 

256

257 

258 

259

260

261 

262 

263

264 

265 

266

267 

268 

269

270

271 

272 

273

274 

275 

276

277 

278 

279

280

281 

282 

283

284 

285 

286

287 

288 

289

290

291 

292 

293

294 

295 

296

297 

298 

299

300

N.

L. 0 1 2 3 4

39 794 811 829 846 863

967 985 *002 #019 *037 

40 140 157 175 192 209 

312 329 346 364 381

483 500 618 53§ 552 

654 671 688 705 722 

824 841 858 875 892

993 #010 *027 ^044 *061 

41 162 179 196 212 229 

330 347 363 380 397

497 514 531 547 564

664 681 697 714 731 

830 847 863 880 896 

996 *012 *029 *045 *062

42 160 177 193 210 226 

325 341 357 374 390 

488 504 521 537 553

651 667 684 700 716 

813 830 846 862 878 

975 991 *008 *024 #040

43 136 152 169 185 201

297 313 329 345 361 

457 473 489 505 521 

616 632 648 664 680

775 791 807 823 838 

933 949 965 981 996 

44 091 107 122 138 164

248 264 279 295 311 

404 420 436 451 467 

560 576 592 607 623

716 731 747 762 778

871 886 902 917 932 

45 025 040 056 071 086 

179 194 209 225 240

332 347 362 378- 393 

484 500 515 530 545 

' 637 652 667 682 697

788 803 818 834 849 

939 954 969 984 *000 

46 090 105 120 135 150

240 255 270 285 300

389 404 419 434 449 

538 553 568 583 598 

687 702 716 731 746

835 850 864 879 894 

982 997 *012 .,,026 *041 

47 129 144 169 173 188

276 290 305 319 334 

422 436 451 465 480 

567 582 596 611 625

712 727 741 756 770

L. 0 12 3 4

5 6. 7 8 9

881 898 915 933 950

#054 *071 *088 *106 *123 

226 243 261 278 295 

398 415 432 449 466

569 580 603 620 637 

739 756 773 790 807 

909 926 943 960 976

*078 *095 *111 *128 *145 

246 263 280 296 313 

414 430 447 464 481

581 597 614 631 647

747 764 780 797 814 

913 929 946 963 979 

*078 *095 *111 *127 #144

243 259 275 292 308 

406 423 439 455 472 

670 586 602 619 635

732 749 765 781 797 

894 911 927 943 959 

*056 #072 *088 #104 *120

217 233 249 265 281

377 393 409 425 441 

537 553 569 584 600 . 

696 712 727 743 759

854 870 886 902 917 

#012 *028 *044 *059 *075 

170 185 201 217 232

326 342 358 373 389 

483 498 514 529 545 

638 654 669 685 700

793 809 824 840 855

948 963 979 994 *010 

102 117 133 148 163 

255 271 286 301 317

408 423 439 454 469 

561 576 591 606 621 

712 728 743 758 773

864 879 894 909 924 

*015 *030 #045 *060 *075 

165 180 195 210 225

315 330 345 359 374

464 479 494 509 523 

613 627 642 657 672 

761 776 790 805 820

909 923 938 953 967 

*056 *070 #085 *100 *114 

202 217 232 246 261

349 363 378 392 407 

494 509 524 538 553 

640 654 669 683 698

784 799 813 828 842

56789

P. P.

1 

2 

3 

4 

5 

6 

7 

8 

9

1 

2 

3 

4 

5 

6 

7 

8 

9

1 

2 

3

4 

5 

6 

7 

8 

9

1

2 

3 

4

5 

6 

7 

8 

9

1 

2 

3 

4 

5 

6 

7 

8 

9

18

1,8 

3,6 

5,4 

7,2 

9,0 

10,8 

12,6 

14,4 

16,2

17

1,7 

3,4 

5,1 

6,8 

8,5 

10,2 

11,9 

13,6 

15,3

16

1,6 

3,2 

4,8 

6,4 

8,0 

9,6 

11,2 

12,8 

14,4

15

1,5 

3,0 

4,5 

6,0 

7,5 

9,0 

10,5 

12,0 

13,5

14

1,4 

2,8 

4,2 

5,6 

7,0 

8,4 

9,8 

11,2 

12,6

P. P.

0° 41' = 2460" S. 4. 68 556 T. 4. 68 560 0° 46' = 2760" S. 4. 68 556 T. 4. 68 560 

0 42 = 2520 4. 68 656 4. 68 560 0 47 = 2820 4. 68 656 4. 68 560 

0 43 = 2580 4. 68 556 4. 68 560 0 48 = 2880 4. 68 556 4. 68 560 

0 44 = 2640 4. 68 556 4. 68 560 0 49 = 2940 4. 68 556 4. 68 560 

0 45 = 2700 4. 68 556 4. 68 560 0 50 = 3000 4. 68 556 4. 68 561
GEOGKAPHIC TABLES AND FOBMULAS. 147

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

SOU

301

302

303

304

305

306

307

308

309

310

311

312

313

314

316

316

317

318

310

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

N.

L. 0 12 3 4

47 712 727 741 756 770

857 871 885 900 914

48 001 015 029 044 058

144 159 173 187 202

287 302 316 330 344

430 444 458 473 487

572 586 601 615 629

714 728 742 756 770

855 869 883 897 911

996 *010 #024 *038 *052

49 136 150 164 178 192

276 290 304 318 332

415 429 443 457 471

654 668 582 696 610

693 707 721 734 748

831 845 859 872 886

969 982 996*010*024

50 106 120 133 147 161

243 256 270 284 297

379 393 406 420 433

515 529 542 556 569

651 664 678 691 705

786 799 '813 826 840

920 934 947 961 974

51 055 068 081 095 108

188 202 215 228 242

322 335 348 362 375

455 468 481 495 508

587 601 614 627 640

720 733 746 759 772

851 865 878 891 904

983 996 *009 *022 *035

52 114 127 140 153 166

244 257 270 284 297

375 388 401 414 427

 504 517 530 543 656

634 647 660 673 686

763 776 789 802 815

892 905 917 930 943

53 020 033 046 058 071

148 161 173 186 199

275 288 301 314 326

403 415 428 441 453

529 542 555 5fi7 580

656 668 681 694 706

782 794 807 820 832

908 920 933 945 958

54033 045 058 070 083

158 170 183 195 208

283 295 307 320 332

407 419 432 444 456

L. 0 1 2 3 4

5

784

929

073

216

359

501

643

785

926

67 8 9

799 813 828 842

943 958 972 986

087 101 116 130

230 244 259 273

373 387 401 416

515 530 544 558

657 671 686 700

799 813 827 841

940 954 968 982

*066 *080 *094 #108 *122

206

346

485

624

762

900

220 234 248 262

360 374 388 402

499 513 527 641

638 651 665 679

776 790 803 817

914 927 941 955

*037 #051 *065 *079 *092

174

311

447

583

718

853

188 202 215 229

325 338 352 365

461 474 488 501

596 610 623 637

732 745 759 772

866 880 893 907

987 #001 *014 *028 *041

121

265

388

521

654

786

917

135 148 162 175

268 282 295 308

402 415 428 441

534 548 561 574

667 680 693 706

799 812 825 838

930 943 957 970

*048 *061 *075 ,088 *101

179

310

440

569

699

827

956

084

212

839

466

693

719

845

970

095

220

345

469

5

0° 50' = 3000" S. 4. 68 556 T. 4. 68 561

0 51 = 3060 4. 68 556 4. 68 661

0 52 = 3120 4. 68 556 4. 68 561

0 53 = 3180 4. 68 556 4. 68 561

0 64 = 3240 4. 68 656 4. 68 661

192 205 218 231

323 336 349 362

453 466 479 492

582 595 608 621

711 724 737 750

840 853 866 879

969 982 994 ,007

097 110 122 135

224 237 250 263

352 364 377 390

479 491 504 517

605 618 631 643

732 744 757 769

857 870 882 895

983 995 *OOS *020

108 120 133 145

233 245 268 270

357 370 382 394

481 494 506 518

6789

P.P.

16

1

2

3

4

5

6

7

8

9

1/5

3,0

4,5

6,0

7,5

9,0 in ^ J-U/J

12,0

13,5

1A

,1

2

3

4 

5

6

7

8

9

1/4

2,8

4,2

5,6 

7,0

8,4

Q a y/o 

11,2

12,6

13

1

2

4

5 

6

7

8

9

1.3

2,6 

3,9

5,2

6,5

7 S /,o

9,1

10,4

11/7

12

1

2

3

4

5

6

7

8

9

1.2

2,4

3,6

4/8

6,0

7,2

8,4

9,6

10,8

P. P.

0° 55' = 3300" S. 4. 68 556 T. 4. 68 561

0 56 = 3360 4. 68 556 4. 38 561

0 57 = 3420 4. 68 555 4. 68 561

0 58 = 3480 4. 68 555 4. 68 562

0 59 = 3540 4. 68 555 4. 68 562
148 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382 

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

N.

L. 0 1 2 3 4

54407 419 432 444 456

531 543 555 568 580

654 667 679 691 704

777 790 802 . 814 827

900 913 925 937 949

55 023 035 047 060 072

145 157 169 182 194

267 279 291 303 315

388 400 413 425 437

509 522 534 546 558

630 642 654 666 678

751 763 775 787 799

871 883 895 907 919

991 *003 #015 *027 *038

56 110 122 134 146 ,158

229 241 253 265 277

348 360 372 384 396

. 467 478 490 502 514

585 597 608 620 632

703 714 726 738 750

820 832 844 855 867

937 949 961 972 984

57 054 066 078 089 101

171 183 194 206 217

287 299 310 322 334

403 415 426 438 449

519 630 542 553 565

634 646 657 669 680

749 761 772 784 795

864 875 887 898 910

978 990 *001 *013 *024

58 092 104 115 127 138

206 218 229 240 252 

320 331 343 354 365

433 444 456 467 478

546 557 569 580 591

659 670 681 692 704

771 782 794 805 816

883 894 906 917 928

995 *006 #017 *028 *040

59 106 118 129 140 151

218 229 240 251 262

329 340 351 362 373

439 450 461 472 483

550 561 572 583 594

660 671 682 693 704

770 780 791 802 813

879 890 901 912 923

988 999 *010 *021 *032

60 097 108 119 130 141

206 217 228 239 249

L. 0 1 2 3 4

5 67 8 9

469 481 494 506 518

593 605 617 630 642

716 728 741 753 765

839 851 864 876 888

962 974 986 998 *011

084 096 108 121 133

206 218 230 242 255

328 340 352 364 376

449 461 473 485 497

570 582 594 606 618

691 703 715 727 739

811 823 835 847 859

931 943 955 967 979

*050 *062 *074 *086 #098

170 182 194 205 217

289 301 312 324 336

407 419 431 443 455

526 538 549 561 573

644 656 667 679 691

761 773 785 797 808

879 891 902 914 926

996 *008 *019 *031 *043

113 124 136 148 159

229 241 252 264 276

345 357 368 380 392

461 473 484 496 507

576 588 600 611 623

692 703 715 726 738

807 818 830 841 852

921 933 944 955 967

*035 *047 *058 *070 *081

149 161 172 184 '195

263 274 286 297 309 

377 388 399 410 422

490 501 512 524 535

602 614 625 636 647

715 726 737 749 760

827 838 850 861 872

939 950 961 973 984

*051 *062 *073-*084 *095

162 173 184 195 207

273 284 295 306 318

384 395 406 417 428

494 506 517 528 539

605 616 627 638 649

715 726 737 748 759

824 835 846 857 868

934 945 956 966 977

*043 *054 ^OeS *076 *086

152 163 173 184 195

260 271 282 293 304

56789

P.P.

13

1

2 

3

4

5

6

7

8

9

i q I/O

2,6 

3,9

5,2

6,5 n Q i </o

9,1

10,4

11,7

"

1

2

3

4

5 

6

7

9

1/2

2,4

3,6

4,8 /? f\ D,U

7,2

8,4

9,6 ift J.I//Oft

11

1

2

4

5

6 

7 

8

9

1/1

2,2 3 <? 0,0 

4,4

5,5

6,6

7,7 

8,8

9,9

1 f\

1 

2

3

4

c0

6

7

9

AV

1/0 

2,0

3,0

4,0

5,0 

6,0

7,0

ft fi o/U

9,0

P.P.

0° 58' = 3480" S. 4. 68 555 T. 4. 68 562 1° 3' = 3780" S. 4. 68 555 T. 4. 68 562

0 59 = 3540 4. 68 555 4. 68 562 14= 3840 4. 68 555 4. 68 563

10= 3600 4. 68 555 4. 68 562 15= 3900 4. 68 555 4. 68 563

1 1 '= 3660 4. 68 555 4. 68 562 16= 3960 4. 68 555 4. 68 563

12= 3720 4. 68 555 4. 68 562 17= 4020 4. 68 555 4. 68 563
GEOGEAPHIC TABLES AND FOEMULAS. 149

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

400

401

402

403

404

. 405 

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

N.

L. 0 1 2 3 4

60 206 217 228 239 249

314 325 336 347 358

423 433 444 455 466

531 541 552 563 674

638 649 660 670 681

746 756 767 778 788 

853 863 874 885 895

959 970 981 991 *002

61 066 077 087 098 109

172 183 194 204 215

278 289 300 310 321

384 395 405 416 426

49Q 500 511 521 532

595 606 616 627 637

700 711 721 731 742

805 815 826 836 847

909 920 930 941 951

62 014 024 034 045 055

118 128 138 149 159

221 232 242 252 263

325 335 346 356 366

428 439 449 459 469

531 .542 552 562 572

634 644 655 665 675

737 747 757 767 778

839 849 859 870 880

941 951 961 972 982

63 043 053 063 073 083

144 155 165 175 185

246 256 266 276 286

347 357 367 377 387

448 458 468 478 488

548 558 568 579 589

649 659 669 679 689

749 759 769 779 789

849 859 869 879 889

949 959 969 979 988

64 048 058 068 078 088

147 167 167 177 187

. 246 256 266 276 286

345 355 365 375 385

444 454 464 473 483

542 552 562 572 582

640 650 660 670 680

738 748 758 768 777

836 846 856 865 875

933 943 953 963 972

65 031 040 050 060 070

128 137 147 157 167

225 234 244 254 263

321 331 . 341 350 360

L. 0 1 2 3 4

5

260

369

477

684

692

799 

906

6789

271 282 293 304

379 390 401 412

487 498 509 520

595 606 617 627

703 713 724 735

810 821 831 842 

917 927 938 949

$013 *023 *034 *045 *055

119

225

331

437

542

648

752

857

962

066

170

273 '

377

480

583

685

788

890

130 140 151 162

236 247 257 268

342 352 363 374

448 458 469 479

553 563 574 584

658 669 679 690

763 773 784 794

868 878 888 899

972 982 993*003

076 086 097 107

180 190 201 211

284 294 304 315

387 397 408 418

490 500 511 521

593 603 613 624

696 706 716 726

798 808 818 829

900 910 921 931

992 *002 *012 #022 *033

094

195

296

397

498

599

699

799

899

104 114 124 134

205 215 225 236

306 317 327 337

407 417 428 438

508 518 528 538

609 619 629 639

709 719 729 739

809 819 829 839

909 919 929 939

998 *008 +018 *028 *038

098

197

296

395

493

591

689

787

885

982

079

176

273

369

5

1° 6' = 3960" S. 4. 68 555 T. 4. 68 563

1 7 = 4020 4. 68 555 4. 68 663

1 8 = 4080 4. 68 555 4. 68 563

1 9 = 4140 4. 68 555 4. 68 563

1 10 = 4200 4. 68 554 4. 68 563

108 118 128 137

207 217 227 237

306 316 326 335

404 414 424 434

503 513 523 532

601 611 621 631

699 709 719 729

797 807 816 826

895 904 914 924

992 *002 *011 *021

089 099 108 118

186 196 205 215

283 292 302 312

379 389 398 408

6789

P.P.

1

2

3

4 

5

6

7

9

1

2

3

4

5

6

7

8

9

1

2

4

5

6

7

8

9

P

11

1/1

2,2

3,3

4,4 

5,6

6,6

7,7 Q Q

o/o 

9,9

10

1/0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

9

0,9

1 J./O& 

2,7 

3,6

4,5

5,4

6,3

7,2

8/1

P.

1° 11'= 4260" S. 4. 68 554 'T. 4. 68 564

1 12 = 4320 4. 68 554

1 13 = 4380 4. 68 564

1 14 = 4440 4. 68 554

1 15 = 4500 4. 68 554

4. 68 564

4. 68 564

4. 68 564

4. 68 564
150 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492 

493

494

495

496

497

498

499

500

N.

L. 0 1 2 3 4

65 321 331 341 350 360

418 427 437 447 456

514 523 533 643 552

610 619 629 639 648

706 715 725 734 744

801 811 820 830 839

896 906 916 925 935

992 *001 *011 #020 #030

66 087 096 106 115 124

181 191 200 210 219

276 285 295 304 314

370 380 389 398 408

464 474 483 492 502

558 567 577 586 596

652 661 671 680 689

745 755 764 773 783

839 848 857 867 876

932 941 950 960 969

67 025 034 043 052 062

117 127 136 145 154

210 219 228 237 247

302 311 321 330 339

394 403 413 422 431

486 495 504 514 523

578 587 596 605 614

669 679 688 697 706

761 770 779 788 797

852 861 870 879 888

943 952 961 970 979

68 034 043 052 061 070

124 133 142 151 160

215 224 233 242 251

305 314 323 332 341

395 404 413 422 431

485 494 502 511 520

574 583 592 601 610

664 673 681 690 699

753 762 771 780 789

842 851 860 869 878

931 940 949 958 966

69 020 028 037 046 055

108 117 126 135 144

197 205 214 223 232 

285 294 302 311 320

373 381 390 399 408

461 469 478 487 496

548 557 566 574 583

636 644 653 662 671

723 732 740 749 758

810 819 827 836 845

897 906 914 923 932

L. 0 1 2 3 4

5 678 9

369 379 389 398 408

466 475 485 495 504

562 571 581 591 600

658 667 677 686 696

753 763 772 782 792

849 858 868 877 887

944 954 963 973 982

*039 *049 *058 *068 *077

134 143 163 162 172

229 238 247 257 266

323 332 342 351 361

417 427 436 445 455

511 521 530 539 549

605 614 624 633 642

699 708 717 727 736

792 801 811 820 829

885 894 904 913 922

978 "987 997 *006 *015

071 080 089 099 108

164 173 182 191 201

256 265 274 284 293

348 357 367 376 385

440 4149 459 468 477

532 541 550 560 569

624 633 642 651 660

* 715 ' 24 . 733 742 752

806 815 825 834 843

897 906 916 925 934

988 997 *006 *015 *024

079 ()88 097 106 115

169 178 187 196 205

260 269 278 287 296

350 359 368 377 386

440 449 458 467 476

629 638 547 556 565

619 628 637 646 655

708 717 726 735 744

797 B06 815 824 833

886 895 904 913 922

975 984 993 *002 »011

064 073 082 090 099

152 161 170 179 188

241 249 258 267 276 

329 338 346 . 355 364

417 425 434 443 452

504 513 522 531 539

592 601 609 618 627

679 688 697 705 714

767 775 784 793 801

854 862 871 880 888

940

5

1° 15'= 4500" S. 4. 68 554 T. 4. 68 564

1 16 = 4560 4. 68 554 4. 68 565

1 17 = 4620 4. 68 554 4. 68 565

1 18 = 4680 4. 68 554 4. 68 661?

1 19 = 4740 '4. 68 554 4. 68 565

949 958 966 975

6789

P.

1

2

3

4 

5

6

7

9

1

2

3

4

5

6

7

8

9

1 

2

0o

4

5 

6 7

8 

9

P.

10

1/0

2,0

3,0

4,0 

5,0

6,0 7 ft I/O

Q f\

O/U

9,0

9

0,9

1,8

2/7

3,6

4,5

5,4

6,3

7,2

8,1

8

0,8 

1/6

2,4

3,2

4,0 

4,8

5,6

6,4 

7,2

P.P.

1° 20'= 4800" S. 4. 68 554 T. 4. 68 565

1 21 = 4860 4. 68 653

1 22 = 4920 4. 68 553

1 23 = 4980 4. 68 553

1 24 - 5040 4. 68 553

4. 68 566

4, 68 566

4. 68 566

4. 68 566
GEOGRAPHIC TABLES AND FORMULAS. 151 

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

500

501

502

603

604

505

506

507

508

609

510

611

512

513

514

615

516

517

518 

619

520

521 

622

523

524

525

526

527

628

529

530

631

632

533

534

535

536

537

538

539

540

541

542

543

544

645

646

647

648

549

550

N.

L. 0 1 2 3 4

69 897 906 914 923 932

984 992 *001 #010 *018

70 070 079 088 096 105

157 165 174 183 191

243 252 260 269 278

329 338 346 355 364

415 424 432 441 449

501 509 518 526 535

586 595 603 612 621

672 680 689 697 706

757 766 774 783 791

842 851 859 868 876

927 .935 944 952 961

71 012 020 029 037 046

096 105 113 122 130

181 189 198 206 214

265 273 282 290 299

349 357 366 374 383

433 441 450 458 466 

517 525 533 642 550

600 609 617 625 634

684 692 700 709 717 

7^7 775 784 792 800

850 858 867 875 883

933 941 950 958 966

72 016 024 032 041 049

099 107 115 123 132

181 189 198 206 214

263 272 280 288 296

346 354 362 370 378

428 436 444 o 452 460

509 518 526 534 542

591 599 607 616 624

673 681 689 697 705

754 762 770 779 787

835 843 852 860 868.

916 925 933 941 949

997 *006 *014 *022 *030

73 078 086 094 102 111

159 167 175 183 191

239 247 255 263 272

320 328 336 344 352

400 408 416 424 432

480 488 496 504 512

560 568 576 584 592

640 648 656 664 672

719 727 735 743 761

799 807 815 823 830

878 886 894 902 910

957 965 973 981 989

74 036 044 052 060 068

L. 0 1 2 3 4

6

940

6789

949 958 966 975

*027 *036 *044 *053 *062

114

200

286

372

458

544

629

714

800

885

969

054

139

223

307

391

475 

559

642

725 

809

892

975

057

140

222

304

387

469

550

632

713

795

876

957

122 131 140 148

209 217 226 234

295 303 312 321

381 389 398 406

467 475 484 492

552 561 569 578

638 646 655 663

723 731 740 749

808 817 825 834

893 902 910 919

978 986 995 *003

063 071 079 088

147 155 164 172

231 240 248 257

315 324 332 341

399 408 ' 416 425

483 492 500 508 

567 575 684 592

650 659 667 675

734 742 750 759 

817 825 834 842

900 908 917 925

983 991 999 *008

066 074 082 090

148 156 165 173

230 239 247 255

313 321 329 337

395 403 411 419

477 485 493 501

658 567 575 583

640 648 656 665

722 730 738 746

803 811 819 827

884 892 900 908

965 973 981 989

#038 *046 *054 *062 *070 .

119

199

280

360

440

520

600

679

759

838

918

127 135 143 151

207 215 223 231

288 296 304 312

368 376 384 392

448 456 464 472

528 536 544 652

608 616 624 632

687 695 703 711

767 775 783 791

846 854 862 870

926 933 941 949

997 *005 *013 *020 #028

076

5

1° 23'= 4980" S. 4. 68 653 T. 4. 68 666

1 24 = 5040 4. 68 553 4. . 68 566

1 26 = 6100 4. 68 553 4. 68 566

1 26 = 6160 4. 68 553 4. 68 567

1 27 = 6220 4. 68 553 4. 68 667

084 092 099 107

6789

P. P.

1 

2

3

4

5

6

7

8

9

1

2

3

4

5

6

7

8

9

1

2J

3

4 

5

 6

7

9

P.

9

0,9 

1/8

2,7

3/6

4,5

5,4

6,3

7,2

8,1

8 ! 0,8 :

1/6

2,4

3,2

4,0

4,8

5,6

6,4

7,2

(

7 i

0,7

1/4

2,1

O Q

£/O

3,5

4,2 i

4,9 ;

5,6 

6,3

P. <

1° 28'= 5280" S. 4. 68 553 T. 4. 68 567

1 29 = 5340 4. 68 553

1 30 = 6400 4. 68 553

1 31 = 6460 4. 68 552

1 32 = 6520 4. -68 552

4. 68 567

4. 68 567

4. 68 568

4. 68 568
152 GEOGRAPHIC TABLES AND FOEMULAS.

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

560

551

552

553

554

555

556

557

658

659

560

561

562

563

564

565

566

567

568

569

570

571

572

573

574

575

576

577

578

579

580

581 

582

583

584

585

586

587

588

589

590

591

592

593

594

595

596

597

598 

599

600

N.

L. 0 1 2 3 4

74 036 044 052 060 068

115 123 131 139 147

194 202 210 218 225

273 280 288 296 304

351 359 367 374 382

429 437 445 453 461

607 515- 523 . 531 539

586 593 601 609 617

663 671 679 687 695

741 749 757 764 772

819 827 834 842 850

896 904 912 920 927

974 981 989 997 *005

75 051 059 066 074 082

128 136 143 151 159

205 213 220 228 236

282 289 297 305 312

358 366 374 381 389

435 442 450 458 465

511 519 526 534 542

587 595 603 610 618

664 671 679 686 694

740 747 755 762 770

815 823 831 838 846

891 899 906 914 921

967 974 982 989 997

76 042 050 057 065 072

118 125 133 140 148

193 200 208 215 223 <

268 275 283 290 298

343 350 358 365 373

418 425 433 440 448 

492 500 507 515 522

567 574 582 589 597

641 649 656 664 671

716 723 730 738 745

790 797 805 812 819

864 871 879 886 893

988 945 953 960 967

77 012 019 026 034 041

085 093 100 307 115

159 166 173 181 188

232 240 247 254 262

305 313 320 327 335

379 386 393 401 408

452 459 466 474 481

525 532 539 546 654

597 605° 612 619 627

670 677 685 692 699 

743 750 757 764 772

815 822 830 837 844

L. 0 1 2 3 4

6 6789

076 084 092 099 107

155 162 170 178 186

233 241 249 257 265

312 320 327 335 343

390 398 406 414 421

468 476 484 492 500

547 554 562 570 578

624 632 640 648 656

702 710 718 726 733

780 788 796 803 811

858 865 873 881 889

935 943 950 958 966

*012 *020 *028 *035 *043

089 097 105 113 120

166 174 182 189 197

243 261 259 266 274

320 328 335 343 351

397 404 412 420 427

473 481 488 496 504

549 557 565 572 580

626 633 641 648 656

702 709 717 724 732

778 785 793 800 803

853 861 868 876 884

929 937 944 952 959

*005 *012 *020 *027 *035

080 087 095 103 r l!0

155 163 170 178 -185

230 238 245 253 .260

305 313 320 328 335

380 388 395 403 410 -

455 462 470 .477 485 

530 537 545 552 559

604 612 619 626 634

678 686 693 701 708

753 760 768 . 775 782

827 834 842 849 856

901 908 916 923 930 '

975 982 989 997 *004

048 056 063 070 078

122 129 137 144 151

195 203 210 217 225

269 276 283 291 298

342 349 357 364 371

415 422 430 437 444

488 495 503 510 517

561 568 576 583 590

634 641 648 656 66?

706 714 721 728 735 

779 786 793 801 808

851 859 866 873 880

5

1° 31' = 5460" S. 4. 68 552 T. 4. 68 568

1 32 = 5520 4. 68 552 4. 68 568

1 33 = 6580 4. 68 552 4. 68 568

1 34 = 6640 4. 68 552 4. 68 568

1 35 = 5700 4. 68 652 4. 68 669

6789

P. P.

1

2

3

4

5

6

7

8

9

1

2

3

4

5

6

7

8

9

8

0,8

1,6

2,4

3,2

4,0

4,8

5,6

6,4

7,2

7

0,7

1/4

2,1

2,8

3,5

4,2 

4,9

5,6

6,3

P.P.

lo 36' = 5760" S. 4. 68 552 T. 4. 68 569

1 37 = 5820 4. 68 552

1 38 = 5880 4. 68 552

1 39 = 5940 4. 68 651

1 40 = 6000 4. 68 551

. 4. 68 569

4. 68 569

4. 68 569

4. 68 670
GEOGEAPHIC TABLES AND FOEMULAS. 153

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

600

601

602

603

604

605

606

607

608

609

610

611

612

613

C14

615

616

617

618

619

620

621

622

623

624

625

626

627

628

629

630

631

632

633

634

635

636

637

638

639

640

641

642

643

644

645 

646

647

. 648

649

650

N.

L. 0 1 2 3 4

77 815 822 830 837 844

887 895 902 909 916

960 967 974 981 988

78 032 039 046 053 061

104 111 118 125 132

176 183 190 197 204

247 254 262 269 276

319 326 333 340 347

390 398 405 412 419

462 469 476 483 490

533 540 547 554 561

604 611 618 625 633

675 682 689 696 704

746 753 760 767 774

817 824 831 838 845

888 895 902 909 916

958 965 972 979 986

79 029 036 043 050 057

099 106 113 120 127

169 176 183 190 197

239 246 253 260 267

309 316 323 330 337

379 386 393 400 407

449 456 463 470 477

518 525 532 539 546

588 595 602 609 616

657 664 671 678 685

727 734 741 748 754

796 803 810 817 824

865 872 879 886 893

934 941 948 955 962

80 003 010 01? 024 030

072 079 085 092 099

140 147 154 161 168

209 216 223 229 236

277 284 291 298 305

346 353 359 366 373

414 421 428 434 441

482 489 496 502 509

550 557 564 570 577

618 625" 632 638 645

686 693 699 706 713

754 760 767 774 781

821 828 835 841 848

889 895 902 909 916

956 963 969 976 983 

81 023 030 037 043 050

090 097 104 111 117

158 164 171 178 184

224 231 238 245 251

291 298 305 311 318

L. 0 1 2 3 4

5

851

924

6789

859 866 873 880

931 938 945 952

996 *003 McOlO *017 *025

068

140

211

283

365 '

426

497

569

640

711

781

852

923

075 082 089 097

147 154 161 168

219 226 233 240

290 297 305. 312

362 369 376 383

433 440 447 455

504 512 519 626

576 583 590 597

647 654 661 668

718 725 732 739

789 796 803 810

859 866 873 880

930 937 944 951

993 *000 *007 *014 *021

064

134

204

274

344

414

484

553

623

692

761

831

900

969

037

106

175

243

312

380

448

616

584

652

720

787

855

922

990 

057

124

191

258

325

5

lo 40' = 6000" S. 4. 68 551 T. 4. 68 570

1 41 = 6060 4. 68 551 4. 68 570

1 42 = 6120 4. 68 551 4. 68 570

1 43 = 6180 4. 68 551 4. 68 570

1 44 = 6240 4. 68 651 4. 68 571

071 078 08$ 092

141 148 155 162

211 218 225 232

281 288 295 302

351 358 365 372

421 428 435 442

491 498 505 511

560 567 574 581

630 637 644 650

699 706 713 720

768 775 782 789

837 844 851 868

906 913 920 927

975 982 989 996

044 051 058 065

113 120 127 134

182 188 195 202

250 257 264 271

318 325 332 339

387 393 400 407

455 462 468 475

523 630 536 543

591 598 604 611

659 665 672 679

726 733 740 747

794 801 808 814

862 868 875 882

929 936 943 949

996 *003 *010 *017 

064 070 077 084

131 137 144 151

198 204 211 218

265 271 278 285

331 338 345 351

6789

P

1

2

3

4 

5

6

7

8 

9

1

2

3 

4

5

6

7

9

1

2

3

4 

5

6

7

9

P

1° 45' = 6300" S. 4. 68 551 T

1 46 = 6360 4. 68 551

1 47 = 6420 4. 68 550

1 48 = 6480 4. 68 5§0

1 49 = 6540 4. 68 650

.P.

0,8

1/6

2,4

4^0

4,8

5,6

6,4 

7,2

7

0,7

1/4

2/1

3,5

4,2

4,9 

5,6

6,3

6

0,6

1/2

1/8

2,4 

3,0

3,6

4,2

4,8 

5,4

P.

. 4. 68 671

4. 68 571

4. 68 572

4. 68 572

4. 68 672
154 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

650

651 

652 

653

654 

655 

656

657 

658 

659

660

661 

662 

663

664 

665 

666

667 

668 

669

670

671 

672 

673

674 

675 

676

677 

678 

679

680

681 

682 

683

684 

685 

686

687 

688 

689

690

691 

692 

693

694 

C95 

696

697 

698 

699

700

N.

L. 0 1 '2 3 4

81 291 298 305 311 318

358 365 371 378 385 

425 431 438 445 451 

491 498 505 611 518

558 564 571 578 584 

624 631 637 644 651 

690 697 704 710 717

757 763 770 776 783 

823 829 836 842 849 

889 895 902 908 915

954 961 968 974 981

82 020 027 033 040 046 

086 092 099 105 112 

151 158 164 171 178

217 223 230 236 243 

282 289 295 302 308 

347 354 360 367 373

413 419 426 432 439 

478 484 491 497 504 

543 549 556 562 569

607 614 620 627 633

672 679 685 692 698 

737 743 750 756 763 

802 808 814 821 827

866 872 879 885 892 

930 937 943 950 956 

995 *001 *008 *014 *020

83 059 065 072 078 085 

123 129 136 142 149 

187 193 200 206 213

251 257 264 270 276

315 321 327 334 340 

378 385 391 398 404 

442 448 455 461 467

506 512 518 525 531 

569 575 582 588 594 

632 639 645 651 658

696 702 708 715 721 

759 765 771 778 784 

822 828 835 841 847

885 891 897 904 910

948 954 960 967 973 

84 Oil 017 023 029 036 

073 080 086 092 098

136 142 148 155 161 

198 205 211 217 223 

261 267 273 280 286

323 330 336 342 348 

386 392 398 404 410 

448 454 460 466 473

510 616 522 628 535

L. 0 1 2 3 4

56789

325 331 338 345 351

391 398 405 411 418 

458 465 471 478 485 

525 531 538 544 551

591 598 604 611 617 

657 664 671 677 684 

723 730 737 743 750

790 796 803 809 816 

856 862 869 875 882 

921 928 935 941 948 ,

987 994 *000 *007 *014

053 060 066 073 079 

119 125 132 138 145 

184 191 197 204 210

249 256 263 269 276 

315 321 328 334 341 

380 387 393 400 406

445 452 458 465 471 

510 517 523 530 636 

575 582 688 595 601

640 646 653 659 C66

705 711 718 724 730 

769 776 782 789 795 

834 840 847 853 860

898 905 911 918 924 

963 969 975 982 988 

*027 *033 *040 *046 *052

091 097 104 110 117 

155 161 168 174 181 

219 225 232 238 245

283 289 296 302 308

347 353 359 366 372 

410 417 423 429 436 

474 480 487 493 499

537 544 550 556 563 

601 607 613 620 626 

664 670 677 683 689

727 734 740 746 753 

790 797 803 809 816 

853 860 866 872 879

916 923 929 935 942

979 985 992 998 *004 

042 048 055 061 067 

105 111 117 123 130

167 173 180 186 192 

230 236 242 248 255 

292 298 305 311 317

354 361 367 373 379 

417 423 429 435 442 

479 485 491 497 504

541 547 553 559 566

56789

P. P.

7

1 0,7 

2 1,4 

3 2,1 

4 2,8 

6 3,5 

6 4,2 

7 4,9 

8 5,6 

9 6,3

6

1 0,6 

2 1,2 

3 1,8 

4 2,4 

5 3,0 

6 3,6 

7 4,2 

8 4,8 

9 5,4

P. P.

1° 48' = 6480" S. 4. 68 550 T. 4. 68 572 1° 53' = 6780" S. 4. 68 550 T. 4. 68 573 

1 49 = 6540 4. 68 550 4. 68 672 1 54 = 6840 4. 68 550 4. 68 573 

1 50 = 6600 4. 68 550 4. 68 572 1 55 =6900 4. 68 549 4. 68 574 

1 51 = 6660 4. 68 550 4. 68 673 1 56 = 6960 4. 68 549 4. 68 674 

1 52 = 6720 4. 68 660 4. 68 573 1 67 = 7020 4. 68 649 4. 68 574
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 25. Five-place logarithms of natural numbers Continued.

155

 N.

700

701 

702 

703

704

705 

706

' 707 

708 

709

710

711 

712 

713

714 

715 

716

717 

718 

719

720

, 721 

722 

723

724 

725

, 726

: 727

: 728

729 

730

731 

732 

733

734 

735 

736

737 

738 

739

740

741 

742 

743

744 

745 

746

747 

748 

749

750

N.

L. 0 >1 2 3 4

84 510 516 522 528 535

572 578 684 590 697 

634 640 646 652 658 

696 702 708 714 720

.757 763 770 776 782 

819 825 831 837 844 

880 887 893 899 905

942 948 954 960 967 

85 003 009 016 022 028 

065 071 077 083 089

126 132 138 144 150

187 193 199 205 211 

248 254 260 266 272 

309 315 321 327 333

370 376 382 388 394 

431 437 443 449 455 

491 497 603 609 616

552 558 564 570 576 

612 618 625 631 637 

673 679 685 691 697

733 739 745 751 757

794 800 806 812 818 

854 860 866 872 878 

914 920 926 932 938

974 980 986 992 998 

86 034 040 046 052 058 

094 100 106 112 118

153 159 165 171 177 

213 219 225 231 237 

273 279 285 291 297

332 338 344 350 356

392 398 404 410 415 

451 457 463 469 475 

510 516 522 528 534

570 576 581 687 593 

629 635 641 646 652 

688 694 700 705 711

747 763 759 764 770 

806 812 817 823 829 

864 870 876 882 888

923 929 935 941 947

982 988 994 999 *005 

87 040 046 052 058 064 

099 105 111 116 122

167 163 169 175 181 

216 221 227 233 239 

274 280 286 291 297

332 338 344 349 355 

390 396 402 408 413 

448 454 460 466 471

506 512 518 523 529

L. 0 12 3 4

5 6789

541 547 653 559 566

603 609 615 621 628 

665 671 677 683 689 

726 733. 739 745 751

788 794 800 807 813 

850 856 862 868 874 

911 917 924 930 936

973 979 986 991 997 

034 040 046 052 058 

095 101 107 114 120

156 163 169 175 181

217 224 230 236 242 

278 28^ 291 297 303 

339 345 352 358 364

400 406 412 418 42§ 

461 467 473 479 485 

522 528 534 540 546

582 588 594 600 606 

643 649 65i? 661 667 

703 709 715 721 727

763 769 775 781 788

824 830 836 842 848 

884 890 896 902 908 

944 950 956 962 968

*004 *010 *016 *022 ,028 

064 070 076 082 088 

124 130 136 141 147

183 189 195 201 207 

' 243 249 255 2C1 267 

303 308 314 320 326

362 368 374 380 386

421 427 433- 439 445 

481 487 493 499 504 

640 546 552 558 564

599 605 611 617 623 

658 664 670 676 682 

717 723 729 735 741

776 782 788 794 800 

835 841 847 853 859 

894 900 906 911 917

953 958 964 970 976

*011 *017 *023 *029 *035 

070 075 081 087 093 

128 134 140 146 151

186 192 198 204 210 

245 251 256 262 268 

303 309 31§ 320 326

361 367 373 379 384 

419 425 431 437 442 

477 483 489 495 500

535 541 547 652 658

5

1° 56' = 6960" S. 4. 68 549 T. 4. 68 574 

1 57 = 7020 4. 68 549 4. 68 574 

1 68 = 7080 4. 68 549 4. 68 675 

1 59 = 7140 4. 68 549 4. 68 67? 

2 0 .= 7200 4.68649 4.68575

6 78 9

P

1 

2 

3 

4 

5 

6 

7 

8 

9

1

2 

3 

4 

5 

6 

7 

8 

9

1

2 

3 

4 

5 

6 

7 

8 

9

P

.P.

7

0,7 

1,4 

2,1 

2,8 

 3,5 

4,2 

4,9 

5,6 

6,3

0

0,6 

1,2 

1,8 

2,4 

3,0 

3,6 

4,2 

4,8 

5,4

6

0,5 

1,0 

1,5 

2,0 

2,5 

3,0 

3,5 

4,0 

4,5

P.

2° 1' = 7260" S. 4. 68 549 T. 4. 68 575 

22= 7320 4. 68 648 4. 68 576 

23= 7380 4. 68 548 4. 68 57C 

24= 7440 4. 68 548 4. 68 576 

25= 7600 4. 68 648 4. 68 577
156 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

750

751 

752 

753

754 

755 

766

757 

758 

759

760

761 

762 

763

764 

765 

766

767 

768 

769

770

771 

772 

773

774 

775 

776

777 

778 

779

780

781 

782 

783

784 

785 

786

787 

788 

789

790

791 

792 

793

794 

795 

796

797 

798 

799

800

N.

L. 0 1 2 3 4

87 506 512 518 523 529

564 570 576 581 587 

622 628 633 039 645 

679 685 691 697 703

737 743 749 754 760 

795 800 806 812 818 

852 858 864 869 875

910 915 921 927 933 

967 973 978 984 990 

88 024 030 036 041 047

081 '087 093 098 104

138 144 150 156 161 

195 201 207 213 218 

252 258 264 270 275

309 315 321 326 332 

366 372 377 383 389 

423 429 434 440 446

480 485 491 497 502 

536 542 547 553 559 

593 598 604 610 615

649 655 660 666 672

705 711 717 722 728 

762 767 773 779 784 

818 824 829 835 840

874 880 885 891 897 

930 936 941 947 953 

986 992 997 $003 *009

89 042 048 053 059 064 

098 104 109 115 120 

154 159 165 170 176

209 215 . 221 226 232

265 271 276 282 287 

321 326 332 337 343 

376 382 387 393 398

432 437 443 448 454 

487 492 498 504 509 

542 548 553 559 564

697 603 609 614 620 

653 658 664 669 675 

708 713 719 724 730

763 768 774 779 785

818 823 829 834 840 

873 878 883 889 894 

927 933 938 944 949

982 988 993 998 *004 

90 037 042 048 053 059 

091 097 102 108 113

146 151 157 162 168 

200 206 211 217 .222 

.255 260 266 271 276

309 314 320 325 331

L. 0 1 2 3 4

66789

535 541 547 552 558

593 599 604 610 616 

651 656 662 668 674 

708 714 720 726 731

766 772 777 783 789 

823 829 835 841 846 

881 887 892 898 904

938 944 950 955 961 

996 *001 *007 .,,013 *018 

053 058 064 070 076

110 116 121 127 133

167 173 178 184 190 

224 230 235 241 247 

281 287 292 298 304

338 343 349 355 360 

395 400 406 412 417 

451 457 463 468 474

508 513 519 525 530 

564 570 576 681 587 

621 627 632 638 643

677 683 689 694 700

734 739 745 750 756 

790 795 801 807 812 

846 852 857 863 868

902 908 913 919 925 

958 964 969 975 981 

*014 *020 *025 #031 *037

070 076 081 087 092 

126 131 137 143 148 

182 187 193 198 204

237 243 248 254 260

293 298 304 310 315 

348 354 360 365 371 

404 409 415 421 426

459 465 470 476 481 

515 520 526 531 637 

570 575 581 586 592

625 631 636 642 647 

680 686 691 697 702 

735 741 746 752 757

790 796 801 807 812

845 851 856 862 867 

900 905 911 916 922 

955 960 966 971 977

*009 *015 *020 *026 *031 

064 069 075 080 086 

119 124 129 135 140

173 179 184 189 195 

227 233 238 244 249 

282 287 293 298 304

336 342 347 352 358

56789

. P. P.

6

1 0,6 

2 1,2 

3 1,8 

4 2,4 

5 3,0 

6 3,6 

7 4,2 

8 4,8 

9 5,4

5

1 0,5 

2 1,0 

3 1,5 ' 4 2,0 ' 

5 2,5 

6 3,0 

7 3,5 

8 4,0 

9 4,6

P.P.

2° 5'= 7500" S. 4. 68 548 T. 4. 68 577 2° 10'= 7800"' S. 4. 68 547 T. 4. 68 578 

26 = 7560 4. 68 548 4. 68 577 2 11 = 7860 4. 68 547 4. 68 579 

27 = 7620 4. 68 648 4. 68 577 2 12 = 7920 4. 68 547 4. 68 579 

2 8 = 7680 4. 68 547 4. 68 578 2 13 = 7980 4. 68 547 4. 68 579 

29 = 7740 4. 68 647 4. 68 678 2 14 = 8040 4. 68 646 4. 68 579
GEOGKAPHIC TABLES AND FOEMULAS. 157

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

800

801 

802 

803

804 

805 

806

807 

808 

809

810

811 

812 

813

814 

815 

816

817 

818 

819

820

821 

822 

823

824 

825 

826

827 

828 

829

830

831 

832 

833

834 

835 

836

837 

838 

839

840

841 

842 

843

844 

845 

846

847 

848 

849

850

N.

L. 0 1 2 3 4

90 309 314 320 325 331

363 369 374 380 385 

417 423 428 434 439 

472 477 482 488 493

526 531 536 542 547 

580 585 590 596 601 

634 639 644 650 655

687 693 698 703 709 

741 747 762 757 763 

795 800 806 811 816

849 854 859 865 870

902 907 913 918 924 

956 961 966 972 977 

91 009 014 020 025 030

062 068 073 078 084 

116 121 126 132 137 

169 174 180 185 190

222 228 233 238 243 

275 281 286 291 297 

328 334 339 344 350

381 387 392 397 403

434 440 445 450 455 

487 492 498 503 508 

540 545 651 556 561

59? 598 603 609 614 

645 651 656 661 666 

698 703 709 714 719

751 756 761 766 772 

803 808 814 819 824 

855 861 866 871 876

908 913 918 924 929

960 965 971 976 981 

92 012 018 023 028 033 

065 070 075 080 085

117 122 127 132 137 

169 174 179 184 189 

221 226 231 236 241

273 278 283 288 293 

324 330 335 .,340 345 

376 381 387 - 392 397

428 433 438 443 449

480 485 490 495 500 

. 531 536 542 547 552 

583 588 593 598 603

634 639 645 650 655 

686 691 696 701 706 

- 737 742 747 752 758

788 793 799 804 809 

840 845 850 855 860 

891 896 901 906 911

942 947 952 957 962

L. 0 1 2 3 4

56789

336 342 347 352 368

390 396 401 407 412 

445 450 455 461 466 

499 504 509 515 620

553 558 563 569 574 

607 612 617 623 628 

660 666 671 677 682

714 720 725 730 736 

768 773 779 784 789 

822 827 832 838 843

875 881 886 891 897

929 934 940 945 950 

982 988 993 998 #004 

036 041 046 052 067

089 094 100 105 110 

142 148 153 158 164 

196 201 206 212 217

249 254 259 265 270 

302 307 312 318 323 

355 360 365 371 376

408 413 418 424 429

461 466 471 477 482 

514 519 524 529 535 

566 572 577 582 587

619 624 630 635 640 

672 677 682 687 69? 

724 730 735 740 745

777 782 787 793 798 

829 834 840 845 850 

882 887 892 897 903

934 939 944 9oO 955

986 991 997 *002 *007 

038 044 049 054 059 

091 096 101 106 111

143 148 153 158 163 

195 200 205 210 215 

247 252 257 262 267

298 304 309 314 319 

350 365 361 366 371 

402 407 412 418 423

454 459 464 469 474

505 511 516 521 526 

557 562 567 572 578 

609 614 619 624 629

660 665 670 675 681 

711 716 722 727 732 

763 768 773 778 783

814 819 824 829 834 

865 870 875 881 886 

916 921 927 932 937

967 973 978 983 988

56789

P.P.

6

1 0,6 

2 1,2 

3 1,8 

4 2,4 

5 3,0 

6 3,6 

7 4,2 

8 4,8 

9 6,4

5

1 0,5 

2 1,0 

3 1,5 

4 2,0 

5 2,5 

6 3,0 

7 3,5 

8 4,0 

9 4,6

P. P.

2° 13' = 7980" S. 4. 68 547 T. 4. 68 579 2° 18'=8280" S. 4. 68 546 T. 4. 68 581 

2 14 =8040 4. 68 546 4. 68 679 2 19 =8340 ' 4. 68 M6 4. 68 581 

2 15 = 8100 4. 68 546 4. 68 580 2 20 =8400 4. 68 645 4. 68 582 

2 16 =8160 4. 68 546 4. 68 580 2 21 =8460 4. 68 545. 4. 68 582 

217= 8220 4. 68 546 4, 68 580 2 22 =8520 4. 68 545 4. 68 582
158 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

850

851

852

853

854

855

856

857

858

859

860

861

862

863

864

865

866

867

868

869

870

871

872

873

874

875

876

877

878

879

880

881

882

883

884

885

886

887 

888

889

890

891

892

893

894

895

896

897

898

899

900

N.

L. 0 1 2 3 4

92 942 947 952 957 962

993 998 *003 *008 *013

93 044 049 054 059 064

095 100 105 110 115

146 151 156 161 166

197 202 207 212 217

247 252 258 263 268

298 303 308 313 318

349 354 359 364 369

399 404 409 414 420

450 455 460 465 470

500 505 510 515 520

651 556 561 566 571

601 606 611 616 621

651 656 661 666 671

702 707 712 717 722

752 757 762 767 772.

802 807 812 817 822

852 857 862 867 872

902 907 912 917 922

952 957 962 967 972

94 002 007 012 017 022

052 057 062 067 072

101 106 111 116 121

151 156 161 166 171

201 206 211 216 221

250 255 260 265 270

300 305 310 315 320

349 354 359 364 369

399 404 409 414 419

448 453 458 463 468

498 503 507 512 517

547 552 557 562 567

596 601 606 611 616

645 650 655 660 665

694 699 704 709 714

743 748 753 758 763

792 797 802 807 812 

841 846 851 856 861

890 895 900 905 910

939 944 949 954 959

988 993 998 *002 *007

95 036 041 046 051 056

085 090 095 100 105

134. 139 143 148 153

182 187 192 197 202

231 236 240 245 250

279 284 289 294 299

328 332 337 342 347

376 381 386 390 395

424 429 434 439 444

L. 0 1 2 3 4

5 6789

967 973 978 983 988

*018 *024 *029 *034 *039

069 075 080 085 090

120 125 131 136 141

171 176 181 186 192

222 227 232 237 242

273 278 283 288 293

323 328 334 339 344'

. 374 379 384 389 394

425 430 435 440 445

475 480 485 490 495

526 531 536 541 546

576 581 586 591 596

626 631 636 641 646

676 682 687 692 697

727

777

732 737 742 747

782 787 792 797

827 832 837 842 847

877 882 887 892 897

927 932 937 942 947

977 982 987 992 997

027 032 037 042 047

077 082 086 091 096

126 131 136 141 146

176 181 186 191 196

226 231 236 240 245

275 280 285 290 295

325 330 335 340 345

374 379 384 389 394

424 429 433 438 443

473 478 483 488 493

522 527 532 537 542

571 576 581 586 591

621 626 630 635 640

670 675 680 685 689

719 724 729 734 738

768 773 778 783 787

817 822 827 832 836

866 871 876 880 885

915 919 924 929 934

963 968 973 978 983

*012 * 017 *022 *027 *032

061 066 071 075 080

109 114 119 124 129

158 163 168 173 177

207 211 216 221 226

255 260 265 270 274

303 308 313 318 323

352 357 361 366 371

400 405 410 415 419

448 453 458 463 468

5

2° 21' = 8460" S. 4. 68 545 T. 4. 68 582

2 22 = 8520 4. 68 '545 4. 68 582

2 23 = 8580 4. 68 545 4. 68 683

2 24 = 8640 4. 68 545 4. 68 583

2 25 = 8700 4. 68 645 4. 68 583

6789

P

1

2

3

4

5

6 

7

9

1

2

3 

4

5

6

7

9

1 

2

3

4 

5

6

7

8

9

P.

6

0,6

1,2

1,8 

2,4

3,0

3,6 

4,2

4,8

5,4

5

0,5

1,0

1,5 

2,0

2,5

3,0

3,5 

4,0

4,5

4

0,4 A Q

U/o

1,2

1,6 

2,0

2,4

2,8

3,2

3,6

P. P.

2° 26' = 8760" S. 4. 68 544 T. 4. 68 584

2 27 = 8820 4. 68 544

2 28 = 8880 4. 68 544

2 29 = 8940 4. 68 544

2 30 = 9000 4. 68 544

4. 68 584

4. 68 584

4. 68 58§

4. 68 585
GEOGKAPHIC TABLES AND FORMULAS. 

TABLE 25. Five-place logarithms of natural numbers Continued.

159

N.

900

901 

902 

903

' 904 

905 

906

907 

908 

909

910

911 

912 

913

914 

915 

916

917 

918 

919

920

921 

922 

923

924 

925 

926

927 

928 

929

930

931 

932 

933

'934 

935 

936

937 

938 

939

940

941 

942 

943

944 

945 

946

947 

948 

949

950

N.

L. 0 1 2 3 4

95 424 429 434 439 444

472 477 482 48? 492 

521 525 -530 535 540 

569 574 578 583 588

617 622 626 631 636 

665 670 674 679 684 

713 718 722 727 732

761 766 770 775 780 

809 813 818 823 828 

856 861 866 871 875

904 909 914 918 923

952 957 961 966 971 

999 #004 #009 *014 #019 

96 047 052 057 061 066

095 099 104 109 114 

. 142 147 162 156 161 

190 194 199 204 209

237 242 246 251 256 

284 289 294 298 303 

332 336 341 346 350

379 384 388 393 398

426 431 435 440 445 

473 478 483 487 492 

520 525 530 534 539

567 572 577 581 586 

614 619 624 628 633 

661 666 670 675 680

708 713 717 722 727 

755 769 764 769 774 

802 806 811 816 820

848 853 858 862 867

895 900 904 909 914 

942 946 951 956 960 

988 993 997 *002 *007

97 035 039 044 049 053 

081 086 090 095 100 

128 132 137 142 146

174 179 183 ' 188 192 

220 225 230 234 239 

267 271 276 280 285

313 317 322 327 331

359 364 368 373 377 

405 410 414 419 424 

451 456 460 465 470

497 502 506 511 516 

543 548 552 557 562 

689 594 598 603 607

635 640 644 649 653 

681 685 690 695 699 

727 731 736 740 745

772 777 782 786 791

L. 0 1 2 3 4

56789

448 453 458 463 468

497 501 506 511 516 

545 550 554 559 564 

593 598 602 607 612

641 646 650 655 660 

689 694 698 703 708 

737 742 746 751 756

785 789 794 799 804 

832 837 842 847 852 

880 885 890 895 899

928 933 938 942 947

976 980 985 990 995 

#023 *028 *033 *038 ,042 

071 076*080 085 090

118 123 12§ 133 137 

166 171 175 180 185 

213 218 223 227 232

261 265 270 275 280 

308 313 317 322 327 

355 360 365 369 374

.402 407 412 417 421

450 454 459 464 468 

497 501 506 511 515 

644 648 553 558 562

591 595 600 605 609 

638 642 647 652 656 

685 689 694 699 703

731 736 741 745 750 

778 783 788 792 797 

825 830 834 839 844

872 876 881 886 890

918 923 928 932 937 

965 970 974 979' 984 

*011 *016 *021 *025 ,030

058 063 067 072 077 

104 109 114 118 123 

161 155 160 165 169

197 202 206 211 216 

243 248 253 257 262 

290 294 299 304 308

336 340 345 350 354

382 387 391 396 400 

428 433 437 442 447 

474 479 483 488 493

520 525 529 534 539 

566 571 575 580 585 

612 617 621 626 630

658 663 667 672 676 

704 708 713 717 722 

749 754 769 763 768

795 800 804 809 813

56789

P.P.

5

1 0,5 

2 1,0 

8 1,5 

4 2,0

5 2,5

6 3,0 

7 3,5 

8 4,0 

9 4,5

4

1 0,4 

2 0,8 

3 1,2 

4 1,6 

6 2,0 

6 2,4 

7 2,8 

8 3,2 

9 3,6

P.P.

2° 30' = 9000" S. 4. 68 544 T. 4. 68 585 2° 35' = 9300" S. 4. 68 543 T. 4. 68 587 

2 31 = 9060 4. 68 544 4. 68 585 2 36 = 9360 4. 68 543 4. 68 587 

2 32 = 9120 4. 68 543 4. 68 586 2 37 = 9420 4. 68 542 4. 68 588 

2 33 = 9180 4. 68 543 4. 68 586 2 38 = 9480 4. 68 542 4. 68 588 

2 34 = 9240 4. 68 643 4. 68 687 2 39 = 9540 4. 68 642 4. 68 588
160 GEOGBAPHIC TABLES AND FOBMULA8.

TABLE 25. Five-place logarithms of natural numbers Continued.

N.

950

951

952

953

954

955

956

957

958

959

960

961

962

963

964 

965

966

967

968

969

970

971

972

973

974

975

976

977 

978

979

980

981

982

983

984

985

986

987

988

989

990

991

992

993

994

995

996

997

998

999

1000

N.

L. 0 1 2 3 4

97 772 777 782 786 791

818 823 827 832 836

864 868 873 877 882

909 914 918 923 928

955 959 964 968 973

98 000 005 009 014 019

046 050 055 059 064

091 096 100 105 109

137 141 146 159 155

182 186 191 195 200

227 232 236 241 245

272 277 281 286 290

318 322 327 331 336

363 367 372 376 381

408 412 417 421 426 

453 457 462 466 471

498 502 507 511 516

543 647 552 556 561

588 592 597 601 605

632 637 641 646 650

677 682 686 691 695

722 726 731 735 740

767 771 776 780 784

811 816 820 825 829

856 860 865 869 874

900 905 909 914 918

945 949 954 958 963

989 994 998 *003 #007 

99 034 038 043 047 052

078 083 087 092 096

123 127 131 136 140

167 171 176 180 185

211 216 220 224 229

255 260 264 269 273

300 304 308 313 317

344 348 352 357 361

388 392 396 401 405

432 436 441 44§ 449

476 480 484 489 493

520 624 628 533 537

564 568 572 577 581

607 612 616 621 625

651 656 660 664 669

695 699 704 708 712

739 743 747 752 756

782 787 791 795 800

826 830 835 839 843

870 874 878 883 887

913 917 92? 926 930

957 961 965 970 974

00 000 004 009 013 017

L. 0 1 2 3 4

5 6789

795 800 804 809 813

841 845 850 855 859

886 891 896 900 905

932 937 941 946 950

978 982 987 991 996

023 028 032 037 041

068 073 078 082 087

114 118 123 127 132

159 164 168 173 177

204 209 214 218 223

250 254 259 263 268

295' 299 304 308 313

340 345 349 354 358

385 390 394 399 403

430 435 439 444 448 

475 480 484 489 493

520 525 529 634 538

565 570 574 579 583

610 614 619 623 628

655 659 664 668 673

700 704 .709 713 717

744 749 753 758 762

789 793 798 802 807

834 838 843 847 851

878 883 887 892 896

923 927 932 936 941

967 972 976 981 985

*012 #016 *021 *025 *029 

056 061 065 069 074

100 105 109 114 118

145 149 154 168 162

189 193 198 202 207

233 238 242 247 251

277 282 286 291 295

322 326 330 335 339

366 370 374 379 383

410 414 419 423 427

454 458 463 467 471

498 502 506 511 515

542 646 650 555 559

585 590 594 599 603

629 634 638 642 647

673 677 682 686 691

717 721 726 730 734

760 765 769 774 778

804 808 813 817 822

848 852 856 861 865

891 896 900 904 909

935 939 944 948 952

978 983 987 991 996

022 026 030 035 . 039'

5

2° 38' = 9480" S. 4. 68 542 T. 4. 68 588

2 39 = 9540 4. 68 542 4. 68 588

2 40. = 9600 4. 68 542 4. 68 589

2 41 = 9660 4. 68 542 4. 68 589

2 42 = 9720 4. 68 541 4. 68 590

6789

P.P.

5

1 0,5

2 1,0

3 1,5 

4 2,0

5 9 &fOf\

6 3,0

7 3,5 

8 4,0

9 4,5

.

4

1 0,4

2 0,8

3 1,2

4 1,6

5 2,0

6 2,4

7 2,8

8 3,2

9 3,6

P.P.

2° 43' = 9780" S. 4. 68 541 T. 4. 68 590

2 44 = 9840 4. 68 641 4. 68 590

2 45 = 9900 4. 68 541 4. 68 591

2 46 = 9960 4. 68 541 4. 68 591

2 47=10020 4.68540 4.68592
GEOGRAPHIC TABLES AND FORMULAS. 161

Formula for using quantities /S and T: 

log sin a = log a" + S. 

log tan a = log a" + 7". 

log cot a a. c. log «" + a. c. log T.

log «" = log sin a 8 = log tan « T.

log cos a = log (90° - a)" + S. 

log cot a = log (90° - a)" + J. 

log tan a = a. c. log (90° a)" + a. c. log T.

log (90° a}" - log cos a 8 = log cot a T.

. 41623° 16 11
162 GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 26. Natural sines and cosines.

Prop.

parts

29

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

M.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36.

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

0°

N.sine

00000

00029

00058

00087

00116

00145

00175

00204

00233

00262

00291

00320

00349

00378

00407

00436

00465

00495

00524

00553

00582

00611

00640

00669'

00698

00727

00756

00785

00814

00844

00873

00902

00931

00960

00989

01018

01047

01076

01105

01134

01164

01193

01222

01251

01280

01309

01338

01367

01396

01425

01454

01483

01513

01542

01571

01600

01629

01658.

01687

01716

01745

N.'COS.

N. cos.

100000

100000

100000

100000

100000

100000

100000

100000

100000

100000

100000

99999

99999

99999

99999

99999

99999

99999

99999

99998

99998

99998

99998

99998

99998

99997

99997

99997

99997

99996

99996

99996

99996

99995

99995

99995

99995

99994

99994

99994

99993

99993

99993

99992

99992

99991

99991

99991

99990

99990

99989

99989

99989

99988

99988

99987

99987

99986

99986

99985

99985

N. sine.

89°

1°

N.sine

01745

01774

01803

01832

01862

01891

01920

C1949

01978

02007

02036

02065

02094

02123

02152

02181

02211

02240

02269

02298

02327

02356

02385

02414

02443

02472

02501

02530

02560

02589

02618

02647

02676

02705

02734

02763

02792

02821

02850

02879

02908

02938

02967

02996

03025

03054

03083

03112

03141

03170

03199

03228

03257

03286

03316

03345

03374

03403

03432

03461

03490

N. cos.

N.cos

99985

99984

99984

99983

99983

99982

99982

99981

99980

99980

99979

99979

99978

99977

99977

99976

99976

99975

99974

99974

99973

99972

99972

99971

99970

99969

99969

99968

99967

99966

99966

99965

99964

99963

99963

99962'

99961

99960

99959

99959

99958

99957

99956

99955'

99954

99953

99952

99952

99951

99950

99949

99948

99947

99946

99945

99944

99943

99942

99941

99940

99939

N.sine.

88°

2°

N.sine

03490

03519

03548

03577

03606

03635

03664

03693

03723

03752

03781

03810

03839

03868

03897

03926

03955

03984

04013

04042

04071

04100

04129

04159

04188

04217

04246

04275

04304

04333

04362

04391

04420

04449

04478

04507

04536

04565

04594

04623

04653

04682

04711

04740

04769

04798

04827

04856

04885

04914

04943

04972

05001

05030

05059

05088

05117

05146

05175

05205

05234

N. cos.

N. cos.

99939

99938

99937

99936

99935

99934

99933

99932

99931

99930

99929

99927

99926

99925

99924

99923

99922

99921

99919

99918

99917

99916

99915

99913

99912

99911

99910

99909

99907

99906

99905

99904

99902

99901

99900

99898

99897

99896

99894

99893

99892

99890

99889

99888

99886

99885

99883

99882

99881

99879

99878

99876

99875

99873

99872

99870

99869

99867

99866

99864

99863

N.sine.

87°

3°

N.sine.

05234

05263

05292

05321

05350

05379

05408

05437

05466

05495

05624

05553

05582

05611

05640

05669

05698

05727

05756

05785

05814

05844

05873

05902

05931

05960

05989

06018

06047

06076

06105

06134

06163

06192

06221

06250

06279

06308

.06337

06366

06395

06424

06453

06482

06511

06540

06569

06598

06627

06656

06685

06714

06743

06773

06802

06831

06860

06889

06918

06947

06976

N. cos.

N. cos.

99863

99861

99860

99858

99857.

99855

99854

99852

99851

99849

99847

99846

99844

99842

99841

99S39

99838

99836

99834

99833

99831

99829

99827

99826

99824

99822

99821

99S19

99817

99815

99813

99812

99810

99808

99806

99804

99803

99801

99799

99797

99795

99793

99792

99790

99788

99786

99784

99782

99780

99778

99776

99774

99772

99770

99768

99766

99764

99762

99760

99758

99756.

tf.sine.

86° '

4°

N.sine

06976

07005

07034

07063

07092

07121

07150

07179

07208

07237

07266

07295

07324

07353

07382

07411

07440

07469

07498

07527

07556

07585

07614

07643

07672

07701

. 07730

07759

07788

07817

07846

07875

07904

07933

07962

07991

08020

08049

08078

08107

08136

08165

08194

08223'

08252

08281

08310

08339

08368

08397

08426

08455

08484

08513

08542

08571

08600

08629

08658

08687

08716

N. cos.

N.cos

99756

99754

99752

99750

99748

99746

99744

99742

99740

99738

99736

99734

99731

99729

99727

99725

99723

99721

99719

99716

99714

99712

99710

99708

99705

99703

99701

99699

99696

99694

99692

99689

99687

99685

99683

99680

99678

99676

99673

99671

99668

99666

99664

99661 

99659

99657

99654

99652

99649

99647

99644

99642

99639

99637

99635

99632

99630

99627

99625

99622

99619

tf.sine.

85°

60

59

58

57

56

55

54

53

52

51

50

49

48

47

46

45

44

43

42

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

M.

Prop.

parts

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1 ' 1

1

1

1

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 26. Natural sines and cosines Continued.

163

Prop.

parts

29

0

0

1

1

2

2

3

3

4

4

5

.5

0

0

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

20

20

27

27

28

28

29

29

M.

0

1

2

3

4

 5

(i

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

.29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

5°

N.sine.

08716

OS745

OS774

08803

08831

OSS60

OS8S9

OSQ18

08947

08976

09005

09034

09063

09092

09121

09150

09179

09208

09237

09266

09295

09324

09353

09382

09411

09440

09469

09498

09527

09556

09585

09614

09642

09071

09700

09729

09758

09787

09816

09S45

09S74

09903

09932

09961

09990

10019

10048

10077

10106

10135

10164

10192

10221

10250

10279

10308

10337

10366

10395

10424

10453

N.cos.

N.cos.

99619

99617

99614

99612

99609

99607

99604

99602

99599

99596

99594

99591

99588

99586

99583

99580

99578

99575

99572

99570

99567

99564

99562

99559

99556

99553

99551

99548

99545

99542

99540

99537

99534

99531

99528

99526

99523

99520

99517

99514

99511

99508

99506

99503

99500

99497

99494

99491

994S8

99485

99482

99479

99476

99473

99470

99467

99464

99461

99458

99455

99452

N.sine.

84°

6°

N.sine.

10453

10482

10511

10540

10569

10597

10626

10655

10684

10713

10742

10771

10800

10829

10S58

10887

10916

10945

10973

11002

11031

11060

110S9

11118

11147

11176

11205

11234

11263

11291

11320

11349

11378

11407

11436

 11465

11494

11523

11552

11580

11609

11638

11667

11696

11725

11754

11783

11812

11840

11869

11898

11927

11956

11985

12014

12043

12071

12100

12129

12158

12187

N. cos.

N. cos.

99452

99449

99446

99443

99440

99437

99434

99431

99428

99424

99421

99418

99415

99412

99409

99400

99402

99399

99396

99393

99390

99386

99383

993SO

99377

99374

99370

99367

99364

99360

99357

99354

99351

99347

99344

99341

99337

99334

99331

99327

99324

99320

99317

99314

99310

99307

99303

99200

99297

99293

99290

99286

99283

99279

99276

99272

99269

99265

99262

99258

99255

N.sine.

83°

7°

N.sine.

12187

12216

12245

12274

12302

12331

12360

12389

12418

12447

12476

12504

12533

12562

12591

12620

12649

12078

12706

12735

12764

12793

12822

12851

12880

12908

12937

12966

12995

13024

13053

13081

13110

13139

13168

13197

13226

13254

13283

13312

13341

13370

13399

13427

13456

13485

13514

13543

13572

13600

13629

13658

13687

13716

13744

13773

13802

13831

13S60

13889

13917

N. cos.

N. cos.

99255

99251

99248

99244

99240

99237

99233

99230

99226

99222

99219

99215

99211

99208

99204

99200

99197

99193

99189

99186

99182

99178

99175-

99171

99167

99163

99160

99156

99152

99148

99144

99141

99137

99133

99129

99125

99122

99118

99114

99110

99106

99102

99098

99094

99091

99087

99083

99079

99075

99071

99067

99063

99059

99055

99051

99047

99043

99039

99035

99031

99027

N.sine.

82°

8°

N.sine.

13917

13946

13975

14004

14033

14061

14090

14119

14148

14177

14205

14234

14263

14292

14320

14349

14378

14407

14436

14464

14493

14522

14551

14580

14608

14637

14600

14095

14723

14752

14781

14810

14838

14807

14896

14925

14954

14982

15011

15040

15069

15097

15126

15155

15184

15212

15241

15270

15299

15327

15356

15385

15414

15442

15471

15500

15529

15557

15586

15615

15643

N. cos.

N. cos.

99027

99023

99019

99015

99011

99006

99002

98998

98994

98990

98986

99982

98978

98973

98969

989G5

98961

98957

98953

9S94S

9S944

98940

98936

98931

98927

98923

98919

98914

98910

98906

98902

98897

98893

98889

98884

98880

98876

98871

98867

98863

98858

98854

98849

98845

98841

98836

98832

98827

98823

98818

98814

98809

98805

98SOO

98796

98791

9S787

98782

98778

98773

98769

N.sine.

81°

9°

N.sine.

15643

15672

15701

15730

15758

15787

15816

15845

15S73

15902

15931

15959

15988

16017

16046

16074

16103

10132

10100

10189

10218

10240

16275

16304

16333

16361

16390

16419

16447

16476

16505

16533

16562

16591

16620

16648

16677

16706

16734

16763

16792

16820

16849

16878

16906

16935

16904

10992

17021

17050

17078

17107

17130

17164

17193

17222

17250

17279

17308

17330

17305

N.cos.

N. cos.

98769

98704

98760

98755

98751

98746

98741

98737

98732

98728

98723

98718

98714

98709

98704

98700

98695

98090

98086

98681

98676

98671

98667

98662

98657

98652

98648

98643

98638

98633

98629

98624

98619

98614

98609

98604

98600

98595

98590

98585

98580

98575

98570

98565

98561

98556

98551

98546

98541

98536

98531

98526

98521

98516

98511

98506

98501

98496

98491

98486

98481

N.sine.

80°

M.

60

59

58

57

56

55

54

53

52

51

50

49

48

47

46

45

44

43

42

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

10

15

14

13

12

11

10

9

8

7

0

5

4

3

2

1

0

M.

Prop.

parts

4

4

4

4

4

4

4

4

4

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

0

- 0

0

0

0

0

0
164 GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 26. Natural sines and cosines Continued.

Prop

parts

28

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

14

15

15

1C

16

17

17

18

18

19

19

20

20

21

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

M.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

23

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

10°

N.sine

17365

17393

17422

17451

17479

17508

17537

17565

17594

17623

17051

17680

17708

17737

17766

17794

17823

17852

17880

17909

17937

17966

17995

18023

18052

18081

18109

18138

18166

18195

18224

18252

1S281

18309

18338

18367

18395

18424

18452

18481

18509

18538

18567

18595

18624

18652

18681

18710

18738

18767

18795

18824

18852

18881

18910

18938

18967

18995

19024

19052

19081

ST. cos.

.N.cos.

98481

98476

98471

98466

98461

98455

98450

98445

93440

98435

98430

98425

98420

98414

98409

98404

98399

98394

98389

98383

98378

98373

98308

98362

98357

98352

98347

9&341

98336

98331

98325

98320

98315

98310

98304

98299

98294

98288

98283

98277

98272

98267

98261

98256

98250

98245

98240

98234

98229

98223

98218

98212

98207

98201

98196

98190

98185

98179

98174

98168

98163

ST. sine.

79°

11°

N.sine

19081

19109

19138

19167

19195

19224

19252

19281

19309

19338

19366

19395

19423

19452

19481

19509

19538

19566

19595

19623

19652

19680

19709

19737

19766

19794

19823

19851

19880

19908

19937

19965

19994

20022

20051

20079

20108

20136

20165

20193

20222

20250

20279

20307

20336

20364

20393

20421

20450

20478

20507

20535

20563

20592

20620

20649

20677

20706

20734

20763

20791

tf.cos.

N.cos

98163

98157

98152

98146

98140

98135

98129

98124

98118

98112

98107

98101

98096

98090

98084

98079

98073

98067

98061

98056

98050

98044

98039

98033

98027

98021

98016

98010

98004

97998

97992

97987

97981

97975

97969

97903

97958

97952

97946

97940

97934

97928

97922

97916

97910

97905

97899

97893

97887

97881

97875

97869

97863

97857

97851

97845

97839

97833

97827

97821

97815

<T.sinc.

78°

12°

N.sine

20791

20820

20848

20877

20905

20933

20962

20990

21019

21047

21076

21104

21132

21161

21189

21218

21246

21275

21303

21331

21360

21388

21417

21445

21474

21502

21530

21559

21587

21616

21644

21672

21701

21729

21758

21786

21814

21843

21871

21899

21928

21956

21985

22013

22041

22070

22098

22120

22155

22183

22212

22240

22268

22297

22325

22353

22382

22410

22438

22467

22495

tf.cos.

N.cos

97815

97809

97803

97797

97791

97784

97778

97772

97766

97760

97754

97748

97742

97735

97729

97723

97717

97711

97705

97698

97692

97086

97680

97673

97667

97661

97655

97648

97642

97636

97630

97623

97617

97611

97604

97598

97592

97585

97579

97573

975C6

97560

97553

97547

97541

97534

97528

97521

97515

97508

97502

97496

97489

97483

97476

97470

97463

97457

97450

97444

97437

tf.sine.

77°

13°

N.sine

22495

22523

22552

22580

22608

22637

22665

22693

22722

22750

22778

22807

22835

22863

22892

22920

22948

22977

23005

23033

23062

23090

23118

23146

23175

23203

23231

23260

23288

23316

23345

23373

23401

23429

23458

23486

23514

23542

23571

23599

23G27

23656

23684

23712

23740

23769

23797

23825

23853

23882

23910

23938

23966

23995

24023

24051

24079

24108

24136

24164

24192

T. cos.

N.cos

97437

97430

97424

97417

97411

97404

97398

97391

97384

97378

97371

97365

97358

97351

97345

97338

97331

97325

97318

97311

97304

. 97298

97291

97284

97278

97271

97264

97257

97251

97244

97237

97230

97223

97217

97210

97203

97196

97189

97182

97176

97169

97162

97155

97148

97141

97134

97127

97120

97113

97106

97100

97093

97086

97079

97072

97065

97058

97051

97044

97037

97030

SLsine.

76°

14°

N.sine

24192

24220

24249

24277

24305

24333

24362

24390

24418

24446

24474

24503

24531

24559

24587

24615

24644

24672

24700

24728

24756

24784

24813

24841

24869

24897

24925

24954

24982

25010

25038

25066

25094

25122

25151

25179

25207

25235

25263

25291

25320

25348

25376

25404

25432

25460

25488

25516

25545

25573

25601

25629

25657

25685

25713

25741

25769

25798

25826

25854

25882

N.cos.

N.cos

97030

97023

97015

97008

97001

96994

96987

96980

96973

96966

96959

96952

96945

96937

96930

96923

96916

96909

96902

96894

96887

96880

96873

96866

96858

96851

96844

96837

96829

96822

96815

96807

96800

96793

96786

96778

96771

96764

96756

96749

96742

96734

96727

96719

96712

96705

96697

96690

96682

96675

96667

96660

96653

96645

96638

96630

96623

96615

96608

96600

96593

N.sine.

75°

60

59

58

57

56

55

54

53

52

51

50

49

48

47

40

45

44

43

42

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

M.

Prop.

parts

6

6

6

6

6

6

6

5

5

5

5

5

5

5

5

5

5

4

4

4

4

4

4

4

4

4

4

3

3

3

3

3

3

3

3

3

3

2

2

2

2

2

2

2

2

2

2

1

1

1

1

1

1

1

1

1

1

0

0

0

0

0
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 26. Natural sines and cosines Continued.

165

Prop

parts

27

0

0

1

1

2

2

:{

3

4

4

5

5

5

6

6

7

7

8

8

9

9

9

10

10

11

11

12

12

13

13

14

14

14

15

15

16

16

17

17

18

18

18

19

19

20

20

21

21

22

22

23

23

23

24

24

25

25

26

26

27

27

M.

0

1

2

3

4

5

0

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

15° . 

N.sine

25882

25910

25938

25966

25994

26022

26050

26079

26107

26135

26163

26191

26219

26247

26275

26303

26331

26359

26387

26415

26443

26471

26500

26528

26556

26584

26612

26640

26668

26696

26724

26752

26780

26808

26836

26864

26892

26920

26948

26976

27004

27032

27060

27088

27116

27144

27172

27200

27228

27256

27284

27312

27340

 27368

27396

27424

27452

27480

27508

27536

27564

N. cos.

N. cos.

96593

96585

96578

96570

96562

96555

96547

96540

96532

96524

96517

96509

96502

96494

96486

96479

96471

96463

96456

96448

96440

96433

96425

96417

96410

96402

96394

96386

96379

96371

96363

96355

96347

96340

96332

96324

96316

96308

96301

96293

90285

96277

96269

96261

96253

96246

96238

96230

96222

96214

96206

96198

96190

96182

96174

96166

96158

96150

96142

96134

96126

N. sine.

74°

16°

N.sine

27564

27592

27620

27648

27676

27704

27731

27759

27787

27S15

27843

27871

27899

27927

27955

27983

28011

28039

28067

28095

28123

28150

28178

28206

28234

28262

28290

28318

28346

28374

28402

28429

28457

28485

28513

28541

28569

28597

28625

28652

28680

28708

28736

28764

28792

28820

28847

28875

28903

28931

28959

28987

29015

29042

29070

29098

29126

29154

29182

29209

29237

tf. cos.

N.cos.

96126

96118

96110

96102

96094

96086

96078

96070

96062

96054

96046

96037

96029

96021

96013

96005

95997

95989

95981

95972

95964

95956

95948

95940

95931

95923

95915

95907

95898

95890

95882

95874

95865

95957

95849

95841

95832

95824

95816

95807

95799

95791

95782

95774

95766

95757

95749

95740

95732

95724

95715

95707

95698

95690

95681

95673

95664

95656

95647

95639

95630

'J.sine.

73°

17°

N.sine.

29237

29265

29293

29321

29348

29376

29404

29432

29460

29487

29515

29543

29571

29599

29626

29654

29682

29710

29737

 29765

29793

29821

29849

29876

29904

29932

29960

29987

30015

30043

30071

30098

30126

30154

30182

30209

30237

30265

30292

30320

30348

30376

30403

30431

30459

30486

30514

30542

30570

30597

30625

30653

30680

30708

30736

30763

30791

30819

30846

30874

30902

tf.cos.

N.cos.

95630

95622

95613

95605

95596

95588

95579

95571

95562

95554

95545

95536

95528

95819

95511

95502

95493

95485

95476

95467

95459

95450

95441

95433

95424

95415

95407

95398

95389

95380

95372

95363

95354

95345

95337

95328

95319

95310

95301

95293

95284

95275

95266

95257

95248

95240

95231

95222

95213

95204

95195

95186

95177

95168

95159

95150

95142

95133

95124

95115

95106

tf.sine.

72°

18°

N.sine.

30902

30929

30957

30985

31012

31040

31068

31095

31123

31151

31178

31206

31233

31261

31289

31316

31344

31372

31399

31427

31454

31482

31510

31537

31565

31593

31620

31648

31675

31703

31730

31758

31786

31813

31841

31868

31896

31923

31951

31979

32006

32034

32061

32089

32116

32144

32171

32199

32227

32254

32282

32309

32337

32364

32392

32419

32447

32474

32502

32529

32557

N. cos.

N..COS.

95106

95097

95088

95079

95070

95061

95052

95043

95033

95024

95015

95006

94997

94988

94979

94970

94961

94952

94943

94933

94924

94915

94906

94897

94888

94878

94869

94860

94851

94842-

94832

94823

94814

94805

94795

94786

94777

94768

94758

94749

94740

94730

94721

94712

94702

94693

94684

94674

94665

94656

94646

94637

94627

94618

94609

94599

94590

94580

94571

94561

94552

N.sine.

71°

19°

N.sine.

32557

32584

32612

32639

32667

32694

32722

32749

32777

32804

32832

32859

32887

32914

32942

32969

32997

33024

33051

33079

33106

33134

33161

33189

33216

33244

33271

33298

33326

33353

33381

33408

33436

33463

33490

33518

33545

33573

33600

33627

33655

33682

33710

33737

33764

33792

33819

33846

33874

33901

33929

33956

33983

34011

34038

34065

34093

34120

34147

34175

34202

N. cos.

N. cos.

94552

94582

94533

94523

94514

94504

94495

94485

94476

94466

94457

94447

94438

94428

94418

94409

94399

94390-

94380

94370

94361

94351

94342

94332

94322

94313

94303

94293

94284

94274

94264

94254

94245

94235

94225

94215

94206

94196

94186

94176

94167

94157

94147

94137

94127

94118

94108

94098

94088

94078

94068

94058

94049

94039

94029

94019

94009

93999

93989

93979

93969

N.sine.

70°

60

59

58

57

56

55

54

53

52

51

50

49

48

47

46

45

44

43

42

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

M.

Prop.

parts

9

9

9

9

9

8

8

8

8

8

8

8

7

7

7

7

7

7

6

6

6

6

6

6

6

5

5

5

5

5

5

5

4

4

4

4

4

4

3

3

3

3

3

3

3

2

2

2

2

2

2

2

1

1

1

1

1

1

0

0

0

0
166 GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 26. Natural sines and cosines Continued.

Prop.

parts

27

0

0

1

1

2

2

3

3

4

4

5

5

5

0

0

7

7

8

8

9

9

9

10

10

It

11

12

12

13

13

14

14

14

15

15

16

1C

17

17

18

18

18

19

19

20

20

21

21

22

22

23

23

23

24

24

25

25

26

26

27

27

M.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

3839-

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56 57

58

59

60

20°

N. sine.

34202

34229

34257

34284

34311

34339

34366

34393

34421

34448

34475

34503

34530

34557

34584

34612

34639

34666

34694

34721

34748

34775

34803

34830

34857

34884

34912

34939

34966

34993

35021

35048

35075

35102

35130

35157

35184

35211

35239

35266

35293

35320

35347

35375

35402

35429

35456

35484

35511

35538

35565

35592

35619

35647

35674

35701

,55728

35755

35782

35810

35837

N. cos.

N. cos.

93969

93959

93949

93939

93929

93919

93909

93899

93889

93879

93869

93859

93849

93839

93829

93819

93809

93799

93789

93779

93769

93759

93748

93738

93728

93718

93708

93698

93688

93677

93667°

93657

93647

93637

93626

93016

93606

93596

93585

93575

93565

93555

93544

93534

93524

93514

93503

93493

93483

93472

93462

93452

93441

93431

93420

93410

93400

933S9

93379

93368

93358

N. sine.

69°

21°

N.sine.

35837

35864

35891

35918

35945

35973

36000

36027

36054

36081

30108

36135

36162

36190

36217

36244

36271

36298

36325

36352

36379

36406

36434

36461

36488

36515

36542

36569

36596

36623

36650

36677

36704

36731

36758

36785

36812

36839

36567

36894

36921

36948

36975

37002

37029

37056

37083

37110

37137

37164

37191

37218

37245

37272

37299

37326

37353

37380

37407

37434

37461

N. cos.

N. cos.

93358

93348

93337

93327

93316

93306

93295

93285

93274

93264

93253

93243

93232

93222

93211

93201

93190

93180

93169

93159

93148

93137

93127

93116

93106

93095

93084

93074

93063

93052

93042

93031

93020

93010

92999

92988

92978

92967

92956

92945

92935

92924

92913

92902

92892

92881

92870

92859

92849

92838

92827

92816

92805

92794

92784

92773

92762

92751

92740

92729

92718

N.sine.

68°

22°

N.sine.

37461

37488

37515

37542

37569

37595

37622

37649

37676

37703

37730

37757

37784

37811

&838

37865 .

37892

37919

37946

37973

37999

38026

38053

38080

38107

38134

38161

38188

38215

38241

38268

38295

38322

38349

38376

38403

38430

38456

38483

38510

38537

38564

38591

38617

38644

38671

38698

38725

38752

38778

38805

38832

38859

38886

38912

3893a

38966

38993

39020

39046

39073

N. cos.

N. cos.

92718

92707

92697

92686

92675

92664

92653

92642

92631

92620

92609

. 92598

92587

92576

92565

92554

92543

92532

92521

92510

92499

92448

92477

92466

92455

92444

92432

92421

92410

92399

92388

92377

92366

92355

92343

92332

92321

92310

92299

92287

92276

92265

92254

92243

92231

92220

92209

92198

92186

92175

92164

92152

92141

92130

92119

92107

92096

92085

92073

92062

92050

N.sine.

67°

23°

N.sine.

39073

39100

39127

39153

39180

39207

39234

39260

39287

39314

39341

39367

39394

39421

39418

39474

39501

39528

39555

39581

39608

39635

39661

39688

39715

39741

39768

39795

39822

39848

39875

39902

39928

39955

39982

40008

40035

40062

40088

40115

40141

40168

40195

40221

40248

40275

40301

40328

40355

40381

40408

40434

40461

40488

40514

40451

40567

40594

40621

40647

40674

N. cos.

N. cos.

92050

92039

92028

92016

92005

91994

91982

91971

91959

91948

91936

91925

91914

91902

91891

91879

91868

91856

91845

91S33

91822

91810

91799

91787

91775

91764

91752

91741

91729

91718

91706

91694

916S3

91671

91660

91648

91636

91625

91613

91601

91590

91578

91566

91555

91543

91531

91519

91508

91496

91484

91472

91461

91449

91437

91425

91414

91402

91390

91378

91366

91355

N.sine.

66°

24°

N.sine.

40674

40700

40727

40753

40780

40806

40833

40860

40886

40913

40939

40966

40992

41019

41045

41072

41098

41125

41151

41178

41204

41231

41257

41284

41310

41337

41363

41390

41416

41443

41469

41496

41522

41549

41575

41602

41628

41655

41681

41707

41734

41760

41787

41813

41840

41866

41892

41919

41945

41972

41998

42024

42051

42077

42104

42130

42156

42183

42209

42235

42262

N. COS.

N. cos.

91355 .

91343

91331

91319

91307

91295

91283

91272

91260

91248

91236

91244

91212

91200

91118

91176

91164

91152

91140

91128

91116

91104

91092

91080

91068

91056

91044

91032

91020

91008

90996

90984

90972

90960

90948

90936

90924

90911

90899

90887

90875

90863

90851

90839

90826

90814

90802

90790

90778

90766

90753

90741

90729

90717

90704

90692

90680

90668

90655

90643

90631

N.sine.

65°

60

59

58

57

56

55

54

53

52

51

50

49

48

47

46

45

44

43

42

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

M.

Prop.

parts

11

11

11

11

10

10

10

10

10

10.

9

9

9

9

9

8

8

8

8

8

8

7

7

7

7

7

6

6

6

6

6

6

5

5

5

5

5

4

4

4

4

4

3

3

3

3

3

3

2

2

2

2

2

1

1

1

1

1

1

0

0

0
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 26. Natural sines and cosines Continued.

167

Prop.

parts

26

. 0

0

1

1

2

2

3

3

3

4

4

5

5

6

C

7

7

7

8

8

9

9

10

10

10

11

11

12

12

13

13

13

14

14

15

15

1C

16

16

17

17

18

18

19

19

20

20

.20

21

21

22

22

23

23

23

24

24

25

25

26

26

M.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

25°

N. sine.

42262

42288

42315

42341

42367

42394

42420

42446

42473

42499

42525

42552

42578

42604

42631

42657

42683

42709

42736

42762

427S8

42815

42841

42867

42894

42920

42946

42972

42999

43025

43051

43077

43104

43130

43156

43182

43209

43235

43201

43287

43313

43340

43366

43392

43418

43445

43471

43497

43523

43549

43575

43602

43628

43054

43680

43706

43733

43759

43785

43811

43837

N.cos.

N.cos.

90631

90618

90606

90594

90582

90569

90557

90545

90532

90520

90507

90495

90483

90470

90458

90446

90-133

90421

90408

90396

903S3

90371

90358

90346

90334

90321

90309

90296

90284

90271

90259

90246

90233

90221

90208

90196

90183

90171

90158

90146

90133

90120

90108

90095

90082

90070

90057

90045

90032

90019

90007

89994

89981

89968

89956

89943

89930

89918

89905

89892

89879

N. sine.

64°

26°

N.sine.

43837

43863

43S89

43916

43942

43968

43994

44020

'44046

44072

44098

44124

44151

44177

44203

44229

44255

44281

44307

44333

44359

44385

44411

44437

44464

44490

44516

44542

44568

44594

44620

44646

44672

44698

44724

44750

44776

44802

44828

44 854

44880

44906

44932

44958

44984

45010

45036

45062

45088

45114

45140

45166

45192

45218

45243

45269

45295

45321

45347

45373

45399

N. cos.

N. cos.

89879

89867

89854

89841

89828

89816

89803

89790

89777

89764

89752

89739

89726

89713

89700

89687

89674

89662

89649

89636

89623

89610

89597

89584

89571

89558

89545

89532

89519

89506

89493

89480

89467

89454

89441

89428

89415

89402

89389

89376

89363

89350

89337

89324

89311

89298

89285

89272

89259

89245

89232

89219

89206

89193

89180

89167

89153

89140

89127

89114

89101

N.sine.

63°

27°

N.sine.

45399

45425

45451

45477

45503

45529

45554

45580

45606

45632

45658

45684

45710

45736

45762

45787

45813

45839

45865

45891

45917

45942

45968

45994

46020

460-16

46072

46097

46123

46149

46175

46201

46226

46252

46278

46304

46330

46355

46381

46407

46433

46458

46484

46510

46536

46561

46587

46613

46639

46664

46690

46716

46742

46767

46793

46819

46844

46870

46896

46921

46947

N.cos.

N. cos.

89101

89087

89074

89061

89048

89035

89021

89008

88995

'88981

88968

88955

88942

88928

88915

88902

88888

88875

88862

88848

88835

88822

88SOS

88795

88782

8S768

88755

88741

88728

88715

88701

88688

88674

88661

88647

88634

88620

88607

88593

88580

88566

88553

88539

88526

88512

88499

88485

88472

88458

88445

88431

88417

88404

88390

88377

88363

88349

88336

88322

88308

88295

N.sine.

62°

28°

N.sine.

46947

40973

46999

47024

47050

47070

47101

47127

47153

47178

47204

47229

47255

47281

47306

47332

47358

47383

47409

47434

47460

47486

47511

47537

47562

47588

47614

47639

47665

47690

47716

47741

47767

47793

47818

47844

47869

47895

47920

47946

47971

47997

48022

48048

48073

48099

48124

48150

48175

48201

48226

48252

48277

48303

48328

48354

48379

48405

48430

48456

484S1

N. cos.

N. cos.

88295

88281

88267

882.54

88240

88226

88213

88199

88185

88172

88158

88144

88130

88117

88103

88089

88075

88062

88048

88034

88020

88006

87993

87979

87965

87951

87937

87923

87909

87896

87882

87868

87854

87840

87826

87812

87798

87784

87770

87756

87743

87729

87715

87701

87687

87673

87659

87645

87631

87617

87603

87589

87575

87561

87546

87532

87518

87504

 87490

87476

87462

N.sine.

61°

29°

N.sine.

48481

48506

48532

48557

48583

48608

48634

48659

48684

48710

48735

48761

48786

48811

48837

48862

48888

48913

48938

48964

48989

49014

49040

49065

49090

49116

49141

49166

49192

49217

49242

49268

49293

49318

49344

49369

49394

49419

49445

49470

49495

49521

49546

49571

49596

49622

49647

49672

49697

49723

49748

49773

49798

49824

49849

49874

49899

49924

49950

49975

50000

N. cos.

N. cos.

87462

87448

87434

87420

87406

87391

87377

87363

87349

87335

87321

87306

87292

87278

87264

87250

87235

87221

87207

87193

87178

87164

87150

87136

87121

87107

87093

87079

87064

87050

87036

87021

87007

86993

86978

86964

86949

86935

86921

86906

86892

86878

86863

86849

86834

86820

86805

86791

86777

86762

86748

86733

86719

86704

86690

86675

86661

86646

86632

86617

86603

N.sine.

60°

60

59

58

57

56

55

54

53

52

51

50

49

48

47

46

45

44

43

42

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

14

11

10

9

8

7

6

5

4

3

2

1

0

M.

Prop.

parts

14

14

14

14

13

13

13

13

12

12

12

12

11

11

11

11

11

10

10

10

10

9

9

9

9

8

8

8

8

7

7

7

7

7

6

0

6

6

5

5

5

5

4

4

4

4

4

3

3

3

3

2

2

2

2

1

1

1

1

0

0

0
168 GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 26. Natural sines and cosines Continued.

Prop.

parts

25

0

0

1

1

2

2

3

3

3

4

4

.5

5

5

6

6

7

7

8

8

8

9

9

10

10

10

11

11

12

12

13

13

13

14

14

15

15

15

16

16

17

17

18

18

18

19

19

20

20

20

21

21

22

22

23

23

23

24

24

25

25

M.

0

1

2

3

4

5

li

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

80°

N.sine.

50000

50025

50050

50076

50101

50126

50151

50176

50201

50227

50252

50277

50302

50327

50352

50377

50403

50428

50453

50478

50503

50528

50553

50578

50603

50628

50054

50679

50704

50729

50754

50779

50804

50829

50854

50879

50904

50929

50954

50979

51004

51029

51054

51079

51104

51129

51154

51179

51204

51229

51254

51279

51304

51329

51354

51379

51404

51429

51454

51479 

51504

N. cos.

N. cos.

86603

86588

86573

86559

86544

86530

86515

86501

86486

86471

86457

86442

86427

86413

86398

86384

86369

86354

86340

86325

86310

86295

86281

86266

86251

86237

86222

86207

86192

86178

86163

86148

86133

86119

86104

86089

86074

86059

86045

86030

86015

86000

85985

85970

85956

85941

85926

85911

85896

85881

85866

85851

85836

85821

85806

85792

85777

85762

85747

85732

85717

N. sine.

59°

31°

N.sine.

51504

51529

51554

51579

51604

51628

51653

51678

51703

51728

51753

51778

51803

51828

51852

51877

51902

51927

51952

51977

52002

52026

52051

52076

52101

52126

52151

52175

52200

52225

52250

52275

52299

52324

52349

52374

52399

52423

52448

52473

52498

52522

52547

52572

52597

52621

52646

52671

52696

52720

52745

52770

52794

52819

52844

52869

52893

52918

52943

52967

52992

N. cos.

N. cos.

85717

85702

85687

85672

85657

85642

85627

85612

85597

85582

85567

85551

85536

85521

85506

85491

85476

85461

85446

85431

85416

85401

85385

85370

85355

85340

85325

85310

85294

85279

85264

85249

85234

85218

85203

85188

85173

85157

85142

85127

85112

85096

85081

85066

85051

85035

85020

85005

84989

84974

84959

84943

84928

84913

84897

84882

84866

84851

84836

84820

84805

N.sine.

58°

82°

N.sine.

52992

53017

53041

53066

53091

53115

53140

53164

53189

53214

53238

53263

53288

53312

53337

53361

53386

53411

53435

53460

53484

53509

53534

53558

53583

53607

53632

53656

53681

53705

53730

53754

53779

53804

53828

53853

53877

53902

53926

53951

53975

54000

54024

54049

54073

54097

54122

54146

54171

54195

54220

54244

54260

54293

54317

54342

54366

54391

54415

54440

54464

N.cos.

N. cos.

84805

84789

84774

84759

84743

84728

84712

84697

84681

84666

84650

84635

84619

84604

84588

84573

84557

84542

84526

84511

84495

84480

84464

84448

84433

84417

84402

84386

84370

84355

84339

84324

84308

84292

84277

84261

84245

84230

84214

84198

84182

84167

84151

84135

84120

84104

84088

84072

84057

84041

84025

84009

83994

83978

83962

83946

83930

83915

83899

83883

83867

N.sine.

57°

goo OO

N.sine.

54464

54488

54513

54537

54561

54586

54610

54635

54659

54683

54708

54732

54756

54781

54805

54829

54854

54878

54902

54927

54951

54975

54999

55024

55048

55072

55097

55121

55145

55169

55194

55218

55242

55266

55291

55315

55339

55363

55388

55412

55436

55460

55484

55509

55533

55557

55581

55605

55630

55654

55678

55702

55726

55750

55775

55799

55823

55847

55871

55895

55919

N. cos.

N. cos.

83867

83851

83835

83819

83804

83788

83772

83756

83740

83724

83708

83692

83676

83660

83645

83629

83613

83597

83581

83565

83549

83533

83517

83501

83485

83469

83453

83437

83421

83405

83389

83373

83356

83340

83324

83308

83292

83276

83260

83244

83228

83212

83195

83179

83163

83147

83131

83115

83098

83082

83066

83050

83034

83017

83001

82985

82969

82953

82936

82920

82904

N.sine.

56°

34°

tf.sine.

55919

55943

55968

55992

56016

56040

56064

56088

56112

56136

56160

56184

56208

56232

56256

56280

56305

56329

56353

56377

56401

56425

56449

56473

56497

56521

56545

56569

56593

56617

56641

56665

56689

56713

56736

56760

56784

56808

56832

56856

56880

56904

56928

56952

56976

57000

57024

57047

57071

57095

57119

57143

57167

57191

57215

57238

57262

57286

57310

57334

57358

N. cos.

N.cos.

82904

82887

82871

82855

82839

82822

82806

82790

82773

82757

82741

82724

82708

82692

82675

82659

82643

82626

82610

82593

82577

82561

82544

82528

82511

82495

82478

82462

82446

82429

82413

82396

82380

82363

82347

82330

82314

82297

82281

82264

82248

82231

82214

82198

82181

82165

82148

82132

82115

82098

82082

82065

82048

82032

82015

81999

81982

81965

81949

81932

81915

N.sine.

55°

60

59

58

57

56

55

54

53

52

51

50

49

48

47

46

45

44

43

42

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

M.

Prop.

parts

16

16

16

15

15

15

15

14

14

14

14

13

13

13

13

12

12

12

11

11

11

11

10

10

10

10

9

9

9

9

8

8

8

7

7

7

7

6

6

6

6

5

5

5

5 

4

4

4

3

3

3

3

2

2

2

2

1

1

1

1

0

0
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 26. Natural sines and cosines Continued.

169

Prop.

parts

23

0

0

1

1

2

2

2

3

3

3

4

4

5

5

5

6

6

7

7

7

8

8

8

9

9

10

10

10

11

11

12

12

12

13

13

13

14

14

15

15

15

16

16

16

17

17

18

18

18

19

19

20

20

20

21

21

21

22

22

23

23

M.

0

1

2

3

4

I;

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

35°

N.sine.

57358

57381

57405

57429

57453

57477

57501

57524

57548

57572

57596

57619

57643

57667

57691

57715

57738

57762

57786

57810

57833

57857

57881

57904

57928

57952

57976

57999

58023

58047

58070

58094

58118

58141

58165

58189

58212

58236

58260

58283

58307

58330

58354

58378

58401

58425

58449

58472

58496

58519

58543

58567

58590

58614

58637

58661

58684

58708

58731

58755

58779

N. cos.

N. cos.

81915

81899

81882

81865

81848

81832

81815

81798

81782

81765

81748

81731

81714

81698

81681

81664

81647

81631

81614

81597

81580

81563

81546

81530

81513

81496

81479

81462

81445

81428

81412

81395

81378

81361

81344

81327

81310

81293

81276

81259

81242

81225

81208

81191

81174

81157

81140

81123

81106

81089

81072

81055

81038

81021

81004

80987

80970

80953

80936

80919

80902

N. sine.

54°

36°

N.sine.

58779

58802

58826

58849

58873

58896

58920

58943

58967

58990

59014

59037

59061

59084

59108

59131

59154

59178

59201

59225

59248

59272

59295

59318

59342

59365

59389

59412

59436

59459

59482

59506

59529

59552

59576

59599

59622

59646

59669

59693

59716

59739

59763

59786

59809

59832

59856

59879

59902

59926

59949

59972

59995

60019

60042

60065

60089

60112

60135

60158

60182

N. cos.

N. cos.

80902

80885

80867

80850

80833

80816

80799

80782

80765

80748

80730

80713

80696

80679

80662

80644

80627

80610

80593

80576

80558

80541

80524

80507

80489

80472

80455

80438

80420

80403

80386

80368

80351

80334

80316

80299

80282

80264

80247

80280

80212

80195

80178

80160

80143

80125

80108

80091

80073

80056

80038

80021

80003

79986

79968

79951

79934

79916

79899

79881

79864

N.sine.

53°

87°

N.sine.

60182

60205

60228

60251

60274

60298

60321

60344

60367

60390

60414

60437

60460

60483

60506

60529

60553

60576

60599

60622

60645

60668

60691

60714

60738

60761

60784

60807

60830

60853

60876

60899

60922

60945

60968

60991

61015

61038

61061

61084

61107

61130

61153

61176

61199

61222

61245

61268

61291

61314

61337

61360

61383

61406

61429

61451

61474

61497

61520

61543

61566

N.cos.

N. cos.

79864

79846

79829

79811

79793

79776

79758

79741

79723

79706

79688

79671

79653

79635

79618

79600

79583

79505

79547

79530

79512

79494

79477

79459

79441

79424

79406

79388

79371

79353

79335

79318

79300

79282

79264

79247

79229

79211

79193

79176

79158

79140

79122

79105

79087

79069

79051

79033

79016

78998

78980

78962

78944

78926

78908

78891

78873

78855

78837

78819

78801

N.sine.

52°

38°

N.sine.

61566

61589

61612

61635

61658

61681

61704

61726

61749

61772

61795

61818

61841

61864

61887

61909

61932

61955

61978

62001

62024

62046

62069

62092

62115

62138

62160

62183

62206

62229

62251

62274

62297

62320

62342

62365

62388

62411

62433

62456

62479

62502

62524

62547

62570

62592

62615

62638

62660

62683

62706

62728

62751

62774

62796

62819

62842

62864

62887

62909

62932

N. cos.

N. cos.

78801

78783

78765

78747

78729

78711

78694

78676

78658

78640

78622

78604

7a586

78568

f8550

78532

78514

78496

78478

78460

78442

78424

78405

78387

78369

78351

78333

78315

78297

78279

78261

78243

78225

78206

78188

78170

78152

78134

78116

78098

78079

78061

78043

78025

78007

77988

77970

77952

77934

77916

77897

77879

77861

77843

77824

77806

77788

77769

77751

77733

77715

N.sine.

51°

39°

N.sine.

62932

62955

62977

63000

63022

63045

63068

63090

63113

63135

63158

63180

63203

63225

63248

63271

63293

63316

63338

63361

63383

63406

63428

63451

63473

63496

63518

63540

63563

63585

63608

63630

63653

63675

63698

63720

63742

63765

63787

63810

63832

63854

63877

63899

63922

63944

63966

63989

64011

64033

64056

64078

64100

64123

64.145

64167

64190

64212

64234

64256

64279

N. cos.

N. cos.

77715

77696

77678

77660

77641

77623

77605

77586

77568

77550

77531

77513

77494

77476

77458

77439

77421

77402

77384

77366

77347

77329

77310

77292

77273

77255

77236

77218

77199

77181

77162

77144

77125

77107

77088

77070

77051

77033

77014

76996

76977

76959

76940

76921

76903

76884

76866

76847

76828

76810

76891

76772

76754

76735

76717

76698

76679

76661

76642

76623

76604

^.sine.

50°

60

59

58

57

56

55

54

53

52

51

50

49

48

47

46

45

44

43

42

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11,

10

9

8

7

6

5

4

3

2

1

0

M.

Prop.

parts

18

18

18

17

17

17 .

17

1C

16

16

15

15

15

14

14

14

14

13

13

13

12

12

12

11

11

11

11

10

10

10

9

9

9

8

8

8

8

7

7

7

6

6

6

5

r,

5

5

4

4

4

3

3

3

2

2

2

2

1

1

1

0

0
170 GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 26. Natural sines and cosines Continued.

Prop.

parts

22

0

0

1

1

1

2

2

3

 3

3

4

4

4

5

5

6

6

6

7

7

7

8

8

8

9

9

10

10

10

11

11

11

12

12

12

13

13

14

14

14

15

15

15

16

16

17

17

17

18

18

18

19

19

19

20

20

21

21

21

22

22

M.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35.

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

40°

N. sine.

64279

64301

64323

64346

64368

64390.

64412

64435

64457

64479

64501

64524

64546

64568

64590

64612

64635

64657

64679

64701

64723

64746

64768

64790

64812

64834

64856

64878

64901

64923

64945

64967

64989

65011

65033

65055

65077

65100

65122

65144

65166

65188

65210

65232

65254

65276

65298

65320

65342

65364

65386

65408

65430

65452

65474

65496

65518

65540

65562

65584

65606

N. cos.

N. cos.

76604

76586

76567

76548

76530

76511

76492

76473

76455

76436

76417

76398

76380

76361

76342

76323

76304

76286

76267

76248

76229

76210

76192

76173

76154

76135

76116

76097

76078

76059

76041

76022

76003

75984

75965

75946

75927

75908

75889

75870

75851

75832

75813

75794

75775

75756

75738

75719

75700

75680

75661

75642

75623

75604

75585

75566

75547

75528

75509

75490

75471

N. sine.

49°

41°

N.sine.

65606

65628

65650

65672

65694

65716

65738

65759

65781

65803

65825

65847

65869

65891

65913

65935

65956

65978

66000

66022

66044

66066

66088

66109

66131

66153

66175

66197

66218

66240

66262

66284

66306

66327

66349

66371

66393

66414

66436

66458

66480

66501

66523

66545

66566

66588

66610

66632

66653

66675

66697

66718

66740

66762

66783

66805

66827

66848

66870

66891

66913

N. cos.

N. cos.

75471

75452

75433

75414

75395

75375

75356

75337

75318

75299

75280

75261

75241

75222

75203

75184

75165

75146

75126

75107

75088

75069

75050

75030

75011

74992

74973

74953

74934

74915

74896

74876

74857

74838

74818

74799

74780

74760

74741

74722

74703

74683

74664

74644

74625

74606

74586

74567

74548

74528

74509

74489

74470

74451

74431

74412

74392

74373

74353

74334

74314

N.sine.

48°

42°

N.sine.

66913

66935

66956

66978

66999

67021

67043

67064

67086

67107

67129

67151

67172

67194

67215

67237

67258

67280

67301

67323

67344

67366

67387

67409

67430

67452

67473

67495

67516

67538

67559

67580

67602

67623

67645

67666

67688

67709

67730

67752

67773

67795

67816

67837

67859

67880

67901

67923

67944

67965

67987

68008

68029

68051

68072

68093

68115

68136

68157

68179

68200

N. cos.

N. cos.

74314

74295

74276

74256

74237

74217

74198

74178

74159

74139

74120

74100

74080

74061

74041

74022

74002

73983

73963

73944

73924

73904

73885

73865

73846

73826

73806

73787

73767

73747

73728

73708

73688

73669

73649

73629

73610

73590

73570

73551

73531

73511

73491

73472

73452

73432

73413

73393

73373

73353

73333

73314

73294

73274

73254

73234

73215

73195

73175

73155

73135

N.sine.

47°

43°

N.sine.

68200

68221

68242

68264

68285

68306

68327

68349

68370

68391

68412

68434

68455

68476

68497

68518

68539

68561

68582

68603

68624

68645

68666

68688

68709

68730

68751

68772

68793

68814

68835

68857

68878

68899

68920

68941

68962

68983

69004

69025

69046

69067

69088

69109

69130

69151

69172

69193

69214

69235

69256

69277

69298

69319

69340

69361

69382

69403

69424

69445

69466

N. cos.

N.cos.

73135

73116

73096

73076

73056

73036

73016

72996

72976

72957

72937

72917

72897

72877

72857

72837

72817

72797

72777

72757

72737

72717

72697

72677

72657

72637

72617

72597

72577

72557

72537

72517

72497

72477

72457

72437

72417

72397

72377

72357

72337

72317

72297

72277

72257

72236

72216

72196

72176

72156

72136

72116

72095

72075

72055

72035

72015

71995

71974

71954

71934

N.sine.

46°

44°

N.sine.

69466

69487

69508

69529

69549

69570

69591

69612

69633

69654

69675

69696

69717

69737

69758

69779

69800

69821

69842

69862

69883

69904

69925

69946

69966

69987

70008

70029

70049

70070

70091

70112

70132

70153

70174

70195

70215

70236

70257

70277

70298

70319

70339

70360

70381

70401

70422

70443

70463

70484

70505

70525

70546

70567

70587

70608

70628

70649

70670

70690

70711

N. cos.

N. cos.

71934

71914

71894

71873

71853

71833

71813

71792

71772

71752

71732

71711

71691

71671

71650

71630

71610

71590

71569

71549

71529

71508

71488

71468

71447

71427

71407

71386

71366

71345

71325

71305

71284

71264

71243

71223

71203

71182

71162

71141

71121

71100

71080

71059

71039

71019

70998

70978

70957

70937

70916

70896

70875

70855

70834

70813

70793

70772

70752

70731

70711

N.sine.

45°

60

59

58

57

56

55

54

53

52

51

50

49

48

47

46

45

44

43

42

41

40

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

M.

Prop.

parts

19

19

19

18

18

18

17

17

17

16

16

16

16

15

15

15

14

14

14

13

13

13

12

12

12

11

11

11

10

10

10

10

9

9

9

8

8

8

7

7

7

6

6

c

5

5

5

4

4

4

3

3

3

3

2

2

2

1

1

1

0

0
GEOGRAPHIC TABLES AND FORMULAS. 171

TABLE 27. Five-place logarithms of circular functions, expressed in arc and time. 

0" 0°

m. s.

0 0 

4 

8 

12 

16

0 20 

24 

28 

32 

36

0 40 

44

48 

52 

56

1 0 

4 

8 

32

10

1 20 

24 

28 

32 

36

1 40 

44 

48 

52 

56

2 0 

4 °8 

12 

16

2 20 

24 

28 

32 

36

2 40 

44

48 

52 

56

3 0 

4 

8 

12 

16

3 20 

24 

28 

32 

36

3 40 

44 

48 

52 

56

4 0

'

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 48 

49

50

61 

52 

53 

54

55 

56 

57 

58 

59

(iO

L. Sin.

6.46 373 

6. 76 476 

6. 94 085 

7. 06 579

7.16 270 

7.24 188 

7. 30 882 

7. 36 682 

7. 41 797

7.46 373 

7. 50 512 

7. 54 291 

7. 57 767 

7. 60 985

7. 63 982 

7.66 784 

7.69417 

7. 7.1 900 

7. 74 248

7. 76 475 

7. 78 594 

7.80 615 

7. 82 545 

7.84 393

7. 86 166 

7.87 870 

7.89 509 

7. 91 088 

7. 92 612

7. 94 084 

7. 95 508 

7. 96 887 

7. 98 223 

7. 99 520

8.00 779 

8.02 002 

8. 03 1 92 

8.04 350 

8. 05 478

8.06 578 

8.07 650 

8.08 696 

8.09 718 

8.10 717

8. 11 693 

8. 12 647 

8.13 581 

8. 14 495 

8. 15 391

8. 16 268 

8.17 128 

8.17 971 

8.18 798 

8. 19 610

8. 20 407 

8.21. 189 

8.21 958 

8.22 713 

8. 23 456

8. 24 186

L. Cos.

d.

30103 

17609 

12494 

9691

7918 

6694 

5800 

5115

4139 

3779 

347G 

3218 

2997

2802 

2G33 

2483 

2348 

2227

2119 

2021 

1930

1848

1704 

1639 

1579 

1524

1472

1424 

1379 

1336 

1297 

1259

1223 

1190 

1158 

1.128 

1100

1072 

1046 

1022 °999

954 

934 

914

896

860 

843 

827 

.812

. 782 

769 

755 

743 

730

d.

L. Tang.

6. 40 373 

6. 76 476 

6. 94 085 

7. 06 579

7.16 270 

7. 24 188 

7. 30 882 

7.36 682 

7.41 797

7.46 373 

7. 60 512 

7. 54 291 

7.57 767 

7. 60 986

7. 63 982 

7. 66 785 

7.69418

7. 71. 900 

7. 74 248

7.76 476 

7. 78 595 

7.80 615 

7. 82 546 

7. 84 394

7.86 167 

7. 87 871 

7.89 510 

7. 91 089 

7. 92 613

7. 94 086 

7. 95 510 

7. 96 889 

7. 98 225 

7. 99 522

8. 00 781 

8.02 004 

8.03 194 

8. 04 353 

8. 05 481

8.06 581 

8.07 653 

8.08 700 

8. 09 722 

8. 10 720

8.1.1 696 

8. 12 651 

3.13 585 

8. 14 500 

8. 15 395

8.16 273 

8.17 133 

8. 17 976 

8. 18 804 

8.19 616

8.20 413 

8.21 195 

8.21 964 

8.22 720 

8. 23 462

. 8.24 192

|L. Cotg.

C. d.

30103 

1.7609 

.12494

OftCH

7918 

6694 

5800 

5115 

4576

4139 

3779 

3476 

321.9 

999(5

2803 

2633 

2482 

2348

OOOft

2119 

2020 

1931 

T848

1704 

1.639 

1579 

1524

1473

1424 

1379 

1336 

1297

1223 

1190 

1159 

1128

1100

1072 

1047 

1022 

998

976

955 

934 

915 

895

O/o

860 

843 

828 

812

797

782 

769 

756 

742

c. d.

L. Cotg.

3. 53 627 

3.23 624 

3.05 915 

2. 93 421

2.83 730 

2. 75 812 

2. 69 118 

 2.63 318 

2. 58 203

2. 53 627 

2. 49 488 

2.45 709 

2. 42 233 

2. 39 014

2. 36 018 

2. 33 215 

2.30582 

.2. 28 100 

2.25 752

2.23 524 

2. 21 405 

2.19 385 

2. 17 454 

2. 15 606

2. 13 833 

2. 12 129 

2. 10 490 

2.08 911 

2. 07 387

2. 05 914 

2. 04 490 

2.03 111 

2.01 775 

2. 00 478

1. 99 219 

1.97 996 

1.96 806 

1 . 95 647 

1. 94 519

1.93 419 

1. 92 347 

1.91 300 

1.90 278 

1.89 280

1.88 304 

1.87 349 

1.86 415 

1. 85 500 

1 . 84 605

1.83 727 

1. 82 867 

.1. 82 024 

.1.81 190 

1. 80 384

1. 79 587 

1.78 805 

1. 78 036 

1. 77 280 

1. 76 538

1.75 808

L. Tang.

L. Cos.

0. 00 000 

0. 00 000 

0. 00 000 

0. 00 000 

0. 00 000

0. 00 000 

0. 00 000 

0. 00 000 

0. 00 000 

0. 00 000

 0. 00 000 

0. 00 000 

0.00 000 

0. 00 000 

0. 00 000

0. 00 000 

0. 00 000 

 9.99 999

9.99 999 

9.99 999

9. 99 999 

9.99 999 

9.99 999 

9.99 999 

9. 99 999

9. 99 999 

9. 99 999 

9. 99 999 

9. 99 999 

9. 99 998

9. 99 998 

9.99 998 

9. 99 998 

9. 99 998 

9. 99 998

9. 99 998 

9. 99 998 

9! 99 997 

9. 99 997 

9. 99 997

9. 99 997 

9. 99 997 

9. 99 997 

9. 99 997 

9. 99 996

9. 99 996 

9. 99 996 

. 9. 99 996 

9. 99 996 

9. 99 996

9. 99 995 

9. 99 995. 

9. 99 995 

9. 99 995 

9. 99 995

9. 99 994 

9.99 994 

9.99 994 

9.99 994 

9. 99 994

9 99 993

L. Sin.

GO

59 

58 

57 

56

55 

54 

53 52 

51

50

49 

48 

47 

46

45 

44 

43 

22 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

so

29 

28 

27 

26

25 

24 

23 

22 

2.1

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

'

00 0 

50 

52 

 48 

44

59 40 

36 

32 

28 

24

59 20 

16 

12 

8 

4

59 0 

06 

52 

48 

44

58 40 

36 

32 

28 

24

58 20 

16 

12 

8 

4

58 0 

56 

52 

48 

44

57 40 

36 

32 

28 

24

57 20 

16 

12 

8 

4

57 0 

50 

52 

48 

44

56 40 

36 

32 

28 

24

66 20 

16 

12 

8 

4

66 0

m. s.

89C
172 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

Oh 1°

in. s.

4 0 

4 

8 

12 

10

4 20 

24

28 

32

ao

4 40 

44 

48 

52 

56

5 0 

4 

8 

12 

10

5 20 

24 

28 

32 

36

5 40 

44

48 

52 

50

0 0 

4 

8 

12 

10

6 20 

24 

28 

32 

36

G 40 

44 

48 

52 

56

7 0 

4 

8 

12 

16

7 20 

24 

28 

32 

30

7 40 

44 

48 

52 

56

8 0

'

0

1

2 

3 

4

5 

6 

7 

8 

9

to

11

12 

13

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

8.24 186 

8.24 903 

8.25 009 

8. 20 304 

8.20 988

8.27 001 

8. 28 324 

8. 28 977 

8. 29 021 

8. 30 255

8. 30 879 

8. 31 495 

8. 32 103 

8.32 702 

8. 33 292

8. 33 875 

8. 34 450 

 8. 35 018 

8.35 578 

8. 36 131

8. 36 678 

8.37 217 

8.37 750 

8. 38 276 

8. 38 796

8. 39 310 

8.39 818 

8. 40 320 

8. 40 816 

8.41 307

8.41 792 

8. 42 272 

8.42 746 

8. 43 216 

8. 43 680

8. 44 139 

8. 44 594 

8.45 044 

8. 45 489 

8. 45 930

8. 46 366 

8. 46 799 

8.47 220 

8.47 050 

8. 48 069

8. 48 485 

8.48 896 

8.49 304 

8.49 708 

8. 50 108

8.50 504 

8. 50 897 

8. 51 287 

8.51 673 

8. 52 055

8.52 434 

8.52 810 

8. 53 183 

8. 53 552 

8. 53 919

8. 54 282

L. Cos.

d.

717 

706 

695 

084

673

603 

653 

644 

634

616 

608 

599 

590

575 

568 

500 

553

539 

533 

520 

520

514

508 

502 

496 

491

485

480 

474 

470 

404

455 

450 

445 

441

433 

427 

424 

419

411 

408 

404 

400

393 

390 

380 

382

370 

373 

369 

367

ouo

d.

L. Tang.

8. 24 192 

8. 24 910 

8. 25 616 

8. 26 312 

8. 26 990

8.27 669 

8.28 332 

8. 28 980 

8. 29 629 

8. 30 263

8. 30 888 

8. 31 505 

8.32 112 

8. 32 711 

8. 33 302

8. 33 886 

8. 34 461 

 8.35 029 

8. 35 590 

8. 30 143

8. 36 089 

8. 37 229 

8. 37 702 

8. 38 289 

8. 38 809

8. 39 323 

8. 39 832 

8. 40 334 

8. 40 830 

8". 41 321

8.41 807 

8. 42 287 

8. 42 762 

8.43 232 

8.43 690

8. 44 150 

8.44 Oil 

8. 45 061 

8. 45 507 

8.45 948

8.46 385 

8.46817

8.47 245 

8.47 669 

8. 48 089

8. 48 505 

8.48 917 

8. 49 325 

8.49 729 

8. 50 130

8. 50 527 

8. 50 920 

8.51 310 

8.51 690 

8.52 079

8. 52 459 

8. 52 835 

8. 53 208 

8. 53 5"8 

8. 53 945

8. 54 308

L. Cotg.

c. d.

718 

700 

090 

084

073

063 

054 

043 

034

025

017 

607 

599 

591

575 

508 

561 

553

540 

533 

527 

520

509 

502 

496 

491

480

480 

475 

470 

404

455 

450 

440 

441

437

432 

428 

424 

420

416

412 

408 

404 

401

393 

390 

380 

383

376 

373 

370 

367

c. d.

L. Cotg.

1. 75 808 

1. 75 090 

1. 74 384 

1.73 688 

1. 73 004

1. 72 331 

1. 71 068 

1.71 014 

1.70 371 

1. 69 737

. 1 . 69 112 

1. 68 495 

1.67 888 

1. 07 289 

1. 66 698

1. 66 114 

1. 05 539 

1. 64 971 

1. 04 410 

1. 03 857

1.03 311 

1.62 771 

1. 62 238 

1.01 711 

1. 01 191

1. 00 077 

1. 60 108 

1. 59 066 

1.59 170 

1. 58 679

1. 58 193 

1.57 713 

1. 57 238 

1.56 768 

1. 56 304

1. 55 844 

1. 55 389 

1.54 939 

1. 54 493 

1. 54 052

1.53 615 

1.53183 

1.52 755 

1.52 331 

1.51 911

1.51 495 

1. 51 083 

1.50 675 

1.50 271 

1. 49 870

1. 49 473 

1.49 080 

1.48 690 

1.48 304 

1.47 921

1.47 541 

1.47 165 

1.40 792 

1.40 422 

1.46 055

1.45 092

L. Tang.

L. Cos.

9. 99 993 

9.99 993 

9. 99 993 

9.99 993 

9. 99 992

9. 99 992 

9. 99 992 

9. 99 992 

9. 99 992 

9. 99 991

9. 99 991 

9. 99 991 

9. 99 990 

9. 99 990 

9. 99 990

9. 99 990 

9. 99 989 

9. 99 989 

9. 99 989 

9 99 ggg

9. 99 988 

9! 99 988 

9. 99 988 

9.99 987 

9. 99 987

9.99 987 

9.99 986 

9. 99 986 

9. 99 980 

9. 99 985

9. 99 985 

9. 99 985 

9. 99 984 

9. 99 984 

9. 99 984

9. 99 983 

9.99 983 

9. 99 983 

9. 99 982 

9. 99 982

9. 99 982 

9.99 981 

9. 99 981 

9. 99 981 

9.99 980

9. 99 980 

9.99 979 

9. 99 979 

9. 99 979 

9. 99 978

9. 99 978 

9. 99 977 

9. 99 977 

9. 99 977 

9. 99 976

9. 99 976 

9. 99 975 

9. 99 975 

9. 99 974 

9. 99 974

9. 99 974

L. Sin.

60

59

58 

57 

50

55 

54 

53 

52 

51

50

49

48 

47 

40

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

.31

;{()

29

28 

27 

26

25 

24 

23 

22 

21

20

]9 

18 

17 

16

15 

14 

13 

12 

11

1.0

9

8 

7 

6

5 

4 

3 

2 

1

0

'

56 0

56 

52 

48 

. 44

55 40 

36

32 

28 

24

55 20 

16 

12

8 

4

55 0 

56 

52 

48 

44

54 40

a;

32 

28 

24

54 20 

16 

12

8 

4

54 0 "56

52 

48 

44

53 40 

36 

32 

28 

24

53 20 

16 

12 

8 

4

53 0 

56 

52

48 

44

52 40 

36 

32 

28 

24

52 20 

16 

128 

4

52 0

m. -s.

88C 5h
GEOGRAPHIC TABLES AND FORMULAS. 173 

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

0" 2°

in. s.

S 0 

4 

8 

.12 

16

8 20 

24 

28 

. 32 

36

8 40 

44 

48- 

52 

56

9 0 

4 

8 

12 

16

9 20 

24 

28 

32 

36

9 40 

44

48 

52 

56

10 0 

4 

8 

12 

16

10 20 

24 

28 

32 

36

10 40 

44 

48

52 

56

11 0 

'I 

S 

12 

16

11 20 

24 

28 

32 

36

11 40 

44, 

48 

52 

56

12 0

/

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

>!0

51 

52 

53 

54

55 

56 

57 

58 

59

CO

L. Sin.

8. 54 282 

8. 54 642 

8. 54 999 

8.55 354 

8. 55 705

8. 56 054 

8. 56 400 

8. 56 743 

8. 57 084 

8. 57 421

8. 57 757 

8. 68 089 

8. 58 419 

8.58 747 

8. 59 072

8.59 395 

8.59 715 

8. 60 033 

8. 60 349 

8. 60 662

8. 60 973 

8. 61 282 

8. 61 589 

8. 61 894 

8. 62 196

8.62 497 

8. 62 795 

8. 63 091 

8. 63 385 

8. 63 678

8. 63 968 

8. 64 256 

8.64 543 

8. 64 827 

8. 65 110

8. 65 391 

8. 65 670 

8. 65 947 

8. 66 223 

8. 66 497

8. 66 769 

8. 67 039 

8. 67 308 

8. 67 575 

8. 67 841

8. 68 104 

8. 68 367 

8. 68 627 

8. 68 886 

8. 69 144

8. 69 400 

8. 69 654 

8. 69 907 

8. 70 159 

8. 70 409

8. 70 658 

8. 70 905 

8. 71 151 

8. 71 395 

8. 71 638

8. 71 880

L. Cos.

d.

360 

357 

355 

351

346 

343 

341 

337

332 

330 

328 

325

00 Q

320 

318 

316 

313

309 

307 

305 

302

298 

296 

294 

293

OQfi

288 

287 

284 

283

OUT

279 

277 

276 

274 

272

270 

269 

267 

266

OAQ

263 

260 

259 

258 

256

254 

253 

252 

250 

249

247 

246 

244 

243

d.

L. Tang.

8. 54 308 

8. 54 669 

8. 55 027 

8. 55 382 

8. 55 734

8. 56 083 

8. 56 429 

8. 56 773 

8.57 114 

8. 57 452

8. 57 788 

8. 58 121 

8. 58 451 

8.58 779 

8. 59 105

8. 59 428 

8.59 749 

8.60068 

8.60 384 

8. 60 698

8. 61 009 

8. 61 319 

8.61 626 

8.61 931 

8. 62 234

8.62 535 

8. 62 834 

8. 63 131 

8. 63 426 

8. 63 718

8. 64 009 

8. 64 298 

8.64 585 

8. 64 870 

8. 65 154

8. 65 435 

8. 65 715 

8. 65 993 

8. 66 269 

8. 66 543

8. 66 816 

8. 67 087 

8. 67 356 

8. 67 624 

8. 67 890

8. 68 154 

8. 68 417 

8. 68 678 

8. 68 938 

8.69 196

8. 69 453 

8: 69 708 

8.69 962 

8.70 214 

8. 70 465

8. 70 714 

8. 70 962 

8. 71 208 

8. 71 453 

8. 71 697

8. 71 940

L. Cotg.

c. d.

361 

358 

355 

352

346 

344 

341 

338

333 

330 

328 

326

321 

319 

316 

314

310 

307 

305 

303

299 

297 

295 

292 

291

289

287 

285 

284

OQ1

280 

278 

276 

274

070

271 

269 

268 

266 

264

263 

261 

260

258 

257

255 

254 

252 

251 

249

248 

246 

245 

244 

243

c.d.

L. Cotg.

1.45 692 

1.45 331 

1.44 973 

1.44 618 

1. 44 266

1.43 917 

1.43 571 

1. 43 227 

1.42 886 

1. 42 548

1.42 212 

1. 41 879 

1.41 549 

1,41 221 

1. 40 895

1. 40 572 

1.40 251 

1.39932 

1.39 616 

1.39 302

1.38 991 

1. 38 681 

L. 38 374 

1. 38 069 

1. 37 766

1. 37 465 

1. 37 166 

1. 36 869 

1. 36 574 

1. 36 282

1. 35 991 

1. 35 702 

1. 35 415 

1.35 130 

1. 34 846

1. 34 565 

1. 34 285 

1. 34 007 

1. 33 731 

1.33 457

1.33 184 

1. 32 913 

1. 32 644 

1. 32 376 

1.32 110

1.31 846 

1.31 583 

1, 31 322 

1.31 062 

1. 30 804

1. 30 547 

1. 30 292 

1. 30 038 

1.29 786 

1. 29 535

1. 29 286 

1.29 038 

1.28 792 

1.28 547 

1. 28 303

1.28 060

L.Tang.

L. Cos.

9.99 974 

9. 99 973 

9. 99 973 

9. 99 972 

9. 99 972

9. 99 971 

9. 99 971 

9.99 970 

9. 99 970 

9. 99 969

9. 99 969 

9. 99 968 

9. 99 968 

9. 99 967 

9.99 967

9. 99 967 

9. 99 966 

9.99966 

9. 99 965 

9.99 964

9.99 964 

9. 99 963 

9. 99 963 

9. 99 962 

9. 99 962

9.99 961 

9. 99 961 

9. 99 960 

9.99 960 

9. 99 959

9. 99 959 

9. 99 958 

9. 99 958 

9. 99 957 

9. 99 956

9. 99 956 

9. 99 955 

9. 99 955 

9. 99 954 

9. 99 95'4

9. 99 953 

9.99 952 

9. 99 952 

9. 99 951 

9. 99 951

9. 99 950 

9. 99 949 

9. 99 949 

9. 99 948 

9.99 948

9. 99 947 

9. 99 946 

9. 99 946 

9.99 945 

9. 99 944

9.99 944 

9. 99 943 

9. 99 942 

9. 99 942 

9. 99 941

9. 99 940

L. Sin.

(10

59 

58 

57 

56

55 

54 

53 

52 

51

60

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

>

52 0 

56 

62 

48 

44

51 40 

36 

32 

28 

24

51 20 

16 

12 

8 

4

51. 0 

56 

52 

48 

44

50 40 

36 

32

28 

24

50 20 

16 12

8 

4

50 0 

66 

52 

48 

44

49 40 

36 

32 

28 

24

49 20 

16 

12 

8 

4

49 0 

56 

52 

48 

44

48 40 

36 

32 

28 

24

48 20 

16 

12 

8 

4

48 0

m. s.

87°
174 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular'functions, etc. Continued. 

Oh 3°

m. s.

12 0 

4 

8 

12 

16

12 20 

24 

28 

32 

36

12 40 

44 

48

OM

56

13 0 

4 

8 

12 

16

13 20 

24 

28 

32 

36

13 40 

44 

 48 

52 

56

14 0 

4 

8 

12 

16

14 20 

24 

28 

32 

36

14 40 

44 

48 

52 

56

15 0 

4 

8 

12 

16

15 20 

24 

28 

32 

36

15 40 

44 

48 

52 

56

16 0

/

0

1 

2 

3 

4

5

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

'20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42. 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

8. 71 880 

8. 72 120 

8. 72 359 

8. 72 597 

8. 72 834

8. 73 069 

8. 73 303 

8. 73 535 

8. 73 767 

8. 73 997

8. 74 226 

8. 74 454 

8. 74 680 

8. 74 906 

8. 75 130

8. 75 353 

8. 75 575 

8. 75 795 

8. 76 015 

8. 76 234

8. 76 451 

8. 76 667 

8. 76 883 

8. 77 097 

8. 77 310

8. 77 522 

8.77 733 

8. 77 943 

8. 78 152 

8. 78 360

8. 78 568 

8.78 774 

8. 78 979 

8. 79 183 

8. 79 386

8. 79 588 

8. 79 789 

8. 79 990 

8. 80 189 

8.80388

8. 80 585 

8. 80 782 

8.80978 

8.81 173 

. 8. 81 367

8. 81 560 

8.81 752 

8.81 944 

8.82 134 

8. 82 324

8. 82 513 

8. 82 701 

8. 82 888 

8.83 075 

8.83 261

8.83 446 

8. 83 630 

8. 83 813 

8. 83 996 

8.84.177

8. 84 358

L. Cos.

d.

240 

239 

238 

237

234 

232 

232 

230

228 

226 

226 

224

222 

220 

220 

219

217

216 

216 

214 

213

211 

210 

209 

208

jZVo

206 

205 

204 

203

201 

201 

199 

199

197 

196 

195 

194

192 

192 

190 

190

188 

187 

187 

186

184 

183 

183 

181

d.

L. Tang.

8. 71 940 

8. 72 181 

8. 72 420 

8. 72 659 

8. 72 896

8. 73 132 

8. 73 366 

8. 73 600 

8. 73 832 

8. 74 063

8. 74 292 

8. 74 521 

8. 74 748 

8. 74 974 

8. 75 199

8. 75 423 

8. 75 645 

8. 75 867 

8. 76 087 

8. 76 306

8. 76 525 

8. 76 742 

8. 76 958 

8. 77 173 

8. 77 387

8. 77 600 

8.77 811 

8. 78 022 

8. 78 232 

8. 78 441

8. 78 649 

8. 78 855 

8. 79 061 

8. 79 266 

8. 79 470

8. 79 673 

8. 79 875 

8. 80 076 

8. 80 277 

8. 80 476

8.80 674 

8. 80 872 

8.81068 

8.81 264 

8.81 459

8. 81 653 

8. 81 846 

8.82 038 

8.82 230 

8. 82 420

8. 82 610 

8.82 799 

8.82 987 

8. 83 175 

8.83 361

8. 83 547 

8.83 732 

8.83 916 

8. 84 100 

8. 84 282

8. 84 464

L. Cotg.

c. d.

241 

239 

239 

237

234 

234 

232 

231

229 

227 

226 

225

224

222 

222 

220 

219

219

217 

216 

215 

214

^JLO

211 

211 

210 

209

206 

206 

205 

204

202 

201 

201 

199

198 

196 

196 

195

193 

192 

192 

190

189

188 

188 

186

185 

184 

184 

182

c. d.

L. Cotg.

1. 28 060 

1. 27 819 

1. 27 580 

1. 27 341 

1. 27 104

1. 26 868 

1. 26 634 

1. 26 400 

1.26 168 

1. 25 937

1. 25 708 

1.25 479 

1. 25 252 

' 1. 25 026 

1. 24 801

1. 24 577 

1. 24 355 

1.24 133 

1. 23 913 

1. 23 694

1.23 475 

1. 23 258 

1. 23 042 

1. 22 827 

1. 22 613

1.22 400 

1. 22 189 

1. 21 978 

1. 21 768 

1. 21 559

1.21 351 

1.21 145 

1. 20 939 

1. 20 734 

1. 20 530

1.20 327 

1.20 125 

1. 19 924 

1. 19 723 

1.19 524

1. 19 326 

1.19 128 

1.18932 

1.18 736 

1. 18 541

1. 18 347 

1. 18 154 

1. 17 962 

1. 17 770 

1. 17 580

1. 17 390 

1. 17 201 

1. 17 013 

1. 16 825 

1. 16 639

1. 16 453 

1. 16 268 

1. 16 084 

1. 15 900 

1. 15 718

1. 15 536

L. Tang.

L. Cos.

9. 99 940 

9. 99 940 

9. 99 939 

9. 99 938 

9. 99 938

9. 99 937 

9. 99 936 

9. 99 936 

9. 99 935 

9. 99 934

9. 99 934 

9. 99 933 

9.99 932 

9. 99 932 

9. 99 931

9. 99 930 

9. 99 929 

9. 99 929 

9. 99 928 

9. 99 927

9. 99 926 

9. 99 926 

9. 99 925 

9. 99 924 

9. 99 923

9. 99 923 

9. 99 922 

9. 99 921 

9. 99 920 

9. 99 920

9. 99 919 

9. 99 918 

9. 99 917 

9.99 917 

9.99 916

.9.99 915 

9. 99 914 

9. 99 913 

9. 99 913 

9. 99 912

9. 99 911 

9. 99 910 

9. 99 909 

9. 99 909 

9. 99 908

9. 99 907 

9. 99 906 

9. 99 905 

9.99 904 

9.99 904

9. 99 903 

9. 99 902 

9. 99 901 

9. 99 900 

9. 99 899

9. 99 898 

9. 99 898 

9. 99 897 

9. 99 896 

9. 99 895

9. 99 894

L. Sin.

60

59

58 

57 

56

55 

54 

53 

52 

61

50

49 

48 

47 

46

45 

44 

43 

42

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29

28 

.27 

26

25 

24 

23 

22 

21

20

19 

IS 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

i

48 56' 0 

52 

48 

44

47 40 

36 

32 

28 

24

47 20 

16 

12 

8 

4

47 0 

56 

52 

48 

44

46 40 

36 

32 

28 

24

46 20 

16 

 12

8 

4

46 0 

56 

52 

48 

44

45 40 

36 

32 

28 

24

45 20 

16 

12 

8 

4

45 0 

56 

52 

48 

44

44 40 

36 

32 

28 

24

44 20 

16 

12 

8 

4

44 0

m. s.

86C
GEOGRAPHIC TABLES AND FORMULAS. 175

TABLE 27. Five-place logarithms of circular functions, etc. Continued.

Oh . 4°

m. s.

16 0 

4 

8 

12 

16

16 20 

24 

28 

32 

36

16 40 

44 

48 

52 

56

17 0 

4 

8 

12 

16

17 20 

24

28 

32 

36

17 40 

44 

48 

52 

56

18 0 

4 

3 

12 

16

18 20 

24 

28 

32 

36

18 40 

44 

48 

52 

56

19 0 

4 8 

12 

16

19 20 

24 

28 

32 

36

19 40 

44 

48 

52 

56

20 0

'

0

1

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13

14

15 

16 

17 

18 

19

 JO

21 

22 

23 '24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

GO

L. Sin.

8. 84 358 

8. 84 539 

8.84 718 

8. 84 897 

8.85 075

8. 85 252 

8. 85 429 

8. 85 605 

8. 85 780 

8. 85 955

8.86 128 

8. 86 301 

8.86 474 

8.86 645 

8. 86 816

8. 86 987 

8.87 156 

8.87 325 

8. 87 494 

8.87 661

8. 87 829 

8. 87 995 

8.88 161 

8.88 326 

8.88 490

8.88 654 

8. 88 817 

8. 88 980 

8.89 142 

8. 89 304

8. 89 464 

8. 89 625 

8. 89 784 

8. 89 943 

8. 90 102

8. 90 260 

8. 90 417 

8. 90 574 

8. 90 730 

8. 90 885

8. 91 040 

8.91 195 

8. 91 349 

8.91 602 

8.91 655

8. 91 807 

8. 91 959 

8. 92 110 

8. 92 261 

8. 92 411

8. 92 561 

8. 92 710 

8. 92 859 

8. 93 007 

8.93 154

8. 93 301 

8.93 448 

8. 93 594 

8.93 740 

8. 93 885

8. 94 030

L. Cos.

d.

181 

179 

179

178 

177

177 

176 

175 

1.75 

173

173 

173 

171 

171 

171

169 

169 

169 

167 

168

166 

166 

165 

164 

164

163 

163 

162 

162 

160

161 

159 

159 

159 

158

157 

157 

156 

155 

155

155 

154 

153 

153 

152

152 

151 

151 

150 

150

149 

1.49 

148 

147 

147

147. 

146 

146 

145 

145

d.

. L. Tang.

8.84 464 

8. 84 646 

8.84826 

8. 85 006 

8.85 185

8. 85 363 

8. 85 540 

8. 85 717 

8. 85 893 

8. 86 069

8. 86 243 

' 8. 86 417 

8.86 591 

8.86 763 

8. 86 935

8.87 106 

8.87 277 

8.87447 

8.87 616 

8.S7 785

8.87 953 

8. 88 120 

8.88 287 

8. 88 453 

8. 88 618

8. 88 783 

8.88 948 

8.89 111 

8. 89 274 

8. 89 437

8. 89 598 

8.89 760 

8.89 920 

8. 90 080 

8. 90 240

8. 90 399 

8. 90 557 

8. 90 715 

8. 90 872 

8. 91 029

8. 91 185 

8. 91 340 

8.91 495 

8. 91 650 

8. 91 803

8. 91 957 

8. 92 110 

8. 92 262 

8. 92 414 

8.92 565

8. 92 716 

8.92 866 

8.93 01 ti 

8.93 165 

8.93 313

8. 93 462 

8. 93 609 

8. 93 756 

8. 93 903 

8. 94 049

8. 94 195

L. Cotg.

c. d.

182 

180 

180 

179 

178

177 

177 

176 

176 

174

174 

174 

172 

172 

171

.171 

170 

169 

169 

168

167 

167 

166 

165

165

165 

163 

163 

163 

161

162 

160 

160 

160 

159

158 

158 

157 

157 

156

155 

155 

155 

153 

154

153 

152 

152 

151 

151

150 

150 

149 

148 

149

147 

147 

147 

146 

146

C. d.

L. Cotg.

1.15 536 

1. 15 354 

1.15 174 

1. 14 994 

1. 14 815

1. 14 637 

1. 14 460 

1. 14 283 

1. 14 107 

1. 18 931

1.13 757 

1. 13 583 

1.13 409 

1.13 237 

1.13 065

1. 12 894 

1.12 723 

1.12553 

1.12 384 

1. 12 215

1. 12 047 

1.11 880 

1.11. 713 

1. 11 547 

1.11 382

1. 11 217 

1. 11 052 

1. 10 889 

1. 10 726 

1. 10 563

1. 10 402 

1.10 240 

1. 10 080 

1.09 920 

1. 09 760

1.09 601 

1. 09 443 

1.09 285 

1. 09 128 

1. 08 971

1.08 815 

1. 08 660 

1.08 505 

1.08 350 

1.08 197

1. 08 043 

1.07 890 

1.07 738 

1.07 586 

1.07 435

1.07 284 

1.07 134 

1. 06 984 

1.06 835 

1. 06 687

1. 06 538 

1 . 06 39.1 

1.06 244 

1. 06 097 

1. 05 951

1. 05 805

L. Tang.

L. Cos.

9. 99 894 

9. 99 893 

9. 99 892 

9.99 891. 

9. 99 891.

9. 99 890 

9. 99 889 

9. 99 888 

9. 99 887 

9. 99 886

9.99 885 

9. 99 884 

9. 99 883 

9. 99 882 

9! 99 881

9. 99 880 

9. 99 879 

9.99879 

9. 99 878 

9. 99 877

9. 99 876 

9. 99 875 

9. 99 874 

9. 99 873 

9. 99 872

9. 99 871 

9.99 870 

9. 99 869 

9. 99 868 

9.99 867

9. 99 866 

9. 99 865 

9. 99 864 

9. 99 863 

9. 99 862

9. 99 861 

9. 99 860 

9. 99 859 

9. 99 858 

9. 99 857

9. 99 856 

9. 99 855 

9. 99 854 

9. 99 853 

9. 99 85?,

9. 99 851 

9. 99 850 

9. 99 848 

9. 99 847 

9. 99 846

9. 99 845 

9.99 844 

9. 99 843 

9. 99 842 

9. 99 841

9.99 840 

9. 99 839 

9. 99 838 

9. 99 837 

9. 99 836

9. 99 834

L. Sin.

00

59

58 

57 

56

55 

.54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

. 7 

6

5 

4 

3

2

1

0

'

44 0 

56 

52 

48 

44

43 40 

36 

32 

28 

24

43 20 

16 

12 

8 

4

43 0 

56

52 

48 

44

42 40 

36 

32 

28 

24

42 20 

16 

12 

8 

4

42 0 

56 

52 

48 

44

41 40 

36 

32 

28 

24

41 20 

16 

12 

8 

4

41. 0 

56 

52 

48 

44

40 40 

36 

32

28 

24

40 20 

16 

12 

8 

4

40 0

in. s.

85C 5h
176 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 27.- 

Oh

-Five-place logarithms of circular functions, etc. Continued.

5° . 

m. s.

20 0 

4

8:i2

16

20 20 

24 

28 

32 

36

20 40 

44

48 

52 

56

21 0 

4 

8 

12 

16

21 20 

24 

28 

32 

36

21 40 

44 

48 

52 

56

22 0 

4 

8 

12 

16

22 20 

24 

28 

32 

36

22 40 

44 

48 

52 

56

23 0 

4 

S 

.12 

16

23 20 

24 

28 

32 

36

23 40 

44 

48 

52 

56

24 0

/

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

66 

57 

58 

59

60

L. Sin.

8. 94 030 

8. 94 174 

8. 94 317 

8. 94 461 

8. 94 603

8.94746 

8. 94 887 

8. 95 029 

8. 95 170 

8. 95 310

8. 95 450 

8. 95 589 

8. 95 728 

8. 95 867 

8. 96 005

8. 96 143 

8. 96 280 

8. 96 417 

8. 96 553 

8. 96 689

8. 96 825 

8. 96 960 

8.97 095 

8.97 229 

8. 97 363

8. 97 496 

8.97 629 

8.97 762 

8.97 894 

8. 98 026

8. 98 157 

8. 98 288 

8. 98 419 

8. 98 549 

8. 98 679

8. 98 808 

8. 98 937 

8. 99 066 

8. 99 194 

8. 99 322

8. 99 450 

8. 99 577 

8.99704 

8. 99 830 

8. 99 956

9. 00 082 

9. 00 207 

9. 00 332 

9. 00 456 

9.00581

9. 00 704 

9. 00 828 

9. 00 951 

9. 0]. 074 

9.01 196

9. 01 318 

9. 01 440 

9.01 561 

9. 01 682 

9. 01 803

9.01 923

L. Cos.

d.

144 

143 

144 

142 

143

141 

142 

141 

140 

140

139 

139 

139 

138 

138

137 

137 

136 

136 

136

135 

135 

134 

134 

133

133 

133 

132 

132 

131

131 

131 

130 

130 

129

129 

129 

128 

128 

128

127 

127 

126 

126 

126

125 

125 

124 

125 

123

124 

123 

123 

122

122

122 

121 

121 

121 

120

d.

L. Tang.

8. 94 195 

8. 94 340 

8. 94 485 

8.94 630 

8. 94 773

8. 94 917 

8. 95 060 

8. 95 202 

8. 95 344 

8. 95 486

8. 95 627 

8. 95 767 

8. 95 908 

8. 96 047 

8.96 187

8. 96 325 

8. 96 464 

8. 96 602 

8. 96 739 

8. 96 877

8. 97 013 

8. 97 150 

8. 97 285 

8. 97 421 

8. 97 556

8. 97 691 

8. 97 825 

8. 97 959 

8. 98 092 

8. 98 225

8. 98 358 

8. 98 490 

8. 98 622 

8. 98 753 

8. 98 884

8.99 015 

8.99 145 

8. 99 275 

8. 99 405 

8. 99 534

8. 99 662 

8. 99 791 

8.99919 

9. 00 046 

9.00 174

9. 00 301 

9. 00 427 

9. 00 553 

9. 00 679 

9. 00 805

9. 00 930 

9. 01 055 

9. 01 179 

9. 01 303 

9. 01 427

9. 01 550 

9.01 673 

9. 01 796 

9. 01 918 

9. 02. 040

9.02 162

L. Cotg.

c. d.

145 

145 

145 

143 

144

143 

142 

142 

142 

141

140 

141 

139 

140

138

139 

138 

137 

138 

136

137 

135 

136 

135 

135

134

134:

133 

133 

133

132 

132 

131 

131 

131

130 

130 

130 

329 

128

1.29 

128 

127 

128 

127

126 

126 

126 

126 

125

125 

124 

124 

124 

123

123 

123 

122 

122 

122

C.d.

L. Cotg.

1. 05 805 

1.05 660 

1.05 515 

1.05 370 

1. 05 227

1. 05 083 

1.04 940 

1. 04 798 

1.04 656 

1. 04 514

1..04 373 

1. 04 233 

1. 04 092 

1.03 953 

1. 03 813

1. 03 675 

1. 03 536 

1.03' 398 

1. 03 261 

1. 03 123

1.02 987 

1. 02 850 

1. 02 715 

1. 02 579 

1. 02 444

1. 02 309 

1. 02 175 

1.02 041 

1. 01 908 

1.01 775

1.01 642 

1. 01 510 

1.01 378 

1.01 247 

1.01 116

1. 00 985 

1. 00 855 

1. 00 72,5 

1. 00 595 

1. 00 466

1. 00 338 

1.00 209 

1.00081 

0. 99 954 

0. 99 826

0. 99 699 

0. 99 573 

0. 99 447 

0.99 321 

0. 99 195

0. 99 070 

0.98 945 

0. 98 82]. 

0. 98 697 

0. 98 573

0. 98 450 

0. 98 327 

0. 98 204 

0. 98 082 

0. 97 960

0. 97 838

L. Tang.

L. Cos.

9. 99 834 

9. 99 833 

9. 99 832 

9. 99 831 

9. 99 830

9. 99 829 

9. 99 828 

9. 99 827 

9. 99 825 

9. 99 824

9. 99 823 

9. 99 822 

9. 99 821 

9. 99 820 

9. 99 819

9.99 817 

9. 99 816 

9. 99 815 

9. 99 814 

9. 99 813

9. 99 812 

9. 99 810 

9.99 809 

9. 99 808 

9. 99 807

9. 99 806 

9. 99 804 

9. 99 803 

9. 99 802 

9. 99 801

9. 99 800 

9. 99 798 

9. 99 797 

9. 99 796 

9. 99 795

9. 99 793 

9. 99 792 

9. 99 791 

9. 99 790 

9.99 788

9. 99 787 

9. 99 786 

9.99 785 

9.99 783 

9. 99 782

9. 99 781 

9. 99 780 

9.99 778 

9. 99 777 

9.99 776

9. 99 775 

9.99 773 

9. 99 772 

9. 99 771 

9.99 769

9.99 768 

9.99 767 

9.99 765 

9. 99 764 

9. 99 763

9. 99 761

L. Sin.

60

59

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

80

29

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

.12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

'

40 0 

56 

52 

48 

44

39 40 

36 

32 

28 

24

39 20 

16 

12 

8 

4

39 0 

56 

52 

48 

44

38 40 

36 

32 

28 

24

38 20 

16 

12 

8 

4

38 0 

56 

52 

48 

44

37 40 

36 

32 

28 

24

37 20 

16 

12 

S 

4

37 0 

56 

52 

48 

44

36 40 

36 

32 

28 

24

36 20 

16 

12

8 

4

36 0

m. s.

84C
GEOGRAPHIC TABLES AND FORMULAS. 177 

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

Oh 6U

m.» s.

24 0 

4 

8 

12 

16

24 20 

24 

28 

32 

36

24 40 

44 

48 

52 

56

25 0 

4 

8 

12 

16

25 20 

24 

28 

32 

36

25 40 

44 

48 

52 

56

26 0 

4 

8 

12 

16

26 20 

24 

28 

32 

36

26 40 

44 

48 

52 

56

27 0 

4 

8 

12 

. 16

27 20 

24 

28 

'36 32 

27 40 

44 

48 

62 

66

28 0

/

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

]3 

14

15 

16

17 

18 

19

20

21 

22 

23

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 '48 

49

50

51. 

. 52 

53 

64

55 

56

57 

58 

59

GO

L. Sin.

9. 01 923 

9. 02 043 

9. 02 163 

9. 02 283 

9. 02 402

9.02 520 

9. 02 639 

9.02 757 

9. 02 874 

9. 02 992

9. 03 109 

9. 03 226 

9. 03 342 

9. 03 458 

9. 03 574

9. 03 690 

9.03805 

9. 03 920 

9. 04 034 ' 

9. 04 149

9. 04 202 

9. 04 376 

9. 04 490 

9. 04 603 

9.04 715

9. 04 828 

9. 04 940 

9. 05 052 

9. 05 164 

9. 05 275

9. 05 386 

9. 05 497 

9. 05 607 

9. 05 717 

9. 05 827

9. 05 937 

 9. 06 046 

9. 06 155 

9. 06 264 

9.06 372

9. 06 481 

9. 06 589 

9. 06 696 

9. 06 804 

9.06 911

9.07 018 

9. 07 124 

9.07 231 

9.07 337 

9. 07 442

9. 07 548 

9. 07 653 

9.07 758 

9. 07 863 

9.07 968

9. 08 072 

9.08 176 

9. 08 280 

9.08383 

9. 08 486

9. 08 589

L. Cos.

d.

120 

120 

120 

119 

118

119 

118 

117 

118 

117

117 

116 

ll(i 

116 

116

115 

.115 

114 

115 

113

114 

114 

113 

112 

113

112 

112 

112 

111 

111

111 

110 

110 

110 

110

109 

109 

109 

108 

109

108 

107 

108 

107 

107

106 

107 

106 

105 

106

105 

105 

105 

105 

104

104 

104 

103 

103 

103

d.

L. Tang.

9. 02 162 

9. 02 283 

9.02 404 

9.02 525 

9. 02 645

9. 02 766 

9. 02 885 

9. 03 005 

9.03 124 

9.03242

9. 03 361 

9. 03 479 

9. 03 597 

9. 03 714 

9. 03 832

9. 03 948

9.04065

9.04181 

9.04 297 

9.04 413

9.04 528 

9.04 643 

9. 04 758 

9.04873 

9. 04 987

9. 05 101 

9. 05 214 

9. 05 328 

9. 05 441 

9.05 553

9. 05 666 

9.05 778 

9. 05 890 

9. 06 002 

9.06 113

9. 06 224 

9. 06 33| 

9. 06 445 

9. 06 556 

9.06 666

9. 06 775 

9. 06 885 

9. 06 994 

9. 07 103 

9. 07 211

9.07 320 

9.07 428 

9. 07 536 

9.07 643 

9.07 751

9. 07 858 

9.07 964 

9. 08 071 

9. 08 177 

9.08283

9. 08 389 

9. 08 495 

9. 08 600 

9. 08 705 

9. 08 810

9.08 914

' L. Cotg.

c. d.

121 

121 

121 

120 

121

119 

120 

119 

118 

119

118 

118 

117 

118 

116

117 

116 

116 

116 

115

115 

115 

115 

114 

114

113 

114 

113 

112 

113

112 

112 

112 

111 

111

111 

110 

111 

110 

109

110 

109 

109 

108 

109

108 

108 

107 

108 

107

106 

107 

106 

106 

106

106 

105 

105 

105 

104

c. d.

L. Cotg.

0. 97 838 

0.97 717 

0. 97 596 

0. 97 475 

0.97 355

0. 97 234 

0. 97 115 

0.96 995 

0. 96 876 

0. 96 758

0. 96 639 

0. 96 521 

0.96 403 

0. 96 286 

0.96 168

0. 96 052 

0.95935 

0.95 819 

0.95 703 

0. 95 587

0.95 472 

0. 95 357 

0. 95 242 

0. 95 127 

0. 95 013

0. 94 899 

0. 94 786 

0.94672 

0. 94 559 

0. 94 447

0. 94 334 

0. 94 222 

0. 94 110 

0. 93 998 

0. 93 887

0.93 776 

0. 93 665 

0. 93 555 

0. 93 444 

0.93 334

0.93 225 

0. 93 115 

0. 93 006 

0. 92 897 

0. 92 789

0.92 680 

0. 92 572 

0. 92 464 

0. 92 357 

0. 92 249

0. 92 142 

0.92 036 

0.91 929 

0.91 823 

0. 91 717

0.91 611 

0. 91 505 

0. 91 400 

0.91 295 

0. 91 190

0. 91 086

L. Tang.

L. Cos.

9. 99 761 

9.99 760 

9. 99 759 

9.99 767 

9. 99 766

9. 99 755 

9.99 753 

9. 99 752 

9.99.751£ 

9. 99 749

9. 99 748 

9. 99 747 

9. 99 745 

9. 99 744 

9. 99 742

9. 99 741 

9.99740 

9.99738 

9. 99 737 

9. 99 736

9. 99 734 

9. 99 733 

9. 99 731 

9. 99 730 

9. 99 728

9. 99 727 

9. 99 726 

9.99 724 

9. 99 723 

9. 99 721

9. 99 720 

9.99 718 

9. 99 717 

9. 99 716 

9. 99 71.4

9. 99 713 

9. 99 711 

9.99 710 

9. 99 708 

9.99 707

9. 99 705 

9. 99 704 

9.99 702 

9. 99 701 

9. 99 699

9. 99 698 

9.99 696 

9. 99 695 

9. 99 693 

9. 99 692

9. 99 690 

9. 99 689 

9. 99 '687 

9. 99 686 

9. 99 684

9. 99 683 

9. 99 681 

9. 99 680 

9. 99 678 

9.99 677

9. 99 675

L. Sin.

(iO

59

58 

57 

56

55 

54 

53 

62 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 '36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

/

36 0 

56 

52 

48 

44

35 40 

36 

32 

28 

24

35 20 

16 

12 

8 

4

35 0 

50 

52 

48 

44

34 40 

36 

32 

28 

24

34 20 

16 

12 

8 

4

34 0 

56 

52 

48 

44

33 40 

36 

32 

28 

24

33 20 

16 

12 

8 

4

33 0 

66 

52 

48 

44

32 40 

36 

32 

28 

24

32 20 

16 

12 

8 

4

32 0

m. s.

41623° 16 12 83°
178 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued.

Qh 70

m. s.

28 0 

4 

8 

12 

16

28 20 

24 

28 

32 

36

28 40 

44 

48 

52 

56

29 0 

4 

8 

12 

16

29 20 

24 

28 

32 

36

29 40 

44 

48 

52 

56

30 0 

4 

8 

12 

16

30 20 

24 

28 

32 

36

30 40 

44

48 

52 

56

31 0 

4 

S 

12 

16

31 20 

24 

28 

32 

36

31 40 

44 

48 

52 

56

32 0

/

0

1 

2 

3 

4

5 

6

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

GO

L. Sin.

9. 08 589 

9. 08 692 

9.03 795 

9. 08 897 

9. 08 999

9.09 101 

9. 09 202 

9.09 304 

o 9. 09 405 

9. 09 506

9. 09 606 

9. 09 707 

9. 09 807 

9. 09 907 

9. 10 006

9. 10 106 

9. 10 205 

9. 10 304 

9. 10 402 

9. 10 501

9. 10 599 

9. 10 697 

9. 10 795 

9. 10 893 

9. 10 990

9. 11 087 

9.11 184 

9.11 281 

9. 11 377 

9. 11 474

9. 11 570 

9. 11 666 

9.11 761 

9. 11 857 

9. 11 952

9. 12 047 

9. 12 142 

9. 12 236 

9. 12 331 

9. 12 425

9. 12 519 

9. 12 612 

9.12706 

9.12 799 

9. 12 892

9.12 985 

9. 13 078 

9. 13 171 

9. 13 263 

9.13 355

9. 13 447 

9. 13 539 

9. 13 630 

9. 13 722 

9. 13 813

9. 13 904 

9. 13 994 

9. 14 085 

9. 14 175 

9. 14 266

9. 14 356

L. Cos.

d.

103 

103 

102 

102 

102

101 

102 

101 

101 

100

101 

100 

100 

99 

100

99 

99 

98 

99

98

98 

 98 

98 

97 

97

97 

97 

96 

97 

96

96 

95 

96 

95 

95

95 

94 

95 

94 

94

93 

94 

93 

93 

93

93 

93 

92 

92 

92

92 

91 

92 

91 

91

90 

91 

90 

91 

90

d.

L. Tang.

. 9. 08 914 

9. 09 019 

9. 09 123 

9. 09 227 

9. 09 330

9. 09 434 

9.09 537 

9.09 640 

9.09 742 

9. 09 845

9.09 947 

9. 10 049 

9. 10 150 

9. 10 252 

9. 10 353

9. 10 454 

9.10 555 

9. 10 656 

9. 10 756 

9.10856

9. 10 956 

9. 11 056 

9. 11' 155 

9. 11 254 

9. 11 353

9. 11 452 

9. 11 551 

9.11 649 

9. 11 747 

9. 11 845

9.11 943 

9. 12 040 

9. 12 138 

9. 12 235 

9. 12 332

9. 12 428 

9.] 2 525 

9. 12 621 

9. 12 717 

9. 12 813

9. 12 909 

9. 13 004 

9.13099 

9.13 194 

9. 13 289

9. 13 384 

9. 13 478 

9. 13 573 

9. 13 667 

9. 13 761

9. 13 854 

9. 13 948 

9.14 041 

9.14 134 

9. 14 227

9.14 320 

9. 14 412 

9. 14 504 

9. 14 597 

9. 14 688

9. 14 780

L. Cotg.

c. d.

105 

104 

104 

103 

104

103 

103 

102 

103 

102

102 

101 

102 

101 

101

101 

101 

100 

100 

100

100 

99 

99 

99 

99

99

98 

98 

98 

98

97 

98 

97 

97 

96

97 

96 

96 

96 

96

95 

95 

95 

95 

95

94 

95 

94 

94 

93

94 

93 

93 

93 

93

92 

92 

93 

91 

92

C.d.

L. Cotg.

0. 91 086 

0.90 981 

0. 90 877 

0. 90 773 

0. 90 670

0. 90 566 

0. 90 463 

0. 90 360 

0. 90 258 

0. 90 155

0. 90 053 

0. 89 953 

0. 89 850 

0.89 748 

0.89 647

0. 89 546 

0. 89 445 

0. 89 344 

0. 89 244 

.0. 89 144

0. 89 044 

0. 88 944 

0. 88 845 

0.88 746 

0. 88 647

0. 88 548 

0.88 449 

0.88 351 

0. 88 253 

0. 88 155

0. 88 057 

0. 87 960 

0. 87 862 

0.87 765 

0. 87 668

0.87 572 

0.87 475 

0. 87 379 

0.87 283 

0.87 187

0. 87 091 

0.86 996 

0.86 901 

0.86 806 

0. 86 711

0. 86 616 

0. 86 522 

0. 86 427 

0.86 333 

0.86 239

0.86 146 

0. 86 052 

0.85 959 

0.85 866 

0. 85 773

0.85 680 

0. 85 588 

0.85 496 

0. 85 403 

0. 85 312

0. 85 220

L. Tang.

L. Cos.

9. 99 675 

9. 99 674 

9. 99 672 

9.99 670 

9. 99 669

9. 99 667 

9. 99 666 

9. 99 664 

9. 99 663 

9. 99 661

9. 99 659 

9. 99 658 

9. 99 656 

9. 99 655 

'9. 99 653

9.99 651 

9. 99 650 

9. 99 648 

9. 99 647 

9. 99 645

9. 99 643 

9. 99 642 

9. 99 640 

9. 99 638 

9. 99 637

9. 99 635 

9. 99 633 

9. 99 632 

9. 99 630 

9. 99 629

9. 99 627 

9.99 625 

9. 99 624 

9. 99 622 

9. 99 620

9.99 618 

9. 99 617 

9.99 615 

9. 99 613 

9.99 612

9. 99 610 

9.99608 

9.99 607 

9.99 605 

9. 99 603

9. 99 601 

9.99 600 

9. 99 598 

9. 99 596 

9.99 595

9. 99 593 

9. 99 591 

9 99 689 

9! 99 588 

9. 99 586

9. 99 584 

9. 99 582 

9. 99 581 

9. 99 579 

9. 99 577

9. 99 575

L. Sin.

CO

59 

58 

57 

56

55 

54 

53 

52 

51

50

59 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29

28 

27 

26

25 

24 

23 

22 

21

20

19

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

'

32 0 

56 

52 

48 

44

31 40 

36 

32 

28 

24

31 20 

16

12 

8 

4

31 0 

56 

52 

48 

44

30 40 

36 

32 

28 

24

30 '20 

16 

12 

8 

4

30 0 

56 

52 

48 

44

29 40 

36 

32 

28 

24

29 20 

16 

12 

8 

4

29 0 

56 

52 

48 

44

28 40 

36 

32 

28 

24

28 20 

16 

12 

.8 

4

28 0

in. s.
GEOGRAPHIC TABLES AND FORMULAS. 179 

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

Oh ' 8°

m. s.

32 0 

4 

 8 

12 

16

32 20 

24 

28 

32 

36

32 40 

44 

48 

52 

56

33 0 

4 

8 

12 

16

33 20 

24 

28 

32 

36

38 40 

44 

48 

52 

56

34 0 

4 

8 

12 

16

34 20 

24 

28 

32 

36

34 40 

44 

48 

52 

56

35 0 

4 

8 

12 

16

35 20 

24 

28 

32 

36

35 40 

44 

48 

52 

56

36 0

/

0

1

2 

3

4

5 

6 

7 

8 

9

10

11 

.1.2 

13 

14

15 

K> 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

80

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

00

L. Sin.

9.14 356 

9. 14 445 

9. 14 535 

9. 14 624 

9. 14 714

9.14 803 

9.14 89.1 

9. 14 980 

9. 15 069 

9. 15 157

9.15 245 

9. 15 333 

9. 15 421 

9. 15 50S 

9. 15 596

9. 15 083 

9.15 770 

9. 15 857 

9. 15 944 

9. 16 030

9. 16 116 

9.16 203 

9. 16 289 

9.16 374 

9. 16 460

9.16 545 

9. 16 631 

9. 16 716 

9. 16 801 

9. 16 886

9. 16 970 

9. 17 055 

9. 17 139 

9. 17 223 

9.17 307

9. 17 391 

9.17 474 

9. 17 558 

9.17 641 

9.17 724

9. 17 807 

9. 17 890 

9.17 973 

9. 18 055 

9.18 137

9. 18 220 

9.18 302 

9.18 383 

9. 18 465 

9.18.547

9. 18 628 

9. 18 709 

9.18 790 

9. 18 871 

9. 18 952

9. 19 033 

9. 19 113 

9. 19 193 

9. 19 273 

9. 19 353

9.19 433

L. Cos.

d.

89 

90

89 

90 

89

88 

89 

89 

88 

88

88 

88 

87 

88 

87

87 

87 

87 

86 

86

87 

86 

85 

86 

85

86 

85 

85 

85 

84

85 84- 

84 

84 

84

83" 

84 

83 

83 

83

83 

83 

82 

82 

83

82 

81 

82 

82 

81

81 

81 

81 

 81 

8.1

80 

80 

80 

80 

80

d.

L. Tang.

9. 14 780 

9. 14 872 

9. 14 963 

9.15 054 

9. 15 145

9. 15 236 

9. 15 327 

9. 15 417 

9. 15 508 

9.15 598

9. 15 688 

9. 15 777 

9. 15 867 

9. 15 956 

9. 16 046

9.16 135 

9.16224 

9. 16 312 

9.16 401 

9. 16 489

9. 16 '577 

9.16 665 

9.16 753 

9.16 841 

9. 16 928

9.17 01.6 

9.17 103 

9. 17 190 

9. 17 277 

9. 17 363

9. 1.7 450 

9. 17 536 

9. 17 622 

9. 17 708 

9.17 794

9. 17 880 

9. 17 965 

9. 18 051 

9.18 136 

9. 18 221

9. 18 306 

9. 18 391 

9. 18 475 

9. 18 560 

9. 18 644

9. 18 728 

9. 18 812 

9. 18 896 

9. 18 979 

9. 19 063

9. 19 146 

9. 19 229 

9. 19 312 

9. 19 395 

9. 19 478

9. 19 561 

9. 19 643 

9. 19 725 

9. 19 807 

9. 19 889

9. 19 971

L. Cotg.

c. d.

92 

9.1 

91 

91 

91

91 

90 

91 

90 

90

89 

90 

89 

90 

89

89

88 

89 

88 

88

88 

88 

88 

87 

88

87 

87 

87 

86 

87

86 

86 

86 

86 

86

85 

86 

85 

85 

85

85 

84 

85 

84 

84

84 

84 

83 

84 

83

83 "83 

83 

83 

83

82

82 

82 

82 

82

c. d.

L. Cotg.

0. 85 220 

0. 85 128 

0. 85 037 

0. 84 946 

0. 84 855

0.84 764 

0. 84 673 

0. 84 583 

0. 84 492 

0. 84 402

0. 84 312 

0. 84 223 

0. 84 133 

0. 84 044 

0.83 954

0. 83 865 

0.83 77C 

0.83688 

0. 83 599 

0. 83 511

0. 83 423 

0. 83 335 

0. 83 247 

0.83 159 

0. 83 072

0. 82 984 

0. 82 897 

0.82 810 

0. 82 723 

0.82 637

0.82 550 

0. 82 464 

0. 82 378 

0.82 292 

0. 82 206

0.82 120 

0.82 035 

0. 81 949 

0.81 864 

0.81 779

0.81 694 

0.81 609 

O.'Sl 525 

0. 81 440 

0. 81 356

0. 81 272 

0.81 188 

0.81 104 

0.81 021 

0. 80 937

0. 80 854 

0. 80 771 

0. 80 688 

0. 80 605 

0. 80 522

0. 80 439 

0.80 357 

0.80 275 

0. 80 193 

0. 80 111

0. 80 029

L. Tang.

L. Cos.

9.99 575 

9. 99 574 

9. 99 572 

9. 99 570 

9.99 568

9. 99 566 

9.99 565 

9. 99 563 

9. 99 561 

9.99 559

9. 99 557 

9. 99 556 

9. 99 554 

9. 99 552 

9. 99 550

9. 99 548 

9. 99 546 

9. 99 545 

9.99 543 

9. 99 541

9. 99 539 

9. 99 537 

9. 99 635 

9. 99 533 

9.99 532

9. 99 530 

9. 99 528 

9. 99 526 

9.99 524 

9.99 522

9.99 520 

9. 99 518 

9. 99 517 

9. 99 515 

9. 99 513

9. 99 511 

9. 99 509 

9. 99 507 

9. 99 505 

9. 99 503

9. 99 501 

9. 99 499 

9. 99 497 

9. 99 495 

9.99 494

9. 99 492 

9. 99 490 

9.99 488 

9.99 486 

9. 99 484

9. 99 482 

9. 99 480 

9. 99 478 

9.99 476 

9.99 474

9. 99 472 

9.99 470 

9. 99 468 

9. 99 466 

9. 99 464

9. 99 462

L. Sin.

(iO

59 

58 

57 

56

55 

54 

63 

52 

51

50

49

48 

4.7 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

:to

29 

28 

27 

26

25 

24 

23 

22 

21

20

19

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

'

28 0 

56 

52 

48 

44

27 40 

36 

32 

28 

24

27 20 

16 

12 

8 

4

27 0 

56 

52 

48 

44

26 40 

36 

32 

28 

24

26 20 

16 

12

8 

4

26 0

56 

52 

48 

44

25' 40 

36 

32 

28 

24

25 20 

16 

12 

8 

4

25 0 

56 

52 

48 

44

24 40 

36 

32 

28 

24

24 20 

16 

12 

8 

4

24 0

111. S.

81C 5h
180 GEOGEAPHIC TABLES AND FORMULAS.

TABLE 27. Mve-place logarithms of circular functions, etc. Continued.

Oh 9°

m. s.

36 0 

4 

8 

12 

16

36 20 

24 

28 

32 

36

36 40 

44 

48 

52 

56

37 0 

4 

8 

12 

16

37 20 

24 

28 

32 

36

37 40 

44 

48 

52 

56

38 0 

4 

8 

12 

16

38 20 

24 

28 

32 

36

38* 40 

44 

48 

52 

50

39 0 

4 

8 

12 

, 16

39 20 

24 

28 

32 

36

39 40 

44

48 

52 

56

40 0

/

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

'20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

GO

L. Sin.

9. 19 433 

9. 19 513 

9. 19 592 

9. 19 672 

9. 19 751

9. 19 830 

9. 19 909 

9.19 988 

9.' 20 067 

9. 20 145

9. 20 223 

9. 20 302 

9. 20 380 

9. 20 458 

9. 20 535

9. 20 613 

9. 20 691 

9. 20 768 

9. 20 845 

9. 20 922

9. 20 999 

9. 21 076 

9.21 153 

9. 21 229 

9. 21 306

9. 21 382 

9.21 458 

9.21 534 

9. 21 610 

9. 21 685

9. 21 761 

9. 21 836 

9.21 912 

9. 21 987 

9.22 062

9.22 137 

9.22 211 

9. 22 286 

9.22 361 

9. 22 435

9. 22 509 

9. 22 583 

9.22657

9.22 731 

9. 22 805

9. 22 878 

9. 22 952 

9. 23 025 

9. 23 098 

9.23 171

9.23 244 

9. 23 317 

9. 23 390 

9.23 462 

9.23 535

9. 23 607 

9.23 679 

9. 23 752 

9. 23 823 

9. 23 895

9.23 967

L. Cos.

d.

80 

79 

80 

79 

79

79 

79 

79

78 

78

79

78 

78 

77 

78

78 

77 

77 

77 

77

77 

77 

76

77 

76

76 

76 

76 

75 

76

75 

76 

75 

75 

75

74 

75 

75 

74 

74

74 

. 74 

74 

74 

73

74 

73 

73 

73 

73

73 

73

72 

73 

72

72 

73 

71

72 

72

d.

L. Tang.

9. 19 971 

9. 20 053 

9. 20 134 

9. 20 216 

9. 20 297

9: 20 378 

9. 20 459 

9. 20 540 

9. 20 621 

9.20 701

9. 20 782 

9.20 862 

9. 20 942 

9.21 022 

9. 21 102

9. 21 182 

9. 21 261 

9.21 341 

9. 21 420 

9. 21 499

9. 21 578 

9. 21 657 

9.21 736 

9. 21 814 

9. 21 893

9.21 971 

9. 22 049 

9.22 127 

9. 22 205 

9. 22 283

9. 22 361 

9. 22 438 

9. 22 516 

9. 22 593 

9.22 670

9. 22 747 

9. 22 824 

9. 22 901 

9. 22 977 

9. 23 054

9. 23 130 

9. 23 20(5 

9.23 283 

9.23 359 

9/23 435

9.23510 

9. 23 586 

9. 23 661 

9. 23 737 

9. 23 812

9.23 887 

9. 23 962 

9. 24 037 

9.24 112 

9. 24 186

9.24 261 

9.24 335 

9. 24 410 

9. 24 484 

9.24 558

9. 24 632

L. Cotg.

c. d.

82 

81

82 

81 

81

81 

81 '81 

80 

81

80 

80 

80 

80 

80

79 

80 

79 

79 

79

79 

79

78 

79 

78

78 

78 

78 

78 

78

77 

78 

77 

77 

77-

77 

77 

76 

77 

76

76

77

76 

76

75

76

75 

76 

75 

75

75 

75 

75 

74. 

75

74 

75 

74 

74 

74

c.d.

L. Cotg.

0. 80 029 

0.79 947 

0. 79 866 

0. 79 784 

0. 79 703

0. 79 622 

0. 79 541 

0. 79 460 

0. 79 379 

0. 79 299

0.79 218 

0. 79 138 

0. 79 058 

0. 78 978 

0. 78 898

0. 78 818 

0. 78 739 

0. 78 659 

0. 78 580 

0. 78 601

0. 78 422 

0. 78 343 

0. 78 264 

0. 78 186 

0. 78 107

0. 78 029 

0. 77 951 

0. 77 873 

0.77 795 

0. 77 717

0.77 639 

0. 77 562 

0. 77 484 

0. 77 407 

0. 77 330

0. 77. 253 

0.77 176 

0. 77 099 

0. 77 023 

0. 76 946

0. 76 870 

0.76 794 

0.76 717 

0. 76 641. 

0.76 565

0. 76 490 

0. 76 414 

0. 76 339 

0. 76 263 

0. 76 188

0. 76 113 

0. 76 038 

0. 75 963 

0. 75 888 

0. 75 814

0.75 739 

0.75 665 

0. 75 590 

0. 75 516 

0. 75 442

0.75 368

L. Tang.

L. Cos.

9. 99 462 

9. 99 460 

, 9. 99 458 

9.99 156 

9. 99 454

9. 99 452 

9. 99 450 

9. 99 448 

9.99 446 

9. 99 444

9. 99 442 

9.99 440 

9. 99 438 

9. 99 436 

9. 99 434

9. 99 432 

9. 99 429 

9. 99 427 

9. 99 425 

9. 99 423

9. 99 421 

9.99 419 

9. 99 417 

9.99 415 

9.99 413

9. 99 411 

9. 99 409 

9.99 407 

9.99 404 

9. 99 402

9. 99 400 

9. 99 398 

9. 99 396 

9. 99 394 

9. 99 392

9. 99 390 

9. 99 388 

9.99 385 

9. 99 383 

9. 99 381

9.99 379 

9.99 377 

9.99 375 

9. 99 372 

9. 99 370

9. 99 368 

9. 99 366 

9. 99 364 

9. 99 362 

9. 99 359

9. 99 357 

9. 99 355 

9. 99 353 

9.99 351 

9.99 348

9.99 346 

9.99 344 

9.99 342 

9. 99 340 

9. 99 337

9. 99 335

L. Sin.

GO

59

58 

57 

56

 55 

54 

53 

52 

51

50

49

48 

47 

46

45 

44. 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

80

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

/

24 0 

56 

52 

48 

 44

23 40 

36 

32 

28 

24

23 20 

16 

12 

8 

4

23 0 

56 

52 

48 

44

22 40 

36 

32

28 

24

22 20 

16 

12 

8 

4

22 0 

56 

52 

48 

44

21 40 

36 

32 

28 

24

21 20 

16 

12

8 

4

21 0 

56 

52 

48 

44

20 40 

36 

32 

28 

24

20 20 

16 

12 

8 

4

20 0

m. s.

80C
C4EOGBAPHIC TABLES AND FORMULAS. 181 

TABLK 27. Five-place logarithms of circular functions, etc. Continued. 

0" 10°

in. s.

40 0

4 

8 

1.2 

16

40 20 

24 

28 

32 

36

40 40 

44 

48 

52 

56

41. 0 

4 

8 

12 

16

4.1. 20 

24 

28 

32 

36

41 40 

44 

48 

52 

56

42 0. 

4 

8 

V 

16

42 20 

24 

28 

32 

36

42 40 

44 

48 

52 

56

43 0 

4 

8 

12 

16

43 20 

24 

28 

32 

36

43 40 

44 

48 

52 

56

44 0

'

0

1

2

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

80

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

00

L. Sin.

9.23 967 

9. 24 039 

9. 24 110 

9. 24 181 

9. 24 253

9.24 324 

9. 24 395 

9. 24 466 

9. 24 536 

9. 24 607

9. 24 677 

9. 24 748 

9.24 818 

9. 24 888 

9. 24 958

9. 25 028 

y. 25 098 

9.25 168 

9. 25 237 

9. 25 307

9.25 376 

9. 25 445 

9. 25 514 

9.25 583 

9. 25 652

9. 25 721 

9. 25 790 

9. 25 858 

9. 25 927 

9. 25 995

9.26 063 

9. 26 131 

9. 26 199 

9. 26 267 

9. 26 335

9. 26 403 

9. 26 470 

9. 26 538 

9. 26 605 

9.26 672

9. 26 739 

9. 26 806 

9.26 873 

9. 20 940 

9.27 007

9.27 073 

9. 27 140 

9.27 200 

9. 27 .273 

9. 27 339

9.27 405 

9. 27 471 

9. 27 537 

9. 27 602 

9. 27 668

9.27 734 

9.27 799 

9. 27 864 

9. 27 930 

9. 27 995

9. 28 060

L. Cos.

d.

72 

71 

' 71 

72

71

71 

71 

70 

71

70

71 

70 

70 

70 

. 70

70 

70 

69 

70

69 

69 

69 

69

09 

68 

69 

68 

68

08 

08 

08 

08

67 

68 

67 

67 

67

67 

67 

67 

67

07 

66 

67 

60

66 

66 

65 

60

65 

65 

66 

65

65

d.

L: Taug.

9. 24 632 

9. 24 706 

9. 24 779 

9. 24 853 

9.24 926

9. 25 000 

9. 25 073 

7. 25 146 

9. 25 219 

9. 25 292

9.25 365 

9. 25 437 

9. 25 510 

9. 25 582 

9. 25 655

9. 25 727 

9.25 799 

9. 25 871 

9. 25 943 

9. 26 015

9.26 080 

9.26 158 

9. 20 229 

9. 26 301 

9. 26 372

9.26 443 

9.26 514 

9.26 585 

9. 26 655 

9. 26 726

9.26 797 

9. 26 867 

9. 26 937 

9. 27 008 

9. 27 078

9. 27 148 

9. 27 218 

9. 27 288 

9. 27 357 

9.27 427

9.27 496 

9.27 560 

9.27 635 

9.27 704 

9.27 773

9. 27 842 

9.27 911 

9.27 980 

9. 28 049 

9. 28 117

9. 28 186 

9.28.254 

9. 28 323 

9. 28 391 

9. 28 459

9. 28 527 

9. 28 595 

9. 28 662 

9. 28 730 

9,28 798

9. 28 865

L. Cotg.

C. d.

74 

73 

74 

73

74

73 

73 

73 

73

72 

73 

72 

73

72

72 

72 

72 

72 

71

72 

71 

72 

71

71 

71 

70 

71 

71

70 

70 

71 

70

70

70 

70 

69 

 70

70 

69 

69 

09

09 

09 

09

68

68 

69 

68 

68

68 

67 

68 

68

67

c. d.

L. Cotg.

0. 75 368 

0. 75 294 

0. 75 221 

0.75 347 

0. 75 074

0. 75 000 

0. 74 927 

0. 74 854 

0. 74 781 

0. 74 708

0. 74 635 

0. 74 563 

0. 74 490 

0. 74 418 

0. 74 345

0. 74 273 

0.74201 

0.74 129 

0. 74 057 

0. 73 985

0. 73 914 

0.73 842 

0. 73 771 

0. 73 699 

0. 73 628

0. 73 557 

0. 73 486 

0. 73 415 

0. 73 345 

0. 73 274

0. 73 203 

0.73 133 

0. 73 063 

0. 72 992 

0. 72 922

0. 72 852 

0.72 782 

0. 72 712 

0. 72 643 

0. 72 573

0. 72 504 

0. 72 434 

0. 72 365 

0. 72 296 

0. 72 227

0.72 158 

0. 72 089 

0. 72 020 

0. 71 951 

0. 71 883

0.71 814 

0.71 746 

0.71 677 

0.71 009 

0. 71 541

0. 71 473 

0. 71 405 

0. 71 338 

0. 71 270 

0.71 202

0.71 135

L. Tang.

L. Cos.

9. 99 335 

9. 99 333 

9. 99 331 

9. 99 328 

9. 99 320

9. 99 324 

9. 99 322 

9.99 319 

9. 99 317 

9. 99 315

9. 99 313 

9. 99 310 

9. 99 308 

9. 99 306 

9. 99 304

9. 99 301 

9.99299 

9. 99 297 

9.99 294 

9. 99 292

9. 99 290 

9.99 288 

9. 99 285 

9. 99 283 

9. 99 281

9. 99 278 

9. 99 276 

9. 99 274: 

9. 99 271 

9. 99 209

9. 99 207 

9. 99 264 

9. 99 262 

9. 99 260 

9. 99 257

9. 99 255 

9. 99 252 

9.99 250 

9.99 248 

9. 99 245

9. 99 243 

9. 99 241 

9. 99 238 

9. 99 236 

9.99 233

9. 99 231 

9. 99 229 

9. 99 226 

9. 99 224 

9.99 221

9.99 219 

9. 99 217 

9. 99 214 

9. 99 212 

9. 99 209

9. 99 207 

9. 99 204 

9. 99 202 

9. 99 200 

9. 99 197

9.99 195

L. Sin.

d.

 2 

2 

3 

2

2

2 

3 

2 

2

2

3 

2 

2 

2

2 

2 

3 

2

£t

2 

3 

2 

2

2 

2 

3 

2

3

2 

2 

3

2

3

2 

2 

3

2 

3 

2 

3

2

2 

3 

2 

3

2 

3 

2 

3

2

3 

2 

2 

3

d.

GO

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

80

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

10

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

'

20 0 

56 

52 

48 

44

19 40 

30 

32 

28 

24

19 20 

10 

12 

8 

4

19 0 

50 

52 

48 

44

18 40 

36 

32 

28 

24

18 20 

10 

12 

8 

4

18 0 

50 

52 

48 

44

.17 40 

30 

32 

28 

24

17 20 

10 

12 

8 

4

17 0 ' 

50 

52 

48 

44

10 40 

30 

32 

28 

24

16 20 

16 

12 

8

4

16 0

m. s.

79° 5h
182 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithm* of circular functions, etc. Continued. 

Oh 11°

m. s.

44 0 

4 

8 

12 

16

44. 20 

24 

28 

32 

36

44 40 

44 

48 

52 

56

45 0 

4 

8 

12 

16

45 20 

24 

28 

32 

36

45 40 

44 

48 

52 

56

46 0 

4 

8 

12 

16

46 20 

24 

28 

32 

36

46 40 

44 

48 

52 

56

47 0 

4 

8 

12 

16

47 20 

24 

28 

32 

36

47 40 

44 

48 

52 

56

48 0

'

0

1 

2 

3 

4

5 

6

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

80

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44.

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 28 060 

9. 28 125 

9. 28 190 

9. 28 254 

9. 28 319

9. 28 384 

9. 28 448 

9. 28 512 

9. 28 577 

9. 28 641

9. 28 705 

9. 28 769 

9.28833 

9.28 896 

9. 28 960

9. 29 024 

9. 29 087 

9.29 150 

9.29 214 

9. 29 277

9.29 340 

9. 29 403 

9. 29 466 

9. 29 529 

9. 29 591

9. 29 654 

9. 29 716 

9.29 779 

9. 29 841 

9. 29 903

9. 29 966 

9. 30 028 

9. 30 090 

9. 30 151 

9. 30 213

9. 30 275 

9. 30 336 

9. 30 398 

9.30-459 

9.30 521

9. 30 582 

9.30643 

9. 30 704 

9. 30 765 

9. 30 826

9.30 887 

9. 30 947 

9.31 008 

9.31 068 

9. 31 129

9. 31 189 

9.31 250 

9.31 310 

9. 31 370 

9. 31 430

9.31 490 

9. 31 549 

9. 31 609 

9. 31 669 

9. 31 728

9. 31 788

L. Cos.

d.

65 

65 

64 

65 

65

64 

64 

65 

64

64 

64 

63 

64

63 

63 

64 

63

63 

63 

63 

62

62 

63 

62 

62 

M

62 

62 

61 

62 

62

61 

62 

61 

62

61

61 

61 

61 

61

-60 

61 

60 

61 

60

61 

60 

60 

60/'A

59 

60 

60 

59

d.

L. Tang.

9. 28 865 

9. 28 933 

9.29 000 

9. 29 067 

9. 29 134

9. 29 201 

9.29 268 

9.29 335 

9. 29 402 

9. 29 468

9.29 535 

9. 29 601 

9.29 668 

9.29 734 

9.29 800

9. 29 866 

9. 29 932 

9. 29 998 

9. 30 064 

9. 30 130

9. 30 195 

9. 30 261 

9. 30 326 

9. 30 391 

9. 30 457

9. 30 522 

9. 30 587 

9. 30 652 

9. 30 717 

9. 30 782

9. 30 846 

9. 30 911 

9. 30 975 

9. 31 040 

9. 31 104

9. 31 168 

9.31 233 

9.31 297 

9. 31 361 

9. 31 425

9. 31 489 

9.31 552 

9.31 616 

9.31 679 

9. 31 743

9. 31 806 

9.31 870 

9. 31 933 

9. 31 996 

9. 32 059

9. 32 122 

9.32 185 

9. 32 248 

9. 32 311 

9. 32 373

9.32 436 

9. 32 498 

9. 32 561 

9. 32 623 

9.32 685

9.32747

L. Cotg.

C.d.

68 

67 

67 

67

67 

67 

67 

66

66 

67 

66 

66

66 

66 

66 

66

66 

65 

65 

66

65 

65 

65 

65 

64

65 

64 

65 

64

65 

64 

64 

64

64

63 

64 

03 

64

oo

64 

63 

63 

63

63

63 

63 

63 

62

62 

63 

62 

62

62

c.d.

L. Cotg.

0. 71 135 

0. 71 067 

0.71 000 

0.70 933 

0. 70 866

0. 70 799 

0. 70 732 

0. 70 665 

0. 70 598 

0.70 532

0. 70 465 

0. 70 399 

0. 70 332 

0. 70 266 

0. 70 200

0.70134 

0.70068 

0. 70 002 

0. 69 936 

0. 69 870

0. 69 805 

0. 69 739 

0. 69 674 

0. 69 609 

0. 69 543

0. 69 478 

0. 69 413 

0. 69 348 

0. 69 283 

0. 69 218

0. 69 154 

0. 69 089 

0. 69 025 

0. 68 960 

0. 68 896

0. 68 832 

0. 68 767 

0.68 703 

0. 68 639 

0. 68 575

0. 68 511 

0.68448 

0. 68 384 

0. 68 321 

0. 68 257

0. 68 194 

0. 68 130 

0. 68 067 

0. 68 004 

0. 67 941

0. 67 878 

.0.67 815 

0. 67 752 

0.67 689 

0.67 627

0. 67 564 

0. 67 502 

0. 67 439 

0. 67 377 

0.67 315

0. 67 253

L. Tang.

L. Cos.

9. 99 195 

9. 99 192 

9.99 190 

9. 99 187 

9. 99 185

9. 99 182 

9. 99 180 

9. 99 177 

9.99 175 

9. 99 172

9. 99 170 

9. 99 167 

9. 99 165 

9. 99 162 

9.99 160

9. 99 157 

9. 99 155 

9. 99 152 

9. 99 150 

9. 99 147

9. 99 145 

9. 99 142 

9. 99 140 

9. 99 137 

9. 99 135

9.99 132 

9. 99 130 

9. 99 127 

9. 99 124 

9. 99 122

9. 99 119 

9. 99 117 

9. 99 114 

9. 99 112 

9. 99 109

9. 99 106 

9. 99 104 

9. 99 101 

9. 99 099 

9.99 096

9. 99 093 

9.99091 

9. 99 088 

9. 99 080 

9. 99 083

9. 99 080 

9. 99 078 

9.99 075 

9. 99 072 

9. 99 070

9.99 067 

9. 99 064 

9. 99 062 

9. 99 059 

9. 99 056

9. 99 054 

9. 99 051 

9.99 048 

9. 99 046 

9. 99 043

9. 99 040

L. Sin.

d.

3 

2 

3 

2

2 

3 

2 

3

3

2 

3 

2

o

2 

3 

2 

3

3 

2 

3 

2

2 

3 

3

2

2 

3 

2 

3

o

2 

3 

2 

3

3

2 

3 

2 

3

2 

3 

3 

2

3 

2 

3 

3

2

3 

3 

2 

3

3

d.

60

59

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

'

16 0 

56 

52

48 

44

15 40 

36 

32 

28 

24

15 20 

16 

12 

8 

4

15 0

56 

52 

48 

44

14 40 

36 

32

28 

24

14 20 

16 

12

8 

4

14 0 

56 

52

48 

44

13 40 

36 

32 

28 

24

13 20 

16 

12 

8 

4

13 0

50 

52 

48 

44

12 40 

36 

32 

28 

24

12 ' 20 

16

' 12 

8 

4

12 0

m. s.

78° 5h
GEOGRAPHIC TABLES AND FORMULAS. 183 

TABLE 27. Five-place logarithms, of circular functions, etc. Continued.

Oh 12°

m. s.

48 0 

4 

8 

12 

16

48 20 

24 

28 

32 

36

48 40 

44 

48 

52 

56

49 0 

4 

8 

12 

16

49 20 

24 

28 

32 

36

49 40 

44 

48 

52 

5G

50 0 

4 

8 

12 

16

50 20 

24 

28 

32 

36

50 40 

44 

48 

52 

56

51 0 

4 

8 

12 

16

51 20 

24 

28 

32 

36

51 40 

44 

48 

52 

56

52 0

/

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

50 

57 

58 

59

60

L. Sin.

9. 31 788 

9. 31 847 

9. 31 907 

9.31 966 

9. 32 025

9. 32 084 

9. 32 143 

9. 32 202 

9. 32 261 

9. 32 319

9.32 378 

9.32437 

' 9. 32 495 

9. 32 553 

9. 32 612

9. 32 670 

9. 32 728 

9. 32 786 

9. 32 844 

9. 32 902

9. 32 960 

9. 33 018 

9. 33 075 

9. 33 133 

9. 33 190

9. 33 248 

9. 33 305 

9. 33 362 

9. 33 420 

9. 33 477

9.33 534 

9. 33 591 

9. 33 647 

9. 33 704 

9.33761

9. 33 818 

9. 33 874 

9. 33 931 

9. 33 987 

9. 34 043

9. 34 100 

9. 34 156 

9. 34 212 

9. 34 268 

9. 34 324

9. 34 380 

9. 34 436 

9.34491 

9. 34 547 

9. 34 602

9. 34 658 

9.'34 713 

9. 34 769 

9. 34 824 

9. 34 879

9. 34 934 

9. 34 989 

9. 35 044 

9. 35 099 

9. 35 154

9. 35 209

L. Cos.

d.

59 

60 

59 

59 

69

59 

59 

59 

58 

59

59 

58 

58 

69 

58

58 

53 

58 

58 

58

58 

57 

58 

57 

58

57 

57 

58 

57 

.57

57 

56 

57 

57 

57

56 

57 

56 

56 

67

56 

56 

56 

56 

56

56 

55 

56 

55 

66

55 

56 

55 

55 

55

55 

55 

55 

55 

55

d.

L. Tang.

9.32 747 

9. 32 810 

9. 32 872. 

9. 32 933 

9. 32 995

9. 33 057 

9. 33 119 

9. 33 180 

9. 33 242 

9. 33 303

9.33 365 

9.33426 

9. 33 487 

9. 33 548 

9. 33 609

9.33 670 

9.33 731 

9.33792

9. 33 853 

9. 33 913

9.33 974 

9.34 034 

9. 34 095 

9.34155 

9. 34 215

9. 34 276 

9. 34 336 

9. 34 396 

9. 34 456 

9. 34 516

9. 34 576 

9.34635 

9. 34 695 

9. 34 755 

9. 34 814

9. 34 874 

9. 34 933 

9. 34 992 

9. 35 051 

9. 35 111

9. 35 170 

9. 35 229 

9. 35 288 

9. 35 347 

9. 35 405

9. 35 464 

9. 35 523 

9. 35 581 

9. 35 640 

9. 35 698

9. 35 757 

9. 35 815 

9.35873 

9.35 931 

9. 35 989

9. 36 047 

9.36 105 

9. 36 163 

9. 36 221 

9. 36 279

9.36 336

L. Cotg.

c. d.

63 

62 

61 

62 

62

. 62 

61 

62 

61 

62

61 

61 

61 

61 

61

61 

61 

61 

60 

61

60 

61 

60 

60 

61

60 

60 

60 

60 

60

59 

60 

60 

59 

60

59 

59 

59 

60 

59

59 

59 

59 

58 

59

59 

58 

59 

58 

59

58 58' 

58 

58 

58

58 

58 

58 

58 

57

c. d.

L. Cotg.

0. 67 253 

0. 67 190 

0. 67 128 

0. 67 067 

0, 67 005

0. 66 943 

0. 66 881 

0. 66 820 

0. 66 758 

0. 66 697

0. 66 635 

0.66 574 

0.66 513 

0. 66 452 

0; 66 391

0. 66 330 

0.66 269 

0.66208

0.66 147 

0. 66 087

0.66026 

0. 65 966 

0. 65 905 

0.65 845 

0. 65 785

0. 65 724 

0. 65 664 

0, 65 604 

0. 65 644 

0. 65 484

0.65424 

0. 65 365 

0. 65 305 

0. 65 245 

0. 65 186

0.65 126 

0. 65 067 

0. 65 008 

0. 64 949 

0. 64 889

0. 64 830 

0.64 771 

0. 64 712 

0. 64 653 

0.64 595

0. 64 530 

0. 64 477 

0. 64 419 

0. 64 360 

0. 64 302

0. 64 243 

0. 64 185 

0. 64 127 

0. 64 069 

0. 64 Oil

0. 63 953 

0. 63 895 

0. 63 837 

0. 63 779 

0. 63 721

0. 63 664

L. Tang.

L. Cos.

9.99 040 

9. 99 038 

9. 99 035 

9.99 032 

9. 99 030

9. 99 027 

9. 99 024 

9.99022 

9.99 019 

9.99 016

9.99 013 

9.99 Oil 

9.99 008 

9. 99 005 

9. 99 002

9. 99 000 

9.98997 

9.98994

9.98 991 

9.98 989

9. 98 986 

9. 98 983 

9. 98 980 

9.98 978 

9. 98 975

9. 98 972 

9. 98 969 

9. 98 967 

9. 98 964 

9. 98 961

9. 98 958 

9. 98 955 

9.98 953 

9. 98 950 

9. 98 947

9. 98 944 

9. 98 941 

9.98 938 

9. 98 936 

9.98 933

9. 98 930 

9. 98 927 

9.98 924 

9. 98 921 

9. 98 919

9.98 916 

9. 98 913 

9. 98 910 

9.98 907 

9. 98 904

9. 98 901 

9. 98 898 

9. 98 896 

9. 98 893 

9. 98 890

9.98887 

9. 98 884 

9. 98 881 

9. 98 878 

9. 98 875

9. 98 872

L. Sin.

d.

2 

3 

3 

2 

3

3 

2 

3 

3 

3

2 

3 

3 

3

2

3 

3 

3 

2 

3

3 

3 

2 

3 

3

3 

2 

3 

3

a

3 

2 

3 

3 

3

3 

3 

2 

3 

3

3 

3 

3 

2 

3

3 

3 

3 

3 

3

3 

2 

3 

3 

3

3 

3 

3 

3 

3

d.

00

59 

58 

57 

56

55 

54 

53 

52 

61

50

49 

48 

47 

46

45 

44

43 

42 

41

40

39 

88 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9 

8

7 

6

5 

4 

3 

2 

1

0

'

12 0 

56 

52 

48 

44

11 40 

30 

32 

28 

24

11 20 

16 

12 

8 

4

11 0 

56 

52

48 

44

10 40 

36 

32 

28 

24

10 20 

16

12 

8 

4

10 0 

56 

52 

48 

44

9 40 

36 

32 

28 

24

9 20 

16 

D2 

8 

4

9 0 

56 

52 

48 

44

8 40 

36 

32 

28 

24

8 20 

16 

12 

8 

4

8 0

m. s.

77°.
184 GEOGKAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued.

Qh 130

m. s.

52 0 

.4 

8 

12 

16

52 20 

24 

28 

32 

36

52 40 

44 

48 

52 

56

53 0 

4 

8 

12 

16

53 20 

24 

28 

32 

36

53 40 

44 

48 

52 

56

54 0 

4 

8 

12 

16

54 20 

24 

28 

32 

36

54 40 

44 

48 

52 

56

55 0 

4 

8 

12 

16

55 20 

24 

28 

32 

36

65 40 

44 

48 

52 

56

56 0

'

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41

42

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 35 209 

9. 35 263 

9. 35 318 

9. 35 373 

9. 35 427

9. 35 481 

9. 35 536 

9. 35 590 

9. 35 644 

9. 35 698

9. 35 752 

9. 35 806 

9. 35 860 

9. 35 914 

9. 35 968

9. 36 022 

9. 36 075 

9. 36 129 

9. 36 182 

9. 36 236

9. 36 289 

9. 36 342 

9. 36 395 

9. 36 449 

9. 36 502

9. 36 555 

9. 36 608 

9.36 660 

9. 36 713 

9. 36 766

9. 36 819 

9. 36 871 

9. 36 924 

9. 36 976 

9. 37 028

9. 37 081 

9. 37 133 

9. 37 185 

9.37 237 

9. 37 289

9. 37 341 

9. 37 393

9.37445

9.37 497 

9.37 549

9. 37 600 

9. 37 652 

9.37 703 

9. 37 755 

9. 37 806

9.37 858 

9. 37 909 

9. 37 960 

9. 38 Oil 

9. 38 062

9.38 113 

9. 38 164 

9. 38 215 

9. 38 266 

9. 38 317

9.38 368

L.Cos.

d.

54 

55 

55 

54 

54

55 

54 

54 

54 

54

54 

54 

54 

54 

54

53 

54 

53 

54 

53

53 

53 

54 

53 

53

53 

52 

63 

53 

53

52 

53 

52 

52 

53

52 

52 

52 

52 

52

52 

52 

52 

52 

 51

52 

51 

52 

51 

52

51 

51 

51 

51 

51

51 

51 

51 

51 

51

d.

L. Tang.

9.36 336 

9. 36 394 

9.36 452 

9. 30 509 

9. 36 566

9.36 624 

9. 36 681 

9. 36 738 

9. 36 795 

9. 36 852

9. 36 909 

9. 36 966 

9. 37 023 

9. 37 080 

9. 37 137

9.- 37 193 

9. 37 250 

9. 37 306 

9. 37 363 

9. 37 419.

9. 37 476 

9.37 532 

9. 37 588 

9. 37 644 

9. 37 700

9. 37 756 

9. 37 812 

9. 37 868 

9. 37 924 

9. 37 980

9. 38 035 

9. 38 091 

9. 38 147 

9. 38 202 

9. 38 257

9. 38 313 

9. 38 368 

9. 38 423 

9. 38 479 

9. 38 534

9. 38 589 

9.38 644

9.38699

9. 38 754 

9. 38 808

9. 38 863 

9. 38 918 

9. 38 972 

9. 39 027 

9. 39 082

9. 39 136 

9. 39 190 

9. 39 245 

9. 39 299 

9. 39 353

9. 39 407 

9. 39 461 

9. 39 515 

9. 39 569 

9. 39 623

9. 39 677

L. Cotg.

c.d.

58 

58 

57 

57 

58

57 

57 

57.

57 

57

57 

57 

57 

57 

56

57 

56 

57 

56

57

56 

56 

56 

56 

56

56 

56 

56 

56 

55

56 

56 

55 

55 

56

55 

55 

56 

55 

55

55 

55

55 

54 

55

55 

54 

55 

55 

54

54 

55 

54 

54 

54

54 

54 

54 

54 

54

c.d.

L. Cotg.

0. 63 664 

0.63 606 

0. 63 548 

0. 63 491 

0. 63 434

0. 63 376 

0. 63 319 

0. 63 262 

0. 63 205 

0. 63 148

0. 63 091 

0.63 034 

0. 62 977 

0. 62 920 

0. 62 863

0. 62 807 

0. 62 750 

0. 62 694 

0. 62 637 

0. 62 581

0. 62 524 

0. 62 468 

0. 62 412 

0. 62 356 

0. 62 300

0. 02 244 

0. 62 188 

0. 62 132 

0. 62 076 

0. 62 020

0. 61 965 

0. 61 909 

0. 61 853 

0.61 798 

0.61 743

0. 61 687 

0. 61 632 

0.61 577 

0.61 521 

0. 61 466

0.61 411 

0. 61 356 

0.61301 

0.61 240 

0.61 192

0. 61 137 

0.61 082 

0. 61 028 

0. 60 973 

0. 60 918

0. 60 864 

0. 60 810 

0. 60 755 

0. 60 701 

0. 60 647

0. 60 593 

0. 60 539 

0. 60 485 

0. 60 431 

0. 60 377

0. 60 323

L. Tang.

L. Cos.

9. 98 872 

9. 98 869 

9.98 867 

9. 98 864 

9. 98 861

9.98 858 

9. 98 855 

9. 98 852 

9.98 849 

9. 98 846

9. 98 843 

9. 98 840 

9.98 837 

9. 98 834 

9. 98 831

9. 98 828 

9. 98 825 

9.98822 

9. 98 819 

9. 98 816

9. 98 813 

9.98 810 

9. 98 807 

9. 98 804 

9. 98 801

9. 98 798 

9. 98 795 

9. 98 792 

9. 98 789 

9.98 786

9.98 783 

9. 98 780 

9. 98 777 

9.98 774 

 9.98 771

9. 98 768 

9. 98 765 

9.98 762 

9. 98 759 

9. 98 756

9. 98 753 

9. 98 750 

9.98 746

9. 98 743 

9.98 740

9. 98 737 

9. 98 734 

9. 98 731 

9. 98 728 

9. 98 725

9. 98 722 

9. 98 719 

9. 98 715 

9. 98 712 

9.98 709

9. 98 706 

9.98 703 

9. 98 700 

9. 98 697 

9. 98 694

9.98 690

L. Sin.

d.

3 

2 

3 

3 

3

3 

3 

3 

3 

3

3 

3 

3 

3 

3

3 

3 

3 

3 

3

3 

3 

3 

3 

3

3 

3 

3 

3 

3

3 

3 

3 

3 

3

3 

3 

3 

3 

3

3 

4 

3 

3 

3

3 

3 

3 

3 

3

, 3 

4 

3 

3 

3

3 

3 

3 

3

4

d.

GO

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18

17 

1C

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

i

8 0 

56 

52 

48 

44

7 40 

36 

32 

28 

24

7 20 

16 

12 

8 

4

7 0 

56 

52 

48 

44

6 40 

36 

32 

28 

24

' 6 20 

16 

12 

8 

4

6 0 

56 

52 

48 

44

5 40 

36 

32 

28 

24

5 20 

16 

12 

8 

4

5 0 

56 

52 

48 

44

4 40 

36 

32 

28 

24

4 20 

16 

12 

8 

4

4 0

m. s.

76C
GEOGEAPH1C TABLES AND FORMULAS. 185

TABLE 27. Five-place logarithm* of circular functions, etc. Continued. 

Oh 14°

111. 8.

50 0 

4 

8 

12 

16

56 20 

24 

28 

32 

36

56 40 

44 

48 

52 

56

67 0 

4 

8 

12 

16

57 20 

24 

28 

32 

36

57 40 

44 

48 

52 

66

58 0 

4 

8 

12 

16

58 20 

24 

28 

32 

36

58 40 

44 

48 

52 

56

59 0 

4 

8 

12 

16

59 20 

24 

28 

32 

36

59 40 

44 

48 

52 

56

60 0

'

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

64

65 

56 

67 

58 

59

CO

L. Sin.

9. 38 368 

9. 38 418 

9. 38 469 

9.38 519 

9. 38 570

9.38 020 

9. 38 670 

9.38 721 

9.38771 

9.38 821

9. 38 87] 

9. 38 921 

9. 38 971 

9. 39 021 

9.39 071

9. 39 121 

9.39 170 

9.39 220 

9. 39 270 

9. 39 319

9.39369 

9. 39 418 

9. 39 467 

9. 39 517 

9. 39 566

9. 39 615 

9. 39 664 

9. 39 713 

9. 39 762 

9. 39 811

9. 39 860 

9. 39 909 

9. 39 958 

9.40 006 

9. 40 055

9. 40 103 

9. 40 152 

9. 40 200 

9. 40 249 

9. 40 297

9. 40 346 

9. 40 394 

9:40 442 

9. 40 490 

9. 40 538

9. 40 580 

9. 40 634 

9. 40 682 

9. 40 730 

9. 40 778

9. 40 825 

9. 40 873 

9. 40 921 

9. 40 968 

9.41 016

9. 41 063 

9.41 111 

9.41 158 

9.41 205 

9.41 252

9.41 300

L. Cos.

d.

50 

51 

60 

51 

50

50 

51 

50 

50

CA

60 

50 

50 

50 

v»

49 

50 

50 

49 

50

49 

49 

50 

49 

49

49 

49 

49 

49 

49

49 

49 

48 

49 

48

49 

48 

49 

48 

49

48 

48 

48 

48 

48

48 48 

48 

48 

47

48 

48 

47

48 

47

48 

47 

47 

47 

48

d.

L. Tang.

9. 39 677 

9. 39 731 

9. 39 785 

9.39 838 

9.39 892

9. 39 945 

9.39 999 

9. 40 052 

9.40 106 

9.40 159

9. 40 212 

9.40 266 

9. 40 319 

9. 40 372 

9. 40 425

9. 40 478 

9.40 531

9.40584

9.40 63G 

9.40 689

9. 40 742 

9. 40 795 

9. 40 847 

9.4.0 900 

9.40 952

9.41 005 

9. 41 057 

9.41 109 

9.41 161 

9. 41 214

9. 41 266 

9.41 318 

9.41 370 

9.41 422 

9. 41 474

9. 41 526 

9.41 578 

9. 41 629 

9. 41 681 

9. 41 733

9.41 784 

9.4.1 836 

9. 41 887 

9. 41 939 

9.41 990

9. 42 041 

9.42 093 

9.42 144 

9. 42 195 

9. 42 246

9. 42 297 

9. 42 348 

9. 42 399 

9. 42 450 

9.42 501

9. 42 552 

9. 42 603 

9.42 653 

9.42 704 

9. 42 755

9. 42 805

L. Cotg.

c. d.

54 

54 

53 

54

53

54 

53 

54 

53 

53

54 

53 

53 

53

53 

53 

52 

53 

53

53 

52 

53 

52

no

52 

52 

52 

53

CO

52 

52 

52 

52 

52

52 

51 

52 

52 

51

52 

51 

52 

51 

51

52 

51 

51 

51 

51

51 

51 

51 

51 

51

51 

50 

51 

51

CA

c. d.

L. Cotg.

0. GO 323 

0. 60 269 

0. 60 215 

0. 60 162 

0. 00 108

0. 60 055 

0. 60 001 

0. 59 948 

0. 59 894 

0. 59 841

0.59 788 

0. 59 734 

0. 59 681 

0.59 628 

0.59 575.

. 0. 59 522 

0.59 469 

0.59416 

0. 59 364 

0. 59 311

0. 59 258 

0. 59 205 

0. 59 153 

0. 59 100 

0.59 048

0.58 995 

0.58 943 

0. 58 891 

0. 58 839 

0. 58 786

0.58 734 

0. 58 682 

0. 58 630 

0.58 578 

0. 58 526

0. 58 474 

0. 58 422 

0.-58 371 

0. 58 319 

0. 58 267

0. 58 216 

0. 58 164 

0.58 113 

0.58061 

0. 58 010

0.5V 959 

0.57 907 

0. 57 856 

0. 57 805 

0. 57 754

0. 57 703 

0.57 652 

0.57 601 

0.57 550 

0. 57 499

0.57 448 

0. 57 397 

0.57 347 

0. 57 296 

0.57 245

0.57 195

L. Tang.

L. Cos.

9.98 090 

9. 98 687 

9.98 084 

9. 98 081 

9. 98 678

9. 98 075 

9. 98 071 

9. 98 668 

9. 98 065 

9. 98 602

9.98 659 

9. 98 656 

9. 98 652 

9. 98 649 

9. 98 646

9. 98 643 

9. 98 640

9.98636

9. 98 633 

9.98 630

9. 98 627 

9. 98 623 

9. 98 620 

9. 98 617 

9. 98 614

9. 98 610 

9. 98 607 

9. 98 604 

9.98 601 

9. 98 597

9. 98 594 

9.98 591 

9. 98 588 

9. 98 584 

9. 98 581

9. 98 578 

9. 98 574 

9. 98 571 

9. 98 568 

9. 98 565

9. 98 561 

9. 98 558 

9.98 555 

9. 98 551 

9. 98 548

9. 98 545 

9. 98 541 

9.98 538 

9. 98 535 

9.98 531

9. 98 528 

9. 98 525 

9. 98 621 

9. 98 518 

9. 98 515

9. 98 511 

9. 98 508 

9. 98 505 

9.98 501 

9. 98 498

9.98 494

L. Sin.

d.

3 

3 

3 

3

3

4 

3 

3 

3

3 

4 

3 

3

3

3 

4 

,3 

3

3

4 

3 

3 

3

3 

3 

3 

4

3 

3 

4 

3 

3

4 

3 

3 

3

3 

3 

4 

3

4 

3 

3 

4

3 

4 

3 

3 

4

3 

3 

4 

3

d.

60

59

58 

67 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

80

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

0

5 

4 

3 

2 

1

0

'

4 0 

 50 

52 

48 

44

3 40 

36 

32 

28 

24

3 20 

16 

12 

8 

4

3 0 

56 . 

52 

48 

44

2 40 

36 

32 

28 

24

2 20 

16 

12 

8 

4

2 0 

66 

52 

48 

44

1 40 

36 

32 

28 

24

1 20 

16 

12 

8 

4

1 0 

56 

52 

48 

44

0 40 

30 

32

28 

24

0 20 

16 

12 

8 

4

0 0

in. s.

75°
186 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

I11 15°

in. s.

0 0 

4 

8 

12 

16

0 20 

24 

28 

32 

. 36

0 40 

44 

48 

53 

56

1 0 

4 

8 

12 

16

1 20 

24 

28 

32 

36

1 40 

44 

48 

52 

56

2 0 

4 

8 

12 

16

2 20 

24 

28 

32 

36

2 40 

44 

48 

52 

56

3 0 

4 

8 

12 

16

3 20 

24 

28 

32 

36

3 40 

44 

48 

52 

56

4 0

/

0

1

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 '39

40

41 

42 

43

44

45 

46 

47 

48 

49

50

51 

52 

53

54

55 

56 

57 

58 

59

60

L. Sin.

9.41 300 

9.41 347 

9.41 394 

9. 41 441 

9.41 488

9.41 535 

9.41 582 

9.41 628 

9.41 675 

9. 41 722

9.41 768 

9. 41 815 

9. 41 861 

9.41 908 

9. 41 954

9.42 001 

9. 42 047 

9. 42 093 

9.42 140

9. 42 186 -

9.42 232 

9. 42 278 

9. 42 324 

9.42 370 

9. 42 416

9. 42 461 

9. 42 507 

9. 42 553 

9. 42 599 

9. 42 644

9. 42 690 

9. 42 735 

9. 42 781 

9. 42 826 

9. 42 872

9. 42 917 

9. 42 962 

9. 43 008 

9. 43 053 

9. 43 098

9. 43 143 

9.43188 

9.43233 

9. 43 278 

9.43 323

9.43 367 

9. 43 412 

9. 43 457 

9. 43 502 

9.43546

9. 43 591 

9. 43 635 

9.43 680 

9.43 724 

9.'43 769

9. 43 813 

9.43 857 

9. 43 901 

9. 43 946 

9. 43 990

9. 44 034

L. Cos.

d.

47 

47

47 

47

47

47 

46 

47 

47

47 

46 

47 

46

47

46 

46 

47 

46

46 

46 

46 

46

^10

46 

46 

46 

45

45 

46 

45 

46

45

45 

46 

45 

45

45

45 

45 

45

45

44

45 

45 

45 

44

45

44 

45 

44 

45

44

44 

44 

45 

44

44

d.

L. Tang.

9.42805 

9. 42 856 

9.42 906 

9.42 957 

9. 43 007

9.43 057 

9.43 108 

9. 43 158 

9. 43 208 

9.43 258

9.43 308 

9.43 358 

9. 43 408 

9.43 458 

9. 43 508

9.43 558 

9. 43 607 

9.43 657 

9.43 707 

9. 43 756

9. 43 806 

9. 43 855 

9.43 905 

9. 43 954 

9. 44 004

9. 44 053 

9. 44 102 

9. 44 151 

9. 44 201 

9. 44 250

9.44 299 

9.44 348 

9. 44 397 

9. 44 446 

9. 44 495

9. 44 544 

9. 44 592 

9. 44 641 

9. 44 690 

9. 44 738

9. 44 787 

9.44836 

9.44884 

9. 44 933 

9. 44 981

9.45 029 

9. 45 078 

9.45 126 

9. 45 174 

9. 45 222

9.45 271 

9.45 319 

9. 45 367 

9. 45 415 

9. 45 463

9.45 511 

9. 45 559 

9.45 606 

9.45 654 

9. 45 702

9. 45 750

L. Cotg.

c. d.

51 

50 

51 

50

51 

50 

50 

50

50

50 

50 

50 

50

*j\j

49 

50 

50 

49

ou

49 

50 

49 

50

49 

49 

50 

49

49 

49 

49 

49

48 

49 

49

48

49 

48 

49 

48

48

49 

48 

48 

48

48 

48 

48 

48

48

48 

47 

48 

48

48

C. d.

L. Cotg.

0. 57 195 

0. 57 144 

0.57 094 

0.57 043 

0. 56 993

0.56 943 

0. 56 892 

0. 56 842 

0. 56 792 

0.56 742

0. 56 692 

0.56 642 

0. 56 592 

0. 56 542 

0. 56 492

0. 56 442 

0. 56 393 

0.56 343 

0. 56 293 

0. 56 244

0. 5C 194 

0.56 145 

0.56 095 

0. 56 046 

0. 55 996

0. 55 947 

0. 55 898 

0. 55 849 

0. 55 799 

0.55 750

0. 55 701 

0.55 652 

0. 55 603 

0. 55 554 

0. 55 505

0. 55 456 

0. 55 408 

0. 55 359 

0. 55 310 

0. 55 262

0. 55 213 

0.55 164 

0.55 116 

0.55 067 

0.55 019

0. 54 971 

0. 54 922 

0. 54 874 

0. 54 826 

0. 54 778

0. 54 729 

0. 54 681 

0. 54 633 

0. 54 585 

0. 54 537

0.54 489 

0. 54 441 

0.54 394 

0. 54 346 

0. 54 298

0. 54 250

L. Tang.

L. Cos.

9. 98 494 

9. 98 491 

9. 98 488 

9. 98 484 

9. 98 481

9. 98 477 

9. 98 474 

9. 98 471 

9. 98 467 

9.98 454

9. 98 460 

9.98 457 

9. 98 453 

9. 98 450 

9. 98 447

9. 98 443 

9. 98 440 

9. 98 436 

9.98433 

9. 98 429

9. 98 426 

9. 98 422 

9. 98 419 

S. 98 415 

9. 93. 412

9. 98 409 

9. 98 405 

9. 98 402 

9. 98 398 

9. 98 395

9. 98 391 

9. 98 388 

9. 98 384 

9. 98 381 

9. 98 377

9. 98 373 

9.98 370 

9.98 366 

9. 98 363 

9. 98 359

9. 98 356 

9.98 352 

9.98349 

9. 98 345 

9. 98 342

9.98 338 

9. 98 334 

9. 98 331 

9.98 327 

9. 98 324

9. 98 320 

9. 98 317 

9. 98 313 

9. 98 309 

9. 98 306

9. 98 302 

9. 98 299 

9. 98 295 

9.98 291 

9. 98 288

9. 98 284

L. Sin.

d.

3 

3 

4 

3 

4

3 

3 

4 

3

3 

4 

3 

3

4

3 

4 

3 

4

4 

3 

4 

3

4 

3 

4 

3

3

'}

4 

4

3

4 

3 

4

4 

3 

4 

3

4 

3 

4 

3

3 

4 

4 

3

3 

4 

4 

3

d.

60

59 

58 

57 

56

55 

54 

53 

52 

51

60

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

'

60 0

56 

52 

48 

44

59 40 

36 

32

28 

24

59 20 

16 

12 

8 

4

59 0 

56 

52 

48 

44

58 40 

36 

32 

28 

24

'58 20 

16 

12 

8 

4

58 0 

56 

52 

48 

44

57 40 

36 

32

28 

24

57 20 

16 

12 

8 

4

57 0 

 56 

52 

48 

44

56 40 

36 

32 

28 

24

66 20 

16 

12 

8 

4

56 0

m. s.

74C
GEOGRAPHIC TABLES AND FORMULAS.. 187

TABLE 27. Fiye-place logarithms of circular functions, etc. Continued. 

1" 16°

m. s.

4 0 

4 

8 

12 

10

4 20 

24 

28 

32 

30

4 40 

44 

48 

52 

50

5 0 

4 

8 

12 

10

5 20 

24 

28 

32 

30

5 40 

44 

48 

52 

56

0 0 

4 

8 

12 

16

0 20 

24 

28 

32 

30

0 40 

44 

48 

52 

50

7 0 

4 

8 

12 

10

7 20 

24 

28 

32 

30

7 40 

44 

48 

52 

50

8 0

/

0 

1

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

20 

27 

28 

29

30

31 

32 

33 

34

35 

30 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

50 

57 

58 

59

60

L. Sin.

9.44 034 

9.44 078 

9. 44 122 

9. 44 106 

9. 44 210

9. 44 253 

9. 44 297 

9.44 341 

9. 44 385 

9.44 428

9.44 472 

9.44 516 

9. 44 559 

9. 44 602 

9. 44 640

9.44 689 

9.44 733 

9. 44 776 

9. 44 819 

9. 44 862

9. 44 905 

9.44 948 

9.44 992 

9. 45 035 

9. 45 077

9. 45 120 

9. 45 163 

9. 45 206 

9. 45 249 

9. 45 292

9. 45 334 

9. 45 377 

9.45 419 

9. 45 462 

9. 45 504

9.45 647 

9.45 589 

9. 45 632 

9. 45 674 

9. 45 716

9.45 758 

9. 45 801 

9.45 843 

9. 45 885 

9.45 927

9.45 969 

9.46 Oil 

9. 46 053 

9. 40 095 

9.40 130

9. 40 178 

9. 46 220 

9. 46 202 

9. 46 303 

9.46 345

9. 46 380 

9. 40 428 

9. 40 469 

9.46 511 

9.46 552

9.46 594

L. Cos.

d.

44 

44 

44 

44 

43

44 44' 

44 

43

44 

43 

43 

44 

43

44 

43 

43 

43 

43

43 

44 

43 

42 

43

43 

43 

43 

43

42

43 

42 

43 

42 

43

42 

43

42 

42 

42

43 

42 

 42 

42 

42

42 

42 

42 

41 

42

42 

42 

41 

42 

41

42 

41 

42 

41 

42

d.

L. Tang.

9.45 750 

9. 45 797 

9. 45 845 

9. 45 892 

9.45 940

9. 45 987 

9.46 035 

9.46 082 

9. 40 130 

9. 46 177

9. 46 224 

9.40 271 

9.46 319 

9.46 360 

9. 46 413

9. 46 460 

9.46507 

9.46554 

9.40 001 

9. 46 648

9. 46 694 

9.46 741 

9. 46 788 

9. 46 835 

9. 46 881

9.46 928 

9.46 975 

9.47 021 

9.47 068 

9.47 114

9.47 100 

9. 47 207 

9. 47 253 

9.47 299 

9. 47 346

9.47 392 

9.47 438 

9. 47 484 

9.47 530 

9. 47 576

9.47 622 

9.47 008 

9.47 714 

9. 47 700 

9.47 806

9. 47 852 

9. 47 897 

9.47 943 

9.47 989 

9. 48 035

9. 48 080 

9.48 126 

9. 58 171 

9. 48 217 

9.48 262

9. 48 307 

9.48 353 

9.48 398 

9. 48 443 

9. 48 489

9. 48 534

L. Cotg.

C. d.

47 

48 

47 

48 

47

48 

47

48 

47

47 

48 

47 

47 

47

47 

47 

47 

47 

46

47 

47 

47 

46 

47

47 

46 

47 

46 

46

47 

46 

46 

47 

46

40 

46 

46 

46 

46

40 

46 

46 

46

46

45 

46 

46 

46 

45

46 

45 

46 

45 

45

46 

45 

45 

' 46 

46

C.d.

L. Cotg.

0. 54 250 

0. 54 203 

0. 54 155 

0.54 108 

0. 54 000

0. 54 013 

0.53 905 

0. 53 918 

0. 53 870 

0. 53 823

0.53 776 

0. 53 729 

0. 53 681 

0.53 034 

0. 53 587

0.53 540 

0.53493 

0.53446 

0. 53 399 

0.53 352

0. 53 300 

0. 53 259 

0. 53 212 

0. 53 165 

0.53 119

0. 53 072 

0. 53 025 

0. 52 979 

0.52 932 

0.52 886

0. 52 840 

0. 52 793 

0. 52 747 

0. 52 701 

0.52 654

0. 52 608 

0.52 562 

0. 52 516 

0. 52 470 

0. 52 424

0. 52 378 

0.52 332 

0. 52 280 

0.62 240 

0. 52 1.94

0. 52 148 

0. 52 103 

0. 52 057 

0. 52 Oil 

0.51 905

0.51 920 

. 0.51 874 

0.51 829 

0.51 783 

0. 51 738

0.51 093 

0.51 647 

0. 51 602 

0. 51 557 

0.51 511

0.51 466

L. Tang.

L. Cos.

9. 98 284 

9. 98 281 

9. 98 277 

9. 98 273 

9. 98 270

9. 98 266 

9. 98 262 

9. 98 259 

9. 98 255 

9. 98 251

9. 98 248 

9. 98 244 

9. 98 240 

9.98 237 

9. 98 233

9.98 229 

9. 98 226 

9.98222 

9.98 218 

9. 98 215

9. 98 211 

9. 98 207 

9. 98 204 

9.98 200 

9. 98 196

9. 98 192 

9.98 189 

9.98 185 

9. 98 181 

9. 98 177

9. 98 174 

9. 98 170 

9. 98 160 

9. 98 162 

9.98 159

9. 98 155 

9. 98 151 

9. 98 147 

9. 98 144 

9. 98 140

9. 98 136 

9.98 132 

9. 98 129 

9.98 125 

9. 98 121

9. 98 117 

9. 98 113 

9. 98 110 

9. 98 100 

9. 98 102

9.98098 

9.98 094 

9. 98 090 

9. 98 087 

9. 98 083

9. 98 079 

9. 98 075 

9. 98 071 

9. 98 007 

9. 98 063

9. 98 060

L. Sin.

d.

3 

4 

4 

3 

4

4 

3 

4 

4 

3

4 

4

3 

4 

4

3 

4 

4 

3 

. 4

4 

3 

4 

4 

4

3

4 

4 

4 

3

4 

4 

4 

3 

4

4 

4 

3 

4 

4

4 

3 

4 

4 

4

4 

3 

4 

4 

4

4 

4 

3 4

4

' 4 

4 

4 

4 

3

d.

GO

59

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

30

35 

34 

33 

32 

31

80

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

10

15 

14 

13 

12 

11

10

9

8

0

5 

4 

3 

2 

1

0

'

56 56' 0 

52 

48 

44

56 40 

36 

32 

28 

24

65 20 

16 

12 

8 

4

55 0 

56 

52 

48 

44

54 40 

36 

32 

28 

24

54 20 

10 

12 

8 

4

54 0 

50 

, 52 

48 

44

53 40 

36 

32 

28 

24

53 20 

' 16 

12 

8 

4

63 0 

56 

52 

48 

44

52 40 

36 

32 

28 

24

62 20 

16 

12 

8 

4

Si 0

m. s.

73°
188 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

1" 17°

m. s.

8 0 

4 

8 

12 

16

8 20 

24 

28 

32 

36

8 40 

44 

48 

52 

56

9 0 

4 

8 

]2 

16

9 20 

24 

28 

32 

36

9 40 

44 

48 

52 

56

10 0 

4 

8 

12 

16

10 20 

24 

28 

32 

36

10 40 

44 

48 

52 

56

11 0 

4 

8 

12 

16

n 20

24 

28 

32 

36

11 40 

44 

48 

52 

56

32 0

'

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23

24

25 

26 

27 

28 

29

80

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

61 

52 

53 

54

55 

56 

57 

58 

59

CO

L. Sin.

9.46 594 

9.46 635 

9.40 676 

9. 46 717 

9.46 758

9.46 800 

.9.46 841 

9. 46 882 

9. 46 923 

9. 46 964

9. 47 005 

9. 47 045 

9.47 086 

9. 47 127 

9.47 168

9. 47 209 

9. 47 249 

9.47 290 

9.47 330 

9.47 371

9.47 411 

9. 47 452 

9. 47 492 

9.47 533 

9. 47 573

9.47 613 

9.47 654 

9.47 694 

9.47 734 

9.47 774

9. 47 814 

9. 47 854 

9. 47 894 

9.47 934 

9.47 974

9. 48 014 

9. 48 054 

9. 48 094 

9.48 133 

9.48 173

9. 48 213 

9. 48 252 

9.48292 

9. 48 332 

9.48 371

9. 48 411 

9.48 450 

9. 48 490 

9. 48 529 

 9.48568

9.48 607 

9. 48 647 

9. 48 686 

9. 48 725 

' 9.48 764

9. 48 803 

9.48 842 

9. 48 881 

9. 48 920 

9. 48 959

9.48 998

L. Cos.

d.

41 

41 

41 

41 

42

41 

41 

41 

41 

41

40 

41 

41 

41 

41

40 

41 

40 

41 

40

41 

40 

41 

40 

40

41 

40 

40 

40 

40

40 

40 

40 

40 

40

40 

40 

39 

40 

40

39 

40 

40 

39 

40

39 

40 

39 

39

<?Q

40 

39 

39 

39 

39

39 

39 

39 

39

QQ

d.

L. Tang.

9. 48 534 

9. 48 579 

9. 48 624 

9. 48 669 

9. 48 714

9.48 759 

9.48 804 

9.48 849 

9. 48 894 

9. 18 939

9. 48 984 

9. 49 029 

9. 49 073 

9.49 118 

9. 49 163

9. 49 207 

9.49 252 

9. 49 296 

9.49 341 

9. 49 385

9. 49 430 

9. 49 474 

9.49 519 

9. 49 563 

9. 49 607

9.49 652 

9. 49 696 

9. 49 740 

9.49 784 

9. 49 828

9. 49 872 

9.49 916 

9.49 960 

9. 50 004 

9. 50 048

9. 50 092 

9. 50 136 

9. 50 180 

9. 50 223 

9. 50 267

9.50 311 

9.50 355

9.50398

9.50 442 

9. 50 485

9. 50 529 

9. 50 572 

9.50 616 

9. 50 659 

9.50 703

9.50 746 

9. 50 789 

9. 50 833 

9. 50 876 

9. 50 919

9. 50 962 

9.51 005 

9.51 048 

9. 51 092 

9.51 135

9.51 178

L. Cotg.

c. d.

45 

45 

45 

45 

45

45 

45 

45 

45 

45

45 

44 

45 

45 

44

45 

44 

45 

44d<i

44 

45 

44 

44 

45

44 

44 

44 

44 

44

44 

44 

44 

,44 

44

44 

44 

43 

44

44 

43 

44 

43

44 

44 

43 

44 

43

43 

44 

43 

43 

as

43 

43 

44 

43 

43

c. d.

L. Cotg.

0. 51 466 

0.51 421 

0. 51 376 

0. 51 331 

0. 51 286

0. 51 241 

0.51 196. 

0. 51 151 

0. 51 106 

0. 51 061

0. 51 016 

0. 50 971 

0. 50 927 

0. 50 882 

0.50837

0. 50 793 

0. 50 748 

0. 50 704 

0. 50 659 

0. 50 615

0. 50 570 

0. 50 526 

0. 50 481 

0. 50 437 

0. 50 393

 0. 50 348 

0. 50 304 

0. 50 260 

0. 50 216 

0. 50 172

0. 50 128 

0. 50 084 

0. 50 040 

0. 49 996 

0. 49 952

0. 49 908 

0. 49 864 

0. 49 820 

0.49 777 

0. 49 733

0. 49 689 

0.49 645 

0.49 602 

0.49 558 

0. 49 515

0. 49 471 

0.49428 

0. 49 384 

0.49 341 

0. 49 297

0. 49 254 

0. 49 211 

0. 49 167 

0. 49 124 

0.49 081

0. 49 038 

0.48 995 

0. 48 952 

0.48 90S 

0. 48 865

0. 48 822

L. Tang.

L. Cos.

9.98 060 

9. 98 056 

9.98 052 

9. 98 048 

9. 98 044

9.98 040 

9. 98 036 

9. 98 032 

9. 98 029 

9. 98 025

9. 98 021 

9. 98 017 

9. 98 013 

9. 98 009 

9. 98 005

.9.98 001 

9. 97 997 

9. 97 993 

9. 97 989 

9! 97 986

9. 97 982 

9. 97 978 

9. 97 974 

9. 97 970 

9.97 966

9.97 962 

9. 97 958 

9. 97 954 

9. 97 950 

9. 97 946

9.97 942 

9. 97 938 

9.97 934 

9.97 930 

9. 97 926

9. 97 922 

9.97 918 

9.97 914 

9.97 910 

9.97 906

9. 97 902 

9. 97 898 

9. 97 894 

9.97 890 

9. 97 886

9. 97 882 

 9. 97 878 

9.97 874 

9. 97 870 

9. 97 866

9. 97 861 

9. 97 857 

9. 97 853 

9. 97 849 

9. 97 845

9. 97 841 

9. 97 837 

9. 97 833 

9. 97 829 

9. 97 825

9.97 821

L. Sin.

d.

4 

4 

4 

4

4 

4 

3 

4 

4

4 

4 

4 

4 

4

4 

4 

4 

3 

4

4 

4 

4 

4

4 

4- 

4 

4 

4

4 

4 

4 

4

4 

4 

4 

4

4 

4 

4

4 

4

4 

4 

4 

4 

5

4 

4 

4

4 

4

4

4 

4 

4

d.

60

59

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 4 : 

3 

2 

1

0

/

52 0 

56 

52 

48 

44

51 40 

36 

32 

28 

24

51 20 

16 

12

8 

4

51 0 

56 

52 

48 

44

50 40 

36 

32 

28 

24

50 20 

16 

12 

8 

4

50 0 

56 

52 

48 

44

49 40 

36 

32 

28 

24

49 20 

1C 

12 

8 

4

49 0 

66 

52 

48 

44

48 40 

36 

32

28 

24

48 20 

16 

12

8

4

48 0

m. s.

72°
GEOGKAPHIC TABLES AND FORMULAS. 189 

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

lh 18°

m. s.

12 0 

4 

8 

12 

16

12 2(? 

24 

28 

32 

36

12 40 

44 

48 

52 

56

13 0 

4

8

12 

16

13 20 

24 

28 

32 

36

13 40 

. 44 

48 

52 

56

14 0 

4

8 

12 

16

14 20 

21 

28 

32 

36

14 40 

44 

48 

52 

56

15 0 

4 

8 

12 

16

15 20 

24 

28 

32 

36

15 40 

44 

48 

52 

56

16 0

'

0

1. 

2 

3 

4

5 

6 

7 

S 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27

.28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

GO

L. Sin.

9. 48 998 

9. 49 037 

9. 49 076 

9.49 115 

9. 49 153

9.49 192 

9. 49 231 

9. 49 269 

9. 49 308 

9. 49 347

9. 49 385 

9.49 424 

9. 49 462 

9. 49 500 

9. 49 539

9. 49 577 

9.49 615 

IK'19654 

9.49 692 

9. 49 730

-9.49768 

9. 49 806 

9.49 844 

9. 49 882 

9. 49 920

9. 49 958 

9.49 996 

9. 50 034 

9. 50 072 

9. 50 110

. 9.50 148 

9. 50 185 

9. 50 223 

9. 50 261 

9. 50 298

9. 50 336 

9. 50 374 

9. 50 411 

9. 50 449 

9.50 486

9. 50 523 

9.50 561 

9. 50 598 

9.50 635 

9. 50 673

9. 50 710 

9. 50 747 

9. 50 784 

9. 50 821 

9. 50 858

9. 50 896 

9. 50 933 

9. 50 970 

9. 51 007 

9.51 043

9.51 080 

9.51 117 

9.51 154 

9. 51 191 

9. 51 227

9. 51 264

L. Cos.

d.

39 

39 

39 

38 

39

39 

38 

39 

39 

38

39 

38

38 

39 

38

38 

39 

38 

38 

38

38 

38 

38 

38 

38

38 

38 

38 

38 

38

37 

38 

38 

37 

38

38 

37 

38 

37 

37

38 

37 

37 

38 

37

37 

37 

37 

37 

38

37 

37 

37 

.36 

37

37 

37 

37 

36 

37

cl.

L. Tang.

9. 51 178 

9. 51 221. 

9. 51 264 

9. 51 306 

9. 51 349

9.51 392 

9. 51 435 

9. 51 478 

9.51 520 

9. 51 563

9. 51 606 

9.51 648 

9.51 691 

9.51 734 

9.51 776

9.51. 819 

9.51 861 

9.51.903 

9.51 94ti 

9. 51 988

9. 52 031 

9. 52 073 

9. 52 115 

9.52 157 

9. 52 200

9.62 242 

9.52284 

9.52 326 

9. 52 368 

9. 52 410

9. 52 452 

9. 52 494 

9. 52 536 

9. 52 578 

9. 52 620

9. 52 661 

9.52 703 

9.52 745 

9. 52 787 

9.52 829

9. 52 870 

9. 52 912 

9.52 95? 

9.52 995 

9. 53 037

9.53 078 

9.53 120 

9. 53 161 

9.53 202 

9. 53 244

9.53 285 

9. 53 327 

9.53 368 

9.53 409 

9.53 450

9. 53 492 

9. 53 533 

9.53 5,4 

9.53 615 

9.53 656

9. 53 697

L. Cotg.

C.d.

43 

43 

42 

43 

43

43 

43 

42 

43 

43

42 

43 

43 

42 

43

42 

42 

43 

42 

43

42 

42 

42 

43 

42

42 

42 

42 

42 

42

42 

42 

42 

42 

41

42 

42 

42 

42 

41.

42 

41 

42 

42 

41

42 

41 

41 

42 

41

42 

41 

41 

41 

42

41 

41 

41 

41 

41

C.d.

L. Cotg.

0. 48 822 

0. 48 779 

0. 48 736 

0.48 694 

0. 48 651

0. 48 608 

0.48 565 

0. 48 522 

0. 48 480 

0.48 437

0. 48 394 

0. 48 352 

0. 48 309 

0.48 266 

0.48 224

0. 48 181 

0.48 139 

0. 48 097 

0.48 054 

0. 48 012

0. 47 969 

0. 47 927 

0. 47 885 

0. 47 843 

0. 47 800

0.47 758 

0. 47 716 

0.47 674 

0.47 632 

0. 47 590

0. 47 548 

0. 47 506 

0. 47 464 

0. 47 422 

0.47 380

0. 47 339 

0. 47 297 

0. 47 255 

0.47 213 

0. 47 171

0. 47 130 

0. 47 088 

0.47 047 

0. 47 005 

0. 46 963

0.46 922 

0.46 880 

0. 46 839 

0. 46 798 

0. 46 756

0.46 715 

0.46 673 

0.46 632 

0.46 591 

0. 46 550

0. 46 508 

0. 46 467 

0. 46 426 

0. 46 385 

0.46 344

0. 46 303

L. Tarig.

L. Cos.

9.97 821 

9.97 817 

9. 97 812 

9. 97 808 

9. 97 804

9. 97 800 

9.97 796 

9. 97 792 

9. 97 788 

9. 97 784

9. 97 779 

9. 97 775 

9. 97 771 

9. 97 767 

9. 97 763

9. 97 759 

9.97 754 

9. 97 750 

9.97 746 

9.97 742

9. 97 738 

9.97 734 

9. 97 729 

9. 97 725 

9. 97 721

9. 97 717 

9. 97 713 

9. 97 708 

9.97 704 

9.97 700

9.97 696 

9. 97 691 

9.97 687 

9.97 683 

9. 97 679

9.97 674 

9.97 670 

9.97 666 

9. 97 662 

9. 97 657

9.97 653 

9.97 649 

9.97 645 

9. 97 640 

9. 97 636

9.97 632 

9.97 628 

9.97 623 

9. 97 619 

9.97 615

9.97 610 

9. 97 606 

9. 97 602 

9. 97 597 

9. 97 593

9. 97 589 

9. 97 584 

9. 97 580 

9.97 576 

9. 97 571

9. 97 567

L. Sin.

d.

4 

5 

4 

4 

4

4 

4 

4 

4 

5

4 

4 

4 

4

4

5 

4 

4 

4 

4

4 

5 

4 

4

4

4 

5 

4 

4 

4

5 

4 

4 

4 

5

4 

4 

4 

5 

4

4 

4 

5 

4 

4

4 

5 

4 

4 

5

4 

4 

5 

4

4

5 

4 

4 

5 

4

d.

CO

69 

58 

57 

56

55 

54 

63 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41.

40

39 

38 

37 

36

35 

34 

33 

32 

31

80

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 3- 

2 

1

0

'

48 0 

56 

52 

48 

44

47 40 

36 

32 

28 

24

47 20 

16 

12 

8 

4

47 0 

5.G 

52 

48 

44

46 40 

36 

32

28 

24

46 20 

16 

12 

8 

4

46 0 

56 

52 

48 

44

45 40 

36 

32 

28 

24

45 20 

16 

12 

8 

4

45 0 

56 

52 

48 

44

44 40 

36 

32 

28 

24

44 20 

16 

12 

8 

4

44 0

m. s.

71°
190 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. : Five-place logarithms of circular functions, etc. Continued. 

lh 19°

m. s.

16 0 

4 

8 

12 

16

16 20 

24 

28 

32 

36

16 40 

44 

48 

52 

56

17 0 

4 

8 

12 

16

17 20 

24 

28 

32 

36

17 40 

44 

48 

52 

56

18 0 

4 

8 

12 

16

18 20 

24 

28 

32 

36

18 40 

44 

48 

52 

56

19 0 

4 

8 

12 

16

19 20 

24 

28 

32 

36

19 40 

44 

48

52 

56

20 0

i

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56

57 

58 

59

60

L. Sin.

9. 51 264 

9.51 301 

9. 51 338 

9.51 374 

9. 51 411

9. 51 447 

9. 51 484 

9. 51 620 

9. 51 557 

9. 51 593

9. 51 629 

9. 51 666 

9.51 702 

9.51 738 

9. 51 774

9. 51 811 

9. 51 847 

9. 51 883 

9. 51 919 

9.51 955

9.51 9C1 

9.52 027 

9. 52 063 

9. 52 099 

9.52 135

9.52 171 

9.52 207 

9. 52 242 

9. 52 278 

9. 52 314

9. 52 350 

9.52 385 

9. 52 421 

9. 52 456 

9. 52 492

9. 52 527 

9. 52 563 

9. 52 598 

9.52 634 

9. 52 669

9. 52 705 

9.52740 

9. 52 775 

9. 52 811 

9. 52 846

9.52 881 

9. 52 916 

9. 52 951 

9.52 986 

9. 53 021

9. 53 056 

9. 53 092 

9.53 126 

9. 53 161 

9. 53 196

9. 53 231 

9. 53 266 

9.53 301 

9. 53 336 

9. 53 370

9. 53 405

L. Cos.

d.

37 

37 

36 

37 

36

37 

36 

37 

36 

36

37 

36 

36 

36 

37

36 

36 

36 

36 

36

36 

36 

36 

36 

36

36 

35 

36 

36 

36

35 

36 

35 

36 

35

36 

35 

36 

35 

36

35 

35 

36 

35 

35

35 

35 

35 

35 

35

36 

34 

35 

35 

35

35 

35 

35 

34 

35

d.

L. Tang.

9.53 697 

9. 53 738 

9. 53 779 

9. 53 820 

9. 53 861

9. 53 902 

9. 53 943 

9. 53 984 

9. 54 025 

9.54065

9.54106 

9. 54 147 

9.54187 

9. 54 228 

9.54269

9. 54 309 

9. 54 350 

9. 54 390 

9. 54 431 

9. 54 471

9. 54 512 

9. 54 552 

9." 54 593 

9. 54 633 

9. 54 67P

9. 54 714 

9. 54 754 

9.54794 

9.54835 

9. 54 875

9. 54 915 

9. 54 95!? 

9. 54 995 

9.55 035 

9.55 075

9. 55 115 

9. 55 155 

9.55 19§ 

9.55 235 

9. 55 275

9. 55 335 

9.55355 

9.55395 

9. 55 434 

9. 55 474

9. 55 514 

9. 55 554 

9. 55 593 

9. 55 633 

9.55 673

9. 55 712 

9. 55 752 

9.55 791 

9. 55 831 

9. 55 870

9.55 910 

9. 55 949 

9. 55 989 

9. 56 028 

9. 56 067

9.56 107

L. Cotg.

c.d.

41 

41 

41 

41 

41

41 

41 

41 

40 

41

41 

40 

41 

41 

40

41 

40 

41 

40

41

40 

41 

40 

40 

41

40 

40 

41 

40 

40

40 

40 

40 

40 

40

40 

40 

40 

40 

40

40 

40 

39 

40 

40

40 

39 

40 

40 

39

40 

39 

40 

39 

40

39 

40 

39 

39 

40

c.d.

L. Cotg.

0. 46 303 

0.46 262 

0. 46 221 

0.46 180 

0. 46 139

0.46 098 

0. 46 057 

0. 46 016 

0. 45 975 

0. 45 935

0. 45 894 

0. 45 853 

0.45813 

0. 45 772 

0.45 731

0. 45 691 

0.45 650 

0.45 610 

0. 45 569 

0. 45 529

0.45 488 

0.45 448 

0. 45 407 

0. 45 367 

0. 45 327

0. 45 286 

0. 45 246 

0. 45 206 

0.45 165 

0. 45 125

0. 45 085 

0.45 045 

0. 45 005 

0. 44 965 

0. 44 925

0.44 885 

0. 44 845 

0.44 805 

0. 44 765 

0. 44 725

0. 44 685 

0.44 645 

0.44605 

0. 44 566 

0. 44 526

0.44486 

0. 44 446 

0. 44 407 

0. 44 367 

0: 44 327

0. 44 288 

0. 44 248 

0.44209 

0. 44 169 

0.44 130

0. 44 090 

0. 44 051 

0. 44 Oil 

0. 43 972 

0. 43 933

0.43 893

L. Tang.

L. Cos.

9. 97 567 

9. 97 563 

9.97 558 

9. 97 554 ' 

9. 97 550

9. 97 545 

9. 97 641 

9. 97 536 

9.97 532 

9. 97 528

9. 97 523 

9.97 519 

9. 97 515 

9. 97 510 

9.97 506

9.97 501 

9. 97 497= 

9. 97 492 

9.97 488 

9. 97 484

9. 97 479 

9. 97 475 

9. 97 470 

9. 97 466 

9. 97 461

9. 97 457 

9. 97 453 

9.97 448 

9.97 444 

9. 97 439

9. 97 435 

9. 97 430 

9.97 426 

9. 97 421 

9. 97 417

9. 97 412 

9.97 408 

9. 97 403 

9.97 399 

. 9. 97 394

9.97 39Q 

9.97 385 

9.97381 

9. 97 376 

9.97 372

9. 97 367 

9.97 363 

9.97 358 

9.97 353 

9.97 349

9.97 344 

9. 97 340 

9. 97 335 

9. 97 331 

9. 97 326

9. 97 322 

9. 97 317 

9. 97 312 

9.97 308 

9. 97 303

9.97 299

L. Sin.

d.

4

5 

4 

4 

5

4 

5 

4 

4 

5

4 

4 

5 

4

5

4 

5 

4 

4 

5

' 4 

5 

4 

5

4

4 

5 

4

5 

4

5 

4 

5 

4 

5

4 

5 

4 

5 

4

5 

4 

5 

4 

5

4 

5 

6 

4 

5

4

5 

4 

5 

4

5 

5 

4 

5

4

d.

«0

59 

58 

57 

56

55 

54 

53 

52 

51

50

49

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

. 35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5. 

4 

3 

2 

1

0

'

44 0 

56 

52 

48 

44

°43 40 

36 

32 

28 

24

43 20 

16 

12 

8 

4

43 0

56 

52 

48 

44

42 40 

36 

32

28 

24

42 20 

16 

12 

8 

4

42 0 

56 

52 

48 

44

41 40 

36 

32 

28 

24

41 20 

16 

12 

8

4

41 0 

56 

52 

48 . 

44

40 40 

36 

32 

28 

24

40 20 

16 

12 

8 

4

40 0

m. s.

70C
C4EOGEAPHIC TABLES AND FOEMULAS. 191

TAMLM 27. Five-place logarithms of circular functions, etc. Continued. 

lh 20°

ni. s.

20 0 

4

8 

12 

10

20 20 

24 

 28 

32 

36

20 40 

'14 

48 

52 

50

21 0 

4 

8 

12 

16

21 20 

24 

28 

32 

36

21 40 

44 

48 

62 

56

22 0 

4 

8 

. 12 

16

22 20 

24 

28 

32 

36

22 40 

44 

48 

52 

56

23 0 

4 

8 

12 

16

23 20 

24 

28 

32 

36

23 40 

44 

48 

52 

56

24 0

'

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15

16 

17 

18 

19

'20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

(JO

L. Sin.

9. 53 405 

9. 53 440 

9. 53 475 

9. 53 509 

9.53 544

9. 53 578 

9. 53 613 

9. 53 647 

9.53 682 

9. 53 716

9.53 751 

9. 53 785 

9. 53 819 

9. 53 854 

9.53888

9. 53 922 

9.53957 

9. 53 991 

9. 54 025 

9. 54 059

9.54093 

9.54 127 

9. 54 161 

9. 54 195 

9. 54 229

9. 54 263 

9. 54 297 

9. 54 331 

9. 54 365 

9.54399

9. 54 433 

9. 54 466 

9. 54 500 

9. 54 534 

9. 54 567

9. 54 601 

9. 54 035 

9. 54 668 

9. 54 702 

9.54 735

9. 54 769 

9. 54 802 

9. 54 836 

9.54869 

9. 54 903

9. 54 936 

9. 54 909 

9.55 003 

9.55 036 

9. 65 069

9. 55 102 

9. 55 136 

9.55 169 

9. 55 202 

9. 55 235

9. 55 268 

9. 55 801 

9. 55 334 

9. 55 367 

9. 55 400

9. 55 433

L. Cos.

d.

35 

35 

34 

35 

34

35 

34 

35 

34

OC

34 

34 

35 

34 

34

35 

34 

34 

34 

34

34 

34 

34 

34 

34

34 

34 

 34 

34 

34

33 

34 

34 

33 

34

34 

33 

34 

33 

34

33 

34 

33 

34 i1 }

33 

34 

33 

33 

<w

34 

33 

33 

33

QO

33 

33 

33 

33

OO

d.

L. Tang.

9. 50 107 

9. 56 140 

9. 50 185 

9.56 224 

9. 50 204

9.56 303 

9.56 342 

9. 56 381 

9. 56 420 

9. 56 459

9. 56 498 

9. 56 537 

9. 56 576 

9. 66 615 

9. 56 654

9.56 693 

9.56732 

0. 56 771 

9.56 810 

9. 56 849

9.56 887 

9. 56 926 

9. 56 965 

9.57 004 

9. 57 042

9. 57 081 

9.57 120 

9. 57 158 

9. 57 197 

9. 57 2&5

9. 57 274 

9.57 312 

9. 57 351 

9.57 389 

9.57 428

9. 57 466 

9. 57 504 

9. 57 543 

9.57 581 

9.57 619

9. 57 658 

9.57 696 

9. 57 734 

9.57 772 

9. 57 810

9.57 849 

9.57 887 

9. 57 925 

9. 57 963 

9. 58 001

9. 58 039 

9.58 077 

9. 58 115 

9.58 153 

9. 58 191

9. 58 229 

9. 58 267 

9.58 304 

9. 58 342 

9. 58 380

9.58418

L. Cotg.

c. d.

39 

39 

39 

40 

39

39 

39 

39 

39 

39

39 

39 

39 

39

SQ

39 

39

39 

39 

38

39 

39 

39 

38 

39

39 

38 

39 

38

SCI

38 

39 

38 

39 

38

38 

39 

38 

38 

39

38 

3s 

38 

38 

39

38 

38 

38 

38

QQ

38 

38 

38 

38

00

38 

37 

38 

38

00

c. d.

L. Cotg.

0.43 893 

0. 43 854 

0. 43 815 

0.43 776 

0.43 736

0.43 697 

0. 43 058 

0.43 619 

0.43 580 

0.43 541

0.43 502 

0. 43 463 

0. 43 424 

0.43 385 

0. 43 340

0. 43 307 

0.43 268 

0.43229 

0.43 190 

0. 43 151

0.43 113 

0.43 074 

0.43 035 

0. 42 996 

0.42 958

0. 42 919 

0. 42 880 

0. 42 842 

0.42 803 

0. 42 765

0. 42 726 

0. 42 688 

0. 42 649 

0. 42 611 

0. 42 572

0.42 534 

0.42 496 

0. 42 457 

0. 42 419 

0.42 381

0.42 342 

0. 42 304 

0. 42 266 

0.42 228 

0. 42 190

0.42 151 

0.42 113 

0. 42 075 

0. 42 037 

0. 41 999

0. 41 961 

0.41 923 

0.41 885 

0.41 847 

0.41 809

0.41 771 

0. 41 733 

0.41 690 

0.41 658 

0. 41 620

0.41 582

L. Tang.

L. Cos.

9.97 299 

9. 97 294 

9. 97 289 

9.97 285 

9.97 280

9.97 276 

9.97 271 

9. 97 266 

9. 97 262 

9.97 257

9.97 252 

9. 97 248 

9.97 243 

9. 97 238 

9. 97 234

9. 97 229 

9. 97 224 

9.97220 

9.97 215 

9.97 210

9.97 206 

9. 97 201 

9. 97 190 

9. 97 192 

9. 97 187

9.97 182 

9. 97 178 

9. 97 173 

9.97 168 

9.97 163

9. 97 159 

9. 97 154 

9.97 149 

9.97 145 

9. 97 140

9.97 135 

9.97 130 

9.97 126 

9.97 121 

9.97 110

9. 97 111 

9. 97 107 

9.97 102 

9.97 097 

9.97 092

9. 97 087 

9. 97 083 

9.97 078 

9.97 073 

9.97 068

9. 97 063 

9. 97 059 

9. 97 054 

9.97 049 

9. 97 044

9. 97 039 

9. 97 035 

9. 97 ,030 

9. 97 025 

9. 97 020

9. 97 015

L. Sin. :

d.

5 

5 

4

5

5 

5 

4 

5

R

4 

5 

5 

4

5 

4 

5 

5

5 

5 

4 

5

C

4 

5 

5 

5 

4

5 

5 

4 

5

5 

4 

5 

5 K

4 

5

5 

5 

5

4 

5 

5 

5

4 

5 

5 

5 

5

4 

5 

5 

5 

5

d.

60

59 

58 

57 

56

55 

54 

53 

52 

51

60

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

'

40 0 

56 

52 

48 

44

39 40 

36 

32 

28 

24

39 20 

16 

12 

8 

4

39 0 

56 

52 

48 

44

38 40 

36 

32 

28 

24 .

38 20 

16 

12 

8 

4

38 0 

56 

52 

48 

44

37 40 

36 

32 

28 

24

37 20 

16 

12 

8 

4

37 0 

56 

52 

48 

44

36 40 

36 

32 

28 

24

36 20 

16 

12

8 

4

36 0

in. s
192 GEOGKAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued! 

lh 21°

m. s.

24 0 

4 

8 

12 

16

24 20 

24 

28 

32 

36

24 40 

44 

48 

52 

56

25 0 

4 

8 

12 

16

25 20 

24 

28 

32 

36

25 40 

44 

. 48 

52 

56

26 0 

4 

8 

12 

16

26 20 

24 

28 

32 

36

26 40 

44 

48 

52 

56

27 0 

4 

8 

12 

16

27 20 

24 

28 

32 

36

27 40 

44 

48 

52 

56

28 0

'

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 55 433 

9. 55 466 

9. 55 499 

9. 55 532 

9. 55 564

9.55 597 

9.55 630 

9. 55 663 

9. 55 695 

9. 55 728

9. 55 761 

9. 55 793 

9. 55 826 

9.55 858 

9. 55 891

9.55 923 

9. 55 956 

9.55 988 

9.66 021 

9.56 053

9. 56 085 

9.56 118 

9.56 150 

9. 56 182 

9. 56 215

9.56 247 

9. 56 279 

9. 56 311 

9.56 343 

9. 56 375

9. 56 408 

9. 56 440 

9. 56 472 

9.56 504 

9. 56 536

9.56 568 

9. 56 599 

9.56 631 

9. 56 663 

9.66 695

9.56 727 

9.56 759 

9.56790

9.56 822 

9.56 854

9.56 886 

9.56 917 

9. 56 949 

9. 56 980 

9.57 012

9.57 044 

9.57 075 

9.57 107 

9.57 138 

9. 57 169

9.57 201 

9. 57 232 

9.57 264 

9.57 295 

9.57 326

9. 57 358

L. Los.

d.

33 

33 

33 

32

OO

33 

33 

32 

33

OO

32 

33 

32 

33 

32

33 

32 

33 

32 

32

33 

32 

32 

33 

32

32 

32 

32 

32

*M

32 

32 

32 

32

Q9

31 

32 

32 

32

00

32 

31 

32 

32 

on

31 

32 

31 

32

OO

31 

32 

31 

31

OO

31 

32 

31 

31 

v>

 d.

L. Tang.

9.58 418 

9. 58 455 

9.58 493 

9.58 531 

9. 58 569

9.58 606 

9.58 644 

9. 58 681 

9. 58 719 

9. 58 757

9. 58 794 

9. 58 832 

9. 58 869 

9. 58 907 

9. 58 944

9. 58 981 

9. 59 019 

9. 59 066 

9.59 094 

9. 59 131

9. 59 168 

9. 59 205 

9. 59 243 

9.59 280 

9. 59 317

9.59 354 

9.59 391 

9. 59 429 

9. 59 466 

9.59 503

9. 59 540 

9.59 577 

9.59 614 

9. 59 651 

9. 59 688

9.59 725 

9. 59 762 

9,59 799 

9. 59 835 

9. 59 872

9. 59 909 

9.59946 

9.59 983 

9. 60 019 

9. 60 056

9.60 093 

9. 60 130 

9.60 166 

9.60 203 

9. 60 240

9. 60 276 

9. 60 313 

9. 60 349 

9. 60 386 

9. 60 422

9. 60 459 

9. 60 495 

9. 60 532 

9. 60 568 

9.60 605

9.60 641

L. Cotg.

c. d.

37 

38 

38 

38 

37

38 

37 

38 

38

07

38 

37 

38 

37 *w

38- 

37 

38 

37 

37

37 

38 

37 

37 

37

37 

38 

37 

37

07

37 

37 

37 

37 

37

37 

37 

36 

37

Q7

37 

37 

36 

37

07

37 

36 

37 

37 

36

37 

36 

37 

36 

37

36 

37 

36 

37 

36

c. d.

L. Cotg.

0.41 582 

0. 41 545 

0.41 507 

0. 41 469 

0. 41 431

0.41 394 

0.41 356 

0.41 319 

0. 41 281 

0. 41 213

0. 41 206 

0.41 168 

0.41 131 

0.41 093 

0.41 056

0. 41 019 

0.40 981 

0.40 944 

0. 40 906 

0. 40 869

0. 40 832 

0. 40 795 

0. 40 757 

0.40 720 

0. 40 683

0.40 646 

0. 40 609 

0. 40 571 

0. 40 534 

0. 40 497

0. 40 460 

0. 40 423 

0. 40 386 

0.40 349 

0.40 312

0.40 275 

0.40 238 

0.40 201 

0.40 165 

0.40 128

0. 40 091 

0.40054 

0. 40 017 

0.39 981 

0. 39 944

0. 39 907 

0. 39 870 

0. 39 834 

0. 39 797 

0.39 760

0. 39 724 

0.39 687 

0. 39 651 

0. 39 614 

0. 39 578

0. 39 541 

0.39 505 

0. 39 468 

0. 39 432 

0.39 395

0. 39 359

L. Tang.

L. Cos.

9. 97 015 

9.97 010 

9. 97 005 

9. 97 001 

9. 96 996

9. 96 991 

9. 96 986 

9. 96 981 

9. 96 976 

9. 96 971

9. 96 966 

9. 96 962 

9. 96 957 

9.96 952 

9. 96 947

9. 96 942 

9. 96 937 

9. 96 932 

9. 96 927 

9. 96 922

9. 96 917 

9. 96 912 

9. 96 907 

9. 96 903 

9. 96 898

9.96 893 

9. 96 888 

9. 96 883 

9.96 878 

9.96 873

9. 96 868 

9. 96 863 

9. 96 858 

9. 96 853 

9. 96 848

9. 96 843 

9. 96 838 

9. 96 833 

9. 96 828 

9. 96 823

9. 96 818

9.96813

9.96 808 

9. 96 803 

9. 96 798

9. 96 793 

9.96 788 

9.96 783 

9.96 778 

9.96 772

9. 96 767 

9. 96 762 

9. 96 757 

9. 96 752 

9. 96 747

9. 96 742 

9.96 ?37 

9. 96 732 

9. 96 727 

9. 96 722

9.96 717

L. Sin.

d.

5 

5 

4 

5 

5

5 

5 

5 

5 

5

4 

5 

5 

5

K

5 

5

5 

5

5 

5 

4 

5

5 

5 

5 

5 

5

5 

5 

5 

5

5

5 

5 

5 

5 

5

5 

5 

5 

5 

5

5 

5 

5 

6 

5

5 

5 

5 

5

5 

5 

5 

5

5

d.

60

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

'

36 0 

56 

52 

48 

44

35 40 

36 32 

28 

24

35 20 

16 

12

8 

4

35 0 

56

52 

48 

44

34 40 

36 

32 

28 

24

34 20 

16 

12 

8 

4

34 0 

56 

52 

48 

44

33 40 

36 

32 

28 

24

33 20 

16

12 

8 4 '

33 0

56 

52 

48 

44

32 40 

36 

32 

28 

24

32 20 

16 

12 

8 

4

32 0

m. s.

68C
GEOGEAPHIC TABLES AND FOEMULAS. 193

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

lh 22°

m. s.

28 0 

4 

8 

12 

16

28 20 

24 

28 

32 

36

28 40 

44 

48

52 

56

29 0 

4 

8 

12 

16

29 20 

24 

28 

32 

36

29 40 

44 

48 

52 

56

30. 0 

4 

8 

12 

16

30 20 

24 

28 

32 

36

30 40 

44

48 

52 

56

31 0 

4 

8 

12 

16

31 20 

24 

28 

32 

36

31 40 

41

48 

52 

56

32 0

'

0

1

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31

32 

33 

34

35 

36 

37 

38 

39

40

41 42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

GO

L. Sin.

9.57 358 

9. 57 389 

9. 57 420 

9. 57 451 

9. 57 482

9.57 514 

9. 57 545 

9.57 676 

9.57 607 

9. 57 638

9. 57 669 

9.57 700 

9.57 731 

9. 57 762 

9. 57 793

9.57 824 

9.57 855

9.57885

9. 67 916 

9.57 947

9. 57 978 

9. 58 008 

9. 58 039 

9. 58 070 

9..5S 101

9. 58 131 

9. 58 162 

9. 58 192 

9.58 223 

9. 58 253

9. 58 284 

9.58 314 

9. 58 345 

9. 58 375 

9.58406

9. 58 436 

9. 58 467 

9. 58 497 

9. 58 627 

9.58 557

9. 58 588 

9. 58 618 

9. 58 648 

9. 58 678 

9. 58 709

9. 58 739 

9. 58 769 

9. 58 799 

9. 58 829 

9. 58 859

9.58 889 

9.58 919 

9.58 949 

9.58 979 

9. 59 009

9. 59 039 

9.59 069 

9. 59 098 

9. 59 128 

9. 59 168

9. 59 188

L. Cos.

d.

31 

31 

31 

31 

32

31 

31 

31 

31 

31

31 

31 

31 

31 

31

31 

30 

31 

31 

31

30 

31 

31 

31 

30

31 

30 

31 

30 

31

30 

31 

30 

31 

30

31 

30 

30 

30 

31

30 

30 

30 

31 

30

30 

30 

30 

30 

30

30 

30 

30 

30 

30

30 

29 

30 

30 

30

d.

L. Ta,ng.

9. 60 641 

9. 60 677 

9. 60 714 

9. 60 750 

9. 60 786

9. 60 823 

9. 60 859 

9. 60 895 

9. 60 931 

. 9. 60 967

9. 61 004 

9. 61 040 

9. 61 076 

9. 61 112 

9.61 148

9. 61 184 

9. 61 220 

9.61256

9.61 292 

9. 61 328

9.61 364 

9. 61 400 

9. 61 436 

9. 61 472 

9. 61 508

9.61 544 

9.61 579 

9. 61 615 

9. 61 651 

9. 61 687

9.61 722 

9.61 758 

9.61 794 

9. 61 830 

9. 61 865

9.61 901 

9.61 936 

9. 61 972 

9. 62 008 

9. 62 043

9. 62 079 

9. 62 114 

9.62 350 

9.62 185 

9. 62 221

9. 62 256 

9. 62 292 

9. 62 327 

9.62 362 

9. 62 398

9. 62 433 

9. 62 468 

9. 62 504 

9. 62 539 

9. 62 574

9. 62 609 

9. 62 645 

9. 62 680 

9. 62 715 

9. 62 750

9.62 785

L. Cotg.

c. d.

36 

37 

36 

36 

37

36 

36 

36 

36 

37

36 

36 

36 

36 

36

36 

36 

36 

36 

36

36 

36 

36 

36 

36

35 

36 

36 

36 

35

36 

36 

36 

35 

36

35 

36 

36 35 

36

35 

36 

35 

36 

35

 36 

35 

35 

36 

35

35 

36 

35 

35 

35

36 

35 

35 

35 

35

c. d.

L. Cotg.

0.39 359 

0. 39 323 

0. 39 286 

0.39 250 

0. 39 214

0. 39 177 

0. 39 141. 

0. 39 105 

0. 39 069 

0. 39 033

0. 38 996 

0.38 960 

0. 38 924 

0. 38 888 

0. 38 852

0. 38 816 

0.38 780 

0.38 744 

0. 38 708 

0. 38 672

0. 38 636 

0.38 600 

0. 38 564 

0. 38 528 

0. 38 492

0. 38 456 

0. 38 421 

0. 38 385 

0. 38 349 

0.38 313

0. 38 278 

0. 38 242 

0. 38 206 

0. 38 170 

0. 38 135

0. 38 099 

0. 38 064 

0. 38 028 

0. 37 992 

0. 37 957

0. 37 921 

0. 37 886 

0.37 850 

0.37 815 

0. 37 779

0.37 744 

0.37 708 

0. 37 673 

0.37 638 

0. 37 602

0. 37 567 

0. 37 632 

0.37 496 

0. 37 461 

0. 37 426

0. 37 391 

0.37 355 

0. 37 320 

0. 37 285 

0. 37 250

0. 37 215

L. Tang.

L. Cos.

9.96 717 

9. 96 711 

9. 96 706 

9.96 701 

9.96 696

9. 96 691 

9. 96 686 

9.96 681 

9. 96 676 

9. 96 670

9. 96 665 

9. 96 660 

9. 96 655 

9. 96 650 

9.96 645

9.96 640 

9.96 634 

9.96629 

9. 96 624 

9.96 619

9. 96 614 

9. 96 608 

9. 96 603 

9. 96 598 

9. 96 593

9. 96 588 

9. 96 582 

9. 96 577 

9. 96 572 

9. 96 567

9. 96 562 

9. 96 556 

9. 96 551 

9. 96 546 

9. 96 541

9. 96 535 

9. 96 530 

9. 96 525 

9. 96 520 

9. 96 514

9. 96 509 

9. 96 504 

9. 96 498 

9. 96 493 

9. 96 488

9. 96 483 

9. 96 477 

9. 96 472 

9. 96 467 

9.96 461

9. 96 456 

9. 96 451. 

9. 96 445 

9. 96 440 

9. 96 435

9. 96 429 

9. 96 424 

9. 96 419 

9. 96 413 

9. 96 408

9.96 403

L. Sin.

d.

6 

5 

5 

5 

5

5 

6 

5 

6 

5

5 

5 

5 

5 

5

6 

5 

5 

5

5

6 

5 

5 

5 

ft

6

5 

6 

5

5

6 

5

5 

5 

6

5

5 

5 

6 

5

5 

6 

5 

5 

5

6 

5 

5 

6 

5

5 

6 

5 

5 

6

5 

5 

6 

5 

5

d.

00

59 

58 

67 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

80

29

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

/

32 0 

56 

62 

48 

44

31 40 

36 

32 

28 

24

31 20 

16 

12 

8 

4

31 0 

56 

52 

48 

44

30 40 

36 

32 

28 

24

30 20 

16 

12 

8 

4

30 0 

56 

52 

48 

44

29 40 

36 

32 

28 

24

29 20 

16 

12

8

"- 4

29 0 

56 

52 

48 

44

28 40 

36 , 

32 

28 

24

28 20 

16 

12 

8 

4

28 0

m. s.

67°

41623° 16 13
194 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

lh - 23°

m. s.

32 0 

4 

8 

12 

16

32 20 

24 

28 

32 

36

32 40 

44 

48 

52 

56

33 0 

4 

8 

12 

16

33 20 

24 

28 

32 

36

33 40 

. 44 

48 

52 

56

34 0 

4 

8 

12 

16

34 20 

24 

28 

32 

36

34 40 

44 

48 

52 

56

35 0 

4 

8 

12 

16

35 20 

24 

28 

32 

36

35 40 

44 

48 

52 

56

36 0

/

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

 43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

GO

L. Sin.

9.59 188 

9. 59 218 

9. 59 247 

9.59 277 

9. 59 307

9. 59 336 

9. 59 366 

9. 59 396 

9. 59 425 

9. 59 455

9. 59 484 

'9.59 514 

9. 59 543 

9. 59 573 

9.59 602

9. 59 632 

9. 59 G61 

9. 59 690 

9.59 720 

9. 59 749

9.59 778 

9. 59 808 

9. 59 837 

9. 59 866 

9. 59 895

9.59 924 

9.59 954 

9. 59 983 

9.60 012 

9. 60 041

9. 60 070 

9. 60 099 

9. 60 128 

9. 60 157 

9. 60 186

9. 60 215 

9. 60 244 

9. 60 273 

9. 60 302 

9. 60 331

9. 60 359

9.60388

9. 60 417 

9. 60 446 

9. 60 474

9. 60 503 

9. 60 532 

9. 60 561 

9. 60 589 

9. 60 618

9. 60 646 

9. 60 675 

9. 60 704 

9. 60 732 

9.60 761

9. 60 789 

9.60 818 

9.60 846 

9. 60 875 ' 

9. 60 903

9. 60 931

L. Cos.

d.

30 

29 

30 

30 

29

30 

30 

29 

30 

29

30 

29 

30 

29 

30

29 

29 

30 

29 

29

30 

29 

29 

29 

29

30 

29 

29 

29 

29

29 

29 

29 

29 

29

29 

29 

29 

29

28

29 

29 

29 

28 

29

29 

29 

28 

29. 

28

29 

29

28 

29 

28

29 

28 

29 

28 

28

d.

L. Tang.

9. 62 785 

9. 62 820 

9. 62 855 

9. 62 890 

9. 62 926

9. 62 961 

9. 62 996 

9.63'031 

9. 63 066 

9. 63 101

9.63 135 

9.63 170 

9. 63 205 

9. 63 240 

9. 63 275

9.63 310 

9. 63 345 

9. 63 379 

9. 63 414 

9. 63 449

9. 63 484 

9. 63 519 

9. 63 553 

9. 63 588 

9. 63 623

9. 63 657 

9. 63 692 

9. 63 726 

9.63 761 

9.63 796

9. 63 830 

9. 63 865 

9. 63 899 

9. 63 934 

9. 63 968

9. 64 003 

9. 64 037 

9. 64 072 

9.64 106 

9.64 140

9. 64 175 

9.64209 

9. 64 243 

9. 64 278 

9. 64 312

9. 64 346 

9.64 381 

9. 64 415 

9. 64 449 

9. 64 483

9. 64 517 

9.64 552 

9. 64 586 

9.64 620 

9.64 654

9. 64 688 

9.64 722 

9.64 756 

9.64 790 

9. 64 824

9. 64 858

L. Cotg.

c. d.

35 

35 

35 

36 

35

35 

35 

35 

35

34

35 

35 

35 

35 

35

35 

34 

35 

35

OK

35 

34 

35 

35 

34

35 

34 

35 

35

3d.

35 

34 

35 

34

Oft

34 

35 

34 

34 

35

34 

34 

35 

34 

3d

35 

34 

34 

34 

34

35 

34 

34 

34 

34

34 

34 

34 

34 

34

c. d.

L. Cotg.

0.37 215 

0. 37 180 

0. 37 145 

0. 37 110 

0. 37 074

0. 37 039 

0. 37 004 

0. 36 969 

0. 36 934 

0.36 899

0. 36 865 

0.36 830 

0. 36 795 

0. 36 760 

0. 36 725

0. 36 690 

0. 36 655 

0. 36 621 

0. 36 586 

0. 36 551

0. 36 516 

0. 36 481 

0. 36 447 

0. 36 412 

0. 36 377

0.36 343 

0.36 308 

0. 36 274 

0. 36 239 

0. 36 204

0. 36 170 

0. 36 135 

0. 36 101 

0. 36 066 

0. 36 032

0.35 997 

0, 35 963 

0. 35 928 

0. 35 894 

0. 35 860

0. 35 825 

0.35791 

0. 35 757 

0. 35 722 

0.35 688

0.35 654 

0.35 619 

0. 35 585 

0. 35 551 

0. 35 517

0. 35 483 

0. 35 448 

0. 35 414 

0.35 380 

0.35 346

0. 35 212 

0. 35 278 

0.35 244 

0.35 210 

0. 35 176

0.35 142

L. Tang.

L. Cos.

9. 96 403 

9. 96 397 

9. 96 392 

9. 96 387 

9. 96 381

9. 96 376 

9. 96 370 

9. 96 365 

9. 96 360 

9. 96 354

9. 96 349 

9.96 343 

9. 96 338 

9. 96 333 

9. 96 327

9. 96 322 

9. 96 316 

9.96 311 

9. 96 305 

9. 96 300

9. 96 294 

9. 96 289 

9. 96 284 

9. 96 278 

9. 96 273

9. 96 267 

9. 96 262 

9. 96 256 

9. 96 251 

9. 96 245

9. 96 240 

9. 96 234 

9. 96 229 

9. 96 223 

9. 96 218

9. 96 212 

9. 96 207 

9. 96 201 

9. 96 196 

9. 96 190

9. 96 185 

9.96179 

9.96 174 

9.96 168 

9. 96 162

9.96 157 

9.96 151 

9. 96 146 

9. 96 140 

9. 96 135

9. 96 129 

9.96 123 

9. 96 118 

9.96 112 

9.96 107

9. 96 101 

9. 96 095 

9. 96 090 

9.96 084 

9.96 079

9. 96 073

L. Sin.

d.

6 

5 

5 

6 

5

6 

5 

5 

6

5

6 

5 

5 

6 

5

6 

5 

6 

5 

6

5 

5 

6 

5 

6

5 

6 

5 

6 

5

6 

5 

6 

5 

6

5 

6 

5 

6 

5

6 

5 

6 

6 

5

6 

5 

6 

5 

6

6 

5 

6 

6 

6

6 

5 

6 

5 

fi

d.

60

59 

58 

57 

56

55 

54 

53 

62 

51

50

49

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

'

28 0 

56 

52 

48 

44

27 40 

36 

32 

 .28 

24

27 20. 

16 

12 

8 

4

27 0 

56 

52 

48 

44

26 40 

36 

32 

28 

24

26 20 

16 

12 

8 

4

26 0 

56 

52 

48 

44

25 40 

36 

32 

28 

24

25 20 

16 

12 

8 

4

25 0 

56 

52 

48 

44

24 40 

36 

32 

28 

24

24 20 

16 

12 

8 

4

24 0

m. s.
GEOGRAPHIC TABLES AND FORMULAS. 195

TABLE 27. Five-place logarithms of circular functions, etc. Continued. . 

lh 24°

m. s.

30 0 

4 

8 

12 

16

36 20 

24 

28 

32 

36

36 40 

44 

48 

52 

56

37 0 

4 

8 

12 

1C

37 20 

24 

28 

32 

36

37 40 

44 

48 

52 

56

38 0 

4 

8 

12 

16

38 20 

24 

28 

32 

36

38 40 

44 

48 

52 

56

39 0 

4 

8 

12 

16

39 20 

24 

28 

32 

36

39 40 

44 

48 

52 

56

40 0

'

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

62 

53 

54

55 

56 

57 

58 

59

GO

L. Sin.

9. 60 931 

9. 60 960 

9. 60 988 

9. 61 016 

9. 61 045

9. 61 073 

9.61 101 

9. 61 129 

9.61 158 

9. 61 186

9. 61 214 

9. 61 242 

9. 61 270 

9. 61 298 

9.61 326

9. 61 354 

9.61382 

9.61411 

9. 61 438 

9. 61 466

9.61 494 

9. 61 522 

9.61 550 

9.61 578 

9.61 606

9.61 634 

9.61 662 

9. 61 689 

9.61 717 

9.61 745

9.61 773 

9. 61 800 

9. 61 828 

9. 61 856 

9. 61 883

9. 61 911 

9. 61 939 

9.61 966 

9. 61 994 

9. 62 021

9. 62 049 

9. 62 076 

9. 62 104 

9. 62 131 

9.62 159

9. 62 186 

9. 62 214 

9.62 241 

9. 62 268 

9. 62 296

9. 62 323 

9. 62 350 

9.62 377 

9. 62 405 

9. 62 432

9. 62 459 

9. 62 486 

9.62 513 

9. 62 541 

9. 62 568

9. 62 595

L. Cos.

d.

29 

28 

28 

29 

28

28 

28 

29 

28 

28

28 

28 

28 

28 

28

28 

29 

27 

28 

28

28 

28 

28 

28 

28

28 

27 

28 

28 

28

27 

28 

28 

27 

28

28 

27 

28 

27

28

27 

28 

27 

28 

27

28 

27 

27 

28 

27

27 

27 

28 

.27

27

27 

27 

28 

27 

27

d.

L. Tang.

9. 64 858 

9. 64 892 

9. 64 926 

9. 64 960 

9. 64 994

9. 65 028 

' 9. 65 062 

9. 65 096 

9. 65 130 

9.65 164

9.65 197 

9.65 231 

9. 65 265 

9. 65 299 

9. 65 333

9. 65 366 

9.65400 

9.65434 

9. 65 467 

9. 65 501

9. 65 535 

9.65 568 

9. 65 602 

9. 65 636 

9.65 669

9. 65 703 

9. 65 736 

9.65770 

9. 65 803 

9. 65 837

9.65 870 

9.65 904 

9. 65 937 

9. 65 971 

9.66 004

9. 66 038 

9. 66 071 

9. 66 104 

9. 66 138 

9. 66 171

9. 66 204 

9. 66 238 

9. 66 271 

9. 66 304 

9. 66 337

9. 66 371 

9. 6C 404 

9. 66 437 

9. 66 470 

9.66 503

9.66 537 

9.66 570 

9. 66 603 

9. 66 636 

9.66 669

9.66 702 

9. 66 735 

9.66 768 

9. 66 SOI 

9. 66 834

9. 66 867

L. Cotg.

c. d.

34 

34 

34 

34 

34

34 

34 

34 

34 

33

34 

34 

34 

34 

33

34 

34 

33 

34 

34

33 

34 

34 

33 

34

33 

34 

33 

34 

33

34 

33 

34 

33 

34

33 

33 

34 

33 

33

34 

33 

33 

33 

34

33 

33 

33 

33 

34

33 

33 

33 

33 

33

33 

33 

33 

33 

33

c. d.

L. Cotg.

0. 35 142 

0. 35 108 

0.35074 

0. 35 040 

0. 35 006

0.34 972 

0. 34 938 

0. 34 904 

0.34 870 

0. 34 836

0. 34 803 

0. 34 769 

0.34 735 

0.34701 

0. 34 667

0. 34 634 

0.34 600 

0.34566

0. 34 533 

0. 34 499

0.34465 

0.34432 

0. 34 398 

0. 34 364 

0. 34 331

0. 34 297 

0. 34 264 

0. 34 230 

0. 34 197 

0. 34 163

0. 34 130 

0. 34 096 

0. 34 063 

0.34 029 

0.33 996

0.33 962 

0. 33 929 

0. 33 896 

0. 33 862 

0. 33 829

0. 33 796 

0. 33 762 

0. 33 729 

0. 33 696 

0. 33 663

0. 33 629 

0.33 596 

0. 33 563 

0. 33 630 

0. 33 497

0. 33 463 

0.33 430 

0. 33 397 

0.33 364 

0. 33 331

0. 33 298 

0. 33 265 

0. 33 232 

0.33 199 

0. 33 166

0. 33 133

L. Tang.

L. Cos.

9. 96 073 

9. 96 067 

9. 96 062 

9. 96 056 

9. 96 050

9. 96 045 

9. 96 039 

9.96034 

9.96 028 

9. 96 022

9. 96 017 

9. 96 Oil 

9. 96 005 

9.96 000 

9. 95 994

9. 95 988 

9.95 982

9,95977

9. 95 971 

9. 96 965

9. 95 960 

9. 95 954 

9. 95 948 

9. 95 942 

9. 95 937

9. 95 931 

9.95925 

9. 95 920 

9. 95 914 

9.95 908

9. 95 902 

9. 95 897 

9. 95 891 

9.95 885 

9. 96 879

9.95 873 

9. 95 868 

9. 95 862 

9. 95 856 

9. 95 850

9. 95 844 

9. 95 839 

9. 95 833 

9. 95 827 

9.95 821

9. 95 815 

9. 95 810 

9. 95 804 

9. 95 798 

9.95 792

9. 95 786 

9.95 780 

9. 95 775 

9. 95 769 

9. 95 763

9.95 757 

9.95 751 

9.95 745 

9.95 739 

9.'95 733

9. 95 728

L. Sin.

d.

6 

5 

6 

6 

5

6 

5 

6 

6 

5

6 

6 

5 

6 

6

6 

5 

6 

6 

5

6 

6 

6 

5 

6

6 

5 

6 

6 

6

5 

6 

6 

6 

6

5 

6 

6 

6 

6

6 

6 

6 

.6 

6

5 

6 

6 

6 

6

6 

5 

6 

6 

6

6 

6 

6 

6 

5

d.

00

69 

58 

57 

56

55 

54 

53 

62 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

 23 

22 

21

20

19 

38 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

/

24 0 

56 

52 

48 

44

23 40 

36 

32 

28 

24

23 20 

16 

12 

8 

4

23 0 

56 

52 

48 

44

22 40 

36 

32 

28 

24

22 20 

16 

12 

8 

4

22 0 

56 

52 

48 

44

21 40 

36. 

32

28 

24

21 20 

16 

12 

8 

4

21 0 

56 

52 

48 

44

20 40 

36 

32 

28 

24

20 20 

16 

12 

8 

4

20 0

m. s.

65C
196 GEOGRAPHIC TABLES AND FORMULAS.

.TABLE 27. Fine-place logarithms of circular functions, etc. Continued. 

lh 25°

m. s.

40 0 

4 

8 

12 

16

40 20 

24 

28 

32 

36

. 40 40 

44 

48 

52 

56

41 0 

4 

8 

12 

16

41 20 

24 

28 

32 

36

41 40 

44 

48 

52 

56

42 0 

4 

8 

12 

16

42 20 

24 

" 28 

32 

36

42 40 

44 '48 

52

50

43 0 

4 

8 

12 

16

43 20 

24 

28 

32 

36

43 40 

44 

48 

52 

56

44 0

i

0

1

2 

3

4

5 

6

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 62 595 

9.62 622 

9. 62 649 

9. 62 676 

9. 62 703

9. 62 730 

9. 62 757 

9.62 784 

9. 62 811 

9.62838

9. 62 865 

9. 62 892 

9. 62 918 

9. 62 945 

9. 62 972

9. 62 999 

9. 63 026 

9. 63 052 

9. 63 079 

9. 63 106

9. 63 133 

9. 63 159 

9. 63 186 

9. 63 213 

9. 63 239

9. 63 266 

9. 63 292 

9. 63 319 

9. 63 345 

9. 63 372

9. 63 398 

9. 63 425 

9. 63 451 

9. 63 478 

9. 63 504

9. 63 531 

9. 63 557 

9. 63 583 

9. 63 610 

9.63 636

9. 63 662 

9. 63 689 

9.63 715 

9.63741 

9. 63 767

9.63 794 

9. 63 820 

9. 63 846 

9. 63 872 

9. 63 898

9. 63 924 

9. 63 950 

9. 63 976 

9. 64 002 

9. 64 028

9.64 054 

9. 64 080 

9.64 106 

9.64 132 

9. 64 158

9.64 184

L. Cos.

d.

27 

27 

27 

27

27

'27 

27 

27 

27

27

27 

26 

27 

27

27

27 

26 

27 

27

27

26 

27 

27 

26

27

26 

27 

26 

27

26

27 

26 

27 

26

27

26 

26 

27 

26

26

27 

26 

26 26

26 

26 

26 

26

26 

26 

26 

26

26 

26 

26 

26

d.

L. Tang.

9. 66 867 

9. 66 900 

9. 66 933 

9. 66 966 

9.66 999

9.67 032 

9.67 065 

9. 67 098 

9. 67 131 

9. 67 163

9. 67 196 

9. 67 229 

9. 67 262 

9. 67 295 

9. 67 327

9. 67 360 

9. 67 393 

9. 67 426 

9. 67 458 

9. 67 491

9. 67 524 

9. 67 556 

9. 67 589 

9. 67 622 

9.67 654

9. 67 687 

9.67 719 

9. 67 752 

9.67 785 

9. 67 817

9. 67 850 

9. 67 882 

9. 67 915 

9. 67 947 

9. 67 980

9. 68 012 

9. 68 044 

9. 68 077 

9. 68 109 

9. 68 142

9. 68 174 

9. 68 206 

9.68239 

9.68 271 

9.68 303

9. 68 336 

9. 68 368 

9.68 400 

9. 68 432 

9.68 465

9. 68 497 

9. 68 529 

9.68 561 

9. 68 593 

9. 68 626

9. 68 658 

9. 68 690 

9. 68 722 

9. 68 754 

9. 68 786

9. 68 818

L. Cotg.

c. d.

33 

33 

33 

33

oo

33 

33 

33 

32

oo

33 

33 

33 

32

oo

.33 

33 

32 

33

oo

32 

33 

33 

32

OO

32 

33 

33 

32

32 

33 

32 

33

32 

33 

32 

33

04

32 

33 

32 

32

OO

32 

32 

32 

33

32 

32 

32 

33

d£

32 

32 

32 

32

oZ

c. d.

L. Cotg.

0. 33 133 

0. 33 100 

0. 33 067 

0. 33 034 

0. 33 001

0. 32 968 

0.32 935 

0. 32 902 

0. 32 869 

0. 32 837

0."32 804 

0. 32 771 

0. 32 738 

0. 32 705 

0. 32 673

0. 32 640 

0. 32 607 

0.32 574 

0. 32 542 

. 0. 32 509

0. 32 476 

0. 32 444 

0. 32 411 

0. 32 378 

0. 32 346

0. 32 313 

0.32 281 

0. 32 248 

0. 32 215 

0. 32 183

0. 32 150 

0.32 118 

0. 32 085 

0. 32 053 

0. 32 020

0. 31 988 

0. 31 956 

0. 31 923 

0. 31 891 

0.31 858

0. 31 826 

0.31 794 

0.31 701 

0. 31 729 

0.31 697

.0. 31 664 

0.31 632 

0.31 600 

0. 31 568 

0. 31 535

0. 31 503 

0. 31 471 

0. 31 439 

0.31 407 

0.31 374

0. 31 342 

0. 31 310. 

0.31 278 

0. 31 246 

0.31 214

0.31 182

L. Tang.

L. Cos.

9.95 728 

9. 95 722 

9. 95 716 

9. 95 710 

9. 95 704

9.95 698 

9. 95 692 

9. 95 686 

9. 95 680 

9. 95 674

9. 95 668 

9.95663 

9. 95 657 

9. 95 651 

9. 95 645

9. 95 639 

9.95 633 

9. 95 627 

9. 95 621 

9. 95 615

9. 95 609 

9. 95 603 

9. 95 597 

9. 95 591 

9. 95 585

9. 95 579 

9. 95 573 

9. 95 567 

9. 95 50>1 

9. 95 555

9. 95 549 

9. 95 543 

9. 95 537 

9. 95 531 

9. 95 525

9. 95 519 

9. 95 513 

9. 95 507 

9.95500 

9. 95 494

9. 95 488 

9. 95 482 

9.95476 

9. 95 470 

9. 95 464

9. 95 458 

9. 95 452 

9. 95 446 

9. 95 440 

9. 95 434

9. 95 427 

9. 95 421 

9. 95 415 

9. 95 409 

9.95 403

9. 95 397 

9. 95 391 

9. 95 384 

9. 95 378 

9. 95 372

9. 95 366

L. Sin.

d.

6 

6 

6 

6

6 

6 

6 

6

5 

6 

6 

6

6 

6 

6 

6

6 

6 

6 

6

6 

6 

6 

6

6 

.6 

6 

6

6

6 

6 

7 

6

6 

6 

C 

6

6

6 

G 

6 

6 

7

6 

6 

6 

6

6 

7 

6 

6

d.

60

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29

28 

27 

26

25 

24 

23 

22 

21

20

19

18

17 

36

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

%

20 0 

56 

52 

48 

44

19 40 

36 

32 

28 

24

19 20 

16 

12 

8 

4

19 0 

56 

52 

48 

44

18 40 

36 

32 

28 

24

18 20 

, 16 

12

8

4

18 0 

56 

52 

48 

44

17 40 

36 

32 

28 

24

17 20 

16 

12

8 

4

17 0 

56 

52 

48 

44

16 40 

36 

32 

28 

24

16 20 

16 

12 

8 

4

16 0

m. s.

64C
GEOGRAPHIC TABLES AND FORMULAS. 197

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

lh 26°

m. s.

44 0 

4 

8 

12 

16

44 20 

24

28 

32 

36

44 40 

44 

48 

52 

56

45 0 

4 

8 

12 

16

46 20 

24 

28 

. 32 

36

45 40 

44 

48 

52 

56

46 0 

4 

8 

12 

16

46 20 

24 

28 

32 

36

46 40 

44 

48 

52 

56

47 0 

4 

8 

12 

16

47 20 

24 

28 

32 

36

47 40 

44 

48 

52 

56

48 0

'

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15

16

17 

18 

19

20

21 

22 

23 

24

26 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

65 

56 

57 

58 

59

CO

L. Sin.

9. 64 184 

9.64210 

9. 64 236 

9. 64 262 

9. 64 288

9. 64 313 

9. 64 339 

9. 64 365 

9. 64 391 

9. 64 417

9. 64 442 

9. 64 468 

9. 64 494 

9. 64 519 

9. 64 545

9. 64 671

9.64596

9. 64 622 

9. 64 647 

9. 64 673

9. 64 698 

9. 64 724 

9. 64 749 

9.64775 

9. 64 800

9. 64 826 

9. 64 851 

9.64 877 

9. 64 902 

9.64927

9. 64 953 

9-64 978 

9. 66 003 

9. 65 029 

9. 65 054

9. 65 079 

9. 65 104 

9. 65 130 

9. 65 155 

9. 65 180

9. 65 205 

9. 65 230 

9. 65 255 

9. 65 281 

9. 65 306

9.65331 

9. 65 356 

9. 65 381 

9. 65 406 

9. 65 431

9. 65 456 

9. 65 481 

9. 65 506 

9. 65 531 

9. 65 556

9. 65 580. 

9. 65 605 

 9. 65 63Q 

9. 65 655 

9. 65 680

9. 65 705

L. Cos.

d.

26 

26 

26 

.26

OK

26 

26 

26 

26 

25

26 

26 

25 

26 

26

25 

26 

25 

26 

25

26 

25 

26 

25 

26

25 

26 

25 

25 

26

25 

25 

26 

25 

25

25 

26 

25 

25 

25

25 

25 

26 

25 

25

25 

25 

25 

25 

25

25 

25 

25 

25 

24

25 

25 

25 

25 

25

d.

L. Tang.

9; 68 818 

9. 68 850 

9. 68 882 

9. 68 914 

9. 68 946

9. 68 978 

9. 69 010 

9. 69 042 

9. 69 074 

9. 69 106

9. 69 138 

9. 69 170 

9. 69 202 

9. 69 234 

9. 69 266

9. 69 298

9.69329

9. 69 361 

9. 69 393 

9. 69 425

9. 69 457 

9. 69 488 

9. 69 520 

9. 69 552 

9. 69 584

9. 69 615 

9. 69 647 

9. 69 679 

9. 69 710 

9. 69 742

9. 69 774 

9. 69 805 

9. 69 837 

9. 69 868 

9. 69 900

9. 69 932 

9.69 963 

9. 69 995 

9. 70 026 

9. 70 058

9. 70 089 

9.70 121 

9.70 152 

9. 70 184 

9. 70 215

9. 70 247 

9. 70 278 

9. 70 309 

9. 70 341 

9. 70 372

9. 70 404 

9. 70 435 

9. 70 466 

9. 70 498 

9. 70 529

9. 70 560 

9. 70 592 

9. 70 623 

9. 70 654 

9. 70 685

9. 70 717

L. Cotg.

C.d.

32 

32 

32 

32 

32

32 

32 

32 

32 

32

32 

32 

32 

32 

32

31 

32 

32 

32 

32

31 

32 

32 

32 

31

32 

32 

31 

32 

32

31 

32 

31 

32 

32

31

32 

31 

32 

31

32 

31 

32 

31 

32

31 

31 

32 

31 

32

31 

31 

32 

31 

31

32 

31 

31 

31 

32

C.d.

L. Cotg.

0. 31 182 

0.31 150 

0. 31 118 

0. 31 086 

0. 31 054

0. 31 022 

0. 30 990 

0.30 958 

0.30 926 

0. 30 894

0.30862 

0. 30 830 

0. 30 798 

0. 30 766 

0. 30 734

0. 30 702 

0.30671 

0.30 639 

0. 30 C07 

0. 30 575

0.30643 

0. 30 512 

0. 30 480 

0.30 448 

0.30 416

0.30385 

0. 30 353 

0. 30 321 

0. 30 290 

0. 30 258

0. 30 226 

0. 30 195 

0. 30 163 

0. 30 132 

0. 30 100

0. 30 068 

0.30037 

0.30005 

0.29974 

0. 29 942

0.29 9H 

0. 29 ,879 

0. 29 848 

0.29 816 

0. 29 .785

0. 29 753 

0. 29 722 

0. 29 691 

0. 29 659 

0. 29 628

0. 29 596 

0.29 565 

0. 29 534 

0. 29 502 

0. 29 471

0. 29 440 

0. 29 408 

0.29 377 

0. 29 346 

0. 29 315

0. 29 283

L. Tang.

L. Cos.

9. 95 366 

9. 96 360 

9. 95 354 

9.95 348 

9. 95 341

9. 95 335 

9. 95 329 

9. 95. 323 

9. 95 317 

9. 95 310

9. 95 304 

9. 95 298 

9. 95 292 

9. 95 286 

9. 95 279

9. 95 273 

9.95267 

9. 95 261 

9.95 254 

9.95 248

9. 95 242 

9. 95 236 

9. 95 229 

9.95223 

9. 95 217

9. 95 211 

9.95204 

9.95 198 

9. 95 192 

9.95 185

9.95 179 

9. 95 173 

9. 95 167 

9.95 160 

9.95 154

9. 95 148 

9. 95 141 

9.95 135 

9.95 129 

9. 95 122

9. 95 116 

9.95 110 

9. 95 103 

9.95 097 

9. 95 090

9. 95 084 

9.95 07; 

9.95 (hi 

. 9. 95 065 

9.95 059

9.95 052 

9. 95 046 

9. 95 039 

9.95033 

9. 95 027

9. 95 020 

9. 95 014 

9. 95 007 

9. 95 001 

9. 94 995

9. 94 988

L. Sin.

d.

6 

6 

6

7 

6

6 

6 

6

7 

f.

6 

6 

6

7 

6

6 

6 

7 

6 

6

6 

7 

6 

6 

6

7 

6 

6

. 7 

6

6 

6 

7 

.6 

6

7 

6 

6 

7 

6

6 

7 

6 

7 

f>

6

7 

6 

6

7

6 

7 

6 

6

7

6 

7 

6 

6 

7

d.

GO

69 

68 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

16 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

/

16 0 

56 

52 

48 

44

16 40 

36 

32 

28 

24

15 20 

16 

12

8 

4

15 0 

56 

52 

48 

44

14 40 

36 

32 

28 

24

14 20 

16 

12 

8 

4

14 0 

56 

62 

48 

44

13 40

36 

32 

28 

24

13 20 

16 

12 

8 

4

13 0

56 

52 

48 

44

12 40 

: 36 

32 

28 

24

12 20 

16 

12

8 

4

12 0

m. s.

63°
198 GEOGRAPHIC! TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

lh 27°

m.

48 0 

4 

8 

12 

16

48 20 

24 

28 

32 

36

48 40 

44 

48 

52 

56

49 0 

4 

8 

12 

16

49 20 

24 

28 

32 

36

49 40 

44 

48 

52 

56

50 0 

4 

8 

12 

16

50 20 

24 

28 

32 

36

50 40 

44 

48 

52 

56

51 0 

4 

8 

12 

16

51 20 

24 

28 

32 

36

51 40 

44 

48 

52 

56

52 0

i

0

1 

2 

3

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9.65 705 

9. 65 729 

9. 65 75-1 

9.65779 

9. 65 804

9. 65 828 

9. 65 853 

1J. 65 878 

9. 65 902 

9. 65 927

9. 65 952 

9. 65 976 

9. 66 001 

9. 66 025 

9. 66 050

9. 66 075 

9. 66 099 

9.66 124 

9.66 148 

9. 66 173

9. 66 197 

9. 66 221 

9. 66 246 

9. 66 270 

9. 66 295

9. 06 319 

9. 66 343 

9. 66 368 

9. 66 392 

9. 66 416

9. 66 441 

9. 66 465 

9. 66 489 

9. 66 513 

9.66 537

9. 66 562 

9. 66 586 

9. 66 610 

9. 66 634 

9. 66 658

9. 66 682 

9.66706 

9. 66 731 

9.66 755 

9. 66 779

9. 66 803 

9. 66 827 

9. 66 851. 

9. 66 875 

9. 66 899

9. 66 922 

9. 66 946 

9. 66 970 

9. 66 994 

9. 67 018

9. 67 042 

9. 67 066 

9. 67 090 

9. 67 113 

9. 67 137

9. 67 161

L. Cos.

d.

24 

25 

25 

25

25 

25 

24 

25

25

24 

25 

24 

25

24 

25 

24 

25 

24

24 

25 

24 

25 

24

24 

25 

24

24 

25

24 

24 

24 

24

24 

24 

24 

24 

24

24 

25 

24 

24

24

24 

24 

24 

24

24 

24 

24 

24

24

24 

24 

23 

24 

24

d.

L. Tang.

9. 70 717 

9. 70 748 

9. 70 779 

9. 70 810 

9. 70 841

9. 70 873 

9. 70 904 

9. 70 935 

9. 70 966 

9. 70 997

9. 71 028 

9. 71 059 

9. 71 090 

9.71 121 

9. 71 153

9.71 184 

9. 71 215 

9. 71 246 

9. 71 277 

9.71 308

9. 71 339 

9.71 370 

9. 71 401 

9.71 431 

9. 71 462

9. 71 493 

9. 71 524 

9. 71 655 

9. 71 586 

9. 71 617

9. 71 648 

9. 71 679 

9.71 709 

9. 71 740 

9.71 771

9. 71 802 

9.71 833 

9. 71 863 

9. 71 894 

9. 71 925

9. 71 955 

9.71986 

' 9. 72 017 

9.72 048 

9. 72 078

9.72 109 

9. 72 140 

9. 72 170 

9. 72 201 

9. 72 231

9. 72 262 

9. 72 293 

9. 72 323 

9. 72 354 

9. 72 384

9. 72 415 

9. 72 445 

9. 72 476 

9. 72 506 

9. 72 537

9. 72 567

L. Cotg.

c.d.

31 

31 

31 

31

32

31 

31 

31 

31

31 

31 

31 

32

Ol

31 

31 31' 

31

31 

31 

30 

31

31 

31 

31 

31

31 

130 

31 

31.

OJ.

31 

30 

31 

31

31 

31 

31 

30

31 

30 

31 

30

31 

30 

31 

30

30 

31 

30 

31

c.d.

L. Cotg.

0.29 283 

0. 29 252 

0. 29 221 

0.29 190 

0.29 159

0.29 127 

0. 29 096 

0.29 065 

0. 29 034 

0. 29 003

0.28 972 

0. 28 941 

0.28 910 

0. 28 879 

0. 28 847

0.28 816 

0. 28 785 

0. 28 754 

0.28 723 

0. 28 692

0.28 661 

0. 28 630 

0. 28 599 

0. 28 669 

0. 28 538

0. 28 507 

0. 28 476 

0. 28 445 

0. 28 414 

0. 28 383

0. 28 352 

0. 28 321 

0.28 291 

0. 28 260 

0. 28 229

0. 28 198 

0. 28 167 

0. 28 137 

0.28 106 

0.28.075

0. 28 045 

0.28014 

0.27983 

0.27 952 

0.27 922

0. 27 891 

0. 27 860 

0. 27 830 

0. 27 799 

0. 27 769

0.27 738 

0.27 707 

0.27 677 

0. 27 646 

0.27 616

0.27 585 

0. 27 555 

0. 27 524 

5. 27 494 

0. 27 463

0. 27 433

L. Tang.

L. Cos.

9. 94 988 

9. 94 982 

9. 94 975 

9. 94 969 

9. 94 962

9. 94 956 

9. 94 949 

9. 94 943 

9. 94 936" 

9. 94 930

9. 94 923 

9. 94 917 

9.94 911 

9. 94 904 

9. 94 898

9. 94 891 

9. 94 885 

9. 94 878 

9.94871 

9. 94 865

9. 94 858 

9.94 852 

9. 94 845 

9. 94 839 

9.94 832

9. 94 826 

9.94 819 

9.94 813 

9. 94 806 

9.94 799

9. 94 793 

9. 94 786 

9. 94 780 

9. 94 773 

9. 94 767

9. 94 760 

9. 94 753 

9. 94 747 

9. 94 740 

9. 94 734

9. 94 727 

9. 94 720 

9.94714 

9. 94 707 

9. 94 700

9. 94 694 

9. 94 687 

9.94 680 

9. 94 674 

9. 94 667

9. 94 660 

9. 94 654 

9. 94 647 

9. 94 640 

9. 94 634

9. 94 627 

9. 94 620 

9. 94 614 

9. 94 607 

9. 94 600

9. 94 593

L. Sin.

d.

6 

7 

6

7

7 

6 

7 

6

7

6 

6 

7 

6

7

6

7 

7 

6

7

6

7 

6 

7

7 

6 

7

7

7 

6 

7 

6

7 

6 

7 

6

7

7 

6

7 

7

7 

7 

6

7

6

7 

7 

6

7

7 

6

7 

7

7

d.

GO

59 

68 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

80

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

/

12 0 

56 

52 

48 

44

11 40 

36 

32 

28 

24

11 20 

16 

12 

8 

4

11 0 

56 

52 

48 

44

ID 40 

36 

32 

28 

24

10 20 

16 

12 

8 

4

10 0 

56 

52 

48 

44

9 40 

36 

32 

28 

24

9 20 

10 

12

8 

4

9 0

56 

52 

48 

44

8 40 

36 

32 

28 

24

8 20 

16 

12 

8 

4

8 0

m. s.

62°
GEOGRAPHIC TABLES AND FORMULAS. 199

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

lh 28°

m. s.

52 0 

4 

8 

12 

16

52 20 

24 

' 28 

32 

36

52 40 

44 

48 

52 

50

53 0 

4 

8 

12 

16

53 20 

24 

28 

32 

36

53 40 

44 

48 

52 

56

54 0 

4 

8 

12 

16

64 20 

24 

28 

32 

36

54 40 

44 

48 

52 

56

55 0 

4 

8 

12 

16

55 20 

24 

28 

32 

36

55 40 

44 

48 

52 

56

56 0

/

0

1

2 

3

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

00

L. Sin.

9. 67 161 

9. 67 185 

9. 67 208 

9. 67 232 

9. 67 256

9. 67 280 

9. 67 303 

9. 67 327 

9. 67 a50 

9.67 374

9. 67 398 

9. 67 421 

9.67 445 

9. 67 468 

9. 67 492

9. 67 515 

9. 67 539 

9.67562 

9. 67 586 

9.67 609

9.67 633 

9. 67 656 

9. 67 680 

9. 67 703 

9.67 726

9. 67 750 

9. 67 773 

9.67 796 

9. 67 820 

9. 67 843

9. 67 866 

9. 67 890 

9. 67 913 

9. 67 936 

9. 67 959

9. 67 982 

9. 68 006 

9. 68 029 

9. 68 052 

9. 68 075

9. 68 098 

9. 68 121 

9. 68 144 

9. 68 167 

9.68 190

9. 68 213 

9. 68 237 

9. 68 260 

9. 68 283 

9. 68 305

9. 68 328 

9. 68 351 

9. 68 374 

9. 68 397 

9. 68 420

9. 68 443 

9. 68 466 

9. 68 489 

9. 68 512 

9. 68 534

9. 68 557

L. Cos.

d.

24 

23 

24 

24 

24

23 

24 

'24 23 

24

23 

24 

23 

24 

23

24 

23 

24 

23 

24

23 

24 

23 

23 

24

23 

23 

24 

23 

23

24 

23 

23 

23 

23

24 

23 

23 

23 

23

23 

23 

23 

23 

23

24 

23 

23 

22 

23

23 

23 

23 

23 

23

23 

23 

23 

22 

23

d.

L. Tang.

9. 72 667 

9. 72 598 

9. 72 628 

9. 72 659 

9. 72 689

9. 72 720 

9. 72 750 

9. 72 780 

9. 72 811 

9. 72 841

9. 72 872 

9. 72 902 

9.72 932 

9. 72 963 

9. 72 993

9. 73 023 

9. 73 054 

9.73084 

9. 73 114 

9. 73 144

9.73 175 

9. 73 205 

9. 73 235 

9. 73 265 

9. 73 295

9. 73 326 

9. 73 356 

9. 73 386 

9.73 416 

9. 73 446

9. 73 476 

9. 73 507 

9. 73 537 

9. 73 567 

9. 73 597

9. 73 627 

9. 73 657 

9. 73 687 

9. 73 717 

9. 73 747

9. 73 777 

9. 73 807 

9. 73 837 

9. 73 867 

9. 73 897

9.73 927 

9.73 967 

9. 73 987 

9. 74 017 

9. 74 047

9. 74 077 

9. 74 107 

9. 74 137 

9. 74 166 

9. 74 196

9. 74 226 

9. 74 256 

9. 74 286 

9. 74 316 

9. 74 345

9. 74 375

L.Cqtg.

C.d.

31 

30 

31 

30 

31

30 

30 

31 

30 

31

30 

30 

31 

30 

30

31 

30 

30 

30 

31

.30 

30 

30 

30 

31

30 

30 

30 

30 

30

31 

30 

30 

30 

30

30 

30 

30 

30 

30

30 

30 

30 

30 

30

30 

30 

30 

30 

30

30 

30 

29 

30 

30

30 

30 

30 

29 

30

c.d.

L. Cotg.

0. 27 433 

0. 27 402 

0.27 372 

0.27 341 

0.27 311

0. 27 280 

0.27 250 

0.27 220 

0. 27 189 

0:27 159

0.27 128 

0. 27 098 

0. 27 068 

0.27 037 

0. 27 007

0.26 977 

0. 26 946 

0.26916 

0. 26 886 

0. 26 856

0.26 825 

0.26 795 

0. 26 765 

0. 26 735 

0. 26 705

0. 26 674 

0.26 644 

0.26 614 

0. 26 584 

0.26 554

0. 26 524 

0. 26 493 

0. 26 463 

0. 26 433 

0. 26 403

0. 26 373 

0. 26 343 

0.26 313 

0. 26 283 

0. 26 253

0.26 223 

0. 26 193 

0.26 163 

0. 26 133 

0. 26 103

0. 26 073 

0. 26 043 

0. 26 013 

0. 25 983 

0. 25 953

0. 25 923 

0. 25 893 

0. 25 863 

0. 25 834 

0. 25 804

0. 25 774 

0. 25 744 

0. 25 714 

0. 25 684 

0. 25 655

0. 25 625

L. Tang.

L. Cos.

9. 94 593 

9. 94 587 

9. 94 580 

9.94 573 

9. 94 567

9. 94 560 

9. 94 553 

9.94 546 

9. 94 540 

9.94 533

9. 94 526 

9. 94 519 

9. 94 513 

9. 94 506 

9. 94 499

9.94 492 

9. 94 485 

9.94479 

9. 94 472 

9. 94 495

9. 94 458 

9. 94 451 

9. 94 445 

9. 94 438 

9. 94 431

9. 94 424 

9. 94 417 

9. 94 410 

9. 94 404 

9. 94 397

9. 94 390 

9. 94 383 

9. 94 376 

9. 94 3C9 

9. 94 362

9.94 355 

9.94 349 

9. 94 342 

9. 94 335 

9. 94 328

9. 94 321 

9. 94 314 

9.94 307 

9. 94 300 

9. 94 293

9. 94 286 

9. 94 279 

9. 94 273 

9.94 266 

9. 94 259

9. 94 252 

9. 94 245 

9. 94 238 

9. 94 231 

9. 94 224

9. 94 217 

9.94 210 

9. 94 203 

9. 94 196 

9. 94 189

9. 94 182

L. Sin.

d.

6

7 

7 

6 

7

7 

7 

6 

7 

7

7 

6

7 

7 

7

7 

G 

7 

7 

7

7 

6 

7

7 

7

7 

7 

6 

7 

7

7 

7 

7 

7 

7

6

7 

7 

7 

7

7 

7 

7 

7 

7

7 

6 

7

7 

7

7 

7 

7 

7 

7

7 

7 

7 

7 

7

d.

60

69 

58 

57 

56

55 

54 

'52 53 

51

50

49 

48 

47 

46

45 

44

.43 

42 

41

40

39 

38 

37 

30

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

'

8 0 

56 

62 

48 

44

7 40 

36 

32 

28

24

7 20 

. 16 

12 

8 

4

7 0 

56 

52 

48 

44

6 40 

36 

32 

28 

24

6 20 

16 

12 

8 , 

4

6 0 

56 

 52 . 

48 

44

5 40 ' 

36 

32 

28 

24

5 20 

16 

12 

8 " 4

6 0 

56 

52 

48 

44

4 40 

36 

32 

28 

24

4 20 

16 

12 

8 

4

4 0

m. s.

61°
200 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued.

lh 29°

m. s.

CO 0 

4 

8 

12 

16

£0 20 

24 

28 

32 

36

CO 40 

44 

48 

52 

56

57 0 

4 

8 

12 

16

57 20 

24 

28 

32 

36

57 40 

44 

48 

52 

56

58 0 

4 

8 

12 

16

58 20 

24 

28 

32 

36

58 40 

44

48

52 

56

59 0 

4 

8 

12 

16

59 20 

24 

28 

32 

36

59 40 

44 

48 

52 

56

60 0

/

0 

]

2 

3 

4

5 

6

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41

42

43

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 68 557 

9. 68 580 

9. 68 603 

9. 68 625 

9. 68 648

9. 68 671 

9. 68 694 

9. 68 716 

9.68 73g 

9. 68 762

9. 68 784 

9. 68 807 

9. 68 829 

9. 68 852 

9. 68 875

9. 68 897 

9. 68 920 

9. 68 942 

9. 68 965 

9.68 987

9. 69 010 

9. 69 032 

9. 69 055 

9. 69 077 

9. 69 100

9.69 122 

9. 69 144 

9. 69 167 

9. 69 189 

9. 69 212

9. 69 234 

9. 69 256 

9. 69 279 

9. 69 301 

9. 69 323

9. 69 345 

9. 69 368 

9. 69 390 

9. 69 412 

9. 69 434

9. 69 456 

9. 69 479 

9.69 501 

9. 69 523 

9. 69 545

9. 69 567 

9. 69 589 

9. 69 611 

9. 69 633 

9. '69 655

9. 69 67-7 

9. 69 699 

9. 69 721 

9. 69 743 

9. 69 765

9. 69 787 

9. 69 809 

9. 69 831 

9. 69 853 

9. 69 875

9. 69 897

L. Cos.

d.

23 

23 

22 

23

93

23 

22 

23 

23 

22

23 

22 

23 

23 

22

23 

22 

23 

22 

93

22 

23 

22 

23 

22

22 

23 

22 

23 

22

22 

23 

22 

22 

22

23 

22 

22 

22 

22

23 

22 

22 

22 

22

22 

22 

22 

22 

22

22 

22 

22 

22

99

22 

22 

22 

22 

22

d.

L. Tang.

9. 74 375 

9. 74 405 

9. 74 435 

9. 74 465 

9. 74 494

9. 74 524 

9. 74 554 

9. 74 583 

9. 74 613 

9. 74 643

9. 74 673 

9. 74 702 

9. 74 732 

9. 74 762 

9. 74 791

9. 74 821 

9. 74 851 

9. 74 880 

9. 74 910 

9.74 939

9. 74 969 

9.74 998 

9. 75 028 

9. 75 058 

9. 75 087

9.75 117 

9. 75 146 

9. 75 176 

9. 75 205 

9. 75 235

9. 75 264 

9. 75 294 

9.75 323 

9. 75 353 

9. 75 382

9. 75 411 

9. 75 441 

9. 75 470 

9. 75 500 

9. 75 529

9. 75 558 

9.75588 

9. 75 617 

9. 75 647 

9. 75 676

9. 75 705 

9. 75 735 

9.75 764 

9. 75 793 

9. 75 822

9. 75 852 

9. 75 881 

9. 75 910 

9. 75 939 

9. 75 969

9. 75 998 

9. 76 027 

9. 76 056 

9. 76 086 

9. 76 115

9. 76 144

L. Cotg.

C. d.

30 

30 

30 

29 

30

30 

29 

30 

30 

30

29 

30 

30 

29 

30

30 

29 

30 

29 

30

29 

30 

30 

29

QA

29 

30 

29 

30 

29

30 

29 

30 

29 

29

30 

29 

30 

29

OQ

30

29

30 

29

9Q

30 

29 

29 

29

on

29 

29 

29 

30 

29

29 

29 

30 

29

9Q

c.d.

L. Cotg.

0. 25 625 

0. 25 595 

0. 25 565 

0. 25 535 

0. 25 506

0. 25 476 

0. 25 446 

0. 25 417 

0. 25 387 

0. 25 357

0. 25 327 

0. 25 298 

0. 25 268 

0. 25 238 

0. 25 209

0. 25 179 

0. 25 149 

0. 25 120 

0. 25 090 

0. 25 061

0.25 031 

0. 25 002 

0. 24 972 

0. 24 942 

0. 24 913

0. 24 883 

' 0. 24 854 

0. 24 824 

0.24 795 

0. 24 765

0. 24 736 

0. 24 706 

0. 24 677 

0. 24 647 

0. 24 618

0. 24 589 

0. 24 559 

0. 24 530 

0. 24 500 

.0.24 471

0. 24 442 

0.24412 

0.24383 

0.24 353 

0.24 324

0. 24 29^ 

0. 24 265 

0. 24 236 

0. 24 207 

0. 24 178

0. 24 148 

0. 24 119 

0. 24 090 

0. 24 061 

0. 24 031

0. 24 002 

0. 23 973 

0. 23 944 

0.23 914 

0. 23 885

0. 23 856

L. Tang.

L. Cos.

9. 94 182 

9.94 175 

9. 94 168 

9. 94 161 

9. 94 154

9. 94 147 

9. 94 140 

9.94133 

9.94 126 

9. 94 119

9. 94 112 

9. 94 105 

9. 94 098 

9. 94 090 

9. 94 083

9. 94 076 

9. 94 069 

9. 94 062 

9. 94 055 

9. 94 048

9. 94 041 

9. 94 034 

9. 94 027 

9. 94 020 

9. 94 012

9. 94 005 

9. 93 998 

9. 93 991 

9. 93 984 

9. 93 977

9. 93 970 

9. 93 963 

9. 93 955 

9. 93 948 

9. 93 941

9. 93 934 

9. 93 927 

9. 93 920 

9.93 912 

9. 93 905

9. 93 898 

9.93891 

9.93884 

9. 93 876 

9. 93 869

9.93 862 

9. 93 855 

9. 93 847 

9. 93 840 

9. 93 833

9. 93 826 

9. 93 819 

9. 93 811 

9. 93 804 

9. 93 797

9. 93 789 

9. 93 782 

9. 93 775 

9. 93 768 

9. 93 760

9. 93 753

L. Sin.

d.

7 

7 

7 

7 

7

7 

7 

7 

7 

7

7 

7 

8

7 

7

7

7 

7 

7 

7

7 

7 

7 

8 

7

7 

7 

7 

7 

7

7 

8 

7 

7 

7

7 

7 

8 

7 

7

7 

7 

8 

7 

7

7 

8 

7 

7 

7

7 

8 

7 

7 

8

7

7 

7 

8 

7

d.

60

59 

58 

57 

56

55 

54 

53 

52 

51

60

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

'

4 0 

56 

52 

48 

44

3 40 

36 

32 

28 

24

3 20 

16 

12 

8 

4

3 0 

56 

52

48 

44

2 40 

36 

32 

28 

24

2 20 

16 

12 

8 

4

2 0 

56 

52 

48 

44

1 40 

36 

32 

28 

24

1 20 

16 

12 

8 

4

1 0 

66 

52 

48 

44

0 40 

36 

32 

28 

24

0 20 

16 

12

8 

4

0 0

m. s.

60C
GEOGRAPHIC TABLES AND FORMULAS. 201 

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

2h 30°

m. s.

0 0 

4 

8 

12 

16

0 20 

 24 

28 

32 

36

0 40 

44 

48 

52 

56

1 0

4

8

12 

16

1 20 

24 

28 

32 

36

1 40 

44 

48 

52 

56

2 0 

4 

8 

12 

16

2 20 

24 

28 

32 

36

2 40 

44 

48 

52 

56

3 0 

4 

8 

12 

16

3 20 

24 

28 

32 

36

3 40 

44 

48 

52 

66

4 0

i

0

1

2 

3 

4

5 

6

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

GO

L. Sin.

9. 69 897 

9.69 919 

9. 69 941 

9. 69 963 

9. 69 984

9. 70 006 

9. 70 028 

9. 70 050 

9. 70 072 

9. 70 093

9. 7.0 115 

9. 70 137 

9. 70 159 

9. 70 180 

9. 70 202

9. 70 224 

9. 70 245

9.70267

9.70 288 

9. 70 310

9. 70 332 

9. 70 353 

9.70 375 

9. 70 396 

9. 70 418

9. 70 439 

9. 70 461 

9. 70 482 

9. 70 504 

9. 70 525

9. 70 547 

9. 70 568 

9. 70 590 

9. 70 611 

9. 70 633

9. 70 654 

9. 70 675 

9. 70 697 

9. 70 718 

9. 70 739

9. 70 761 

9. 70 782 

9. 70 803 

9. 70 824 

9. 70 846

9. 70 867 

9. 70 888 

9. 70 909 

9. 70 931 

9. 70 952

9. 70 973 

9. 70 994 

9.71 015 

9. 71 036 

9. 71 058

9. 71 079 

9.71 100 

9. 71 121 

9. 71 142 

9. 71 163

9.71 184

L. Cos.

d.

22 

22 

22 

21 

22

22 

22 

22 

21 

22

22 

22 

21 

22 

22

21 

22 

21 

22 

22

21 

22 

21 

22 

21

22 

21 

22 

21 

22

21 

22 

21 

22 

21

21 

22 

21 

21 

22

21 

21 

 21

22 

21

21 

21 

22 

21 

21

21 

' 21 

21 

22 

21

21 

21 

21 

21 

21

d.

L. Tang.

9.76 144 

9. 76 173 

9.76202 

9. 76 231 

9. 76 261

9. 76 290 

9. 76 319 

9. 76 348 

9. 76 -377 

9. 76 406

9. 76 435 

9. 76 464 

9.76493 

9. 76 622 

9. 76 651

9.76 580 

9.76 609 

9.76639

9. 76 668 

9. 76 697

, 9.70 725 

9. 76 754 

9. 76 783 

9. 76 812 

9. 76 841

9. 76 870 

9. 76 899 

9. 76 928 

9. 76 957 

9. 76 986

9. 77 015 

9.77 044 

9. 77 073 

9.77 101 

9. 77 130

9. 77 159 

9. 77 188 

9. 77 217 

9. 77 246 

9. 77 274

9. 77 303 

9. 77 332 

9. 77 361 

9. 77 390 

9. 77 418

9. 77 447 

9. 77 476 

9. 77 505 

9. 77 533 

9.77 562

9. 77 591 

9. 77 619 

9. 77 648 

9.77 677 

9. 77 706

9. 77 734 

9. 77 763 

9. 77 791 

9. 77 820 

9. 77 849

9. 77 877

L. Cotg.

c. d.

29 

29 

29 

30 

29

29 

29 

29 

29 

29

29 

29 

29 

29 

29

29 

30 

29 

29 

28

29 

29 

29 

29 

29

29 

29 

29 

29 

29

29 

29 

28 

29 

29

29 

29 

29 

28 

29

29 

29 

29 

28 

29

29 

29 

28 

29 

29

28 

29 

29 

29 

28

29 

28 

29 

29 

28

c. d.

L. Cotg.

0. 23 856 

0.23827 

0. 23 798 

0. 23 769 

0. 23 739

0.23710 

0. 23 681 

0. 23 652 

0. 23 623 

0.23 594

0. 23 565 

0. 23 636 

0.23 507 

0. 23 478 

0. 23 449

0. 23 420 

0.23391 

0.23361 

0. 23 332 

0. 23 303

0.23 275 

0. 23 246 

0.23 217 

0.23 188 

0.23 159

0. 23 130 

0. 23 101 

0. 23 072 

0. 23 043 

0.23 014

0. 22 985 

0.22 956 

0. 22 927 

0. 22 899 

0. 22 870

0. 22 841 

0. 22 812 

0.22 783 

0.22754 

0. 22 726

0. 22 697 

0. 22 668 

0.22 639 

0.22 610 

0.22 582

0. 22 553 

0. 22 524 

0.22 495 

0.22 467 

0.22:438

0. 22 409 

0. 22 381 

0. 22 352 

0.22 323 

0. 22 294

0.22 266 

0. 22 237 

0.22 209 

0. 22 180 

0. 22 151

0.22 123

L. Tang.

L. Cos.

9. 93 753 

9. 93 746 

9. 93 738 

9. 93 731 

9. 93 724

9. 93 717 

9. 93 709 

9. 93 702 

9. 93 695 

9. 93 687

9. 93 680 

9. 93 673 

9. 93 665 

9.93 658 

9. 93 650

9. 93 643 

9.93636 

9.93 628 

9.93 621 

9. 93 614

9.93 606 

9.93 599 

9. 93 591 

9.93 584 

9.93 577

9. 93 569 

9.93 562 

9. 93 554 

9. 93 547 

9. 93' 539

9. 93 532 

9. 93 525 

9.93 617 

9. 93 510 

9.93 602

9. 93 495 

9. 93 487 

9.93480 

9. 93 472 

9. 93 465

9. 93 457 

9. 93 450 

9. 93 442 

9. 93 435 

9. 93 427

9. 93 420 

9. 93 412 

9. 93 405 

9. 93 397 

9. 93 390

9.93 382 

9. 93 375 

9. 93 367 

9.93 360 

9.93 352

9. 93 344 

9. 93 337 

9. 93 329 

9. 93 322 

9.93 314

9. 93 307

L. Sin.

d.

7

8 

7 

7 

7

8 

7 

7 

8 

7

7 

8 

7 

8 

7

7 

8

7 

7 

8

7 

8 

7 

7 

8

7 

8

7 

8 

7

7 

8 

7 

8 

7

8 

7 

8 

7 

8

7 

8 

7 

8 

7

8 

7 

8 

7 

8

7 

8 

7 

8 

8

7 

8 

7 

8 

7

d.

GO

59 

58 

57 

56

55 

54 

53 

52 

51

60

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

80

29 

28 

27 

26

25 

24 

23 

22 

21

20

19

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

i

60 0 

56 

52 

48 

44

59 40 

36 

32 

28 

24

59 -20 

16 

12 

8 

4

59 0 

56 

62 

48 

44

58 40 

36 

32 

28 

24

58 20 

16 

12 

8 

4

58 0 

56 

52 

48 

44

57 40 

36 

32 

28 

24

57 20 

16 

12 

8 

4

57 0 

56 

52 

48 

44

56 40 

36 

32 

28 

24

56 20 

16 

12 

8 

4

56 0

m. s.

59C
202 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

2h 31°

m. s.

4 0 

4 

8 

12 

16

4 20 

24 

28 

32 

36

4 40 

44 

48 

52 

56

5 0 

4 

8 

12 

16

5 20 

24 

28 

32 

36

5 40 

44 

48 

52 

56

6 0 

4 

» 

12 

16

6 20 

24 

28 

32 

36

6 40 

44 

48 

52 

56

7 0 

4 

8 

12 

16

7 20 

24 

28 

32 

36

7 40 

44 

48 

52 

56

8 0

/

0

1 

2 

3 

4

5 

6

7 

8 

9

10

11

12 

13 

14

15 

16 

17 

18 

19

20

21 '22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41

42

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 71 184 

9.71 205 

9. 71 226 

9.71 247 

9. 71 268

9.71 289 

9.71 310 

9. 71 331 

9. 71 352 

9.71 373

9. 71 393 

9. 71 414 

9. 71 435 

9. 71 456 

9. 71 477

9. 71 498 

9.71 519 

9. 71 539 

9. 71 560 

9,71 581

9. 71 602 

9.71 622 

9.71 643 

9.71 664 

9.71 685

9.71 705 

9.71 726 

9.71 747 

9.71 767 

9.71 788

9. 71 809 

9. 71 829 

9.71 850 

9. 71 870 

9. 71 891

9. 71 911 

9.71 932 

9.71 952 

9. 71 973 

9. 71 994

9. 72 014 

9.72 034

9.72055

9.72 075 

9. 72 096

9. 72 116 

9. 72 137 

9. 72 157 

9. 72 177 

9.72 198

9. 72 218 

9. 72 238 

9. 72 259 

9. 72 279 

9.72 299

9.72 320 

9. 72 340 

9. 72 360 

9. 72 381 

9. 72 401

9. 72 421

L. Cos.

d.

21 

21 

21 

21 

21

21 

21 

21 

21 

20

21 

21 

21

21 

21

21 

20 

21 

21 

21

20 

21 

21 

21 

20

21 

21 

20 

21 

21

20 

21 

20 

21 

20

21 

20 

21 

21 

20

20 

21 

20 

21 

20

21 

20 

20 

21 

20

20 

21 

20 

20 

21

20 

20 

21 

20 

20

d.

L. Tang.

9.77 877 

9. 77 906 

9. 77 935 

9. 77 963 

9. 77 992

9. 78 020 

9. 78 049 

9. 78 077 

9. 78 106 

9.78 135

9.78 163 

9. 78 192 

9. 78 220 

9. 78 249 

9.78277

9. 78 306 

9. 78 334 

9.78 363 

9. 78 391 

9. 78 419

9. 78 448 

9. 78 476 

9.78 505 

9.78 533 

9. 78 562

9. 78 690 

9. 78 618 

9. 78 647 

9. 78 675 

9. 78 704

9. 78 732 

9. 78 760 

9. 78 789 

9. 78 817 

9. 78 845

9. 78 874 

9. 78 902 

9.78 930 

9. 78 959 

9. 78 987

9. 79 015 

9. 79 043

9.79072

9.79 100 

9.79 128

9. 79 156 

9. 79 185 

9. 79 213 

9. 79 241 

9.79269

9. 79 297 

9. 79 326 

9. 79 354 

9. 79 382 

9. 79 410

9. 79 438 

9. 79 466 

9. 79 495 

9. 79 523 

9. 79 551

9. 79 579

L. Cotg.

c.d.

29 

29 

28 

29 

28

29 

28 

29 

29 

W

29 

28 

29 

28 

29

28 

29 

28 

28 

29

28 

29 

28 

29 

28

28 

29 

28 

29 

28

28 

29 

28 

28 

29

28 

28 

29 

28 

28

28 

29 

28 

28 

28

29 

28 

28 

28 

28

29

28 

28 

28 

28

28 

29 

28 

28 

28

c.d.

L. Cotg.

0.22 123 

0.22 094 

0. 22 065 

0. 22 037 

0. 22 008

0.21 980 

0.21 951 

0. 21 923 

0. 21 894 

0.21 865

0. 21 837 

0. 21 808 

0.21 780 

0. 21 751 

0.21 723

0.21 694 

0. 21 666 

0. 21 637 

0.21 609 

0. 21 581

0.21 552 

0.21 524 

0. 21 495 

0. 21 467 

0. 21 438

0. 21 410 

0.21 382 

0.21 353 

0.21 325 

0. 21 296

0.21 268 

0.21 240 

0.21 211 

0. 21 183 

0. 21 155

0. 21 126 

0. 21 098 

0. 21 070 

0.21 041 

0.21 013

0. 20 985 

0. 20 957

0.20928

0. 20 900 

0.20 872

0.20 844 

0.20 815 

0. 20 787 

0. 20 759 

0. 20 731

0. 20 703 

0. 20 674 

0. 20 646 

0.20 618 

0. 20 590

0. 20 562 

0. 20 534 

0. 20 505 

0. 20 477 

0.20 449

0.20421

L. Tang.

L. Cos.

9. 93 307 

9. 93 299 

9. 93 291 

9.93 284 

9.93 276

9. 93 269 

9.93 261 

9. 93 253 

9. 93 246 

9. 93 238

9.93230 

9. 93 223 

9.93 215 

9. 93 207 

9.93 200

9.93 192 

9. 93 184 

9. 93 177 

9. 93 169 

9.93161

9. 93 154 

9.93 146 

9. 93 138 

9. 93 131 

9. 93 123

9.93 115 

9. 93 108 

9. 93 100 

9. 93 092 

9. 93 084

9. 93 077 

9. 93 069 

9. 93 061 

9. 93 053 

9. 93 046

9. 93 038 

9. 93 030 

9. 93 022 

9. 93 014 

9. 93 007

9. 92 999 

9.92 991

9.92983

9.92 976 

9.92 968

9. 92 960 

9.92 952 

9.92 944 

9.92 936 

9.92 929

9. 92 921 

9.92 913 

' 9.92 905 

9. 92 897 

9. 92 889

9. 92 881 

9. 92 874 

9. 92 866 

9. 92 858 

9. 92 850

9.92 842

L. Sin.

d.

8 

8 

7 

8 

7

8 

8 

7 

8 

8

7 

8 

8 

7

a

8 

7 

8 

8 

7

8 

8 

8'7 

a

7 

8 

8 

8 

7

8 

8 

8 

7 

8

8 

8' 8 

7 8"

8 

8 

7

8 

8

8 

8 

8

8

8 

8 

8 

8 

8

7 

8 

8 

8 

8

d.

GO

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18. 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

'

56 0 

56 

52 

48 

44

55 40 

36 

32 

28, 

24

55 20 

16 

12 

8 

4

55 0 

56 

52, 

48 

44

54 40 

36 

32 

28 

24

54 20 

16 

12 

8 

4

54 0 

56 

52 

48 

44

53 40 

36 

32 

28 

24

53 20 

16 

12 

8 

4

53 0 

56

52 

48 

44

52 40 

36 

32 

28 

24

52 20 

16 

12 

8 

4

62 0

m. s.

58°
GEOGRAPHIC TABLES AND FORMULAS. 203 

TABLE 27. Five-place logarithms of circular functions, etc. -Continued. 

2h 32°

m. s.

8 0 

4 

8 

12 

16

8 20 

24 

28 

32 

36

8 40 

44 

48 

52 

66

9 0 

4 

8 

12 

16

9 20 

24

1 28 

32 

36

9 40 

44 

48 

52 

56

10 0 

4 

8 

12 

16

10 20 

24 

28 

32 

36

10 40

44 

48 

52 

56

11 0 

4 

8 

12 

16

11 20 

24 

28 32 

36

11 40 

44 

48 

52 

56

12 0

/

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24.

25 

26 

27 

28 

29

80

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53

54

55 

56 

57 

58 

59

60

L. Sin.

9.72 421 

9. 72 441 

9. 72 461 

9. 72 482 

9. 72 502

9. 72 522 

9. 72 542 

9. 72 562 

9. 72 582 

9. 72 602

9. 72 622 

9. 72 643 

9.72 663 

9.72 683 

9. 72 703

9. 72 723 

9.72 743 

9.72 763 

9. 72 783 

9. 72 803

9. 72 823 

9. 72 843 

9. 72 863 

9. 72 883 

9. 72 902

9. 72 922 

9. 72 942 

9. 72 962 

9. 72 982 

9. 73 002

9. 73 022 

9. 73 0 11 

9. 73 061 

9. 73 081 

9. 73 101

9. 73 121 

9. 73 140 

9. 73 160 

9. 73 180 

9. 73 200

9. 73 219 

9. 73 239 

9. 73 259 

9.73278 

9. 73 298

9.73 318 

9. 73 337 

9.73 357 

9. 73 377 

 9. 73 396

9. 73 416 

9. 73 435 

9. 73 455 

9. 73 474 

9. 73 494

9. 73 513 

9. 73 533 

9. 73 552 

9. 73 572 

9. 73 591

9. 73 611

L. Cos.

d.

20 

20 

21 

20 

20

20 

20 

20 

20 

20

21 

20 

20 

20 

20

20 

20 

20 

20 

20

20 

20 

20 

19 

20

20 

20 

20 

20 

20

19 

20 

20 

20 

20

19 

20 

20 

20 

19

20 

20 

19 

20 

20

19 

20 

20 

19 

20

19 

20 

19 

20 

19

20 

19 

20 

19 

20

d.

L. Tang.

9. 79 579 

9. 79 607 

9. 79 635 

9. 79 663 

9. 79 691

9. 79 719 

9. 79 747 

9.79 776 

9. 79 804 

9. 79 832

9. 79 860 

9. 79 888 

9^79 916 

9. 79 944 

9. 79 972

9. 80 000 

9.80028 

9.80056 

9. 80 084 

9. 80 112

9. 80 140 

9. 80 168 

9. SO 195 

9. 80 223 

9.80251

9. 80 279 

9. 80 307 

9. 80 335 

9.80 363 

9. 80 391

9. 80 419 

9. 80 447 

9.80 474 

9.80 502 

9.80 530

9. 80 558 

9. 80 586 

9.80 614 

9. 80 642 

9. 80 669

9. 80 697 

9.80 725 

9. 80 753 

9.80 781 

9. 80 808

9. 80 836 

9. 80 864 

9.80'892 

9. 80 919 

9.80 947

9. 80 975 

9.81 003 

9. 81 030 

9.81 058 

9. 81 086

9. 81 113 

9.81 141 

9.81 169 

9. 81 196 

9.81 224

9. 81 252

L. Cotg.

c.d.

28 

28 

28 

28

Oft

28 

29 

28 

28

OQ

28 

28 

28 

28 

28

28 

28 

28 

28 

28

28 

27 

28 

28

OQ

28 

28 

28 

28 

28

28 

27 

28 

28

Oft

28 

28 

28 

27 

28

28 

28 

28 

27 

28

28 

28 

27 

28 

28

28 

27 

28 

28 

27

28 

28 

27 

28

08

c.d.

L. Cotg.

0. 20 421 

0 20 393 

0. 20 365 

0. 20 337 

. 0. 20 309

0. 20 281 

0. 20 253 

0. 20 224 

0.20 196 

0. 20 168

0.20 140 

0.20 112 

0. 20 084 

0. 20 056 

0. 20 028

0. 20 000 

0.19 972 

0.19944 

0. 19 916 

0. 19 888

0. 19 860 

0. 19 832 

0.19 805 

0. 19 777 

0. 19 749

0. 19 721 

0.19 693 

0. 19 665 

0.19 637 

0. 19 609

0. 19 581 

0. 19 553 

0. 19 426 

0. 19 498 

0.19 470

0. 19 442 

0. 19 414 

0. 19 386 

0. 19 358 

0.19 331

0.19 303 

0. 19 275 

0. 19 247 

0. 19 219 

0. 19 192

0. 19 164 

0. 19 136 

0. 19 108 

0.19 081 

0. 19 053

0. 19 025 

0. 18 997 

0. 18 970 

0.18 942 

0. 18 914

0. 18 887 

0. 18 859 

0. 18 831 

0. 18 804 

0. 18 776

0. 18 748

L. Tang.

L. Cos.

9. 92 842 

9.92 834 

9. 92 826 

9. 92 818 

9. 92 810

9. 92 803 

9. 92 795 

9. 92 787 

9. 92 779 

9. 92 77,1

9.92 763 

9.92 755 

9. 92 747 

9. 92 739 

9. 92 731

9. 92 723 

9. 92 715 

9.92707 

9.92 699 

9. 92 691

9.92 683 

9.92 675 

9. 92 667 

9. 92 659 

9. 92 651

9. 92 643 

9.92 635 

9. 92 627 

9. 92 619 

9. 92 611

9. 92 603 

9. 92 595 

9. 92 587 

9.92 579 

9. 92 571

9. 92 563 

9. 92 555 

9. 92 546 

9. 92 538 

9. 92 530

9.92 522 

9. 92 514 

9.92 606 

9. 92 498 

9. 92 490

9. 92 482 

9. 92 473 

9. 92 465 

9. 92 457 

9.92 449

9. 92 441 

9. 92 433 

9. 92 425 

9. 92 416 

9. 92 408

9. 92 400 

9. 92 392 

9. 92 384 

9. 92 376 

9. 92 367

9. 92 359

L. Sin.

d.

8 

8 

8 

8

8 

8 

8 

8

8 

8 

8 

8 

8

8 

8 

8 

8 

8

8 

8 

8 

8 

8

8 

8 

8 

8 

8

8 

8 

8 

8 

8

8 

9

8 

8

8 

8 

8 

8

9

8 

8 

8

8 

8 

9

8

8 

8 

8 

9

d.

GO

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 '48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

]2 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

/

52 0 

56 

52 

48 

44

51 40 

36 

32 

28 

24

51 20 

16 

12

8 

4

51 0 

56 

52 

48 

44

50 40 

36 

32 

28 

24

50 20 

16 

12 

8 

4

50 0 

56 

52 

48 

44

49 40 

36 

32 

28 

24

49 20 

16 

12 

8 

4

49 0 

56 

52 

48 

44

48 40 

36 

32 

28 

24

48 20 

16 

12 

8 

4

48 0

m. s.

57°
204 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

2h 33°

m. s.

12 0 

4 

8 

12 

16

12 20 

24 

28 

32 

36

12 40 

44

48 

52 

56

13 0 

4 

8 

12 

16

13 20 

24 

28 

32 

36

13 40 

44 

48 

52 

56

14 0 

4 

8 

12 

16

14 20 

24 

28 

32 

36

14 40 

44

48

52 

56

15 0 

4 

8 

12 

16

15 20 

24 

28 

32 

36

15 40 

44 

48 

52 

56

16 0

/

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21

22 

23

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 73 611 

9. 73 630 

9. 73 650 

9. 73 669 

9. 73 689

9. 73 708 

9. 73 727 

9. 73 747 

 9. 73 766 

9. 73 785

9. 73 805 

9. 73 824 

9. 73 843 

9. 73 863 

9. 73 882

9. 73 901 

9.73 921 

9. 73 940 

9. 73 959 

9. 73 978

9. 73 997 

9.74 017 

9. 74 036 

9. 74 055 

9. 74 074

9. 74 093 

9. 74 113 

9. 74 132 

9.74 151 

9. 74 170

9. 74 189 

9. 74 208 

9. 74 227 

9. '4 246 

9. 74 265

9.74 284 

9. 74 303 

9. 74 322 

9. 74 341 

9. 74 360

9. 74 379 

9.74398 

9.74417 

9. 74 436 

9. 74 455

9. 74 474 

9. 74 493 

9. 74 512 

9. 74 531 

9. 74 549

9. 74 568 

9. 74 587 

9. 74 606 

9. 74 625 

9. 74 644

9. 74 662 

9. 74 681 

9. 74 700 

9. 74 719 

9. 74 737

9. 74 756

L. Cos.

d.

19 

20 

19 

20

19 

20 

19 

19

20

19 

19 

20 

19

20 

19 

19 

19

20 

19 

19 

19

20 

19 

19 

19

19 

19 

19 

19 

19

19 

19 

19 

19 

19

19 

19 

19 

19 

19

19 

19 

19 

18 

19

19 

19 

19 

19

1 Q

19 

19 

19 

18 

19

d.

L. Tang.

9.81 262 

9.81 279 

9.81 307 

9.81 335 

9. 81 -362

9. 81 390 

9. 81 418 

9.81 445 

9. 81 473 

9.81 500

9.81 528 

9.81 556 

9. 81 583 

9.81 611 

9. 81 638

9.81 666 

9.81 693 

9. 81 721 

9.81 748 

9.81 776

9.81 803 

9. 81 831 

9. 81 858 

9. 81 886 

9.81 913

9.81 941 

9.81 968 

9.81 996 

9. 82 023 

9.82 051

9. 82 078 

9. 82 106 

9.82 133 

9. 82 161 

9. 82 188

9. 82 215 

9. 82 243 

9. 82 270 

9. 82 298 

9.82 325

9. 82 352 

9.82380 

9.82407 

9. 82 435 

9.82 462

9.82 489 

9.82 517. 

9. 82 544 

9.82 571 

9.82 599

9. 82 626 

9. 82 653 

9. 82 681 

9.82 708 

9. 82 735

9.82 762 

9.82 790 

9. 82 817 

9.82 844. 

9. 82 871

9. 82 899

oL. Cotg.

c. d.

27 

28 

28 

27

28 

27 

28 

27

28 

27 

28 

27

Zo

27 

28 

27 

28

27

28 

27 

28 

27

27 

28 

27 

28 

27

28 

27 

28 

27 

27

28 

27 

28 

27 

27

28

27

28 

27 

27

28 

27 

27 

28 

27

27 

28 

27 

27 

27

28 

27 

27 

27

OQ

c. d.

L. Cotg.

0. 18 748 

0. 18 721 

0. 18 693 

0. 18 665 

0. 18 638

0. 18 610 

0. 18 582 

0.18 555 

0. 18 527 

0. 18 500

0. 18 472 

0.18 444 

0. 18 417 

0. 18 389 

0. 18 362

0. 18 334 

0. 18 307 

0.18279 

0. 18 252 

0.18224

0. 18 197 

0. 18 169 

0.18 142 

0. 18 114 

0. 18 087

0. 18 059 

0. 18 032 

0. 18 004 

0. 17 977 

0. 17 949

0. 17 922 

0. 17 894 

0. 17 867 

0. 17 839 

0. 17 812

0. 17 785 

0. 17 757 

0. 17 730 

0.17 702 

0. 17 675

0. 17 648 

0.17 620 

0.1759? 

0. 17 565 

0. 17 638

0. 17 511 

0. 17 483 

0. 17 456 

0. 17 429 

0. 17 401

0. 17 374 

0. 17 347 

0. 17 319 

0. 17 292 

0. 17 265

0. 17 238 

0. 17 210 

0.17 183 

0. 17 156 

0. 17 129

0. 17 101

L. Tang.

L. Cos.

9. 92 359 

9. 92 351 

9. 92 343 

9. 92 335 

9. 92 326

9. 92 318 

9.92 310 

9. 92 302 

 9. 92 293 

9. 92 285

9. 92 277 

9. 92 269 

9. 92 260 

9. 92 252 

9. 92 244

9. 92 2*5 

9. 92 227 

9. 92 219 

9. 92 211 

9. 92 202

9. 92 194 

9. 92 186 

9.92 177 

9. 92 169 

9. 92 161

9. 92 152 

9.92 144 

9. 92 136 

9. 92 127 

9. 92 119

9. 92 111 

9.92 102 

9.92 094 

9.92 086 

9. 92 077

9. 92 069 

9. 92 060 

9. 92 052 

9. 92 044 

9. 92 035

9. 92 027 

9.92 018 

9.92 010 

9.92 002 

9. 91 993

9. 91 985 

9. 91 976 

9. 91 968 

9.91 959 

9. 91 951

9. 91 942 

9. 91 934 

9. 91 925 

9.91 917 

9.91 908

9.91 900 

9. 91 891 

9. 91 883 

9.91 874 

9.91 866

9. 91 857

L. Sin.

d.

8 

8 

8 

9

8 

8 

9 

8

8 

9 

8 

8

8 

8 

8 

9

8 

9 

8 

8- 

g

8 

8 

9 

8

9

8 

8 

9

9 

8 

8 

9

9 

8 

8 

9

9 

8 

9 

8 

g

8 

9 

8 

. 9

9

8 

9 

8 

9

d.

60

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

i

48 0 

56 

52 

48 

44

47 40 

36 

32 

28 

24

47 20 

16 

12

8 

4

47 0 

56

52 

48 

44

46 40 ' 36 

32 

28 

24

46 20 

16 

12 ' 8 

4

46 0 

56 

52 

48 

44

45 40 

36 

32 

28 

24

45 20 

16 

12 

8 

4

45 0 

56 

52 

48 

44

44 40 

36 

32 

28 

24

44 20 

16 

12 

8 

4

44 0

m. s.

56°
C4EOGEAPHIC TABLES AND FOKMULAS. 205

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

n 34°

m. s.

16 0 

4 

8 

12 

16

16 20 

24 

28 

32 

36

16 40 

44 

48 

52 

56

17 0 

4 

8 

12 

16

17 20 

24 

28 

32 

36

17 40 

44 

48 

52 

56

18 0 

4 

8 

12 

16

18 20 

24 

28 

32 

36

18 40 

44 

48 

52 

56

19 0 

4 

8 

12 

16

19 20 

24 

28 

32 

36

19 40 

44 

48 

52 

56

20 0

/

0

1

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 74 756 

9. 74 775 

9. 74 794 

9. 74 812 

9. 74 831

9. 74 850 

9. 74 868 

9. 74 887 

9. 74 906 

9. 74 924

9. 74 943 

9. 74 961 

9. 74 980 

9. 74 999 

9. 75 017

9. 75 036 

9.75054 

9.75073 

9.75-091 

9. 75 110

9.75.128 

9. 75 147 

9. 75 165 

9. 75 184 

9. 75 202

9. 75 221 

9.75239 

9. 75 258 

9.75276 

9. 75 294

9. 75 313 

9. 75 331 

9. 76 350 

9. 75 368 

9. 75 386

9. 75 405 

9. 75 423 

9. 75 441 

9. 75 459 

9. 75 478

9. 75 496 

9. 75 514 

9. 75 533 

9. 75 551 

9. 75 669

9. 75 587 

9. 75 605 

9. 75 624 

9. 75 642 

9.75 660

9. 75 678 

9. 75 696 

9. 75 714 

9. 75 733 

9. 75 761

9. 75 769 

9. 75 787 

9. 75 805 

9. 75 823 

9. 75 841

9. 75 859

L. Cos.

d.

19 

19 

18 

' 19 

19

18 

19 

19 

18 

19

18 

19 

19 

18 

19

18 

19 

18 

19 

18

19 

18 

19 

18

10

18 

19 

18 

18 

19

18 

19 

18 

18 

19

18 

18 

18 

19 

18

18 

19

18 

18

1Q

18 

. 19 

18 

18 

18

18 

18 

19 

18 

18

.18 

18 

18 

18

1 ft

d.

L. Tang.

9.82 899 

9. 82 926 

9. 82 963 

9. 82 980 

9..S3 008

9. 83 035 

9. 83 062 

9. 83 089 

9. 83 117 

9.83 144

9.83 171 

9.83 198 

9. 83 225 

9. 83 252 

9.83 280

9.83 307 

9.83 334 

9.83361 

9. 83 388 

9. 83 415

9.83442 

9. 83 470 

9. 83 497 

9. 83 524 

9.83551

9. 83 578 

9.83 605 

9. 83 632 

9.83 659 

9. 83 686

9.83 713 

9. 83 740 

9. 83 768 

9.83 795 

9. 83 822

9. 83 849 

9.83 876 

9.83 903 

9. 83 930 

9. 83 957

9. 83 984 

9.84 Oil 

9. 84 038 

9.84 065 

9. 84 092

9.84 119 

9.84 146 

9.84 173 

9. 84 200 

9.84 227

9. 84 254 

9. 84 280 

9.84 307 

9.84 334 

9.84 361

9.84 388 

9.84.415 

9.84 442 

9.84 469 

9. 84 496

9.84 523

L. Cotg.

c. d.

27 

27 

27 

28 

27

27 

27 

28 

27 

27

27 

27 

27 

28 

27

27 

27 

27 

27 

27

28 

27 

27 

27

27

27 

27 

27 

27 

27

27 

28 

27 

27 

27

27 

27 

27 

27

27 

27 

27 

27

27 

27 

27 

27 

27

26 

27 

27 

27 

27

27 

27 

27 

27 

27

c. d.

L. Cotg.

0. 17 101 

0. 17 074 

0. 17 047 

0. 17 020 

0. 16 992

0. 16 965 

0. 16 938 

0.16 911 

0. 16 883 

0. 16 856

0. 16 829 

0. 16 802 

0. 16 775 

0. 16 748 

0. 16 720

0. 16 693 

0. 16 666 

0. 16 639 

0.16 612 

0. 16 585

0.16 558 

0. 16 530 

0. 16 503 

0.16 476 

0.16 449

0. 16 422 

0. 16 395 

0. 16 368 

0. 16 341 

0. 16 314

0. 16 287 

0. 16 260 

0. 16 232 

0.16 205 

0. 16 178

0.16 151 

0.16 124 

0.16 097 

0.16 070 

0. 16 043

0. 16 016 

0. 15 989 

0. 15 962 

0. 16 935 

0. 15 908

0. 15 881 

0. 16 854 

0. 15 827 

0. 15 800 

0. 15 773

0. 15 746 

0. 15 720 

0. 15 693 

0. 15 666 

0. 15 639

0.15 612 

0.15 585 

0. 15 558 

0. 15 531 

0. 15 504

0. 15 477

L. Tang.

L. Cos.

9.91 857 

9. 91 849 

9.91 840 

9. 91 832 

9.91 823

9.91 815 

. 9. 91 806 

9. 91 798 

9. 91 789 

9. 91 781

9. 91 772 

9. 91 763 

9.91 755 

9. 91 746 

9.91 738

9. 91 729 

9. 91 720 

9.91 712 

9. 91 703 

9. 91 695

9. 91 686 

9.91 677 

9. 91 669 

9. 91 660 

9.91 651

9. 91 643 

9. 91 534 

9. 91 625 

9. 91 617 

9. 91 608

9.91 599 

9. 91 591 

9. 91 582 

9. 91 573 

9. 91 565

9.91 556 

9. 91 547 

9. 91 538 

9. 91 530 

9. 91 521

9. 91 512 

9.91 504 

9.91 495 

9. 91 486 

9.91. 477

9.91 469 

9.91 460 

9. 91 451 

9. 91 442 

9. 91 433

9.91 425 

9.91 416 

9.91 407 

9.91 398 

9.91 389

9. 91 381 

9.91 372 

9.91 363 

9.91 354 

9.91 345

9.91 336

L. Sin.

d.

8 

9 

8 

9

9 

8 

9 

8 

g

9 

8 

9 

8

9 

8 

9 

8

9 

8 

9 

9

9 

9 

8 

9 

g

8 

9 

9 

8 

g

9 

9 

8 

9 

9

8 

9 

9 

9

8

9 

9 

9 

9

8

9 

9 

9 

9

8

9 

9 

9 

9 

9

d.

GO

59

58 

57 

56

55 

54 

53 52' 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

80

29 

28 

27 

26

25 

24 

23 

22 

21

20

19

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

'

44 0 

56 

52 

48 

44

43 40 

36 

32 

° 28 

24

43 20 

16 

12 

8 

4

43 0 

56 

52 

48 

44

42 40 

36 

32 

28 

24

42 20 

16 

12 

8 

4

42 0 

56 

52 

48 

44

41 40 

36 

32 

28 

24

41 20 

16 

12 

8 

4

41 0 

56 

52 

48 

44

40 40 

36 

32 

28 

24

40 20 

16 

12 

8 

4

40 0

m. s.

55C
20G GEOGRAPHIC TABLES AND FOEMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

2h 35°

m. s.

20 0 

4 

8 

12 

16

20 20 

24 

28 32° 

36

20 40 

44 

48 

52 

56

21 0 

4 

8 

12 

16

21 20 

24 

28 

32 

36

21 40 

44 

48 

62 

56

22 0 

4 

8 

12 

16

22 20 

24 

28 

32 

36

22 40 

44 

48 

52 

56

23 0 

4 

8 

12 

16

23 20 

' 24 

28 

32 

36

23 40 

44 

48 

52 

56

24 0

'

0

1 

2 

3

4

5 

6 

7 '8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 75 859 

9. 75 877 

9. 75 895 

9.75 913 

9. 75 931

9. 75 949 

9. 75 967 

9. 75 985 

9. 76 003 

9. 76 021

9. 76 039 

9. 76 057 

9. 76 075 

9. 76 093 

9. 76 111

9. 76 129 

9. 76 146 

9. 76 164 

9. 76 182 

9. 76 200

9. 76 218 

9. 76 236 

9.76253 

9. 76 271 

9.76 289

9. 76 307 

9. 76 324 

9. 76 342 

9. 76 360 

9. 76 378

9. 76 395 

9. 76 413 

9. 76 431 

9. 76 448 

9. 76 466

9. 76 884 

9. 76 501 

9. 76 519 

9. 76 537 

9. 76 554

9. 76 572 

9.76 590 

9.76607 

9. 76 625 

9. 76 642

9.76 660 

9. 76 677 

9. 76 695 

'9. 76 712 

9. 76 730

9. 76 747 

9. 76 765 

9.76782 

9. 76 800 

9. 76 817

9.76 835 

9. 76 852 

9. 76 870 

9. 76 887 

9.76904

9. 76 922

L.Cos.

d.

18 

18 

18 

18

18 

18 

18 

18

lo

18 

18 

18 

18

17 

18 

18 

18

18 

17 

18 

18

17 

18 

18 

18 

17

18 

18 

17 

18

17 

18 

18. 

17

18 

17 

18 

17

1 Q

17 

18 

17 

18 

17

18 

17 

18 

17

no

17 

18 

17 

17

d.

L. Tang.

9.84 523 

9. 84 550 

9. 84 576 

9. 84 603 

9. 84 630

9.84 657 

9.84 684 

9. 84 711 

9. 84 738 

9.84764

9. 84 791 

9.84 818 

9. 84 845 

9. 84 872 

9.84899

9. 84 925 

9.84 952 

9.84979 

9. 85 006 

9.85033

9.85059 

9. 85 086 

9.85113 

9.85 140 

9.85166

9. 85 193 

9.85 220 

9. 85 247 

9.85 273 

9.85 300

9. 85 327 

9. 85 354 

9. 85 380 

9.85 407 

9.85 434

9. 85 460 

9. 85 487 

9.85 514 

9. 85 540 

9.85 567

9. 85 594 

9. 85 620 

9.85647 

9. 85 674 

9. 85 700

9.85 727 

9. 85 754 

9. 85 780 

9.85807 

9.85 834

9. 85 860 

9. 85 887 

9.85 913 

9.85 940 

9.85 967

9.85993 

9. 86 020 

9. 86 046 

9. 86 073 

9.86 100.

9. 86 126

L. Cotg.

c. d.

27 

26 

27 

27 

27

27 

27 

27 

26

27 

27 

27 

27

26

27 

27 

27

27

27 

27 

27 

26 

27

27 

27 

26 

27

27

27 

26 

27

27

26

27 

27 

26 

27

27

26 

27 

27 

26

27

27 

?6

27 

27

26

27 

26 

27 

27 

26

27 

26 

27 

27

26

c. d.

L. Cotg.

0.15 477 

0. 15 450 

0. 15 424 

0. 15 397 

0.15-370

0. 15 343 

0.15316 

0. 15 289 

0. 15 262 

0.15236

0.15 209 

0. 15 182 

0.15155 

0.16128 

0.15101

0. 15 075 

0.15048 

0. 15 021 

0. 14 994 

0.14 967

0. 14 941 

0. 14 914 

0.14887 

0. 14 860 

0. 14 834

0. 14 807 

0. 14 780 

0.14753 

0. 14 727 

0.14 700

0. 14 673 

0.14 646 

0. 14 620 

0. 14 593 

0. 14 566

0.14 540 

0. 14 513 

0.14 486 

0. 14 460 

0. 14 433

0. 14 406 

0.14380 

0.14353 

0. 14 326 

0. 14 300

0. 14 273 

0. 14 246 

0. 14 220 

0. 14 193 

0. 14 166

0.14 140 

0.14 113 

0. 14 087 

0. 14 060 

0. 14 033

0. 14 007 

0. 13 980 

0. 13 954 

0.13927 

0.13900

0. 13 874

L. Tang.

L. Cos.

9.91 336 

9. 91 328 

9. 91 319 

9. 91 310 

9. 91 301

9. 91 292 

9. 91 283 

9.91 274 

9. 91 266 

9. 91 257

9. 91 248 

9. 91 239 

9. 91 230 

9. 91 221 

9.91 212

9. 91 203 

9. 91 194 

9.91 185 

9. 91 176 

9. 91 167

9. 91 158 

9. 91 149 

9.91 141 

9.91 132 

9. 91 123

9. 91 114 

9.91 105 

9. 91 096 

9. 91 087 

9. 91 078

9. 91 069 

9.91 060 

9. 91 051 

9. 91 042 

9.91 033

9. 91 023 

9. 91 014 

9. 91 005 

9. 90 996 

9. 90 987

9.90 978 

9.90969 

9.90 960 

9. 90 951 

9. 90 942

9. 90 933 

9. 90 924 

9. 90 915 

9.90906 

9. 90 896

9. 90 887 

9. 90 878 

9. 90 869 

9. 90 860 

9. 90 851

9. 90 842 

9. 90 832 

9. 90 823 

9.90 814 

9. 90 805

9. 90 796

L. Sin.

d.

8 

9 

9 

9

9 

9 

8 

9

9 

9 

9 

9

9 

9 

9 

9 

9

9 

8 

9 

9 

9

9 

9 

9 

9 

9

' 9 

9 

9 

9 

10

9 

9 

9 

9 

9

9 

9 

9 

9 

9

9 

9 

9 

10 

9

9 

9 

9 

9 

9

10 

9 

9 

9

d.

60

59 

58 

. 57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

/

40 0 

56 

52 

48 

44

39 40 

36 

32

28 

24

39 20 

16 

12 

8 

4

39 0 

56 

52 

48 

44

38 40 

36 

32 

28 

24

38 20 

16 

12 

8 

4

38 0 

56 

52 

48 

44

37 40 

36 

32 

28 

24

37 20 

16 

12 

8 

4

37 0 

56 

52 

48 

44

36 40 

.36 

32 

28 

24

36 20 

16 

12 

8 

4

36 0

m. s.
GEOGRAPHIC TABLES AND FORMULAS. 207 

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

2h 36°

m. s.

24 0 

4 

8 

12 

16

 24 20 

24 

28 

32 

36

24 40 

44 

48 

52 

56

25 0 

4: 

8 

12 

16

 25 20 

24 

28 

32 

36

25 40 

44 

48 

52 

56

26 0 

4 

8 

12 

16

26 20 

24 

28 

32 

36

26 40 

44 

48 

52 

56

27 0 

4 

8 

12 

16

27 20 

24 

28 

32 

. 36

27 40 

44 

48 

52 

56

28 0

i

0 

1

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 76 922 

9. 76 939 

9. 76 '957 

9. 76 974 

9. 76 991

9. 77 009 

9. 77 026 

9. 77 043 

9. 77 061 

9. 77 078

9. 77 095 

9.77 112 

9.77 130 

9. 77 147 

9. 77 164

9. 77 181 

9.77 199 

9.77216 

9.77233 

9.77 250

9. 77 268 

 9.77 285 

9. 77 302 

9. 77 319 

9. 77 336

9. 77 353 

9.77 370 

9. 77 387 

9. 77 405 

9. 77 422

9. 77 439 

9. 77 456 

9. 77 473 

9. 77 490 

9. 77 507

9. 77 524 

9. 77 541 

9. 77 558 

9.77 575 

9. 77 592

9.77 609 

9. 77 626 

9. 77 643 

9. 77 660 

9.77 677

9. 77 694 

9. 77 711 

9.77 728 

9. 77 744 

9. 77 761

9. 77 778 

9.77 795 

9. 77 812 

9. 77 829 

9. 77 846

9. 77 862 

9. 77 879 

9. 77 896 

9. 77 913 

9.77 930

9. 77 946

L. Cos.

d.

17 

18 

17 

17 

18

17 

17 

18 

U 

17

17 

18 

17 

17 

17

18 

17 

17 

17 

18

17 

17 

17 

17 

17

17 

17 

18 

17 

17

17 

17 

17 

17 

17

17 

17 

17 

17 

17

17 

17 

17 

17 

17

17 

17 

16 

17 

17

17 

17 

17 

17 

16

17 

17 

17 

17 

16

d.

L. Tang.

9. 86 126 

9. 86 153 

9.86179 

9. 86 206 

9. 86 232

9. 86 259 

9. 86 285 

9. 86 312 

9. 86 338 

9.86 365

9. 86 392 

9. 86 418 

9. 86 445 

9. 86 471 

9.86498

9.86 524 

9. 86 551 

9.86577 

9. 86 603 

9. 86 630

9. 86 656 

9. 86 683 

9. 86 709 

9. 86 736 

9.86 762

9.86 789 

9.86 815 

9. 86 842 

9. 86 868 

9. 86 894

9. 86 921 

9. 86 947 

9. 86 974 

9. 87 000 

9.87 027

' 9. 87 053 

9.87 079 

9.87 106 

9. 87 132 

9.87 158

9.87 185 

9. 87 211 

9. 87 238 

9. 87 264 

9.87 290

9. 87 317 

9.87 343 

9.87 369 

9. 87 396 

9. 87 422

9. 87 448 

9. 87 475 

9.87 501 

9. 87 527 

9. 87 554

9.87 580 

9.87 606 

9. 87 633 

9. 87 659 

9. 87 685

9. 87 711

L. Cotg.

c.d.

27 

26 

27 

26 

27

26 

27 

26 

27 

27

26 

27 

26 

27 

26

27 

26 

26 

27 

26

27 

26

27 

26 

27

26 

27 

26 

26 

27

26 

27 

26 

27 

26

26 

27 

26 

26

27

26 

27 

26 

26 

27

26 

26. 

27 

26 

26

27 

26 

26 

27 

26

26 

27 

26 

26 

26

c. d.

L. Cotg.

0. 13 874 

0.13847 

0.13 821 

0.13 794 

0. 13 768

0. 13, 741 

0. 13 715 

0.13 688 

0. 13 662 

0. 13 635

0.13 608 

0. 13 582 

0. 13 555 

0. 13 529 

0. 13 502

0. 13 476 

0.13449 

0.13423 

0. 13 397 

0. 13 370

0. 13 344 

0. 13 317 

0.13 291 

0. 13 264 

0. 13 238

0. 13 211 

0. 13 185 

0.13 158 

0. 13 132 

0.13106

0.13 079 

0. 13 053 

0. 13 026 

0. 13 000 

0. 12 973

0. 12 947 

0. 12 921 

0. 12 894 

0. 12 868 

0. 12 842

0. 12 815 

0. 12 789 

0.12 762 

0. 12 736 

0. 12 710

0. 12 683 

0. 12 657 

0. 12 631 

0. 12 604 

0. 12 578

0. 12 552 

0. 12 525 

0.12499 

0. 12 473 

0. 12 446

0. 12 420 

0. 12 394 

0. 12 367 

0. 12 341 

0. 12 315

0.12289

L. Tang.

L. Cos.

9. 90 796 

9. 90 787 

9. 90 777 

9. 90 768 

9. 90 759

9. 90 750 

9. 90 741 

9. 90 731 

9. 90 722 

9. 90 713

9. 90 704 

9. 90 694 

9. 90 685 

9. 90 676 

9. 90 667

9.90 657 

9.90648 

9. 90 639 

9. 90 630 

9.90 620

9. 90 611 

9. 90 602 

9. 90 592 

9.90683 

9. 90 574

9.90 56§ 

9. 90 555 

9. 90 546 

9. 90 537 

9. 90 527

9. 90 518 

9. 90 509 

9. 90 499 

9. 90 490 

9.90480

9. 90 471 

9. 90 462 

9. 90 442 

9. 90 443 

9. 90 434

9. 90 424 

9. 90 4li? 

9. 90 405 

9. 90 396 

9. 90 386

9. 90 377 

9. 90 368 

9. 90 358 

9. 90 349 

9. 90 339

9. 90 330 

9. 90 320 

9. 90 311 

9. 90 301 

9. 90 292

9.90282 

9. 90 273 

9. 90 263 

9. 90 254 

9. 90 244

9. 90 235

L. Sin.

d.

9 

10 

9 

9 

9

9 

10 

9 

9 

9

10 

9 

9 

9 

10

9 

9 

9 

10 

9

9 

10 

9 

9 

9

10 

9 

9 

10 

9

9 

10 

9 

10 

9

9 

10 

9 

9 

10

9 

10 

9 

10 

9

9 

10 

9 

10 

9

10 

9 

10 

9 

10

9 

10 

9 

10 

9

d.

GO

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

/

36 0 

56 

52 

48 

44

35 40 

36 

32 

28 

24

35 20 

16 

12 

8 

4

35 0 

56 

52 

48 

44

34 40 

36 

32 

28 

24

34 20 

16 

12 

8 

4

34 0 

56 

52 

48 

44

33 40 

36 

32 

28 

24

33 20 

16 

12 

8 

4

33 0

56 

52 

48 

44

32 40 

36 

32 

28 

24

32 20 

16 

12 

8 

4

32 0

m. s.

53C
208 .GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, ete. Continued. 

2h 370

m. s.

28 0 

4 

8 

12 

16

28 20 

24 

28 

32 

36

28 40 

44 

48 

52 

56

29 0 

4 

8 

12 

16

29 20 

24 

28 

32 

36

29 40 '44 

48 

52 

56

30 0 

4 

8 

12 

16

30 20 

24 

28 

32 

36

30 40 

44 

48 

62 

56

31 0 

4 

8 

12 

16

31 20 

24 

28 

32 

36

31 40 

44 

48 

52 

56

32 0

i

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

80

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

61 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 77 946 

9. 77 963 

9. 77 980 

9. 77 997 

9. 78 013

9. 78 030 

9. 78 047 

9. 78 063 

9.78080 

9. 78 097

9. 78 113 

9.78 130 

9. 78 147 

9. 78 163 

9. 78 180

9. 78 197 

9. 78 213 

9.78 230 

9. 78 24C 

9. 78 263

9. 78 280 

9. 78 296 

9. 78 313 

9. 78 329 

9; 78 346

9. 78 362 

9. 78 379 

9. 78 395 

9. 78 412 

9. 78 428

9. 78 445 

9. 78 461 

9. 78 478 

9. 78 494 

9. 78 510

9. 78 527 

9. 78 543 

9. 78 660 

9. 78 576 

9. 78 592

9. 78 609 

9.78625 

9. 78 642 

9. 78 658 

9. 78 674

9. 78 691 

9. 78 707 

9. 78 723 

9. 78 739 

9.78 756

9. 78 772 

9. 78 788 

9. 78 805 

9. 78 821 

9. 78 837

9. 78 853 

9. 78 869 

9. 78 886 

9. 78 902 

9. 78 918

9. 78 934

L. Cos.

d.

17

17 

17 

16 

17

17 

16 

17 

17 

16

17 

17 

16 

17 

17

16 

17 

16 

17 

17

16 

17 

16 

17 

16

17 

16 

' 17 

16 

17

16 

17 

16 

16 

17

16 

17 

16 

16 

17

16 

17 

16 

16 

17

16 

16 

16 

17 

16

16 

17 

16 

16 

16

16 

 17 

16 

]6 

16

d.

L. Tang.

9. 87 711 

9.87 738 

9. 87 764 

9.87 790 

9. 87 817

9.87843 

9. 87 869 

9. 87 895 

9. 87 922 

9. 87 948

9.87 974 

9.88000 

9.88 027 

9. 88 053 

9.88079

9.88105 

9.88131 

9.88 158 

9.88 184 

9. 88 210

9. 88 236 

.9.88 262 

9. 88 289 

9.88 315 

9. 88 341

9. 88 367 

9. 88 393 

9. 88 420 

9. 88 446 

9. 88 472

9.88498 

9.88524 

9. 88 550 

9. 88 577 

9. 88 603

9. 88 629 

9.88655 

9. 88 681 

9.88 707 

9.88 733

9. 88 759 

9.88786 

9.88812 

9.88 838 

9. 88 864

9. 88 890 

9. 88 916 

9. 88 942 

9. 88 968 

9.88994

9. 89 020 

9.89 046 

9. 89 073 

9. 89 099 

9. 89 125

9. 89 151 

9. 89 177 

9. 89 203 

9. 89 229 

9.89 255

9. 89 281

L. Cotg.

c. d.

27 

26 

26 

27 

26

26 

26 

27 

26 

26

26 

27 

26 

26 

26

26 

27 

26 

26 

26

26 

27 

26 

26 

26

26 

27 

26 

26 

26

26 

26 

27 

26 

26

26 

26 

26 

26 

26

27 

26 

26 

26 

26

26 

26 

26 

26. 

26

26 

27 

26 

26 

26

26 

26 

26 

26 

26

C. d.

L. Cotg.

0. 12 289 

0. 12 262 

0. 12 -236 

0. 12 210 

0.12 183

0.12 157 

0. 12 131 

0. 12 105 

0.12078 

0. 12 052

0. 12 026 

0.12 000 

0.11 973 

0. 11 947 

0. 11 921

0. 11 895 

0. 11 869 

0. 11 842 

0. 11 816 

0.11 790

0. 11 764 

0. 11 738 

0. 11 711 

0. 11 685 

0.11 659

0. 11 633 

0.11 607 

0. 11 580 

0. 11 554 

0. 11 628

0.11 502 

0. 11 476 

0. 11 450 

0.11 423 

0. 11 397

0. 11 371 

0. 11 345 

0. 11 319 

0. 11 293 

.0. 11 267

0. 11 241 

0. 11 214 

0.11 188 

0.11 162 

0.11 136

0.11 110 

0. 11 084 

0. 11 058 

0.11 032 

0. 11 006

0. 10 980 

0. 10 954 

0. 10 927 

0. 10 901 

0. 10 875

0. 10 849 

0. 10 823 

0. 10 797 

0. 10 771 

0.10745

0. 10 719

L. Tang.

L. Cos.

9.90 235 

9.90 225 

9. 90 216 

9.90 206 

9. 90 197

9. 90 187 

9. 90 178 

9.90168 

9. 90 159 

.9.90149

9.90 139 

9. 90 130 

9.90 120 

9. 90 111 

9. 90 101

9.90091 

9.90082 

9.90072 

9.90063 

9.90 053

9. 90 043 

9.90034 

9.90024 

9. 90 014 

9. 90 005

9.89995 

9. 89 985 

9.89 976 

9.89 966 

9. 89 956

9.89 947 

9. 89 937 

9. 89 927 

9.89 918 

9.89 908

9. 89 898 

9.89 888 

9. 89 879 

9.89 869 

9. 89 859

9.89849 

9. 89 840 

9.89 830 

9.89820 

9. 89 810

9. 89 801 

9.89791 

9.89 781 

9.89 771 

9. 89 761

9.89 7{>2 

9. 89 742 

9.89 732 

9.89 722 

9.89 712

9. 89 '702 

9. 89 693 

9. 89 683 

9. 89 673 

9. 89 663

9.89653

L. Sin.

d.

10 

9 

10 

9 

10

9 

10 

9 

10 

10

9 

10 

9 

10 

10

9 

10 

9 

10 

10

9 

10 

10 

9 

10

10 

9 

10 

10 

9

10 

10 

9 

10 

10

10 

9 

10 

10 

10

9 

10 

10 

10 

9

10 

10 

10 

10 

9

10 

10 

10 

10 

10

9 

10 

10 

10 

10

d.

60

59 

58 

57 

56

65 

54 

53 

62 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

i

32 0 

56 

52 

48 . 

44

31 40 

36 

32 

28 

24

31 20 

16 

12 

8 

4

31 0

66 

52 

48 

44

30 40 

36 

32 

28 

24

30 20 

16 

12 

8 

4

30 0 

56 

62 

48 

44

29 40 

36 

32 

28 

24

29 20 

16 

12 

8 

4

29 0 66 

52 

48 

44

28 40 

36 

32 

28 

24

28 20 

16 

12

8 

4

28 0

m. s.

52C
GEOGEAPHIC TABLES AND FOKMULAS. 209 

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

2h 38°

m. s.

32 0 

4 

8 

12 

16

.32 20 

24 

28 

32 

36

32 40 

44 

48 

52 

56

33 0 

4 

8 

12 

16

33 20 

24 

28 

32 

36

33 40 

44 

48 

52 

56

34 0 

4

8 

12 

16

34 20 

24 

28 

32 

36

34 40 

44 

48 

52 

56

35 0 

4 

8 

12 

16

35 20 

24 

28 

32 

36

35 40 

44 

48 

52 

56

36 0

i

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

80

31 

32 

33 

34

35 

36 

37 

38 

89

40

41

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

GO

L. Sin.

9. 78 934 

9. 78 950 

9. 78 967 

9. 78 983 

9. 78 999

9. 79 015 

9. 79 031 

9. 79 047 

9. 79 063 

9. 79 079

9. 79 095 

9. 79 111 

9. 79 128 

9. 79 144 

9. 79 160

9. 79 176 

9.79192 

9. 79 208 

9. 79 224 

9. 79 240

9. 79 256 

9. 79 272 

9. 79 288 

9.79304 

9. 79 319

9. 79 335 

9. 79 351 

9. 79 367 

9. 79 383 

9. 79 399

9. 79 415 

9. 79 431 

9. 79 447 

9. 79 463 

9. 79 478

9. 79 494 

9. 79 610 

9. 79 526 

9. 79 542 

9. 79 558

9. 79 573 

9. 79 589 

9.79 605 

9. 79 621 

9. 79 636

9. 79 652 

9. 79 668 

9. 79 684 

9. 79 699 

9.79 715

9. 79 731 

9. 79 746 

9.79 762 

9. 79 778 

9. 79 793

9. 79 809 

9. 79 825 

9. 79 840 

9. 79 856 

9. 79 872

9.79 887

L. Cos. .

d.

16 

17 

16 

16

16 

16 

16 

16

16 

17 

16 

16

1(5 

16 

16 

16

16 

16 

16 

15

16 

16 

16 

16

16 

16 

16 

15

16 

16 

16 

16

15

16 

16 

16 

15

16 

16 

15 

16

15 

16 

16 

15

16 

15 

16 

16

15

d.

L. Tang.

9. 89 281 

9. 89 307 

9. 89 333 

9. 89 359 

9. 89 385

9. 89 411 

9. 89 437 

9.89 463 

9. 89 489 

9. 89 515

9. 89 541 

9. 89 567 

9.89 593 

9.89 619 

9. 89 645

9. 89 671 

9.89697 

9. 89 723 

9. 89 749 

9. 89 775

9. 89 801 

9.89 827 

9.89 853 

9.89879 

9. 89 905

9. 89 931 

9. 89 .957 

9. 89 983 

9. 90 009 

9. 90 035

9. 90 061 

9. 90 086 

9.90 112 

9.90 138 

9. 90 164

9. 90 190 

9. 90 216 

9. 90 242 

9. 90 268 

9. 90 294

9. 90 320 

9. 90 346 

9. 90 371 

9. 90 397 

9. 90 423

9. 90 449 

9. 90 475 

9. 90 501 

9. 90 527 

9. 90 553

9. 90 578 

9. 90 604 

9. 90 630 

9. 90 656 

9. 90 682

9. 90 708 

9. 90 734 

9.90 759 

9. 90 785 

9. 90 811

9. 90 837

L. Cotg.

c.d.

26 

26 

26 

26

26

26 

26 

26 

26

26

26 

26 

26 

26

26

26 

26 

26 

26

26 

26 

26 

26

26 

26 

26 

26

26

25 

26 

26 

26

26 

26 

26 

26

26

26 

25 

26 

26

26 

26 

26 

26

zO

26 

26 

26 

26

26

26 

25 

26 

26

26

C.d.

L. Cotg.

0.10 719 

0. 10 693 

0. 10 667 

0. 10 641 

0. 10 615

0. 10 589 

0. 10 563 

0. 10 537 

0. 10 511 

0. 10 485

0. 10 459 

0. 10 433 

0. 10 407 

0. 10 381 

0. 10 355

0.10329 

0.10303 

0. 10 277 

0. 10 251 

0. 10 225

0. 10 199 

0. 10 173 

0. 10 147 

0. 10 121 

0. 10 095

0. 10 069 

0. 10 OJ3 

0.10 017 

0. 09 991 

0. 09 965

0. 09 939 

0. 09 914 

0. 09 888 

0. 09 862 

0. 09 836

0. 09 810 

0.09 784 

0.09 758 

0.09 732 

0. 09 706

0.09 680 

0. 09 654 

0. 09 629 

0. 09 603 

0. 09 577

0. 09 551 

0.09 525 

0. 09 499 

0.09 473 

0.09 447

0. 09 422 

0. 09 396 

0.09 370 

0.09 344 

0. 09 318

0. 09 292 

0. 09 266 

0. 09 241 

0. 09 215 

0.09 189

0.09 103

L. Tang.

L. Cos.

9. 89 653 

9. 89 643 

9. 89 633 

9.89 624 

9. 89 614

9. 89 604 

9. 89 594 

9.89 584 

9. 89 574 

9.89 564

9. 89 554 

9.89 544 

9. 89 534 

9. 89 524 

9.89 514

9. 89 504 

9.89 495 

9. 89 485 

9. 89 475 

9. 89 465

9.89455 

9. 89 445 

9. 89 435 

9. 89 425 

9. 89 415

9. 89 405 

9. 89 395 

9.89 385 

9. 89 375 

9.89 364

9.89 354 

9. 89 344 

9.89 334 

9. 89 324 

9.89 314

9. 89 304 

9. 89 294 

9. 89 284 

9. 89 274 

9. 89 264

9. 89 254 

9.89 244 

9. 89 233 

9. 89 223 

9. 89 21 3

9.89 203 

9.89 193 

9. 89 183 

9.89 173 

9. 89 162

9.89 152 

9.89 142 

9.89 132 

9. 89 122 

9.89 112

9.89 101 

9. 89 091 

9. 89 081 

9. 89 071 

9. 89 060

9. 89 050

L. Sin.

d.

10 

10 

9 

10

10

10 

10 

10 

10

10

10 

10 

10 

10

10

9 

10 

10 

10

10

10 

10 

10 

10

10

10 

10 

1011

10

10 

10 

10 

10

10

10 

10 

10 

10

10 

1011

10 

10

10

10 

10 

1011

10

10 

10 

10 

1011

10 

10 

1011

10

d.

CO

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

/

28 0 

56 

52 

48 

44

27 40 

36 

32 

28 

24

27 20 

16 

12 

8 

4

27 0 

56 

52 

48 

44

26 40 

36 

32 

28 

24

26 20 

16 

12 

8 

4

26 0 

56 

52 

48 

44

25 40 

36 

32 

28 

24

25 20 

16 

12 

8 

4

25 0 

56 

52 

43 

44

24 40 

36 

32 

28 

24

24 20 

16 

12 

8 

4

24 0

m. s.

41623° 1

51°
210 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued.

2h 39°

m. s.

36 0 

4 

8 

12 

16

36 20 

24 

28 

32 

36

36 40 

44 

48 

52 

56

37 0 

4 

8 

12 

16

37 20 

24 

28 

32 

36

37 40 

44 

48 

52 

56

38 0 

4 

8 

12 

16

38 20 

24 

28 

32 

36

38 40 

44 

48 

52 

56

39 0 

4 

8 

12 

16

39 20 

24 

28 

32 

36

39 40 

44 

48 

52 

56

40 0

i

0 

1

2 

3

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56. 

57 

58 

59

60

L. Sin.

9. 79 887 

9. 79 903 

9. 79 918 

9. 79 934 

9. 79 950

9. 79 965 

9. 79 981 

9. 79 996 

9. 80 012 

9. 80 027

9.80043 

9. 80 058 

9. 80 074 

9.80 089 

9. 80 105

9. 80 120 

9. 80 136 

9. 80 151 

9.80 166 

9. 80 182

9. 80 197 

9.80213 

9. 80 228 

9. 80 244 

9. 80 259

9. 80 274 

9. 80 290 

9. 80 305 

9. 80 320 

9. 80 336

9. 80 351 

9. 80 366 

9. 80 382 

9. 80 397 

9. 80 412

9. 80 428 

9. 80 443 

9. 80 458 

9. 80 473 

9.80489

9. 80 504 

9.80 519 

9. 80 534 

9. 80 550 

9.80 565

9. 80 580 

9. 80 595 

9. 80 610 

9. 80 625 

9. 80 641

9. 80 656 

9. 80 671 

9. 80 686 

9.80 701 

9.80 716

9. 80 731 

9. 80 746 

9. 80 762 

9.80 777 

9. 80 792

9. 80 807

L. Cos.

d.

16 

15 

16 

16

16 

15 

16 

15

1.0 

16 

15 

16

15

16 

15 

15 

16

-Li)

16 

15 

16 

15

15.

16 

15 

15 

16

15

15 

16 

15 

15

15 

15 

15 

16

15

15 

15 

16 

15

J.O

15 

15 

15 

16

15

15 

15 

15 

15

15

15 

16 

15 

15

15

d.

L. Tang.

9.90 837 

9. 90 863 

9. 90 889 

9. 90 914 

9. 90 940

9. 90 966 

9. 90 992 

9. 91 018 

9. 91 043 

9.91069

9. 91 095 

9. 91 121 

9.91 147 

9.91 172 

9. 91 198

9. 91 224 

9.91 250 

9.91 276 

9.91 301 

9. 91 327

9.91 353 

9.91 379 

9. 91 404 

9.91 430 

9,91 456

9. 91 482 

9. 91 507 

9. 91 533 

9.91 559 

9.91 685

9. 91 610 

9.91 636 

9.91 662 

9. 91 688 

9.91 713

9. 91 739 

9.91 765 

9.91 791 

9.91 816 

9. 91 842

9. 91 868 

9.91 893 

9.91 919 

9.91 945 

9. 91 971

9. 91 996 

9. 92 022 

9. 92 048 

9. 92 073 

9. 92 099

9. 92 125 

9. 92 150 

9. 92 176 

9. 92 202 

9. 92 227

9. 92 253 

9. 92 279 

9. 92 304 

9. 92 330 

9.92 356

9. 92 381

L. Cotg.

C. d.

26 

26 

25 

26

26

26 

26 

25 

26

Ofi

26 

26 

25 

26

26

26 

26 

25 

26

26

26 

25 

26 

26

26

25 

26 

2ti 

26

26 

26 

26 

25

26

26 

26 

25 

26

25 

26 

26 

26

25

26 

26 

25 

26

26

25 

26 

26 

25 

oc

26 

25 

26 

26

c. d.

L. Cotg.

0.09 163 

0. 09 137 

0. 09 111 

0. 09 086 

0.09 060

0.09034 

0. 09 008 

0.08 982 

0. 08 957 

0. 08 931

0. 08 90S 

0. 08 879 

0.08 853 

0. 08 828 

0.08802

0. 08 776 

0.08 750 

0. 08 724 

0.08 699 

0. 08 673

0. 08 647 

0. 08 621 

0. 08 596 

0. 08 570 

0. 08 644

0. 08 518 

0. 08 493 

0. 08 467 

0. 08 441 

0.08 415

0. 08 390 

0. 08 364 

0. 08 338 

0. 08 312 

0. 08 287

0.08261 

0. 08 235 

0. 08 209 

0. 08 184 

0.08 158

0.08132 

0.08107 

0.08 081 

0. 08 055 ' 

0. 08 029

0. 08 004 

0. 07 978 

0.07 952 

0. 07 927 

0. 07 901

0.07 875 

0.07 850 

0.07 824 

0. 07 798 

0. 07 773

0.07 747 

0. 07 721 

0. 07 696 

0. 07 670 

0. 07 644

0.07 619

L. Tang.

L. Cos.

9. 89 050 

9.89 040 

9. 89 030 

9. 89 020 

9.89 009

9. 88 999 

9.88 989 

9. 88 978 

9. 88 968 

9.88958

9. 88 948 

9.88 937 

9.88 927 

9. 88 917 

9. 83 906

9.88 896 

9.88 886 

9. 88 875 

9. 88 865 

9. 88 855

9.88 844 

9. 88 834 

9. 88 824 

9. 88 813 

9. 88 803

9. 88 793 

9.88 782 

9.88 772 

9.88 761 

9. 88 751

9. 88 741 

9.88 730 

9.88 720 

9. 88 709 

9. 88 699

9.88 688 

9.88 678 

9. 88 668 

9. 88 657 

9.88 647

9.88636 

9.88 626 

9.88 615 

9.88 605 

9.88 594

9.88 584 

9. 88 573 

9. 88 563 

9. 88 552 

9.88 542

9. 88 531 

9. 88 521 

9. 88 510 

9.88 499 

9.88 489

9. 88 478 

9. 88 468 

9.88 457 

9. 88 447 

9. 88 436

9. 88 425

L. Sin.

d.

10 

10 

10 

11

10

10 

11 

10 

10

10

11 

10 

10 

11

10

10 

11 

10 

10

11

10 

10 

11 

10

10

11

1011

10

10

11

1011

1011

10 

1011

1011

10

11 

1011

10

11

1011

1011

1011 11

1011

1011

101111

d.

CO

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

i

24 0 

56 

52 

48 

44

23 40 

36 

32 

28 

24

23 20 

16 

12 

8 

4

23 0 

56 

52 

48 

44

22 40 

36 

32 

28 

24 .

22 20 

16 

12 

8 

4

22 0 

56 

52 

48 

44

21 40 

36 

32

28 

24

21 20 

16 

128' 

4

21 0 

56 

52 

48 

44

20 40 

36 

32 

28 

24

20 20 

16 

12 

8 

4

20 0

m. s.

50°
GEOGEAPHIC TABLES AND FOEMULAS. 211

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

2h 40°

m. s.

40 0 

4 

8 

12 

16

40 20 

24 

28 

32 

36

40 40 

44 

48 

52 

56

41 0 

4 

8 

12 

16

41 20 

24 

28 

32 

36

41 40 

44 

48 

52 

66

42 0 

4 

8 

12 

16

42 20 

24 

28 

32 

36

42 40 

44

48 

52 

56

43 0 

4 

8 

12 

16

43 20 

24 

23 

32 

36

43 40 

44 

48 

52 

56

44 0

'

0

1 

2 

3 

4

6 

6 

7 

8 

9

JO

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

80

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53

54

55 

56 

57 

58 

59

60

L. Sin.

9. 80 807 

9. 80 822 

9. 80 837 

9. 80 852 

9. 80 867

9. 80 882 

9. 80 897 

9. 80 912 

9. 80 927 

9/80 942

9.80 957 

9. 80 972 

9. 80 987 

9. 81 002 

9. 81 017

9. 81 032 

9.81 047 

9. 81 061 

9.81 076 

9.81 091

9. 81 106 

9.81 121 

9.81 136 

9.81 151 

9.81 166

9.81 180 

9.81 195 

9. 81 210 

9.81 225 

9. 81 240

9. 81 254 

9. 81 269 

9. 81 284 

9.8.1 299 

9. 81 314

9. 81 328 

9.81 343 

9.81358 

9.81 372 

9. 81 387

9. 81 402 

9.81 417 

9. 81 431" 

9. 81 446 

9.81 461

9.81 475 

9.81 490 

9. 81 505 

9. 81 519 

9. 81 534

9.81 549 

9. 81 563 

9. 81 578 

9. 81 592 

9. 81 607

9.81 622 

9.81 636 

9.81 651 

9.81 665 

9.81 680

9.81 694

L. Cos.

. d.

"15 

15 

15 

15 

15

15 

15 

15 

15 

15

15 

15 

15 

15 

15

15 

14 

15 

15 

15

15 

15 

15 

15 

14

15 

15 

15 

15 

14

15 

15 

15 

15 

14

15 

15 

14 

15 

15

15 

14 

15 

15 

14

15 

15 

14 

15 

15

14 

15 

14 

15 

15

14 

15 

14 

15 

14

d.

. L. Tang.

9.92 381 

9.92407 

9. 92 433 

9. 92 458 

9. 92 484

9.92 510 

9. 92 535 

9. 92 561 

9. 92 587 

9. 92 612

9. 92 638 

9.92 663 

9. 92 689 

9.92 715 

9.92 740

9. 92 766 

9.92 792 

9.92 817 

9.92 843 

9.92 868

9.92894 

9. 92 92Q 

9. 92 945 

9. 92 971 

9.92 996

9.93 022 

9. 93 048 

9. 93 073 

9. 93 099 

9. 93 124

9. 93 150 

9.93 175 

9. 93 201 

9. 93 227 

9. 93 252

9. 93 278 

9. 93 303 

9. 93 329 

9. 93 354 

9. 93 380

9. 93 406 

9. 93 431 

9. 93 457 

9. 93 482 

9. 93 508

9. 93 533 

9. 93 559 

9.93 584 

9.93 610 

9.93 636

9. 93 661 

9.93 687 

9. 93 712 

9.93 738 

9. 93 763

9. 93 789 

9. 93 814 

9. 93 840 

9. 93 865 

9. 93 891

9. 93 916

L. Cotg.

C. d.

26 

26 

25 

26 

26

25 

26 

26 

25 

26

25 

26 

26 

25 

26

26 

25 

26 

25 

26

26 

25 

26 

25 

26

26 

25 

26 

25 

26

25 

.26 

26 

25 

26

25 

26 

25 

26 

26

25 

26 

25 

26 

25

26 

25 

26 

26 

25

26 

25 

26 

25 

26

25 

26 

25 

26 

25

c. d.

L. Cotg.

0. 07 619 

0. 07 593 

0. 07 567 

0.07 542 

0.07 516

0. 07 490 

0. 07 465 

0. 07 439 

0. 07 413 

0. 07 388

0. 07 362 

0.07 337 

0. 07 311 

0.07 2S5 

0. 07 260

0.07 234 

0.07208 

0. 07 183 

0.07 157 

0. 07 132

0.07 106 

0. 07 080 

0. 07 055 

0.07 029 

0. 07 004

0. 06 978 

0.06 952 

0. 06 927 

0. 06 901 

0. 06 876

0.06 850 

0. 06 825 

0. 06 799 

0.06 773 

0. 06 748

0.06 722 

0.06 697 

0.06 671 

0. 06 646 

0. 06 620

0.06 594 

0.06 569 

0.06 543 

0.06 518 

0. 06 492

0. 06 467 

0.06 441 

0. 06 416 

0.06 390 

0. 06 364

0.06 339 

0. 06 313 

0. 06 288 

0. 06 262 

0. 06 237

0. 06 211 

0.06 186 

0. 06 160 

0. 06 135 

0.06 109

C. 06 084

L. Tang.

. L. Cos.

9. 88 425 

9. 88 415 

9. 88 404 

9. 88 394 

9.88 383

9. 88 372 

9. 88 362 

9. 88 351 

9. 88 340 

9. 88 330

9. 88 319 

9.88 308 

9. 88 298 

9. 88 287 

9. 88 276

9.88266 

9.88255 

9. 88 244 

9. 88 234 

9. 88 223

9.88 212 

9. 88 201 

'9.88 191 

9.88 180 

9.88 169

9.88 158 

9.88 148 

9.88 137 

9.88 126 

9.88 115

9.88 105 

9. 88 094 

9. 88 083 

9.88072 

9. 88 061

9. 88 051 

9.88 040 

9. 88 029 

9. 88 018 

9.88007

9. 87 996 

9.87 985 

9.87 975 

9.87 964 

9. 87 953

9.87 942 

9- 87 931 

9.87 920 

9.87 909 

9. 87 898

9. 87 887 

9. 87 877 

9.87 866 

9.87 855 

9.87 844

9. 87 833 

9. 87 822 

9. 87 811 

9.87 800 

9.87 789

9.87 778

L. Sin.

d.

10 

11 

10 

11 

11

.10 

11 

11 

10 

11

11 

10 

11 

11 

10

11 

11 

10 

11 

11

11 

10 

11 

11 

11

10 

11 

11 

11 

10

11 

11 

11 

11 

10

11 

11 

11 

11 

11

11 

1011 11 11

11 11 11 11 11

1011 11 11 11

11 11 11 1111

d.

(10

59

58 

57 

56

55 

54 

63 

52 

61

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9 

8 

7 

6

5 

4 

3 

2 

1

0

'

20 0 

. 56 

52 

48 

44

19 40 

36 

32 

28 

24

19 20 

16 

12 

8 

4

19 0 

66

. 52 

48 

44

18 40 

36 

32 

28 

24

18 20 

16 

12 

8 

4

18 0 

56 

52 

48 

44

17 40 

36 

32 

28 

24

17 20 

16

12 

8 

4

17 0 

56 

52 

48 

44

16 40 

36 

32 

28 

24

16 20 

16 

12 

8 

4

16 0

111. S

49°
212 GEOGEAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

2h 41°

m. s.

44 0 

. 4 

8 

12 

16

44 20 

24 

28 

32 

36

44 40 

44 

48 

52 

66

45 0 

4 

8 

12 

16

45 20 

24 

28 

32 

36

45 40 

44 

48 

52 

56

46 0 

4 

8 

12 

16

46 20 

24 

28 

32 

36

46 40 

44 

48 

52 

56

47 0 

4 

 8 

12 

16

47 20 

24 

28 

32 

36

47 40 

44 

48 

52 

56

48 .0

'

0

1 

2 

3 

4

5 

'7 6 

8 

9

10

31 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

61 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9. 81 694 

9.81 709 

9.81 723 

9.81 738 

9. 81 752

9.81 767 

9.81 781 

9.81 796 

9. 81 810 

9. 81 825

9. 81 839 

9.81 854 

9.81 868 

- 9. 81 882 

9. 81 897

9.81 911 

9.81 926 

9. 81 940 

9. 81 955 

9.81 969

9.81 983 

9.81 998 

9. 82 012 

9. 82 026 

9. 82 041

9. 82 055 

9. 82 069 

9. 82 084 

9. 82 098 

9. 82 112

9.82 126 

9. 82 141 

9.82 155 

9.82 169 

9. 82 184

9.82 198 

9. 82 212 

9. 82 226 

9. 82 240 

9.82 255

9.82 269 

9.82283 

9. 82 297 

9. 82 311 

9.82 326

9.82 340 

9.82 354 

9.82 368 

9. 82 382 

9.82 396

9. 82 410 

9.82 424 

9. 82 439 

9. 82 453 

9. 82 467

9. 82 481 

9. 82 495 

9. 82 509 

9.82523 

9. 82 537

9.82 551

L. Cos.

d.

15 

14 

15 

14 

15

14 

15 

14 

15 

14

15 

14 

14 

15 

14

15 

14 

15 

14 

14

15 

14 

14 

15 

14

14 

15 

14 

14 

14

15 

3.4 

14 

15 

14

14 

14 

14 

15 

14

14 

14 

'15 14 

14

14 

14 

14 

14 

14

14 

15 

14 

14 

14

14 

14 

34 

14 

14

d.

L. Tang.

9.93 916 

9. 93 942 

9. 93 967 

9. 93 993 

9. 94 018

9. 94 044 

9. 94 069 

9. 94 095 

9. 94 120 

9. 94 146

9. 94 171 

9. 94 197 

9. 94 222 

9. 94 248 

9. 94 273

9. 94 299 

9. 94 324 

9. 94 350 

9. 94 375 

9. 94 401

9. 94 426 

9. 94 452 

9. 94 477 

9.94 503 

9. 94 528

9. 94 551 

9. 94 579 

9.94 604 

9. 94 630 

9. 94 655

9. 94 681 

9. 94 706 

9. 94 732 

9. 94 757 

9. 94 783

9. 94 808 

9.94834 

9.94 859 

9. 94 884 

9.94 910

9. 94 935 

9.94961 

9.94 986 

9. 95 012 

9.95 037

9. 95 062 

9. 95 088 

9. 95 113 

9.95 139 

9. 95 164

9. 95 190 

9. 95 215 

9. 95 240 

9. 95 266 

9. 95 291

9. 95 317 

9. 95 342 

9. 95 368 

9. 95 393 

9. 95 418

9. 95 444

L. Cotg.

c.d.

26 

25 

26 

25 

 26

25 

26 

25 

26 

25

26 

25 

26 

25 

26

25 

26 

25 

26 

25

26 

25 

26 

25 

26

25 

25 

26 

25 

26

25 

26 

25 

26 

25

26 

25 

25 

26 

25

26 

25 

26 

25 

25

26 

25 

26 

25 

26

25 

25 

26 

25 

26

25 

26 

25 

25 

26

c.d.

L. Cotg.

0. 06 084 

0.06 058 

'0. 06 033 

0.06 007 

0. 05 982

0.05 956 

0. 05 931 

0. 05 905 

0.05880 

0. 05 854

0. 05 829 

0. 05 803 

0.05 778 

0. 05 752 

0.05 727.

0. 05 701 

0.05 676 

0. 05 650 

0.05 625 

0. 05 599

0.05 574 

0. 05 548 

0. 05 523 

0.05497 

0. 05 472

0. 05 446 

0. 05 421 

0. 05 396 

0. 05 370 

0. 05 345

0.05 319 

0. 05 294 

0. 05 268 

0. 05 243 

0. 05 217

0. 05 192 

0. 05 166 

0. 05 141 

0.05 116 

0. 05 090

0. 05 065 

0.05039 

0. 05 014 

0. 04 988 

0.04 963

0.04 938 

0.04 912 

0.04 887 

0. 04 861 

0. 04 836

0. 04 810 

0. 04 785 

0.04 760 

0. 04 734 

0. 04 709

0.04 683 

0. 04 658 

0. 04 632 

0. 04 607 

0. 04 582

0. 04 556

L. Tang.

L. Cos.

9.87 778 

9.87 767 

9.87 756 

9. 87 745 

9.87734

9.87 723 

9. 87 712 

9.87 701 

9. 87 690 

9. 87 679

9. 87 668 

9.87 657 

9. 87 646 

9.87 635 

9. 87 624

9. 87 613 

9. 87 601 

9. 87 590 

9.87 579 

9.87 568

9.87 557 

9. 87 546 

9.87 535 

9. 87 524 

9.87513

9. 87 501 

9. 87 490 

9. 87 479 

9.87 468 

9. 87 457

9.87 446 

9. 87 434 

9. 87 423 

9. 87 412 

9.87 401

9.87 390 

9. 87 378 

9. 87 367 

9.87 356 

9.87 345

9.87 334 

9.87322 

9.87 311 

9. S7 300 

9. 87 288

9.87 277 

9. 87 266 

9.87 255 

9.87 243 

9. 87 232

9. 87 221 

9.87 209 

9. 87 198 

9.87 387 

9.87 175

9.87 164 

9.87 153 

9.87 141 

9.87 130 

9.87 119

9.87 107

L. Sin.

d.

11 

11 

11 

11 

11

11 

11 

11 

11 

11

11 

11 

11 

11 

11

12 

11 

11 

11 

11

11 

11 

11 

11 

12

11 

11 

11 

11 

11

12 

11 

11 

11 

11

12 

11 

11 

11 

11

12 

11 

11 

12

11

11 

11 

12 

11 

11

12 

11 

11 

12 

11

11 

12 

.11 

11 

12

d.

60

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

'

16 0 

56 

52 

48 

44

15 40 

36 

32 

28 

24

15 20 

16 

12

8 

4

15 0 

56 

52 

48 

44

14 40 

36 

32 

28 

24

14 20 

16 

12 

8 

4

14 0 

56 

52 

48 

44

13 40 

36 

32

28 

24

13 20 

16 

12 

8 

4

13 0 

56 

52 

48 

44

12 40 

36 

32 

28 

24

12 20 

16 

12 

8 

4

12 0

m. s.

48C
GEOGRAPHIC TABLES AND FORMULAS. 213 

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

2h 42°

m. s.

48 0 

4 

8 

12 

16

48 20 

24 

28 

32 

36

48 40 

44 

48 

52 

56

49 0 

4 

8 

12 

16

49 20 

24 

28 

32 

36

49 40 

44 

48 

52 

56

50 0 

4 

8 

12 

16

50 20 

24 

28 

32 

36

50 40 

44 

48 

52 

56

51 0 

4 

8 

12 

16

61 20 

24 

28 

32 

36

51 40 

44 

48 

52 

56

52 0

'

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

66 

57 

68 

59

60

L. Sin.

9.82 551 

9.82 565 

9. 82 579 

9. 82 593 

9. 82 607

9. 82 621 

9. 82 635 

9.82 649 

9. 82 663 

9. 82 677

9. 82 691 

9. 82 705 

9. 82 719 

9. 82 733 

9. 82 747

9. 82 761 

9.82 775 

9. 82 788 

9. 82 802 

9. 82 816

9.82 830 

9. 82 844 

9.82 858 

9.82 872 

8. 82 885

9.82 899 

9.82 913 

9. 82 927 

9. 82 941 

9.82 955

9. 82 968 

9. 82 982 

9. 82 996 

9. 83 010 

9. 83 023

9.83 037 

9. 83 051 

9.83 065 

9. 83 078 

9. 83 092

9. 83 106 

9. 83 120 

9.83 133 

9.83 147 

9.83 161

9. 83 174 

9. 83 188 

9. 83 202 

9. 83 215 

9. 83 229

9. 83 242 

9. 83 256 

9. 83 270 

9. 83 283 

9. 83 297

9.83 310 

9. 83 324 

9. 83 338 

9. 83 351 

9. 83 365

9. 83 378

L. Cos.

d.

14 

14 

14 

14 

14

14 

14 

14 

14 

14

14 

14 

14 

14 

14

14 

13 

14 

14 

14

14 

14 

14 

13 

14

14 

14 

14 

14 

13

14 

14 

14 

13 

14

14 

14 

13 

14 

14

14 

13 

14 

14 

13

14 

14 

13 

14 

13

14 

14 

13 

14-1Q

14 

14 

13 

14 

11

d.

L. Tang.

9. 95 444 

9. 95 469 

9. 95 495 

9. 95 520 

9.95 645

9. 95 571 

9. 95 596 

9. 95 622 

9. 95 647 

9. 95 672

9. 95 698 

9. 95 723 

9. 95 748 

9. 95 774 

9. 95 799

9. 95 825 

9.95850 

9.95875 

9. 95 901 

9. 95 926

9. 95 952 

9. 95 977 

9. 96 002 

9. 96 028 

9. 96 053

9. 96 078 

9. 96 104 

9. 96 129 

9.96 155 

9. 96 180

9. 96 205 

9. 96 231 

9.96 256 

9. 96 281 

9. 96 307

9. 96 332 

9. 96 357 

9.96 383 

9. 96 408 

9. 96 433

9. 96 459 

9. 96 484 

9.96 510 

9.96 535 

9.96 560

9. 96 586 

9. 96 611 

9. 96 636 

9. 96 662 

9. 96 687

9.96 712 

9. 96 738 

9. 96 763 

9. 96 788 

9. 96 814

9. 96 839 

9. 96 864 

9. 96 890 

9. 96 915 

9. 96 940

9. 96 966

L. Cotg.

c. d.

25 

26 

25 

25 

26

25 

26 

25 

25 

26

25 

25 

26 

25 

26

25 

25 

26 

25 

26

25 

25 

26 

25 

25

26 

25 

26 

25 

25

26 

25 

25 

26 

25

25 

26 

25 

25 

26

25 

26 

25 

25 

26

25 

25 

26 

25 

25

26 

25 

25 

26 

25

25 

26 

25 

25 

26

c. d.

L. Cotg.

0. 04 55G 

0. 04 531 

0. 04 505 

0. 04 480 

0. 04 455

0. 04 429 

0. 04 404 

0. 04 378 

0. 04 353 

0. 04 328

0. 04 302 

0. 04 277 

0.04 252 

0. 04 226 

0.04201

0. 04 175 

0. 04 150 

0.04125 

0. 04 099 

0.04 074

0. 04 048 

0. 04 023 

0.03 998 

0.03 972 

0. 03 947

0. 03 922 

0. 03 896 

0. 03 871 

0.03845 

0. 03 820

0. 03 795 

0. 03 769 

0. 03 744 

0. 03 719 

0. 03 693

0. 03 668 

0. 03 643 

0.03 617 

0. 03 592 

0. 03 567

0. 03 541 

0.03 516 

0. 03 490 

0. 03 465 

0. 03 440

0.03 414 

0.03 389 

0. 03 364 

0. 03 338 

0. 03 313

0. 03 288 

0. 03 262 

0. 03 237 

0. 03 212 

0. 03 186

0. 03 161 

0. 03 136 

0. 03 110 

0. 03 085 

0. 03 060

0. 03 034

L. Tang.

L. Cos.

9.87 107 

9. 87 096 

9.87 085 

9. 87 073 

9. 87 062

9. 87 050 

9.87 039 

9. 87 028 

9. 87 016 

9.87 005

9. 86 993 

9. 86 982 

9.86 970 

9.86 959 

9. 86 947

9. 86 936 

9. 86 924 

9.86913 

9.86 902 

9. 80 890

9. 86 879 

9. 86 867 

9. 86 855 

9. 86 844 

9.86 832

9. 86 821 

9. 86 809 

9. 86 798 

9. 86 786 

9.86 775

9. 86 763 

9. 86 762 

9. 86 740 

9. 86 728 

9.86 717

9. 86 705 

9.86 694 

9. 86 682 

9. 86 670 

9. 86 659

9. 86 647 

9. 86 635 

9. 86 624 

9.86 612 

9.86 600

9. 86 589 

9. 86 577 

9. 86 565 

9. 80 554 

9. 86 542

9.86 530 

9. 86 518 

9. 86 507 

9. 86 495 

9.86 483

9. 86 472 

9.86 460 

9.86 448 

9.86 436 

9. 86 425

9. 86 413

L.Sin.

d.

11 

11 

12 

11 

1?

11 

11 

12 

11 

1?,

11

12 

11 

12- 

11

12 

11 

11 

12 

11

12 

12 

11 

12 

11

12 

11 

12 

11 

1?

11 

12 

12 

11 

1?

11 

12 

12 

11 

1?

12 

11 

12 

12 

11

12 

12 

11 

12 

12

12 

11 

12 

12 

11

12

12 

12 

11

d.

GO

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

80

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

16 

14 

13 

12 

11

10

9 

8 

7 

6

6 

4 

3 

2 

I

0

i

12 0 

56 

52 

48 

44

11 40 

36 

32 

28 

24

11 20 

16 

12 

8 

4

11 0 

56 

52 

48 

44

10 40 

36 

32 

28 

24

10 20 

16 

12

8 

4

10 0 

56 

52 

48 

44

9 40 

36 

32 

28 

24

9 20 

16 

12 

8 

4

9 0 

56 

52 

48 

44

8 40 

36 

32 

28 

24

8 20 

16 

12

8 

4

8 0

m. s.

47c
214 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

2h 43°

m. s.

52 0 

4 

8 

12 

16

52 20 

24 

28 

32 

36

52 40 

44 

48 

52 

56

53 0 

4 

8 

12 

16

53 20 

24 

28 

32 

36

53 40 

44 

48 

52 

56

64. 0 

4 

8 

12 

16

54 20 

24 

28 

32 

36

54 40 

44 

48 

52 

56

55 0 

4 

8 

12 

16

55 20 

24 

28 

32 

36

55 40 

44 

48 

52 

56

56 0

/

0

1 

2 

3 

4

5 

6 

7 

8 

9

10

11 

12 

13 

14

15 

16 

17 

18 

19

20

21 

22 

23 

24

25 

26

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50 ' 

51 

52 

53 

54

55 

56 

57 

58 

59

60

L. Sin.

9.83 378 

9. 83 392 

9.83 405 

9. 83 419 

9. 83 432

9.83 446 

9. 83 459 

9. 83 473 

9. 83 486 

9.83500

9.83 513 

9.83 527 

9.83 540 

9. 83 554 

9.83 567

9. 83 581 

9. 83 594 

9.83 608 

9.83 621 

9.83 634

9. 83 648 

9. 83 661 

9. 83 674 

9.83 688 

9. 83 701

9. 83 715 

9. 83 728 

9.83 741 

9.83 755 

9. 83 768

9.83 781 

9. 83 795 

9. 83 808 

9. 83 821 

9.83 834

9. 83 848 

9. 83 861 

9. 83 874 

9. 83 887 

9. 83 901

9.83 914 

9. 83 927 

9.83940 

9. 83 954 

9.83 967

9.83 980 

9.83 993 

9.84 006 

9. 84 020 

9.84 033

9. 84 046 

9. 84 059 

9. 84 072 

9.84 085 

9. 84 098

9.84 112 

9.84 125 

9.84 138 

9.84 151 

9.84 164

9.84 177

L. Cos.

d.

14 

13 

14 

13 

14

13 

14 

13 

14

10

14 

13 

14 

13 

14

13 

14 

13 

13 

14

13 

13 

14 

13 

14

13 

13 

14 

13 

13

14 

13 

13 

13 

14

13 

13 

13 

14 

13

13 

13 

14 

13 

13

13 

13 

14 

13 

13

13 

13 

13 

13 

14

13 

13 

13 

13 

13

d.

L. Tang.

9. 96 966 

9. 96 991 

9. 97 016 

9. 97 042 

9. 97 067

9. 97 092 

9. 97 118 

9. 97 143 

9.97 168 

9.97 193

9.97 219 

9. 97 244 

9.97 269 

9.97 295 

9.97 320

9.97 345 

9. 97 371 

9. 97 396 

9. 97 421 

9. 97 447

9. 97 472 

9. 97 497 

9. 97 523 

9. 97 548 

9. 97 573

9. 97 598 

9.97 624 

9.97 649 

9.97 674 

9. 97 700

9. 97 725 

9.97 750 

9.97 776 

9. 97 801 

9. 97 826

9. 97 851 

9. 97 877 

9.97 902 

9. 97 927 

9. 97 953

9. 97 978 

9.98 003 

9.98029 

9. 98 054 

9. 98 079

9. 98 104 

9. 98 130 

9. 98 155 

9. 98 180 

9.98 206

9. 98 231 

9. 98 256 

9. 98 281 

9. 98 307 

9. 98 332

9.98 357 

9. 98 383 

9. 98 408 

9. 98 433 

9. 98 458

9.98484

L. Cotg.

C. d.

25 

25 

26 

25

91

26 

25 

25 

25 

26

25 

25 

26 

25 

25

26 

25 

25 

26 

25

26 

26 

25 

25 

25

26 

25 

25 

26 

25

25 

26 

25 

25 

25

26 

25 

25 

26 

25

25 

26 

25 

25 

25

26 

25 

25 

26 

25

25 

25 

26 

25 

25

26 

25 

25 

25 

26

c. d.

L. Cotg.

0. 03 034 

0. 03 009 

0.02 984 

0.02 958 

0.02 933

0.02 908 

0.02 882 

0. 02 857 

0.02 832 

0. 02 807

0. 02 781 

0.02 756 

0.02 731 

0.02 705 

0.02 680

0.02 655 

0.02 629 

0.02 604 

0.02 579 

0. 02 553

0. 02 528 

0. 02 503 

0.02 477 

0.02 452 

0. 02 427

0. 02 402 

0. 02 376 

0.02 351 

0. 02 326 

0. 02 300

0. 02 275 

0. 02 250 

0. 02 224 

0.02 199' 

0. 02 174

0. 02 149 

0. 02 123 

0. 02 098 

0. 02 073 

0. 02 047

0.02 022 

0. 01 997 

0.01971 

0. 01 946 

0.01 921

0.01 896 

0.01 870 

0. 01 845 

0. 01 820 

0. 01 794

0.01 769 

0. 01 744 

0.01 719 

0. 01 693 

0. 01 668

0. 01 643 

0.01 617 

0. 01 592 

0. 01 567 

0. 01 542

0. 01 516

L. Tang.

L. Cos.

9. 86 413 

9. 86 401 

9.86389 

9. 86 377 

9. 86 366

9.86 354 

9. 86 342 

9.86 330 

9. 86 318 

9.86 306

9.86 295 

9.86 283 

9. 86 271 

9. 86 259 

9.86 247

9.86 235 

9.86 223 

9.86 211 

9.86 200 

9. 86 188

9.86 176 

9. 86 164 

9.86 152 

9.86 140 

9. 86 128

9.86 116 

9.86 104 

9.86 092 

9. 86 080 

9. 86 068

9. 86 056 

9.86 044 

9. 86 032 

9. 86 020 

9.86 008

9. 85 996 

9. 85 984 

9.85 972 

9. 85 960 

9. 85 948

9. 85 936 

9.85 924 

9.85912 

9. 85 900 

9. 85 888

9. 85 876 

9. 85 864 

9. 85 851 

9. 85 839 

9.85 827

9. 85 815 

9. 85 803 

9. 85 791 

9.85779 

9.85 766

9. 85 754 

9. 85 742 

9. 85 730 

9. 85 718 

9.85 706

9. 85 693

L. Sin.

d.

12 

12 

12 

11 

12

12 

12 

12 

12 

11

12 12' 

12 

12 

12

12 

12 

11 

12 

1?,

12 

12 

12 

12 

19

12 

12 

12 

12 

12

12 

12 

12 

12 

1?,

12 

12 

12 

12 

1?,

12 

12 

12 

12 

1?

12 

13 

12 

12 

1?

12 

12 

12 

13 

1?

12 

12 

12 

12 

13

d.

f.O

59 

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2 

1

0

/

8 0 

56 

52 

48 

44

7 40 

36 

32 

28 

24

7 20 

16 

12 

8 

4

7 0 

56 

62 

48 

44

6 40 

36 

32

28 

24

6 20 

16 

12 

8 

.4

6 0 

56 

52 

48 

44

5 40 

36 

32

28 

24

5 20 

16 

12 

8 

4

5 0 

56 

52 

48 

44

4 40 

36 

32 

28 

24

4 20 

16 

12 

8 

4

4 0

m. s.

46C
GEOGRAPHIC TABLES AND FOEMULAS. 215

TABLE 27. Five-place logarithms of circular functions, etc. Continued. 

2h 44°

m. s.

56 0 

4 

8 

12 

16

56 20 

24 

28 

32 

36

56 40 

44 

48 

52 

56

57 0 

4 

8 

12 

16

57 20 

24 

. 28 

32 

36

57 40 

44 

48 

52 

56

58 0 

4 

8 

12 

16

58 20 

24 

28 

32 

36

58 40 

44 

48 

52 

56

69- 0 

4 

8 

12 

16

59 20 

24 

28 

32 

36

59 40 

44 

48 

52 

56

60 0

/

0

1 

2 

3 

4

5 

6 

7 8 

9

10

11 

12 

13 

14

15 

J6 

17 

18 

19

20

21 

22 

23 

24

25 

26 

27 

28 

29

30

31 

32 

33 

34

35 

36 

37 

38 

39

40

41 

42 

43 

44

45 

46 

47 

48 

49

50

51 

52 

53 

54

55 

56 

57 

58 

59

00

L. Sin.

9.84 177 

9.84 190 

9. 84 203 

9.84 216 

9. 84 229

9. 84 242 

9. 84 255 

9. 84 269 

9.84 282 

9. 84 295

9.84 308 

9.84 321 

9.84334 

9. 84 347 

9. 84 360

9.84 373 

9.84385 

9.84398 

9.84411 

9. 84 424

9.84437 

9. 84 450 

9. 84 463 

9. 84 476 

9. 84 499

9. 84 502 

9. 84 615 

9.84 528 

9. 84 540 

9. 84 553

9. 84 566 

9.84 579 

9. 84 592 

9. 84 605 

9. 84 618

9. 84 630 

9. 84 643 

9. 84 656 

9. 84 669 

9. 84 682

9. 84 694 

9. 84 707 

9. 84 720 

9. 84 733 

9.84 745

9.84 758 

9.84 771 

9. 84 784 

9. 84 796 

9. 84 809

9. 84 822 

9. 84 835 

9. 84 847 

9.84 860 

9. 84 873

9. 84 885 

9. 84 898 

9. 84 911 

9.84 923 

9. 84 936

9. 84 949

L. Cos.

d.

13 

13 

13 

13 

13

13 

14 

13 

13 

13

13 

13 

13 

13 

13

12 

13 

13 

13 

13

13 

13 

13 

13 

13

13 

13 

12 

13 

13

13 

13 

13 

13 

12

13 

13 

33 

13

12

13 

13 

13 

12 

13

13 

L3 

32 

13 

13

13 

12 

13 

13 

12

13 

13 

12 

13 

13

d.

L. Tang.

9. 98 484 

9.98 509 

9.98 534 

9. 98 560 

9. 98 585

9. 98 610 

9. 98 635 

9. 98 661 

9.98 686 

9. 98 711

9. 98 737 

9.98 762 

9. 98 787 

9. 98 812 

9. 98 838

9. 98 863 

9. 98 888 

9.98913 

9.98939 

9.98 964

9. 98 989 

9.99 015 

9. 99 040 

9. 99 065 

9.99 090

9. 99 116 

9.99 HI 

9. 99 166 

9.99 191 

9. 99 217

9. 99 242 

9. 99 267 

9.99 293 

9. 99 318 

9. 99 343

9.99 368 

9. 99 394 

9. 99 419 

9. 99 444 

9. 99 469

9.99 495 

9. 99 520 

9. 99 545 

9. 99 570 

9. 99 596

9. 99 621 

9. 99 646 

9. 99 672 

9. 99 697 

9. 99 722

9.99 747 

9. 99 773 

9. 99 798 

9. 99 823 

9. 99 848

9. 99 874 

9. 99 899 

9. 99 924 

9. 99 949 

9. 99 975

0.00 000

L. Cotg.

c. d.

25 

25 

26

25 

25

25 

26 

25 

25 

26

25 

25 

25 

26 

25

25 

25 

26 

25 

25

26 

25 

25 

25 

26

25 

25 

25 

26 

25

25 

26 

25 

25 

25

26 

25 

25 

25 

26

25 

25 

25 

26 

25

25 

26 

25 

25 

25

26 

25 

25 

25 

26

25 

25 

25 

26 

25

c. d.

L. Cotg.

0. 01 516 

0.01 491 

0.01 466 

0.01 440 

0. 01 415

0.01 390 

0.01 365 

0.01 339 

0. 01 314 

0.01 289

0. 01 263 

0.01 238 

0. 01 213 

0. 01 188 

0. 01 162

0.01 137 

0.01 112 

0.01 087 

0.01 061 

0.01 036

0. 01 Oil 

0.00 985 

0. 00 960 

0. 00 935 

0.00 910

0.00 884 

0.00859 

0. 00 834 

0.00 809 

0. 00 783

0.00 758 

0.00 733 

0. 00 707 

0. 00 682 

0.00 657

0. 00 632 

0. 00 606 

0.00581 

0.00 556 

0. 00 531

0. 00 505 

0. 00 480 

0. 00 455 

0. 00 430 

0. 00 404

0.00 379 

0. 00 354 

0.00 328 

0.00 303 

0. 00 278

0.00253 

0. 00 227 

0. 00 202 

0. 00 177 

0.00 152

0. 00 126 

0. 00 101 

0. 00 076 

0. 00 051 

0. 00 025

0.00 000

L. Tang.

L. Cos.

9. 85 693 

9.85 681 

9.85 669 

9.85 657 

9.85 645

9. 85 632 

9.85 620- 

9.85 608 

9. 85 590 

9.85 583

9. 85 571 

9.85 559 

9. 85 547 

9.85 534 

9. 85 522

9. 85 510 

9. 85 497 

9.85485

9. 85 473 

9. 85 460

9. 85 448 

9. 85 436 

9. 85 423 

9.85 411 

9.85 399

9. 85 386 

9. 85 374 

9. 85 361 

9.85 349 

9. 85 337

9.85 324 

9. 85 312 

9. 85 299 

9. 85 287 

9.85274

9. 85 262 

9.85 250 

9.85 237 

9.85 225 

9.85 212

9. 85 200 

9.85 187 

9.85 175 

9.85 102 

9. 85 150

9. 85 137 

9.85 125 

9.85 112 

9. 85 100 

9.85 087

9. 85 074 

9. 85 062 

9. 85 049 

9. 85 037 

9. 85 024

9. 85 012 

9. 84 999 

9. 84 986 

9. 84 974 

9. 84 961

9.84 949

L. Sin.

d.

12 

12 

12 

12 

]3

32 

12 

12 

13 

32

12 

12 

13 

32 

32

13 

12 

12 

13 

12

12 

13 

12 

32 

13

12 

13 

12 

32 

33

12 

13 

12 

13 

32

12 

13 

32 

13 

32

33 

12 

33 

32 

13

32 

13 

12 

33 

33

32 

33 

12 

13 

32

13 

33 

32 

33 

32

d.

00

59

58 

57 

56

55 

54 

53 

52 

51

50

49 

48 

47 

46

45 

44 

43 

42 

41

40

39 

38 

37 

36

35 

34 

33 

32 

31

30

29 

28 

27 

26

25 

24 

23 

22 

21

20

19 

18 

17 

16

15 

14 

13 

12 

11

10

9

8 

7 

6

5 

4 

3 

2

1

0

/

4 0 56 

52 

48 

44

3 40 

36 

32 

28 

24

3 20 

16 

12 

8 

4

3 0 

56 

52 

48 

44

2 40 

36 

32 

28 

24

2 20 

16 

32 

8 

4

2 0 

56 

52 

48 

44

1 40 

36 

32 

28 

24

1 20 

16 

12

8 

4

1 0 

56 

52 

48 

. 44

0 40 

36 

32 

28 

24

0 20 

36 

12 

8 

4

°. °

m. s.

45°
216 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. GEODETIC POSITION COMPUTATIONS.

TABLE OF LOGARITHMS OF FACTORS A, B, C, D, E, F, BASED UPON THE CLARKE SPHEROID OF 1866 AND THE METRIC SYSTEM, BETWEEN LATITUDES 0° AND 72°.

[Extracted from reports of the U. S. Coast and Geodetic Survey.] 

CONSTANTS.

(1 e2 sin2 <p)' A=

B =

/"I _ m

a arc V 

(1 e2 sin2 <

a (1 e2 ) arcl" 

(1 g2 sin2 <p) 2 tan <p 

2a? (l el ) arcl" 

f g2 sin <p cos <p arc Vf 

~ 1 e2 sin2 cp

(1 + 3 tan2 <p) (1 e2 sin2 E ~ 6a2 

F = Y1^ sin q> cos2 <p arc2 V

log a = 6.804 698 57 

log b = 6. 803 223 78 

oe2 = 7.830 502 57

log = 8.50972656

log (| e2 arc l/x) =2.692 168 7

log (^ arc2 1^) = §.291 96

The formulas for the computation of the geodetic differences in latitude Aq>, in 

longitude /7A, and in azimuth A a. are as follows:

 A<p=s cos a . B-\-s2 sin2 a . C+(<5<p) 2 D h . s2 sin2 a . E

A7(.=s sin a sec <px . A 

. Aa.=A\. sin \ (^-f^) sec 

where

an(j / 8<p=s cos a . J?-)-s2 sin2 a . C h . s2 sin2 a . E

* also 7i=s cos a . B 

For subordinate triangulation when the sides, do not exceed say 25 kilometers, or 

about 15 statute miles, the term involving E in A<p and the factor sec \ (Aq>), as 

well as the term involving F in A a, may be omitted.
GEOGRAPHIC TABLES AND FORMULAS. 217

EXAMPLES OF COMPUTATION OF GEODETIC COORDINATES.

Azimuth a: 1 

Spherical angle:

Azimuth of: ] 

5 a+180°

Azimuth (a): rt 

Latitude.

o / //

0: 35 25 13.473 J 

d 0 -17 47. 546 Geo. P

0' 35 07 25.927 Z 

Geo. P 

Computation for 

latitude:

log s 4. 6236305 

" B . 8.5111933 

" cos a' 9.8930500

log (I) 3. 0278738

logs2 9.24726 

" C 1.25696 

" sinV 9.58986

log (II) 0. 09408

log D 2. 3674 

" [I+II]2 6.0568

log (III) 8. 4242

log E 6. 0124 

" sftanV 8.8371 

" (I) 3.0279

log (IV) 7. 8774

(I) 1066. 286+ 

(II) 1. 242+

(III) .026+ [I+II] 10( 

(IV) .008- log " 

 "[I+IIP

-rf0 1067. 546+

0 / //

^ell Chusca. 159 29 08. 728 

120 54 13.980

'Jell Zuni. 38 34 54.748 

179 50 02. 124

5uni Nell. 218 24 56. 872 

Longitude.

o

Ml. A: 108 

os. No. 5. d A +

uni. A' 108 

os. No. 6. 

Computation for 1

 logs " sin a/ 

" A' 

" sec 0 

Corr. for diff. arc &,

log (V) 

dA

Computation of a> 

log(V)'

sin (^ 2

/ //

37 24. 925 

17 15. 360

54 40.285 

angitude:

4. 6236305 

9. 7949286 

8. 5092394 

0. 0872944

3. 0150914 

1035".360

dmuth: 

3. 015091

) 0.000001

log (VI) 2. 776614 

da . - 597".876 

-9' 57".S76

Azimuth check.

57. 528 

3.0283792 Check: 

6. 0567584 Spher. angle

of itt
218 GEOGRAPHIC TABLES AND FORMULAS.,

Azimuth a: 

Spherical angle:

Azimuth a': 

da+180°

Azimuth (a): 

Latitude.

0 / //

0: 35 53 06.746 Cl 

d $ 45 40. 818 Geo. I

0> 35 07 25.928 2 

Geo. I 

Computation for 

latitude:

log s 4. 9280539 

"B 8.5111594 

"-cose/ 9.9986260

log (I) 3.

log s2 

« C " sin2 ^

log (II)

logD 

" [I+II]2

log (III)

logE " s2sin2ax

" (I)

4378393

9. 85610 

1. 26435 

7. 79982

8. 92027

2. 3698 

6. 8757

9. 2460

6. 0214 

7. 6559 

3. 4378

log (IV) 7: 1151

(I) 2740. 560+ 

(II) .083+

(III) 

(IV)

.176+ [I+II] ^ 

.001- log "

L J.-r-lAJ

-dL +2740.818

Chusca Nell. 339 21 40.150 

25 11 38.601

Chusca Zuni. 4 33 18.751 

179 57 25.650

Zuni Chusca. 184. 30 44.401 

Longitude.

o / //

lusca. A: 108 50 14.518

(os. No. 4. dX +4 25.768

toni. V 108 54 40.286 

'os. No. 6. 

Computation for longitude:

log s 4. 9280539 

" sin a" 8.8999280 

" A' 8.5092394 

-" sec 0' 0.0872944 

Corr. for diff. arc & sine 129

log (V) 2. 4245028 

d A +265". 768

Computation of azimuth:

log (V) 2. 424503 

" °in (^^"^ ~\ 9 76400°

" °nr ( ^ ^\ 0 000000

log (VI) 2. 188514 

d a - 154". 350 

-2' 34". 350

Azimuth check:

0 / //

218 24 56. 872 

184 30 44.401

3.4378525 Check: 33 54 12.471 

6. 875705 Spher. angle 

at Zuni 33 54 12.469
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 0°.

219

Lat.

o /

00 00 ' 1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

1819 -

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40 .

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A

8.509 7266

66

66

66

66

66

66

66

66

66

8.509 7266

65

65

65

65

65

65

65

65

65

8.509 7265

65

65

65

65

65

65

65

55

65

8. 509 7265

64

64

64

64

64

64

64

64

64

8.509 7264

64

64

64

63

63

63

63

63

63

8.509 7263

63

62

62

62

62

62

62

61

61

8.509.7261

logB

8.512 6761

61

61

61

61

61

 61

61

61

61

8.512 6761

61

61

61

61

61

61

60

60

60

8.512 6760

60

60

60

59

59

59

59

59

58

8. 512 6758

58

58

57

57

57

57

56

56

56

8. 512 6756

55

55

55

54

54 

64

53

53

53

8. 512 6752

52

51

51

51

50

50

49

49

49

8. 512 6748

logC

o-°°

2- 8707

8.1737

3477

4727

5696

6488

7158

7740

8249

8. 8707

9121

9499

8.9846

9.0168

0468

0748

1011

1259

1494

9. 1717

1929

2131

2324

2509

2686

2857

3020

3178

3331

9. 3478

3620

3758

9. 3892

9. 4022

4148

4270

4389

4505

4618

9..472S

4835

9.4939

9. 5042

5141

5239

5335

6428

5519

5609

9. 5697

5783

5866

9. 5950

9.6031

6111

6189

6266

6341

6416

9. 6489

logD

=-co

9. 156

457

633

758

= 855

9.934

0.001

059

110

0.156

197

235

270

302

QQO OOZ

360

386

411

435

0.457

478

498

518

536

554

571

587

' 603

618

0.633

647

661

674

687

700

712

724

736

747

0.758

769

779

789 

799

809

819

828

837

846

0.855

863

872

880

888

896

904

912

919

927

0.934

logE

5. 6125

6

5

5

5

5

5

5

5

5

5.6325

5

5

5

5

5

5

5

5

5

5. 6125

5

5

5

5

5

5

5

5

5

5. 6126

6

6

6

6

6 " 6

6

6

6

5.6126

6

6

6

7

7

7

7

7

7

5.6127

7

7

7

8

8

8

8

8

8

5. 6128

logF

-00

6.057

6.358

0.534
220 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 1°.

Lat.

o /

1 00

1

2

3

4

' 05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

 27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43 '

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A

8.509 7261

61

61

61

61

60

60

60

60

60

8. 509 7260

59

59

59

59

59

58

58

58

58

8.509 7258

57

57

57

57

57

56

56

66

56

8. 509 7256

55

55

55

55

54

54

54

54

53

S.509 7253

53

5352 '

52

52

52

51

51

51

8.509 7251

50

50

50

49

49

49

49

48

48

8.509 7248

logB

8.512 6748

48

47 .

47

46

46

45

46

44

44

8. 512 6743

43

42

42

41

41

40

39

39

38

8.512 6738

37

36

36

35

35

34

33

33

32

8.512 6731

31

30

29

29

28

27

26

26

25

8. 512 6724

23

23

22

21

20

20

19

18

17

8.512 6716 .

16

15

14

13

12

11

10

10

09

8.512 6708

logC

9.6489

560

631

701

769

836

903

9. 6968

9. 7032

096

9.7158

220

281

341

400

458

516

572

628

684

9. 7738

792

846

898

9.7950

9. 8002

053

103

152

202

9. 8250

298

346

393

439

485

531

576

620

664

9.8708

751

794

836

878

920

961

9.9002

042

082

9. 9122

161

200

239

277

315

353

390

427

464

9. 9500

logD

0.934

941

948

955

962

969

975

982

988

0. 995

1.001

007

013

019

025

031 037-

042

048

053

1.059

064

070

075

080

085

090

095

100

105

1.110

115

119

124

129

133

138

142

147

151

1.156

160

164

168

173

177

181

185

189

193

1.197

201

205

209

212

216

220

224

227

231

1.2347

logE

5. 6128

29

29

29

29

29

29

29

30

30

5. 6130

30

30

30

31

31

31

31

31

31

5. 6132

32

32

32

32

32

33

33

33

33

5. 6133

34

34

34

34

34

35

35

35

35

5. 6136

36

36

36

36

37

37

37

37

38

5.6138

38

38

39

39

39

39

40

40

40

5. 6140

logF

6.534

6.658

6.755

6.834
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 28. Geodetic position computations Continued.

LATITUDE 2°.

221

Lat.

O 1

2 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

5859 '

60

log A

8.509 7248 -

47

47

47

47

46

46

46

45

45

8.509 7245

44

44

44

43

43

43

42

42

42

8. 509 7241

41

41

40

40

40

39

39

38

38

8. 509 7238

37

37

37

36

36

35

35

35

34

8. 509 7234

33

33

33

32

32

31

31

31

30

8.509 7230

29

29

28

28

28

27

27

26

26

8.509 7225

logB

8. 512 6708

07

06

05

04

03

02

01

6700

6699

8.512 6698

97

97

96

95

94

93

91

90

89

8.512 6688

87

86

85

84

83

82

81

80

79

8. 512 6678

76

75

74

73

72

71

70

68

67

8. 512 6666

65

64

62

61

60

59

58

56

55

8. 512 6654

52

51

50

49

47

46

45

43

42

8.512 6641

logC

9. 95002

5363

5721

6076

6428

6777

7123

7467

7808

8146

9. 98482

8815

9145

9473

9.99799

0.00122

0443

0762

1078

1392

0. 01703

2013

2320

2625

2928

3229

3528

3826

4119

4412

0.04703

4992

5279

5564

5847

6129

6408

6686

6962

7237

0. 07509

7780

8050

8317

8583

8848

9111

9372

9631

0. 09890

0. 10146

0401

0655

0907

1158

1407

1655

1902

2147

2390

0. 12633

log D

1.2347

383

419

454

489

624

659

593

627

661

1.2694

727

760

793

826

858

890

922

953

1.2984

1. 3015

046

077

107

138

168

197

227

256

285

1.3314

343

372

400

428

456

484

512

539

567

1.3594

621

648

674

701

727

753

779

805

831

1. 3856

882

907

932

957

. 1. 3982

1.4007

031

055

080

1. 4104-

log E

5. 6140

41

41

41

41

42

42

42

43

43

6. 6143

43

44

44

44

45

45

45

45

46

5. 6146

46

47

47

47

48

48

48

49

49

5. 6149

50

50

50

51

51

51

52

52

52

5. 6153

53

53

54

54

54

55

55

56

56

5. 6156

57 .

57

57

58

58

59

59

59

60

5. 6160

logF

6.834

6.901

6.959

7.010
222 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 3°.

Lat.

o / 

3 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

 30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

64

55

66

57

58

59

60

log A

8. 509 7225

25

24

24

24

23

23

22

22

21

8. 509 7221

20

20

19

19

18

18

17

17

16

8.509 7216

15

15

14

14

13

13

12

12

11

8.509 7211

10

10

09

09

08

08

07

.07

06

8. 509 7206

05

04

04

03

03

02

02

01

01

8. 509 7200

7199

99

98

98

97

96

96

95

95

8,509 7194

logB 

diff. 1"=-0.03

8. 512 6641

39

38

37

35 .

34

33

31

30

28

8. 512 6627

26

24

23

21

20

18

17

15

14

8.512 6612

11

09

08

06

05

03

02

6600

6599

8.512 6597

96

94

92

91

89

88

86

84

83

8. 512 6581

80

78

76

75

73

71

69

68

66

8. 512 6564

63

61

59

58

56

54

52

50

49

.. 8.512 6547 ..

logC

0. 12633

. 2874

3113

3352

3589

3825

4059

4293

4525

4756

0. 14985

5214

5441

5667

5892

6116

6338

6560

6780

6999

0. 17217

7434

7650

7665

8079

8292

8504

8715

8925

9133.

0. 19341

9548

9754

19959

20163

0366

0568

0769

0969

1168

0. 21367

1564

1761

1956

2151

2345

2538

2731

2922

3113

0. 23302

3491

3680

3867

4053

4239

4424

4608

4792

4974

0.25156

logD

1.4104

28

52

75

1. 4199-

1. 4222

46

69

1. 4292

1.4315

1.4338

60

1. 4383

1. 4405

28

50

72

1.4494

1. 4516

38

1. 4560

1. 4581

1. 4603

24

45

66

1.4687

1. 4708

29

50

1. 4770

1.4791

1.4811

32

52

72

1.4892

1.4912

32

52

1.4971

1. 4991

1. 5011

30

49

68

1. 5088

1. 5107

26

45

1.5163

1.5182

1. 6201

19

38

56

75

1.5293

1. 5311

29

. 1. 5347. ._

log E log F

5. 6160 f. 010

61

61

61

62

62

62,

63

63

64

5.6164

65

65

65

66

66

67

67

68

68

5.6168 7.055

69

69

70

70

71

71

72

72

72

5. 6173

73

74

74

75

75

76

76

77

77

5. 6178 7. 096

78

79

79

80

80

81

81

81

82

5. 6182

83

84

84

85

85

86

86

 87

87

-..6..6188 7.JL33. ..
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 4°

223

Lat.

0 /

4 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

66

57

58

59

60

log A

8. 509 7194

93

93

92

92

91

91

90

89

89

8.509 7188

87

87

86

86

85

84

84

83

82

8.5097182

81

80

80

79

78

78

77

76

76

8. 509 7175

74

74

73

72

72

71

70

70

69

' 8. 509 7168

67

67

66

66

65

64

63

63

62

8.509 7161

60

60

69

58

57

57

56

55

55

8.509 7154

logB 

diff.l"=-0.04

8.5126547

45

43

42

40

38

36

34

32

31

8. 512 6529

27

25

23

21

19

17

16

14

12

8.5126510

08

06

04

02

6500

6498

96

94

92

8.512 6490

88

86

84

82

80

78

76

74

72

8.512 6470

68

65

63

61

59

57

55

53

51

8. 512 6448

46

44

42

40

38

35

33

31

29

8.612 6427

logC

0. 25156

6337

5518

5697

5876

6055

6232

6409

6585

6760

0. 26935

7109

7282

7455

7627

7798

7968

8138

8308

8476

0. 28644

8812

8978

9144

9310

9475

9639

9802

0.29965

0. 30128

0. 30290

0451

0611

0771

0931

1090

1248

1406

1563

1719

0. 31875

' 2031

2186

2340

2494

2647

2800

2953

3104

3255

0. 33406

3556,

3706

3855

4004

4152

4300

4447

4594

4740

0.34885

logD

1. 5347

65

1.6383

1. 5401

18

36

64

71

1.5489

1.5506

1. 6523

40

58

76

1.5592

1.5609

25

42

59

76

1.5692

1.6709

25

42

58

74

1. 5791

1.5807

23

39

1.6855

71

1.5887

1.5902

18

34

50

65

81

1.5996

1.6011

27

42

57

73

1.6088

1. 6103

18

33

48

1. 6163

77

1.6192

1. 6207

21

36

51

65

80

1.6294

1.6308

logE

I>. 6188

88

89

89

90

90

91

91

92

92

5. 6193

93

94

95

95

96

96

97

97

98

5.6199

5.6199

5.6200

00

01

01

02

03

03

04

5. 6204

05

05

06

07

07

08

08

09

10

5. 6210

11

12

12

13

13

14

 ISIS

16

5. 6216

17

18

18

19

20

20

21

22

22

5. 6223

logF

7.133

7.168

7.200

7.229
224 GEOGBAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 5°.

Lat;

o /

5 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

66

57

58

59

60

log A

8. 509 7154

53

53

52

51

50

49

49

48

47

8. 509 7146

46

45

44

43

43

42

41

40

39

8.509 7139

38

37

36

35

35

34

33

32

31

8. 509 7131

.30

29

28

27

27

26

25

24

23

8.509 7122

21

21

20

19

18

17

16

16

15

8.509 7114

13

12

11

10

09

09

08

07

06

8.509 7105

logB 

diff. 1"=-0.04

8.512 6427

24

22

20

18

15

13

11

08

06

8. 512 6404

6402

6399

97

95

92

90

88

85

83

8. 512 6381

78

76

73

71

69

66

64

61

59

8. 512 6356

54

52

49

47

44

42

39

37

34

8. 512 6332

29

27

24

21

19

16

14

11

09

8.512 6306

03

6301

6298

96

93

90

88

85

82

8.512 6280

lOgC

0. 34885

5030

5175

5320

5464

5607

6750

5892

6034

6176

0. 36317

6457

6597

. 6737

6876

7015

7154

7292

7429

7566

0. 37703

7839

7975

8111

8246

8380

8514

8648

8781

8914

0.39047

9179

9311

9442

9573

9704

9834

0. 39964

0.40094

0223

0.40351

0480

0608

0735

0863

0990

1116

1242

1368

1493

0.41619

1743

1868

1992

2115

2239

2362

2484

2607

2729

0. 42850

logD 

diff. 1"= +0.22

1. 6308

23

37

51

65

79

1. 6393

1.6407

21

35

1. 6449

63

77

1.6491

1.6504

18

32

45

59

72

1. 6586

1.6599

1. 6612

26

39

52

65

78

1. 6692

1. 6705 _

1. 6718

31

44

56

69

82

1.6795

1.6808

20

33

1.6846

58

71

83

1. 6896

1.6908

21

33

45

58

1.6970

82

1.6994

1. 7006

19

31

43

55

67

79

1.7090

logE.

5.6223

24

24

25

26

2fi

27

28

28

29

5.6230

30

31

32

32

33

34

34

35

36

5.6236

37

38

38

39

40

41

41

42

43

5. 6243

44

45

46

46

47

48

48

49

50

5.6251

51

52

53

54

54

55

56

57

57

5. 6258

59

60

60

61

62 

63

63

64

65

5. 6266

logF

7.229

7.256

7.282

7.306
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 6°.

225

Lat.

0 /

6 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22 .

23

24

25

26

27

28

29

80

31

32

.33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.02

8. 509 7105

04

03

02

01

01

7100

7099

98

97

8.5097096

95

94

93

92

91

91

90

89

88

8.509 7087

86

86

84

83

82

. 81

80

79

78

8.509 7077

76

75

74

73

72

7170 '

70

69

8. 509 7068

67

66 .

65

64

63

62

61

60

59

8.509 7058

57

56

55

53

52

51

50

49

48

8.509 7047

logB 

diff.l"=-0.05

8. 512 6280

77

74

72

69

66

64

61

58

55

8.512 6253

50

47

44

42

39

36

33

31

28

8.512 6225

22

19

16

14

11

08

05

6202

6199

8.512 6196

94

91

88

85

82

79

76

73

70

8.5126167

64

61

58

55

52

49

46

43

40

8.512 6137

34

31

28

25

22

19

16

13

10

8. 512 6107

logC

0. 42850

2972

3093

3213

3334

3454

3573

3693

3812

3931

0. 44049

4167

4285

4402

4519

4636

4753

4869

4985

5101

0.45216

5331

5446

5560

5674

5788

5902

6015

6128

6241

0.46353

6465

6577

6689

6800

6911

7022

7132

7242

7352

0.47462

7671

7681

7789

7898

8006

8114

8222

8330

8437

0. 48544

8651

8757

8864

8970

, 9075

9181

9286

9391

9496

0.49600

logD 

diff.l"=+0.18

1. 7090

7102

14

26

38

50

61

73

85

1.7196

1. 7208

19

31

42

54

65

76

88

1. 7299

1.7310

1.7322

33

44

55

66

78

1.7389

1.7400

11

22

1.7433

44

54

65

76

87

1. 7498

1.7508

19

30

1.7541

51

62

73

83

1. 7594

1. 7604

15

25

36

1. 7646

56

67

77

87

1. 7698

1. 7708

18

28

38

1. 7749

logE

1.6266

67

67

68

69

70

70

71

72

73

5. 6274

74

75

76

77

78

78

79

80

81

5.6282

83

83

84

85

86

87

88

88

89

5.6290

91

92

93

93

94

95

96

97

98

5.6299

5. 6299

5. 6300

01

02

03

04

. 05

06

06

5.6207

08

09

10

11

12

13

13

14

15

5. 6216

logF

f.306

.

7.329

7.361

7.371

41623° 16 15
226 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 7°.

Lat.

o / 

7 00

1

2

3

4

05

6

X7

8

9

10

11

12

13

14

15

16

, 17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43 ,

44

 45

46

47

48

49

50

51

62

53

54

55

56

57 .

68

59

60

log A 

diff.l"=-0.02

8. 509 7047

46

45

44

43

42

41

40

39

38

8.509 7037

36

35

34

33

32

30

29

28

27

8. 509 7026

25

24

23

22

21

20

19

17

16

8.509 7015 .

14

13

12

11

10

09

07

06

05

8.609 7004

03

02

01

7000

6998

97

96

96

94

8. 509 6993

91

90

89

88

87

86

84

83

82

8. 509 6981

logB 

diff.l"=-0.06

8. 512 6107

03

6100

6097

94

91

88

85

82

78

8. 512 6075

72

69 '

66

62

59

56

53

50

46

8.512 6043

40

37

33

30

27

23

20

17

14

8.512 6010

07

04

6000

5997

94

90

87

83

80-

8. 512 5977

73

70

66

63

60

56

53

49

46

8. 512 5942

39

35

32

28

25

21

18

14

11

8. 512 5907

logC

0. 49600

705

809

0.49913

0. 50016

119

222

325

428

530

0. 50632

734

836

0.50937

0.51039

140

240

341

441

541

0. 51641

741

840

0. 51939

0. 52038

137

236

334

432

530

0. 52628

725

822

0.52919

0.53016

113

209

306

402

497

0. 53593

688

784

879

0. 53973

0.54068

162

257

351

444

0.54538

631

725

818

0. 54911

0.55003

*096

188

280

372

0.65464

logD 

diff.l"=+0.16

1. 7749

59

69

79

89

1. 7799

1. 7809

19

29-

39

1.7849

59

68

78

88

1.7898

1. 790817 '

27

37

1. 7946

56

66

75

85

1. 7994

1.8004

13

23

32

1.8042

51

61

70

79

89

1.8098

1.8107 .

17

26

1.8135

44

53

63

72

81

90

1.8199

1. 8208

17

1. 8226

35

44

53

62

71

80

89

1. 8298

1.8307

1.8315

logE

5. 6316

17

18

19

20

21

22

23

23

24

5.6325

26

27

28

29

30

31

32

33

. 34

5.6335

36

37

37

38

3940 =

41

42

43

5.6344

45

46

47

48

49

60

51

52

53

5.6354

55

56

57

58

59

60

61

62

63

5. 6364

65

66

67

68

69

70

71

72

73

5.6374

logF

7\371

7.391

7.409

7.427
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 8°.

227

Lat.

O 1

8 00

1

2

3

4

' 056

7

8

9

10

11

A2

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

64

55

56

57

58

59

60

log A 

diff. 1"=-0.02

8. 509 6981

80

79

77

76

75'

74

73

71

70

8.509 6969

68

67

65

64

63

62

61

59

58

8.509 6957

56

54

63

52

51

49

48

47

46

8. 509 6945

43

42

41

39

38

37

36

34

33

8.509 6932

31

29

28

27

25

24

23

22

20

8. 509 6919

18

16

15

14

12

11

10

09

07

8.609 6906

logB 

diff. 1"=- 0.06

8. 512 5907

04

5900

5897

93

90

86

82

79

75

8.512 5872

68 ' 64

61

57

54

50

46

. 43

39

8. 512 5835

82

28

24

20

17

13

09

06

5802

8. 512 5798

94

91

87

83

79

75 ' 72

68

64

8. 512 5760

56

53

49

45

41

37

33

29

26

8. 512 5722

18

14

10

06

5702

5698

94

90

86

8.612 5682

logC

0. 55464

556

646

738

829

0. 55919

0. 56010

100

191

281

0. 56371

460

550

639

728

817

906

0. 56995

0.57083

172

0.57260

348

436

623

611

698

785

872

0. 57959

0. 58045

0.58132

213

304

390

476

562

647

732

818

903

0. 58987

0. 59072

157

241

325

409

493

577

660

744

0.59827

910

0. 59993

0. 60076

159

241

324

406

488

670

0. 60652

logD 

diff. 1"=+0.14

1.8315

24

33

42

50

59

68

77

85

1.8394

1.8403

12

20

28

37

45

54

62

71

79

1.8488

1.S496

1.8505

13

21

30

38

46

55

63

1. 8571

80

88

1.8596

1. 8604

13

21

29

37

45

1.8653

61

69

77

85

1. 8693

1.8701

09

17

25

1.8733

41

49

57

65

73

81

89

1.8796

1. 8804

1.8812

log E log F 

diff. 1"=+0.02

5.6374 7.427

75

76

77

78

79

80

81

82

83

5. 6384

85

86

87

88 .

90

91

92

93

94

. 6395 7.444

96

97

98

99

f>. 6400

5. 6401

02

03

04-

5. 6406

07

08

09

10

11

12

13

14

15

5. 6416 7. 461

18

19

20

21

22

23

24

25

26

5. 6428

29

30

31

32

33

34

36

37

38

5.6439 7.476
228 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 9°.

Lat.

0 /

9 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.02

8. 509 6906

05

03

02

6901

6899

98

97

95

94

8.509 6893

91

90

89

87

86

84

83

82

80

8. 509 6879

78

76

75

74

72

71

69

68

67

8. 509 6865

64

62

61

60

58

57

55

54

53

8. 509 6851

60

48

47

45

44

43

41

40

38

8.509 6837

35

34

33

31

30

28

27

25

24

8.509 6822

logB 

diff.l"=-0.07

8. 512 5682

78

74

70

66

62

58

54

50

46

8. 512 5642

38

34

30

26

22

18

14

10

06

8.512 5602

5598

93

89

85

81

77

73

69

64

8.512 5560

56

52

48

43

39

35

31

2722 

8. 512 5518

14

10

05

5501

5497

92

88

84

80

8. 512 5475

71

67

62

58

54

49

45

40

36

8.512 5432

logC

0. 60652

733

815

896

0. 60977

0. 61058

139

220

301

881

0. 61461

542

622

702

781

861

0. 61941

0. 62020

099

178

0. 62257

336

415

493

572

650

728

806

884

0. 62962

0. 63039

117

194

271

349

426

502

579

656

732

0. 63808

885

0.63961

0. 64037

112

188

264

339

415

490

0. 64565

640

715

789

864

0. 64938

0. 65013

087

161

235

0: 65309

logD 

diff.l"=+6.12

1.8812

20

27

35

43

51

58

66

74

81

1.8889

1.8897

1. 8904

12

19

27

34

42

50

57

1. 8964

72

79

87

1. 8994

1. 9002

09

17

24

31

1. 9039

46

53

61

68

75

82 '

90

1.9097

1.9104

1. 9111

19

26

. 33

40

47

54

61

69

76

1. 9183

90

1. 9197

1.9204

11

18

25

32

39

46

1. 9253

logE 

diff.l"=+0.02

5.6439

40

41

42

44

45

, 46

47

48

49

5. 6450

52

53

54

55

56

57

59

60

61

5. 6462

63

65

66

67

68

69

70

72

73

5. 6474

75

76

78

79

80

81

83

84

85

5. 6486

87

.89

90

91

92

94

95

96

97

5.6498

5. 6500

01

02

03

05

06

07

08

10

5.6411

logF

7.476

7.490

7.505

7.518
GEOGKAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 10°.

229

Lat.

O I

10 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45 "

46

47

48

49

50

51

52

53

54

55

5657 

58

59

60

log A 

cliff. 1»= -0.03

8. 509 6822

21

19

1817-

15

14

12

11

9

8.509 6808

06

05

03

.02

6800

6799

97

96

94

8.509 6793

91

90

88

87

85

84

82

81

79

8. 509 6777

76

74

73

71

70

68

67

65

64

8.509 6762

60

59

57

56

54

53

51

50

48

8. 509 6746

45

43

42

40

38

37

35

34

32

8.509 6730

logB 

Cliff. 1"= -0.08

8.512 5432

27

23

19

14

10'

05

5401

5396

92

8. 512 5388

83

79

74

70

65

61

56

52

47

8. 512 5343 *

38

33

29

24

20

15

11

06

5302

8.512 5297

92

88

83

79

74

69

65

60

55

8. 512 5251

46

41

37

32

27

23

18

13

08

8. 512 5204

5199

94

89

85

80

75

70

66

61

8. 512 5156

logC

0. 65309

383

456

530

603

677

750

823

896

0.65968

' 0.66041

114

186

259

331

403

475

547

619

691

0. 66762

834

905

0. 66976

0. 67047

118

189

260

331

401

0. 67472

542

613

683

753

823

893

0. 67962

0. 68032

102

0. 68171

240

 310

379

448

517

686

654

723

791

0. 68860

928

0. 68996

0. 69064

132

200

268

336

404

471

0. 69539

logD 

diff.l"=+0.11

1. 9253

60

67

74

. 80

87

1. 9294

1.9301

08

15

1. 9322

28

35

42

49

56

62

69

76

82

1. 9389

1. 9396

1. 9403

09

16

23

29

36

42

49

1.9456

62

69

75

82

88

1. 9495

1. 9501

08

14

1. 9521

27

34

40

47

53

60

66

72

79

1.9585

91

1. 9598

1. 9604

10

17

23

29

36

42

1. 9648

logE 

cliff. 1"= +0.02

f>. 6511

12

13

15

16

17

18

20

21

22

5. 6524

26

26

27

29

30

31

33

34

35

5.6536

38

39

40

42

43

44

46

47

48

5. 6549

51

52

63

55

56

57

59

60

. 61

5. 6563

64

65

67

68

69

71

72

73

75

5. 6576

78

79

80

82

83

84

86

87

88

5. 6590

logF

7.518

7.532

7.544

7.556
230 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 11°. ' '

Lat.

o / 

11 00

1

 2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.03

8.509 6730

29

27

26

24

22

21

19

18

16

8. 509 6714

13

11

09

08

06

05

03

01

6700

8.509 6698

96

95

93

91

90

88

86

85

83

8. 509 668180 '

78

76

75

73

71

70

68

66

8. 509 6665

63

61

59

58

56

54

53

61

49

8.509 6647

46

44

43

41

39

37

35

34

32

8. 509 6630

logB 

diff.l"=-0.08

8.512 5156

51

46

41

37

32

27

22

17

12

8. 512 5108

5103

5098

5093

88

83

78

73

68

63

8.512 5058

53

49

44

39

34

29

24

19

14

8. 512 5009

04

4999

94

89

83

78

73

68

63

8. 512 4958

53

48

43

38

33

28

22

17

12

8.512 4907

4902

4897

92

86

81

76

71

66

60

8. 512 4855

logC

0. 69539

606

673

740

807

874

0. 69941

0. 70008

074

141

0. 70208

274

340

406

473

539

604

670

736

802

0.70867 '

933

0. 70998

0.71063

128

194

259

323

388

453

0. 71518

582

647

711

775

840

904

0. 71968

0.72032

095

0. 72159

223

286

350

413

477

540

603

666

729

0. 72792

855

918

0. 72980

0. 73043

106

168

230

293 '

355

0. 73417

logD 

diff.l"=+0.10

1.9648

54

61

67

73

79

86

92

1.9698

' 1.9704

1.9710

16

23

29

35

41

47

53

59

65

1.9771

77

83

89

1. 9795

1. 9801

07

13

19

25

1. 9831

37

43

49

55

61

67

73

79

85

1. 9890

1.9896

1. 9902

08

14

20

25

31 ' 37

43

1.9949

54

60 

66

72

77

83

89

94

1. 9900

2.0006

logE 

diff.l"=+0.02

5.6590

91

93

94

95

97

98

5.6599

5. 6601

02

5. 6604

05

06

08

09

11

12

13

15

16

5. 6618

19

20

22

23

25

26

27

29

30

5. 6632

33

35

36

37

39

40

42

43

45

5.6646

47

49

50

52

53

55

56

58

59

5. 6661

62

64

65

66

68

69

71

72

74

5. 6675

logF

7.556

7.568

7.580

7.591
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 28. Geodetic position computations -Continued.

LATITUDE 12°.

231

Lat.

o /

12 00

1

. 2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

66

57

. 58

59

60

log A diff.l'°=-0.03

8. 609 6630

29

27

25

23

21

20

18

16

14

8. 509 6613

11

09

07

06

04

02

6600

6599

97

8. 509 6595

93

91

90

88

86

84

82

81

79

8.509 6577

75

73

72

70

G8

66

64

62

61

8. 609 6559

57

55

53

51

50

48 46

44

42

8. 509 6540

39

. 37

36

33

31

29

27

25

24

8.509 6522

logB 

diff.l"=-0.09

8.512 4855

50

45

39

34

29

24

18

13

08

8. 612 4803

4797

92

87

81

76

71

65

60

55

8. 512 4749

44

39

33

28

23

17

12

06

4701

8 512 4690

90

85

79

74

68

63

57

62

46

8. 512 4641

35

30

24

19

13

08

4602

4697

91

8. 512 4686

80

75

69

63

58

52

47

41

35

8. 512 4530

logC

0. 73417

479

541

603

664

726-

788

849

911

0. 73972

0. 74033

094

156

217

278

339

399

460

521

581

0. 74642

702

763

823

883

0.74943

0. 75003

063

123

183

0.75243

302

362

422

481

540

600

659

718

777

0. 75836

895

0. 76954

0. 76013

072

130

189

247

306

364

0.76422

481

539

597

655

713

771

828

886

0. 76944

0. 77001

logD 

diff.l"=+0.09 d

2.0006

11

17

23

28

34

40

45

51

57

2. 0062

67

73

79

84

90

2.0096

2.0101

07

12

2.0118

23

29

34

40

45

60

56

61

67

2. 0172

77

83

88

94

2. 0199

2. 0205

10

15

21

2.0226

32

37

42

47

53

58

63

69

74

2. 0279

84 90

2.0295

, 2. 0300

05

10

16

21

26

2.0331

logE 

iff. 1"- +0.04

1. 6676

77

78

80

81

83

84

86

87

89

5.6690

92

93

95

96

98

99

5.6701

02

04

' 5. 6705 .

07

08

10

11

13

14

16

17

19

5. 6720

22

24

25

27

28

30

31

33

34

5. 6736

37

39

41

42

44

45

47

48

50

5.6751

53

55

56

58

59

61

62

64

66

5. 6767

logF

7.591

7.601

7.611

s

7.621
232 GEOQBAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 13°.

Lat.

o /

13 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

. 27

28

29

30

31

32

33

34

36

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff. 1"=-0.03

8. 509 6522

20

18

16

14

12

10

09

07

05

8. 509 6503

6501

6499

97

95

93

91

90

88

86

8. 509 648482'

80

78

76

74

72

70

68

66

8. 509 6464

63

61

59

. 57

55

53

51

49

47

8. 509 6445

43

41

39

37

35

33

31

29

27

8. 509 6425

23

21

19

17

15

13

, 11

09

07

8. 509 6405

logB 

diff. 1"=-0.10

8. 512 4530

24

19

13

07

4502

4496

90

85

79

8: 512 4473

67

62

56

50

45

39

33

27

22

8. 512 4416

10

4404

4399

93

87

81

76

70

64 '

8. 512 4358

52

46

41

35

29

23

17

11

4305

8. 512 4299

94

88

82

76

70

64

58

52

46

8. 512 4240

34

28

^ 22

16

i

10

4204

4198

92

86

8. 512 4180

logC 

diff. 1"= +0.93

0. 77001

059

116

174

231

288

346

403

460

517 .

0. 77574

630

687

744

801

857

914

0. 77970

0. 78027

083

0.78139.

195

251

307

363

419

475

531

587

642

o! 78698

754

809

865

920

0.78975

0. 79030

086

141

196

0. 79251

306

360

415

470

525

579

634

588

743

0. 79797

851

905

0. 79960

0. 80014

068

122

176

230

284

* 0.80337

logD 

diff. 1"=+0.(

2. 0331

36

42

47

52

57

62

67

73

78

2.0383

88

93

2. 0398

2.0403

08

13

18

23

28

2. 0433

38

44

49

54

59

64

69

74

78

2.0483

88

93

2. 0498

2.0503

08

13

18

23

28

2.0533

38

42

47

52

57

62

67

72

76

2. 0581

86

91

2. 0596

2.0601

05

10

15

20

24

' 2.0629

logE 

)8 diff. 1"= +0.03

5. 6767

69

70

72

74

75

77

78

80

82

5.6783

85

86

88

90

91

93

94

96

98

5. 6799

5. 6801

03

04

06

07

09

11

12

14

5. 6816

' 17

19

20

22 .

24

25

27

29

30

5. 6832

34.

35

37

39

40

42

4445'

47

5. 6849

50

52

54

55

57

59

60

62

64 .

5. 6865

logF

7.621

.

7.631

7.640

7.649
GEOGEAPHIC TABLES AND FOEMULAS. 

TABLE 28. Geodetic position computations Continued.

LATITUDE 14°.

233

Lat.

o / 

14 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

. 24

25

i 26

27 ' 28

' 29

30

31

32

33

. . 34

. 35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

5S

59

60

log A 

diff.l"=-0.03

8. 509 6405

03

6401

6399

97

96

93

91

89

87

8. 509 6385

83

81

79

77

75

73 ' 71

69

67

8. 509 6365

63

61

58

56

54

52

60

48

46

8. 509 6344

42

' 40

38

36

34

32

29

27

25

8. 509 6323

21

19

17

15

13

11

08

06

04

8. 509 6302

6300

6298

96

94

92

89

87

85

83

8. 509 6281

logB 

diff.l"=-0.10

8.512 4180

74

68

62

56 

50

44

38

32

26

8. 512 4120

14

, 08

4101

4095

89

83

77

71

65

8.512 4059

52

46

40

34

.28

21

15

09

4003

8. 512 3997

90

. 84 '

78

72

65

59

53

47

40

8. 512 3934

28

22

15

09

3903

3896

90

84

77.

8. 512 3871

65

58

52

45

39

33

26

20

13

8.512 3807

logC 

diff.l"=+0.87

0.80337

391

445

498

552

605

. 659

712

765

819

0. 80872

925

0.80978

0. 81031

084

137

190

243

295

348

0. 81401

453

506

558

611

663

715

767

820

872

0. 81924

0.81976

0. 82028

080

131

183

235

287

338

390

0. 82441

493

544

596

647

698

749

800

852

903

0. 82954

0. 83005

055

106

157

208

258

309

360

410

0. 83461

lOgD 

diff.l"=+0.08

2.0629

34

39

43

48

53

58

62

67

72

2. 0676

81

86

90

. 2.0695

2. 0700

04

09

14

18

2.0723

28

32

36

41

46

51

65

60

64

2. 0769

73

78

83

87

92

2. 0796

2. 0801

05

10

2.0814

19

23

28

. 32

37

41

46

50

54

2. 0859

63

68

72

77

81

85

90

94

2. 0899

2. 0903

logE 

diff.l"=+0.03

5. 6865

67

69

71

72

74

76

77

79

81

5. 6882

84

86

88

89

91

93

94

96

98

5. 6900

01

03

05

06

08

10

12

13

15

5. 6917

19

20

22

24

26

27

29

31

33

5. 6934

36

38

40

41

43 '

45

47

48

50

5. 6952

54

55

57

59

61

63

64

66

68

5. 6970

logF

7.649

7.658

7.667

7.675
234 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 2& Geodetic position computations Continued.

LATITUDE 15°.

Lat.

o / 

15 00

1

2

3

4

05

6

78'

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

63

64

55

56

67

68

59

60

log A 

diff.l"=-0.04

8. 509 6281

79

77

74

72

70

68

66

64

62

8. 509 6259

67

55

53

51

49

46

44

42

40

8. 509 6238

35

33

31

29

27

24

22

20

18

. 8. 509 621614 

11

09

07

05

02

6200

6198

96

8.509 6194

91

89

87

85

82

80

78

76

73

8. 609 6171

69

67

64

62

60

58

55

53

51

8. 509 6149

logB 

diff.l"=-0.11

8. 512 3807

3801

3794

88

81

75

68

62

56

49

8. 512 3743

36

30

23

17

10

3704

3697

91

84.

8. 512 3677

71

64

58

51

45

38 

31

25

18

8. 512 3612

3605

3598

92

. 85

79

72

65

59

52

8. 512 3545

39

 32

25

19

12

3506

3498

92

85

8.5123478

71

65

58

51

44

38

31

24

17

8. 512 3411

logC 

diff.l"=+0.82 (

0. 83461

511

561 612'

662

712 762'

813

863

913

0.83963

0. 84012

062

112

162

212

261

311

361

410

0. 84460

509

558

608

657

706

755

804

854

903

0.84952

0.85001

049

098

147

196

245

293

342

390

0.85439

487 

536

584

633

681

729

777

825

874

0. 85922

0. 85970

0. 86018

066

113

161

209

257

304

352

0.86400

log D

2.0903

07

12

16

21

25

29

34

38

42

2.0947

51

5559 -

64

68

72

77

81

85

2.0990

94

2.0998

2.1002

.07

11

15

19

23

28

2. 1032

36

HO

44

49

53

57

61

65

69

2. 1074

78

82

86

90

94

2. 1099

2. 1103

07

11

2. 1115

19

23

27

31

35

39

44

48

52

2. 1156

log E log P 

diff.l"=+0.03

5. 6970 7. 675

72

73

75

77

79

80

82

84

86

5.6988

89

91

93

95

97

5.6999

5. 7000

02

04

5.7006 7.683

08

09

11

13

15

17

19

20

22

5.7024

26

28

30

31

33

35

37

39

41

5. 7042 7. 691

44

46

48

50

52

64

55

57

59

5.7061

63

65

67

69

70

72

74

76

78

5. 7080 7. 698
GEOGKAPHIO TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 16°.

235

Lat.

o /

1C 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

GO

log A 

diff.l"=-0.04

8. 509 6149

46

44

42

40

37

35

33

30

28

8. 509 6126

24

21

19

17

14

12

10

08

05

8. 509 6103

6101

6098

96

94

91

89

87

84

82

8. 509 6080

77

75

73

70

68

66

63

61

59

8.509 6056

54

52

49

47

45

42

40

37

35

8. 509 6033

30

28

26

23

21

18

16

14

. 11

8. 509 6009

logB 

diff.l"=-0.12

8.512 3411

3404

3397

90

83

'76

70

63

56

49

8. 512 3342

35

28

22

15

08

3301

' 3294

87

80

8. 512 3273

66

59

52

45

39

32

25

18

11

8. 512 3204

3197

90

83

76

69

62

55

48

41

8.512 3133

26

19

12

3105

3098

91

84

77

70

8. 512 3063

56

48

41

34

27

20

13

3006

2998

8. 512 2991

logC 

diff.l"=+0.77

0. 86400

447

495

542

590

637

684

732

779

826

" 0. 86873

921

0.86968

0.87015

062

109

156

202

249

296

0. 87343

389

436

483

529

576

622

669

715

761

0. 87808

854

900

947

0. 87993

0. 88039

085

131

177

223

0. 88269

315

360

406

452

498

543

589

634

680

0. 88726

771

816

862

907

. 952

0. 88998

0.89043

088

133

0. 89178

logD 

diff.l"=+0.06

2. 1156

60

64

68

72

76

80

84

88

92

2. 1196

2. 1200

04

08

12

16

20

24

28

32

2. 1236

40

44

47

51

55

59

63

67

.71

2. 1275

79

83

87

90

94

2. 1298

2.1302

06

10

2. 1314

17

21

25

29

33

37

40

44

48

2. 1352

56

59

63

67

71

74

78

82

86

2. 1390

log E 

diff.l"=+0.03

5. 7080

82

84

85

87

89

91

93

95

97

5. 7099

5. 7101

03

04

06

08

10

12

14

16

5.7118

20

22

24

25

27

29

31

33

35

5. 7137

39

41

43

45

47

49

61

52

54

5. 7156

58

60

62

64

66

68

70

72

74

5. 7176

78

80

82

84

86

88

90

92

94

5. 7196

logF

7.698

7.705

7.712

7.719
236 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 17°.

Lat.

0 / 

17 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

> 23 ' 24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43.

44

45

46

47

48

49

50

51

62

53

54

55

56

57

58 59

60

log A 

diff.l"=-0.04

8.5096009

06

04

6002

5999

97

94

92

90

* 87

8.5095985

82

80

78

75

73

70

68

65

63

8. 509 5961

58

56

53

51

48

" 46

44

41

39

8.509 5936

34

31

. 29

26

24

21

19

16

14

8. 509 5912

09

07

04

5902

5899

97

94

92

89

8.5095887

84

82

79

77

74

72

69

67

64

8.509 5862

logB 

diff.l"=-0.12

8. 512 2991

84

77

70

62

55

48

41

34

26

8.512 2919

12

2905

2897

90

83

76

68

61

54

8.512 2846

39

32

24

17

10

2802

2795

88

80

8.512 2773

66

58

51

44

36

29

21

14

2707

8. 512 2699

92

84

77

69

62

65

47

40

32

8.512 2625

17

10

2602

2595

87

80

72

65

57

8.512 2550

logC 

diff.l"=-0.73

0. 89178

223

268

313

358

403

448

493

638

583

0. 89627

672

717

761

806

850

895

939

0. 89984

0. 90028

0. 90072 '

117

161

205

249

294

338

382

426

470

0. 90514

558

602

646

689

733

111

821

864

908

0. 90952

0.90995

0. 91039

082

126

169

212

256

299

342

0. 91386

429

472

515

558

601

644

687

730

773

0.91816

logD 

diff.l"=+0.06

2. 1390

93

2. 1397

2.1401

04

08

12

16

19

23

2. 1427

30

34

38

42

45

49

53

56

60

2.1464

67

71

75

78

' 82

85

89

93

2. 1496

2. 1500

04

07

11

14

18

22

25

29

32

2. 1536

39

43

47

50

54

57

61

64

68

2. 1571

75

78

82

85

89

92

96

2. 1599

2. 1603

2. 1606

logE 

diff.l"=+0.03

5. 7196

97

99

5. 7201

03

05

07

09

11

13

5. 7215

17

19

21

23

25

27

29

31

33

5.-7235

37

39

41

43

45

47

49

51 .

53

5. 7255

57

59

61

64

66

68

70

72

74

5. 7276

78

80

82

84

86

88

90

92

94

5. 7296

5. 7298

5. 7300

02

04

06

08

11

13

15

5.7317

logF

77719

7.726

7.732

7.738
GEOGEAPHIO TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 18°.

237

Lat.

o / 

18 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

66

57

58

59

60

log A. 

diff.l"=-0.04

8.509 5862

59

57

54

52

49

46

44

41

39

8. 509 5836

34

31

29

26

24

21

19

16

13

8. 609 5811

08

06

03

8.509 5801

8. 509 5798

96

93

90

88

8.509 5785

83

80

78

75

72

70

67

65

62

8. 509 5759

67

54

52

49

46

44

41

39

36

8. 609 5733

31

28

25

23

20

18

15

12

10

8. 609 5707

logB 

(Jiff. 1"= -0.13

8. 512 2550

42

35

27

19

12

8.5122504

8. 512 2497

89

81

8. 612 2474

66

59

51

43

36

28

20

13

8.512 2405

8. 512 2397 .

90

82

74

67

59

51

44

36

28

8.512 2320

13

8. 512 2305

8. 512 2297

90

82

74

66

58

51

8. 512 2243

35

27

19

12

8. 512 2204

8. 512 2196

' 8088

72

8. 512 2165

57

49

41

33

25

17

10

8.512 2102

8. 512 2094

8.5122086

logC 

diff.l"=+0.70

0. 91816

859

902

945

0. 91987

0.92030

073

115

168

201

0. 92243

286

328

371

413

456

498

640

582

625

0. 92667

709

751

793

836

, 878

920

0. 92962

0.93004

046

0. 93088

129

171

213

256

296

338

380

421

463

0. 93505

546

588

629

671

712

753

795

836

877

0. 93919

0.93960

0.94001

042

083

126

166

207

248

289

0. 94330

logD 

diff. 1"=+0.06 cliff

2. 1606

10

13

17

20

24

27

31

34

38

2. 1641 '44

48

51

55

58

62

65

68

72

2. 1675

79

82

85

89

92

95

2. 1699

2. 1702

06

2.1709 '

12

16

19

22

26

29

. 3236 '

39

2. 1742

46

49

52

56

69

62

65

69

72.

2. 1775

79

82

85

88

92

95

2. 1798

2. 1801

05

2.1808

logE 

1"=+0.03

5. 7317

19

21

23

25

27

29

31

33

35

5.7337

39

41

44

 46

48

50

52

54

56

5. 7358

60

62

64

67

69

71

73

75

77

5.7379

81

83

85

88 '

90

92

94

96

5.7398

5. 7400

02

05

07

09

11

13

15

17

19

5.7422

24

26

28

30

32

34

37

39

41

5.7443

logF 

diff. 10'= +3.0

7.738

7.744

7.750

7.766
238 GEOGBAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 19°.

Lat.

o / 

19 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff. 1"=- 0.04

8.509 5707

04

8.509 5702

8. 509 5699

96

94

91

89

86

83

8. 609 5681

78

75

73

70 

67

65

62

59

57

8.509 5654

52

49

46

43

41

38

35

33

30

8.509 5627

25

22

19

16

14

11

08

06

03

8. 509 5600

8.5095598

96

92

89

87

84

81

78

76

8.509 5573

70

68

65

62

59

57

54

51

48

8. 509 5646

log B log C log D 

diff.l"=-0.13 diff.l" = +0.67 diff. 1"= +0.06

8. 512 2086

78

70

62

54

46

38

30

22

14

8.512 2006

8.512 1999

91

83

75

67

59

51

43

35

8. 512 1927

19

11

8.512 1903

8. 512 1895

87

79

71

63

55

8. 612 1847

38

30

22

14

8.512 1806

8. 512 1798

90

82

74

8.512 1766

57

49

41

33

25

17

08

8.512 1700

8.512 1692

8.512 1684

75

67

59

51

43

34

26

18

10

8. 512 1602

0. 94330

370

411

452

493

534

575

615

656

697

0.94737

778

819

859

900

940

0. 94981

0. 95021

061

102

0.95142

182

223

263

303

344

384

424

464

504

0. 95544

584

624

664

704

744

784

824

863

903

0.95943

0.95983

0. 96022

062

102

142

181

221

260

300

0.96339

379

418

457

497

536

575

615

654

693

0.96733

2. 1808

11

14

18

21

24

27

30

34

37

2.1840

43

46

50

53

56

59

62 ,

66

69

2. 1872 '75

78

81

84

88

91

 94

2. 1897

2. 1900

2. 1903

07

10

13

16

19

22

25

28

31

2.1934

38

41

44

47

50

53

56 .

59 

62

2. 196568-

71

74

77

80

83

86

89

92

2. 1996

Jog E log F 

diff. 1"= +0.04 diff. 10' = +2.7

5.7443 7.756

45

47

49

52

54

56

58

60

62

5.7464

67

69

71

73

75

78

80

82

84

5. 7486 7. 761

88

91

93

95

97

5.7499

5. 7501

04

06

5.7508

10

12

15

17

19

21

23

26

28

5. 7530 7. 767

32

34

37

39

41

43

46

48

60

5. 7552

54

57

59

61

63

65

68

70

72

5.7574 7.772
GEOGEAPHIC TABLES AUD FOEMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 20°.

239

Lat.

' o / 

20 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

88

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

65

56

67

58

59

60

log A 

diff.l"= -0.05

8.509 5546

43

40

37

35

32

29

26

' 24

21

8. 509 5518

15

12

10

07

04

8. 609 5501

8. 509 5499

96

93

8.509 6490

87

85 o

82

79

76

73

71

68

65

8.609 5462

59

57

64

51

48

45

42

40

37

8.509 5434

31

28

25

23

20

17

14

11

08

8. 509 5406

03

8. 609 5400

8. 509 5397

94

91

88

86

83

80

8.509 6377

logB 

diff.l"=-0.14

8. 512 1602

8. 512 1593

85

77

68

60

52

44

35

27

8. 512 1519

.10

8.512 1502

8. 512 1494

85

77

69

60

52

44

8. 512 1435

27

18.

10

8. 512 1402

8. 512 1393

85

76

68

60

8.512 1351

43

34

26

17

09

8.512 1301

8.612 1292

84

76

8.512 1267

58

50

41

33

24

16

8.512 1207

8.512 1199

90

8.512 1182

73

64

56

47

39

30

21

13

8.512 1104

8. 512 1096

logC 

diff.l"=+0.64

0.96733

772

811

850

889

928

0. 96967

0.97006

045

084

0. 97123

162

201

240

279

318

356

395

434

472

0. 97511

550

588

627

666

704

743

781

819

858

0. 97896

935

0. 97973

0.98011

050

088

126

164

203

241

0. 98279

317

355

393

431

469

507

545

583

621

0.98659

697

736

773

811

848

886

924

962

0. 98999

0.99037

logD 

diff.l"=+0.05

2. 1996

2. 1999

2.2002

05

08

11

14

17

20

23

2.2026

28

31

34

37

40

43

46

49

52

2.2055

68

61

64

67

70

7376'

79

81

2.2084

87

90

93

96

2. 2099

2. 2102

05

08

10

2. 2113

16

19

22

25

28

81

33

36

39

2. 2142

45

48

50

53

56

59

62

65

67

2.2170

log E log F 

diff.l"=+0.04 diff.lO'=+2.5

5. 7574 7. 772

77

79

81

83.

86

88

90

92

94

5.7597

5. 7599

5.76Q1 i

03

06

08

10

12

15

17

ft. 7619 7. 777

21

24

26

28

30

33 ' 35

37

40

5. 7642

44

46

49

51

 53

55

58

60

62

5.7664 7.782

67

69

71

74

76

78

81

83

85

5.7688

90

92

94

97

5.7699

5. 7701

04

06

08

5.7711 7.787
240 GEOGBAPHIC TABLES AND FOKMULAS. 

TABLE 28. Geodetic position computations Continued.

LATITUDE 21°.

Lat.

o / 

21 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18 

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

66

57

68

59

60

log A 

diff.l"=-0.05

8. 509 5377

74

71

68

66

63

60

57

54

51

8.5095348

46

43

40

37

34

31

28

25

22

8.509 5320

17

14

11

08

05

8.509 5302

8. 509 5299

96

93

8. 509 5290

88

85

82

79

76

73

70

67

64

8. 609 5261

58

55

52

49

46

44

41

38

35

8.509 5232

29

2623'

20

17

14

11

08

05

8.509 5202

logB 

diff.l"=-0.15

8. 512 1096

87

79

70

62

53

45

36

27

19

8.512 1010

8.512 1002

8. 512 0993

84

76

67

58

50

41

32

8. 512 0924

15

8. 512 0906

8. 512 0897

89

80

71

62

54

45

8.512 0836

27

19

10

8. 512 0801

8. 512 0792

84

75

66

57

8. 512 0748

39

31

22

13

8. 512 0704

8.512 0695

86

78

69

8. 512 0660

51

42

33

24

15

8. 512 0606

8.' 512 0598

89

80

8. 512 0571

 log C log D 

diff.l"= +0.062 diff.l"=+0.04

0. 99037

075

112

150

187

225

262

300

337

375

0. 99412

450

487

524

562

599

636

673

711

748

0. 99785

822

859

896

933

0. 99971

1. 00008

045

082

119

1. 00156

192

229

266

303

340

377

413

450

487

1. 00524

560

597

634

670

707

743

780

816

853

1.00890

926

962

1. 00999

1.01035

072

108

144

181

217

1. 01253

2. 2170

73

76

79

81

84

87

90

93

95

2. 2198

2. 2201

04

07

09

12

15

18

20

23

2. 2226

29

31

34

37

40

42

45

48

50

2.2253

56

59

61

64

67

69

72

75

78

2. 2280

83

86

88

91

94

96

2. 2299

2.2301

04

2. 2307

09

12

15

17

20

23

25

28

31

2.2333

logE 

diff.l"=+0.04

5. 7711

13

15

18

20

22

24

27

29

31

5.773436'

38

41

43

45

48

50

52

55

5. 7757

59

62

64

66

69

71

73

76

- 78

5.7780

83

85

87

. 90

92

94

97

5.7799

5. 7802

5.7804

06

09

11

13 

16

18

20

23

25

5.7828

30

32

35

37

40

42

44

47

49

5.7861

lOgF 

diff.lO'=+2.2

7.787

7. 791

j

7; 796

7.800
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 22°.

241

Lat.

o /

22 00

1

2

3

4

05

' 76

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

69

60

log A 

diff.l"=-0.05

8. 509 5202

8. 509 5199

96

93

90

87

84

81

78

75

8.509 5172

69

66

63

60

57

54

51

48

45

8. 509 5142

39

36

33

30

27

24

21

18

15

8. 509 5112

09

06

03

8.509 5100

8.509 5097

94

91

88

85

8. 509 6082

79

76

72

69

66

63

60

57

54

8. 509 5051

48

45

42

39

36

33

30

27

23

8.509 5C20

lOgB 

diff.l"=-0.15

8. 512 0571

62

53

44

35

26

17

8. 512 0508

8.512 0499

90

8. 512 0481

72

63

54

45

36

27

18

09

8. 512 0400

8.5120391

82

73 <64

55

46

37

28

19

10

8. 512 0301

8.512 0292

83

73

64

55

46

37

28

19

8. 512 0210

8. 512 0200

8.512 0191

82

73

64

55

46

36

27

8.512 0118

09

8.512 0100

8. 512 0090

81

72

63

54

44

35

8. 512 0026

logC 

diff.l"=+0.59

1. 01253

289

326

362

398

434

470

506

542

578

1. 01615

651

687

723

759

794

830

866

902

938

1. 01974

1. 02010

045

081

117

153

 , 188

224

260

295

1. 02331

367

402

438

473

509

544

580

615

651

1. 02686

721

757

792

828

863

898

933

1 -02969

1 -03004

1. 03039

074

109

145

180

215

« 250

285

320

355

1.03390

logD 

diff.l"=+0.04

2.2333

36

38

41

44

46

49

51

54

57

2.2359

62

64

67

70

72

75

77

80

83

2.2385

88

90

93

95

2.2398

2. 2400

03

06

08

2. 2411

13

16

18

21

23

26

28

31

33

2. 2436

38

41

43

46

48

51

53

56

58

2.2461

63

66

68

70

73

75

78

80

83

2.2485

log E log F 

diff.l"=+0.04 diff.lO'=+2.0

5.7851 7.800

54

56

59

61

63

66

68

71

73

5. 7875

78

80

83

86

87

90

92

95

97

5. 7899 7. 804

5. 7902

 04

07

09

11

14

16

19

21

6. 7924

26

28

31

33

36

38

41

43

45

5. 7948 7. 808

.50

53

55

58

60

62

65

67

70

5.7972

75

77

80

82

84

87

89.

92

94 

5.7997 7.812 *

41623° 16 16.
242 QEOGBAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 23°.

Lat.

0 /

23 00

1

2

3

4

! 05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

63

54

55

56

57

58

59

. 60

log A 

diff.l"=-0.05

8. 509 5020

17

14

11

08

05

8. 509 5002

8. 509 4999

96

93

8. 509 4990

87

83

80

77

74

71

68

 65

62

8. 509 4959

55

52

49

46

43

40

37

34

31

8. 509 4927

24

21

18

15

12

09

05

8. 509 4902

8. 509 4899

8. 509 4896

93

90

87

83

80

77

74

71

68

8. 509 4865

61

58

55

52

49

45

42

39

36

8. 509 4833

logB 

diff.l"=-0.16

8. 512 0026

17

8.5120008

8. 511 9998

89

80

71

61

52

43

8. 511 9934

24

15

8. 511 9906

8. 511 9896

87

' 78

 68

59

50

8.511 9840

31

22

12

8.511 9803

8.511 9794

84

75

66

56

8.511 9747

37

28

19

09

8.511 9700

8. 511 9690

81

71

62

8.511 9653

43

34

24

15

8.511 9605

8.511 9596

86

77

67

8.511 9558

48

39

29

20

10

8.511 9501

8.511 9491

82

72

8.511 9463

logC 

diff.l"=+0.57

1. 03390

425

460

495

530

565

600

634

669

704

1. 03739

774

809

843

878

913

947

1. 03982

1. 04017

052

1. 04086

121

155

190

224

259

293

328

362

397

1.04431

466

500

534

569

603

637

672

706

740

1. 04775

809

843

877

911

945

1.04980

1. 05014

048

082

1. 05116

150

184

218

252

286

320

354

388

422

1.05456

logD 

diff.l"=+0.04

2. 2485

88

90

93

95

2. 2497

2.2500

02

05

07

2. 2510

12

14

17

19

22

24

26

29

31

2.2534

36

3&

41

43

45

48

50

53

55

2. 2557

60

62

64

67

69

71

74

76

78

2. 2581

83

85

88

90

92

95

97

2. 2599

2. 2601

2. 2604

06

09

11

13

16

18

20

23

25

2. 2627

log E log F 

diff.l"=+0.04 diff.lO'=+1.8

5. 7997 7. 812

5. 7999

5. 8002

04

07

09

12

14

16

19

5. 8021

24

26

29

31

34

36

39

41

44

5. 8046 7. 816

49

51

54

56

59

61

64

66

69

5. 8071

74

76

79

81

84

86

89

91

93

5.8096 7.819

5. 8099

5. 8101

04

06

09

11

14

16

19

5. 8121

24

26

29

31

. 34

36

39

41

44

5. 8146 7. 823
.GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 28. Geodetic position computations Continued.

LATITUDE 24°.

243

Lat.

O '

24 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

 49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.05

8. 509 4833

30

26

23

20

17

14

10

07

04

8.609 4801

8.509 4798

94

91 . 88

85

82

78

75

72

8.609 4769

66

62

59

56

53

50

46

43

40

8. 509 4737

33

30

27

24

20

17

14

11

07

8. 509 4704

8. 509 4701

8. 509 4698

94

91

38

85

81

78

75

8. 509 4672

. 68

' 65

62

59

55

52

49

45

42

8. 509 4639

logB 

cliff. 1"= -0.16

8. 511 9463

63

44

34

24

15

8. 511 9405

8. 511 9396

86

77

8.511 9367

58

48

38

29

19

09

8.511 9300

8.511 9290

81

8. 611 9271

61

52

42

32

23

13

8. 511 9203

8.511 9194

84

8.511 9174

65

55

45

35

26

16

8.511 9106

8. 511 9096

87

8.511 9077

67

58

48

38

28

18

8.511 9009

8.511 8999

89

8. 511 8979

70

60

50

40

30

21

11

8.511 8901

8. 511 8891

8.611 8881

logC 

cliff. 1"= +0.56

1. 05456

490

523

557

591

625

658

692

726

760

1. 05794

827

861

894

928

962

1. 05995

1.06029

062

096

1.06130

163

197

230

263

297 

330

364

397

431

1. 06464

497

530

564

597

630

664

697

730

763

1.06797

830

863

896

929

962

1. 06995

1. 07028

061

095

1.07128

161

194

226

259

292

326

358

391

424

1.07457

logD 

diff.l"=+0.04

2. 2627

29

31

34

36

b8

41

43

45

47

2.2650

52

54

56

59

61

63

65

68

70

2.2672

74

77

79

81

83

85

88

90

92

2. 2694

96

2. 2699

2. 2701

03

05

07

10 ' 12

14

2.2716

18

20

23

25

27

29

31

33

36

2. 2738

40

42

44

46

49

51

53

55

57

2.2759

log E log F 

cliff. 1"= +0.04 cliff. 10'= +1.6

5. 8146 7. 823

49

51

54

57

59

62

64

 67

69

5. 8172

74

77

79

82

85

. 87

90

92

95

5.8197 7.826

5. 8200

02

05

07

10

13

15

18

20

5. 8223

25

28

31

33

36

38

41

43

46

5. 8249 7. 829

51

54

56

59

61

64

67

69

72

5. 8274

77

80

82

85

87

90

92

95

5. 8298

6.8300 7.832
244 GEOGKAPHIC TABLES AND FORMULASt 

TABLE 28. Geodetic position computations Continued.

LATITUDE 25°.

Lat.

o /

25 00 ' 1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0-06

8. 509 4639

36

32

29

26

23

19

16

1309 "

8. 509 4606

03

8. 509 4600

8. 509 4596

93

90

86

83

80

76

8. 509 4573

70

66 .

63

60

56

53

50

46

43

8.509 4540

37

33

30

26

23

20

17

13

10

8. 509 4507

03

8.5094500

8.509 4496

93

90

86

83

80

76

8. 509 4473

70

66

63

60

56

53

50

46

43

8. 509 4439

logB 

diff.l"=-0-16

8. 511 8881

. 71

62

52

42

32

22

12

8.511 8802

8.511 8793

8.511 8783

73

63

53

43

33

23

13

8. 511 8704

8.511 8694

8.511 8684

74

64

54

44

34

24

14

8.511 8604

8. 511 8594

8. 511 8584

 74

64

54

44

34

24

14

8.511 8504

8.511 8494

8. 511 8484

74

64

54

44

34

24

14

8. 511 8404

8.511 8393

8.511 8383

73

63

53

43

33

23

13

8. 511 8303

8. 511 8293

8. 511 8283

- logC 

diff.l"=-rO-54

1. 07457

490

523

555

588

621

654

687

719

752

1. 07785

817

850

883

915

948

1.07981

1.08013

046

078

1. 08111

143

176

208

241

. 273

306

338

370

403

1. 08435

468

500

532

565

697

629

662

694

726

1. 08758

791

823

855

887

919

951

1. 08984

1. 09016

048

1.09080

112

144

176

208

240

272

304

336

368

1. 09400

logD 

diff.l"=+0-03

2. 2759

61

63

66

68

70

72

74

76

78

2. 2780

82

85

87

89

91

93

95

97

2. 2799

2.2801

03

05

07

10

12 .

14

16

18

20

2. 2822

24

26

28

30

32

34

36

38

40

2.2842

44

46

48

50

52

54

56

58

60

2. 2862

64

66

68

70

72

74

76

78

80

2. 2882

logE 

diff.l"=+0-04

6.8300

03

05

08

11

13

16

18

21

24

5. 8326

29

32

34

37

39

42

45

47

50

5.8352

55

59

60

63

66

68

71

73

76

5. 8379

81

84

87

. 89

92

94

5.8397

5.8400 02

5. 8405

08

10

13

16

18

21

24 -

26

29

5. 8431

3437 °

39

42

45

47

50

53

55

5. 8458

logF 

diff.!0'=+l-5

7.832

7.835

7.838

7.841
GEOGRAPHIC TABLES ADD FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 26°.

245

Lat.

0 /

26 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

' 21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

- 40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

68

59

60

log A 

diff.l"=-0-06

8. 509 4439

36

33

29

26

22

19

16

12

09

8. 509 4406

8. 509 4402

8.509 4399

 95

92

88

85

82

78

75.

8. 509 4372

68

65

61

58

54

51

48

44

41

8. 509 4337

34

31

27

24

20

17

13

10

07

. 8. 509 4303

8. 509 4300

8. 509 4296

93

89

86

83

79

76

72

8. 509 4269

65

62

58

65

52

48

46

41

38

8. 609 4234

logB 

diff.l"=-0-17

8.511 8283

72

62

52

42

32

22

12

8.511 8201

8. 511 8191

8.511 8181

71

61

51

40

30

20

10

8. 511 8100

8.611 8089

8.511 8079

69

59

48

38

28

18

8.511 8008

8.511 7997

87

8.511 7977

67

66

46

36

25

15

8.511 7905

8.511 7895

84

8. 511 7874

64

53

43

33

'22

12

8.511 7802

8. 511 7791

81

8.511 7771

60

50

40

29

19

8.511 7709

8.511 7698

88

77

8.511 7667

logC 

diff.l"=+0-52

1. 09400

432

464

496

527

559

591

623

655

687

1. 09718

750

782

814

845

877

909

940

1. 09972

1.10004

1. 10036

067

099

130

162

194

225

257

288

320

1. 10351

383

414

.446

477

509

640

571

603

634

1.10666

697

728

760

791

822

854

885

916

947

1. 10979

1. 11010

041

072

103

134

166 197

228

259

1. 11290

logD 

diff.l"=+0-03

2.2882 ' 84

86

88

90

92

94

96

2.2898

2. 2900

2.2902 ' 04

06

08

10

12

14

16

18

20.

2.2922

23

25

27

29

31

33

35

3739 '

2. 294143'

45

47

48

50 :' 52 -

54

56

58

2.2960 ' '

62 .' 63 '

65

67

69

71

73

75

77

2. 2978

80

82

84

86

88

89

91

93

95

2. 2997

log E log F 

diff.l"=+0-04 difE.10'=+l-3

5.8468

61

63

66

69

71

74

77

79

82

5.8485

88

90

9396 "

5.8498

5.8501

04

06

09

5.8512

14

17

20

22

25

28

30

33

36

6.8539

41

44

47

49

52

55

57

60

63

5.8566

68

71

74

76

79

82

85

87

90

5. 8593

95

5.8598

5.8601

04

06

09

12 .

14

17

5.8620

7.841

7.844

7.846

7.849
246 GEOGKAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 27°.

Lat.

o / 

27 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

62

53

54

55

56

57

58

59

60

log A diff.l"=-0.0'6

8. 509 4234

31

27

24

20

17

13

10

06

03

8. 509 4200

8. 509 4196

93

89

86

82

79

75

72

68

8. 509 4165

61

68

54

51

47

44

40 37

33

8.509 4130.

26

23

19

16

12

08

05

8.5094101

8.509 4098

8. 509 4094

91

87

84

80

77

73

70

66

63

8. 509 4059

56

52

49

45

41

38

34

' 31

27

8.509 4024

logB 

diff.l"=-0.18

8.511 7667

57-

46

36

25

15

8.511 7605

8.511 7594

84

73

8.511 7563

53

42

32

21

11

8.511 7500

8. 511 7490

79

69

5.511 7458

48

37

27

16

8.511 7406

8.511 7395

85

74

64

8.511 7353

43

32

22

11

8.511 7301

8.511 7290

80

69

58

8.511 7248

37

27

16

8.511 7206

8.511 7195

84

74

63

53

8.511 7142

31

21

10

8.511 7100

8.511 7089

78

68

57

46

8.511 7036

logC 

diff.l"=+0.51

1. 11290

321

352

383

414

445

476

507

538

569

1. 11600

631

662

693

724

755

786

817

848

878

1.11909

940

1. 11971

1. 12002

032

063

094

125

156

186

1. 12217

248

278

309

340

370

401

432

462

493

1. 12523

554

584

615

646

676

707

737

768

798

1. 12829

859

889

920

950

1. 12981

1.13011

041

072

102

1. 13132

logD 

diff.l"=+0.03

i. 2997

2. 2999

 2. 3001

03

04

06

08

10

12

14

2.3015

17

19

21

23

24

26

28

30

32

2. 3033

35

37

39

41

42

44

46

48

50

2.3051

53

55

57

58

60

62

64

65

67

2. 3069

70

72

74

76

78

79

81

83

85

2. 3086

88

90

91

93

95

97

2.3099

2.3100

02

2.3104

logE 

diff.l"=+0.05

5. 8620

23

25

28

31

34

36

39

42

44

5.8647

50

53

55

58

61

64

66

69

72

6.8675

77

80

83

86

88

91

94

97

5.8699

5.8702

05

08

10

13

16

19

22

24

27

5. 8730

33

35

38

41

44

46

49

52

55

5. 8757

60

63

66

.69

72

74

77

80

83

6.8785

logF 

diff.lO'=+l.l

7.849

7.851

7.853

7.855
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 28. Geodetic position computations Continued.

LATITUDE 28°.

247

Lat.

0 /

28 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

16

16

17

18

19

20

2122-

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.06

8.509 4024

20

17

13

10

06

8. 609 4002

8. 509 3999

95

92

8.509 3988

85

81

78

74

70

67

63 .

60

66

8.509 3952

49

45

42

38

35

81

27

24

20

8. 509 3917

1309 -'

06

8. 509 3902

8. 509 3899

95

92

88

84

8.509 3881

77 .

73

70

66

63

69

65

62

48

8. 509 3845

41

37

34

30

26

23

19

16

12

8. 509 3808

logB 

diff. 1"=-0.18

8. 511 7036

25

14

8. 511 7004

8.511 6993

 82

72

61

5040 

8. 511 6929

18

8.511 6908

8.511 6897

86

75

65

54

43

33

8.511 6822

11 .

8.511 6800

8. 611 6790

79

68

67

47

36

26

8. 511 6714

8.511 6704

8.511 6693

82

71

61

50

39

28

17

8.511 6607

8.511 6696

85

74

63

52

42

31

20

8.511.6509

8.511 6498

87

76

66

55

44

33

22

11

8.511 6400

8. 511 6389

logC 

diff. 1"= +0.50

1. 13132

163

193

223

254

284

314

345

375

405

1. 13435

465

496

526

556

586

616

646

677

707

1.13737

767

797

827

857

887

917

j 947

1. 13977

1.14007

1.14037

067

097

127

157

187

217

247

277

307

1. 14337

366

396

426

456

486

516

545

575

605

1. 14635

664

694

724

754 

783

813

843

872

902

1.14932

logD 

diff. 1"= +0.03

2. 3104

05

07

09

10

12

14

16

17

19

2. 3121

22

24

26

27

29

81

32

84

36

2. 3187

39

41

.42

44

46

47

49

61

52

2.3164

56

67

59

61

62

64

65

67

69

2. 3170

72

74

75 .

77

78

80

82

83

85

2.3187

88

90

91

93

95

96

98

2. 3199

2. 3201

2. 3203

' logE 

diff. 1»= +0.05

6.8785

88

91

94

97

5.8799 

5.8802

05

08.

11

5. 8813

16

19

22

25

27

30

33

86

39

5.8841

44

47

50

53

55

68

61

64

67

5. 8870

72

75

78

81

84

87

89

92

95

5. 8898

5. 8901

04

06

09

12

15

18

21

23

5.8926

29

32

35

3*

40

43

46

4952 '

6.8956

lOgF 

diff. 10"= +1.0

7.855

;

'

7.857

7.859

7.861
248 GEOGRAPHIC TABLES AND FORMULAS..

TABLE 28. Geodetic position computations Continued.

LATITUDE 29°.

Lat.

0 /

29 00.

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

67

68

69

60

log A 

diff.l"=-0.06

8.509 3808

05

8.509 3801

8. 509 3797

94

90

86

83

79

76

8. 509 3772

68

65

61

57

54

50

46

43

39

8.509 3735

32

28

24

21

17

13

10

06

8. 509 3702

8.509 3699

95

91

88

84

80

77

73

69

66

8.609 3662

58

55

51

47

44

40

36

33

29

8.509 3625

21

18

14

10

07

8. 509 3603

8.509 3599

96

92

8. 509 3588

' logB 

diff.l"=-0.18

8. 511 6389

78

68

57

46

35

24

13

8. 511 6302

8.511 6291

8. 611 6280

69

58

47

36

26

15

8. 511 6204

8.511 6193

82

8.511 6171

.60

49

38

27

16

8.511 6105

8. 511 6094

83

72

8.511 6061

50

39 -

28

17

8.511 6006

8.511 6995

84

73

61

8.511 6950

39

28

17

8. 511 5906

8.511 5895

84

73

62

51

8.611 5840

29

18

8. 511 6806

8. 511 5795

84

73

62

61

40

8.6115729

. Jog C 

diff.l"=+0.49

1. 14932

961

1. 14991

1.15021

050

080

109

139

168

198

1.15228 S

257

287

316

346

375

405

434

464

493

i: 15522

552

681

611

640

670

699

728

758

787

1. 16816

846

876

904

934

963

1. 15992

1.16021

051

. 080

1. 16109

138

167

197

226

255

284

313

343

372

1. 16401

430

459

488

517

646

575

604

633

663

1.16692

logD 

diff.l"=+0.03

2.3203

04

06

07

09

10

12

14

15

17

2. 3218

20

21

23

25

26

28

29

31

. 32

2.3234

35

37

38

40

42

43

o 45

46

48

2.3249

61

52

54

55

57

58

60

61

63

. 2. 3264

66

67

69

70

72

73

75

76

78 .

2. 3279

81

82

84

85

87

88

90

91

93

2.3294

log E 

diff.l"=+0.05

5.8955

58

60

63

66

69

72

75

78

80

5.8983

86

89

92

95

5. 8998

5.9000

03

06

09

5. 9012

15

18

21

23

26

29

32

35

38

5.9041

43 0 46

49

62

55

"'. 68

61

64

67

5. 9069

. 72

75

78

81

84

87

90

93

96

5. 9098

5. 9101

04

07

10

13

16

19

22

25

5. 9127

logF 

diff.lO'=+0.8

7.861

7.863

7.864

7.866
GEOGKAPHIC TABLES AND FOBMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 30°.

249

Lat.

o / 

30 00

1

2

3.

4

05

6

7

8

9

10

11

12

13

14

16

16

17

18

, 19

20

21

22 ' 23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

 45

46

47

48

49

50

61

52

« 53

54

65

56

67

58

59

60

log A 

diff.l''=-0.06

8.609 3588

84

81

77

73

09

66

62

58

55

8. 509 3551

47

43

40

36

32

29

25

21

17

8.609 3514

10

06

8.609 3502

8.609 3499

95

91

88

84

80

8. 509 3476

72

69

65

61

57

54

50

46

42

8. 509 3439

35

31

27

24

20

16

. . 12

09

05

8. 509 3401

8. 609 3397

94

90

86

82

78

75

71

67

8.509 3363

logB 

diff.l"=-0.19

8.511 5729

18

8. 511 5706

8.511 5695

84

73

62

61

40

28

8.511 5617

8.511 5606

8.511 5595

84

73

61

60

39

28

17

8.5115605

8.511 5494

83

72

61

49

38

27

16

8. 511 6404

8. 511 5393

82

71

59

48

37

26

14

8.511 6303

8. 611 6292

8.511 5281

69

68

47

35

24

13

-8.511 5202

8.511 5190

79

8. 511 5168

56

45

34

22

11

8. 511 5100

8. 511 5088

77

66

8.511 5064

logC 

diff.l"=+0.48

1. 16692

721

750

778

807

836

865

894

923

952

1. 16981

1. 17010

039

068

097

126

155

184

212

241

1.17270

299

328

357

385

414

443

472 500'

529

1.17658

687

615

644

673

701

730

759

788

816

1. 17845

874

902

931

959

1. 17988

1.18017

045

074

102

1.18131

160

188

217

245

274

302.

331

359

388

1. 18416

logD 

diff.l"=+0.02

2. 3294

96

97

. 2.3298

2.3300

01

03

04

06

07

2. 3309

10

12

13

14

16

17

18

20

22

2.3323

24

26

27

29

30

32

33

34

36

2. 3337

39

40

41

43

44

46

47

48

50

2.3351

53

54

65

57

58

59

61

62

64

2.3365

66

68

69

70

72

73

74

76

77

2.3379

logE 

diff.l"=+0.05

5. 9127

30

33

36

39

42

45

48

51.

54

5.9157

69

62

65

68

71

74

77

80

83

5. 9186

89

92

95

5. 9198

5.9200

03

06

09

12

5.9215

18

21

24

27

30

33

36

39

42

5.9246

48

61

63

66

59

62

65

68

71

5.9274

77

80

83

86

89

92

95

5.9298

6.9301

5.9304

logF 

diff.lO'=+0.7

7.866

7.867

7.869

7.870
250 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 31°.

Lat.

o / 

31 00

1

2

3

4

05 .

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

. 46

47

48

49

50

51

52

53-

54

55

56

57

58

59

60

log A 

diff.l" = -0.06

8. 509 3363

60

56

52

48

44

41

37

 33

29

8. 509 3326

22

18

14

10

06

8.509 3303

8. 509 3299

95

91

8. 509 3287

84

80

76

72

68

65

61

57

53

8. 509 3249

46

42

38

34

30

26

23

19

 15

8. 509 3211

07

03

8.509 3200

8. 509 3196

92

88

84

81

77

8.509 3173

69

66

61

57

54

50

46

42

38

8. 509 3134

logB 

diff.l"=-0.19

8.511 CJ54

43

32

20

8.511 5009

8.511 4998

86

75

64

52

8. 511 4941

29

18

8. 511 4907

8. 611 4895

84

72

61

50

38

8.511 4827

15

8.511 4804

8. 511 4793

81

70

58

47

36

24

8. 511 4713

8. 511 4701

8. 511 4690

78

67

55

44

32

21

8.5114609

8. 511 4598

86

75

63

52

40

29

17

8.511 4506

8.511 4494

8. 511 4483

71

60

48

37

25

14

8. 511 4402

8.511 4391

79

8.511 4368

logC 

diff.l"=+0.47

1.18416

445

473

501

530

558

587

615

643

672

1.18700

729

757

785

813

842

870

898

927

955

1.18988

1. 19012

040

068

096

125

153

181

209

238 .

1. 19266

294

322

351

379

407

435

463

491

520

1. 19548

576

604

632

660

688

716

744

772

800

1. 19828

856

884

912

940

968

1. 19996

1.20024

052

080

1.20108

logD 

diff.l"=+0.02

2. 3379

80

81

83

84

85

87

88

89

91

2.3392

93

96

96

97

2.3399

2.3400

01

03

04

2. 3405

06

08

09

10

12

13

14

16

17

2. 3418

20

21

22

23

25

26

27

29

30

2.3431

32

34

35

36

37

39

40

41

43

2.3444

45

46

48

49

50

51

53

54

55

2. 3456

logE 

diff.l"=+0.05

5. 9304

07

10

13

. 16

19

22

25

28

31

5.9334

37

39

42

45

48

51

54

57

60

5.9368

66

69

72

76

78

81

84

87

90

5. 9393

96

5.9399

5.9402

05

08

11

14

17

20

5. 9423

26

29

32

35

38

41

44

47

50

6.9453

56

59

62

65

68

72

75

78

81

5.9484

logF 

diff.lO'=+0.5

7.870

7.871

7.872

7.873

..
GEOGBAPHIC TABLES AND FOKMULAS.

TABLE 28. Geodetic position compulations Continued. 

LATITUDE 32°.

251

Lat.

o /

32 00

1

2

3

4

05,,

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

I 40

' 41

42

43

44

45

46

47

48 49

50

51

52

53

64

55 1 56

57

58

69

60

log A 

cliff. 1"= -0.06

8. 509 3134

31

27

23

19

15

11

07

04

8.509 3100

8. 509 3096

92

88

84

80

76

73

69

65

61

8,509 3057

63

49

46

42

38

34

30

26

22

8.509 3018

15

11

07

8. 609 3003

8.609 2999

96

91

87

83

8.509 2980

76

72

68

64

60

66

52

48

44

8.509 2940

37

33

29

25

21

17

13

09

05

8.609 2901

logB 

cliff. 1"= -0.19

8. 511 4368

56

44

33

21

8.511 4310

8. 511 4298

87

75

63

8. 511 4252

40

29

17

8.511 4205

8. 511 4194

82

71

59

47

8.511 4136

24

13

8. 511 4101

8. 611 4089

78

66

54

43

31

8. 611 4020

8.511 4008

8.611 3996

86

73

61

50

38

26

15

8. 511 3903

8.611 3891

79

68

56

44

33

21

8.511 3809

8.511 3798

8.511 3786

74

63

51

39

27

16

8.511 3704

8.511 3692

80

8.611 3669

. log C 

(Jiff. 1"= +0.46

1.20108

136

164

192

220

248

276

304

332

360

1.20387

415

443

471

499

527

555

582

610

638

1.20666

694

722

749

777

805

833

860 .

888

916

1.20944

971

1. 20999

1. 21027

054

082

110

137

165

193

1. 21220

248

276

303

331

358

386

414

441

469.

1. 21496

524

551

579

607

634

662

689

717

744

1. 21772

logD 

cliff. 1"= +0.02

2.3456

57

59

60

61

62

64

66

66

67

2. 3469

70

71

72

73

75

76

77

78

79

2.3481

82

83

84

85

87

88

89

90

91

2. 3493

94

95

96

97

2. 3499

2.3500

01

02

03

2. 3504

. 06

07

08

09

10

11

13

14

15 .

2. 3516

17

18

19

21

22

23

24

26

26

2.3527

log E log F 

cliff. 1"= +0.05 diff.lO'=+0.3

5. 9484 7. 873

87

90

93

96

5. 9499

' 5.9502

05

08

11

5. 9514

17

20

23

26

29

32

36

38

41

5.9544 7.874

47

50

53

66

60

63

66

69

72

5. 9575

78

81

84

87

90

93

96

5. 9599

5. 9602

5. 9605 7. 875

08

11

15

18

21

24

27

30

33

5.9636

39

42

45

48

51

64

68

61

64

5.9667 7.876
252 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 33°.

Lat.

o / 

33 00 .

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

.24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

1 58

59

60

lop A 

diff.l"=-0.07

8. 509 2901

8.5092897

94

90

86

8278 

74

70

66

8. 509 2862

58

54

51

47

43

39

35

31

27

8. 509 2823

19

15

11

07

8.509 2803

8. 509 2799

95

91

88

8. 509 2784

80

76

72

68

64

60

56

52

48

8. 509 2744

40

36

32

28

24

20

16

12

08

8. 609 2704

8. 509 2701

8. 509 2697

93

89

85

8177-

73

69

8. 509 2665

logB 

diff.l"=-0.20

8. 511 3669

57

45

33

22

8.511 3610

8.611 3598

86

75

63

8.511 3551

39

28

16

8.511 3504

8. 511 3492

80

69

57

45

8.511 3433

21

8.511 3410

8.511 3398

86

74

62

51

39

27

8.511 3315

8.511 3303

8.511 3291

80

68

56

44

32

20

8.611 3209

8.511 3197 '

85

73

61

49

37

25

13

8.511 3102

8.511 3090

8.511 3078

66

54

42

30

18

8.511 3006

8. 611 2995

83

71

8.6112959

logC 

diff.l"=+0.45

1. 21772

799

827

854

882

909

937

964

1.21992

1. 22019

1.22047

074

101

129

156

184

211

238

266

293

1.22321

348

376

403

430

457 .

485

512

539

567

1.22594

621

648

676

703

730

757

785

812

839

. 1.22866

893

921

948

1 -22975

1.23002

029

057

084

111

1.23138

165

192

220

247

274

301

328

355

382

1.23409

logD 

diff.l"=+0.02

2. 3527

 29

30

31

32

33

34

35

36

38

2. 3539

40

41

42

43

44

45

46

48

49

2.3550

51

52

53

54

55

66

57

58

60

2. 3561

62

63

64

65

66

67

68

69

70

2.3571

72

73

75

76

77

78

79

80

81

2.3582

83

84

85

86

87

88

89

90

91

2.3592

logE 

diff.l"=+0.05

5. 9667

70

73

76

79

82

85

88

92

95

5. 9698

5.9701

04

07

10

13

16

19

22

26

5. 9729

32

35

38

41

44

47

50

53

57

5. 9760

63

66

69

72

75

78

81

85

88

- 5.9791

94

5.9797

5.9800

03

06

10

13

16

19

5. 9822

25

28

31

35

38

41 " 44

47

50 .

5.9853

log-F 

diff.lO'=+0.2

7.875

7.876

7.876

7.877
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 28. Geodetic position computations Continued.

LATITUDE 34°.

253

Lat.

0 /

34 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

. 22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45 46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff. 1"= -0.07

8.509 2665

61

57

53

49

45

41

37

33

29

8. 509 2625

21

17

13

09

05

8.609 2601

8.5092597

93

89

8.609 2585

81

77

73

69

65

61

67

53

49

8. 509 2545

41

37

33

29

25

21

17

13

09

8.509 2505

8. 509 2501

8. 509 2497

93

89

85

81

77

73

69

8. 509 2465

61

57

53

49

45

4137"

33

29

8.509 2425

logB 

diff. 1"=-0.20

8.511 2959

47

35

23

8.511 2911

8. 511 2899

87

75

63

51

8.511 2840

28

16

8.511 '.804

8.511 2792

80

68

56

44

32

8. 511 '2720

 8.511 2708

8. 511 2096

o 84

72

60

48

36

24

12

8.511 2600

8.511 2588

76

64

52

40

28

16

8.511 2504

8.511 2492

8.511 2480

68

56

44

32

20

8.511 2408

8. 511 2396

84

72

8.511 2360

48

35

23

8.511 2311

8. 511 2299

87

75

63

51

8. 511 2239

logC 

diff. 1"= +0.45

1. 23409

437

464

491

518

545

572

599

626

653

1. 23680

707

734

761

788

815

842

869

896

923

1.23950

1.23977

1. 24004

031

058

085

112

139

165

192

] . > 219

246

273

300

327

354

381

408

434

461

1. 24488

515

542

569

595

622

649

676

703

729

1. 24756

783

810

837

863

890

917

944

970

1. 24997

1.26024

logD 

diff. 1"= +0,02

2. 3592

93

94

95

96

97

98

2. 3599

2.3600

01

2. 3602

03

04

05

06

07

08

09

10

11

2.3612

13

14

15

16

17

18

19

20

21

2. 31.22

23

24

25

26

27

28

29

30

31

2. 3632

33

34

35

36

37

38

39

40

41

2. 3642

43

43

44

45

46.

47

48

49

50

2.3651

log E log F 

diff.l"=+0.05 diff.lO'=+0.0

5. 9853 * 7. 877

57

60

63

66

69

72

75

79

82

5.9885

88

91

94

5. 9897

5.9901

04

07

10

13 .

5.9916 7.877

19

23

26

29

32

35

38

42

45

5.994851'

54

57

61 -

64

67

70

73

76 .

5. 9980 7. 877

83

86

89

92

96

5. 9999

6.0002

05

08

6.0011

15

18

21

24

27.

31

34

' 37

40

6.0043 7.877
254 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 35°.

Lat.

0 /

35 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

on 

oa

40

41

42

43

44

45

46

47

48

49

50

61

62

63

54

55

56

57

58

59

60

log A 

diff.l"= 0.07

8. 509 2425

21

17

13

09

' 05

8. 509 2401

' 8. 509 2396

92

88

8. 509 2384

80

76

72

68

64

60

56

52

48

8. 509 2344

40

36

32

28

24

20

16

12

08

8. 509 2304

8. 609 2300

8. 509 2296

92

87

83

79

75

71

. 67

8. 509 2263

59

55

51

47

43

39

35

31

27

8. 509 2222

18

14

10

06

8. 509 2202

8.609 2198

94,

90

86

8. 609 2182

logB 

diff.l"=-0.20

8. 511 2239

27

15

8.511 2203

8. 511 2191

78

66

54

42

30

8.511 2118

8. 511 2106

8. 511 2094

82

70

57

45

33

21

8.511 2009

8.511 1997

85

72

60

48

36

24

12

8.511 1900

8.511 1887

8.511 1875

63

51

39

27

15

8.511 1802

8.511 1790

78

66

8.511 1754

41

29

17

8.511 1705

8.511 1693

80

68

56

44

8.511 1632

20

8.511 1607

8. 511 1595

83

71

58

46

34

22

8.511 1510

logC 

diff.l"=+0.44

1.25024

050

077

104

131

157

184

211

237

264

1.25291

317

344

371

397

424

451

477

504

531

1. 25557

584

610

637

664

690

717 '

743

770

796

1. 25823

850

876

903

929

956

1.25982

1. 26009

035

062

1.26088 

115

141

. 168

194

221

247

274

300

327

1.26353

380

406

432

459

485

512

538

565

591

1. 26617

logD 

diff.l"=+0.01

2.3651

52

53

54

55

56

56

57

58

59

2.3660

61

62

63

64

65

66

66

67

68

2.3669

70

71

72 .

73

74

75

75

76

77

2. 3678

79

80

81

82

82

83

84

8586'

2.3687

88

88

89

90

91

92

93

94

94

2. 3695

96

97

98

99

2.3699

2.3700

01

02

03

2.3704

logE 

diff.l"=+0.05

6.0043

47

50

53

56

59

63

66

69

72

6.0075

79

82

85

88

91

95

6. 0098

6.0101

04

6. 0107

11

14

17

20

23

27

30

33

36

6. 0140

43

46

49

52

56

59

62

65

69

6. 0172

75

78

81

85

88

91.

94

6. 0198

6.0201

6. 0204

07

11

14

17

20

24 ' 27

30

33

6.0237

logF 

diff.lO'=+0.0

7.877

7.877

7.877

7.877
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 36°.

255

Lat.

0 1

36 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47 

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.07

8.509 2182

78

74

70

65

61

57

53

49

45

8. 509 2141

37

33

29

25

21

16

12

08

04

8.5092100

8. 509 2096

92

88

84

80

75

71

67

63

8. 509 2059

55

51

47

43

39

35

30

26

22

8. 509 2018

14

10

06

8.509 2002

8.509 1998

93

89

85

81

8. 509 1977

73

69

65

61

56

52

48

44

40

8. 609 1936

logB 

diff.l"=-0.20

8.511 1510

8. 511 1497

85

73

61

48

36

24

8.511 1412

8.511 1399

8.511 1387

75

63

60

38

26

14

8.511 1301

8.611 1289

77

8.511 1265

52

40

28

15

 8.511 1203

8.511 1191

79

66

54

8.511 1142

29

17

8. 511 1105

8.511 1092

80

68

56

43

31

8. 511 1019

8.511 1006 

8.511 0994

82

69

57

45

32

20

8.511 0908

8.511 0895

83

71

58

46

34

21

8.511 0809

8.511 0797

84

8.611 0772

logC 

diff.l"=+0.44

1.26617

644

670

69?

723

749

776

802

828

855

1.26881 .

908

934

960

1.26987

1. 27013

039

066

092

118

1.27145

171

197

223

250

276

302

329

355

381

1.27407

434

460

486

512

539

565

591

617

644

1.27670

696

722

748

775

801

827

853

879

905

1.27932

958

1.27984

I.^SOIO

036

062

088

114

141

167

1. 28193

logD 

diff.l"=+0.01

2.3704

04

05

06

07

08

09

09

10

11

2. 3712

13

13

14

15

16

17

17

18

19

2. 3720

21

21

22

23

24

25

26

26

27

2. 3728

29

29

30

31

32

32

33

.34

35

2. 3735

36

37

38

39

39

40

41

42

42

2. 3743

44

45

45

46

47

48

48

49

50

2.3760

logE. 

diff.l"=+0.05'

6.0237

40

43

46

50

53

56

59

63

66

6. 0269

72

76

79

82

a 85

89

92

95

6..0299

6.0302

05

08

12

15

18

21

 25

28

31

6. 0334

38

41

44

48

51

54

57

61

64

6.0367

71

74

77

80

84

87

90

94

6. 0397

6. 0400

03

07

10

13

17

20

23

27

30

6.0433

logF 

diff.!0'=-0.2

7.877

7.877

7.877

7. 876
266 GEOGKAPHIC TABLES AND FOKMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 37°.

Lat.

o i 

37 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

 42

43

44

45

46

47

48

49

50

51

52

53

54

' 55

56

57

58

59

60

log A 

diff.-l"=-0.07

8.509 1936

32

28

23

19

15

11

07

85.09 1903

85.09 1899

8. 509 1895

90

86

82

78

74%

70

66

62

57-

8. 509 1853

49

45

41

37

33

2824 

20

16

8. 509 181208 '

04

8. 509 1800

8. 509 1795

91

87

83

79

75

8.509 1771

66

62

58

54

50

46

41

37

33

8. 509 1729

25

21

16

12

08

04

8. 509 1700

8. 509 16%

92

8. 509 1687

logB 

diff.l"=-0.21

8.511 0772

60

47

35

2?.

8.511 0710

8.511 0698

85

' 73

61

8. 511 0648

36

23

8.511 0611

8. 511 0599

86

74

61

49

37

8.511 0524

12

8.511 0500

8. 511 0487

75

62

50

37

25

13

8.511 0400

8. 511 0388

75

63

51

38

26

13

8.511 0301

8. 511 0288

8. 511 0276

64

51

39

26

14

8.511 0201

8.511 0189

76

64

8. 511 0151

39

26

14

8.511 0102

8.511 0089

77

64

52

39

8. 511 0027

logC 

diff.l"=+0.43

1. 28193

219

245 '271

297

324

. 350

376

402

428

1.28454

480

506

532

558

584

610

636

662

688

1. 28715

741

767

793

819

845

871

897

923

949

1.28975

1. 29001

027

053

079

104

130

156

182

208

1.29234

260

286

312

338

364

390

416

442

468

1. 29494

520

546

671

597

623

649

675

701

727

1.29753

logD 

diff.l"=+0.01

2. 3750

51

52

53

53

54

55

56

56

57

2. 3758

59

59

60

61

61

62

63

73

64

2. 376566 '

66

67

68

68 

69

70

70

71

2. 3772

72

73

74

74

75

76

76

77

78

2. 3779

' 79

80

81

81

82

82

83

84

84

2.3785

86

. 86

87

88

88

89

90

90

91

2.3792

logE 

diff.l'°=+0.06

6. 0433

37

40

43

46

50

53

56

60

63

6.0466

70

73

76

80

83

86

89

93

96

6.0499

6. 0503

06

09

13

16

19

23

26

29

6. 0533

36

39

43

46

49

53

56

59

6D

6.0566

69

73

76

79

83

86

89

93

6. 0596

6.0600

03

06

10

13

16

20

23

26

30

6.0633

log. F 

difl.lO'=-0.3

7.876

7.876

7.875

,

7.874
GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 38°.

257

Lat.

o / 

38 00

1 ' 2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

; 29

30

31

32

33

34

35

36

37

38

' 39

40

41

42

: 43

44

45

'4746

48

49

1 

50

51

, 52

: 53

j 54

; 55

56

57

58

59

60

log A 

diff.l"=-0.07

8. 509 1687

 83

79

75

71

67 62

58

54

60

8. 509 1646

42

. 37

33

29

25

21

17 .

12

08

8. 509 1604

8.509 1600

8. 509 1596

92

87

83

79

75

71

66

8. 509 1562

58

54

50

46

41

37

33

29

25

8. 509 1521

16

]2

08

04

8. 509 1500

8. 509 1495

91

87

83

8. 609 1479

75

70

66

62

58

63

49

45

41

8.609 1437

logB 

diff.l''=-0.21

8.511 0027

14

8.511 0002

8.5109989

77

64

52

39

27

14

8. 510 9902

8. 510 9889

. 77

64

. 52

39

27

14

8.510 9802

8. 510 9789

8. 510 9777

64 '52

39

27

14

8.510 9701

8.5109689

77

64

8. 510 9652

39

27

14

8.510 9601

8. 510 9589

76

64

51

39

8.510 9526

14

8. 510 9501

8. 510 9488

76

63

51

38

26

13

8. 510 9401

8. 610 9388

76

63

50

38

25

13

8. 610 9300

8.510 9287

8.510 9275

logC 

diff.l"=+0.43

1.29753

778

804

830

856

882

908

934

959

1.29985

1.30011

037

063

089

114

140

166

192

218

243

1.30269

295

321

347

372

398

424

450

476

501

1.30527

553

579

604

630

656

682

707

733

759

1.30785

810

836

862

887

913

939

965

1. 30990

1. 31016

1.31042 .

067

093

119

144

170

196

221

247

273

1. 31299

logD 

diff.l"=+0.01

2. 3792

92

93

93

94 .

95

95

96

97

97

2.3798

2. 3799

2.3800

00

01

01

02

02

03

03

2.3804

05

05

06

06

07

08

08

09

09

 2. 3810

11

11

12

12

13

14

14

]5

15

2. 3816

16

' 17

18

18

19

19

20

20

21

 2. 3822

22

23

23

24

24

25

25

26

27

2f3827

logE 

diff.l"=+0.06

6. 0633

36

40

43

47

50

53

57

60

63

6.0667

70

73

77

80

84

87

90

94

6. 0697

6. 0701

04

07

11

14

17

21

24

28

31

6. 0734

38

41

44

48

51

55

58

61

65

6. 0768

72

75

78

82

85

89

92

95

6. 0799

6.0802

 06

09

13

16

19

23

26

30

33

6.0836

logF 

diff.lO'=-0.4

7.874

7.874

7.873

7.872

41623° 16- -17
258 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 39°.

Lat.

o /

39 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

68

59

60

log A 

diff.l"=-0.07

8. 609 1437

33

28

24

20

16

12

07

8.509 1403

8.509 1399

8.509 1395

91

86

82

78

74

70

65

61

57

8.609 1353

49

44

40

36

32

28

23

19

15

8. 509 1311

07

8. 609 1302

8. 509 1298

94

90

86

81

77

73

8. 509 1269

64

60

56

52

48

43

39

35

31

8. 509 1227

22

18

14

10

06

8. 509 1201

8. 509 1197

93

89

8.609 1184

logB 

diff.l"=-0.21

8.510 9275

62

50

37 25

8. 510 9212

8. 510 9199

87

74

62

8. 510 9149

36

24

8. 510 9111

8. 510 9098

86

73

61

48

36

8. 510 9023

8. 510 9010

8. 510 8998

85

73

60

47

35

22

8.510 8909

8. 510 8897

84

72

59

46

34

21

8.5108808

8.510 8796

83

8.510 8771

58

45

33

20

8. 510 8707

8. 510 8695

82

69

57

8. 510 8644

31

19

8. 510 8606

8. 510 8593

81

68

55

43

30

8. 610 8517

logC 

diff.l"=+0.43

1. 31299

324

350

375

401

427

452

478

504

529

1.31555

581

606

632 658-

683

. 709

734

760

786

1.31811

837

862

888

913

939

965

1. 31990

1. 32016

041

1.32067

092

118

144

169

195

220

246

271

297 

1.32323

348

374

399

425

450

476

501

527

552

1. 32578

603

629

654

680

705

731

756

782

807

1.32833

logD 

diff.l"=+0.01

2. 3827

28

28

29

29

30

30

31

31

32

2. 3832

33

33

34

35

35

36

36

37

37

2. 3838

38

39

39

40

40

41

41

42

42

2.3843

43

44

44

45

45

46

46

47

47

2. 3848

48

49

49

50

50

51

51

52

52

2.3852

53

53

54

54

55

55

56

56

57

2.3857

logE 

diff.l"=+0.06

6. 0836

40

43

47

50

53

57

60

64

67

6/0871

74

77

81

84

88

91

95

6. 0898

6.0902

6. 0905

08

12

15

19

22

26

29

32

36

6.0939

43

46

50

53

57

60

63

67

70

6. 0974

77

81

84

88

91

95

6. 0998

6. 1002

05

6.1008

12

15

19

22

26

29

33

36

40

6.1043

logF 

diff.lO'=-0.5

7.872

7.871

7.870

7.869
GEOGKAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 40°.

259

Lat.

o /

40 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff. 1"= -0.07

8. 509 1184

80

76

72

67

63

59

55

50

46

8. 509 1142

38

34

29

25

21

17

12

08

04

8.509 1100

8.509 1096

91

87

83

79

74

70

66

62

8. 509 1057

53

49

45

41

36

32

28

24

19

8. 509 1015

11

07

8. 509 1002

8. 509 0998

94

90

85

81

77

8.509 0973

68

64

60

56

52

47

43

39

34

8.509 0930

logB 

cliff. 1"= -0.21

8.5108517

8. 510 8505

8. 510 8492

79

67

54

41

29

16

8. 510 8403

8. 510 8391

78

65

53

40

27

15

8. 510 8302

8. 510 8289

77

8. 510 8264

51

38

26

13

8.5108200

8.5108188

75

62

50

8. 510 8137

24

8. 510 8111

8. 510 8099

86

73

61

48

35

23

8. 510 8010

8. 510 7997

84

72

59

46

33

21

8. 510 7908

8. 610 7895

8.510 7883

70

57

44

32

19

8. 510 7806

8. 510 7793

81

68

8.510 7755

logC 

diff. 1"= +0.42

1. 32833

858

884

909

935

960

1. 32986

1. 33011

037

062

1.33088

113

139

164

189

215

240

266

291

317

1.33342

368

393

418

444

469

495

520

546

571

1.33596

622

647 

673

698

723

749

774

800

825

1. 33850

876

901

926

952

1.33977

1. 34003

028

053

079

1.34104

129

155

180

206

. 231

256

282

307

332

1.34358

logD 

diff. 1"= +0.01

2.3857

68

68

58

59

59

60

60

60

61

2.3861

62

62

63

63

64

64

65

65

65

2. 3866

66

67

67

68

68

68

69

69

70

2.3870

70

71

71

72

72

72

73

73

74

2.3874

74

75

75

76

76

76

77

77

77

2.3878

78

79

79

79

80

80

80

81

81

2.3882

logE 

diff. 1"= +0.06

6. 1043

47

50

54

57

61

64

67

71

74

6. 1078

81

85

88

92

95

6. 1099

6.1102

06

09

6. 1113

16

20

23

27

30

34

37

41

44

6. 1148

51

55

68

62

65

69

72

76

79

6. 1183

86

90

93

6. 1197

6.1200

04

07

11

15

6.1218

22

25

29

32

36

39

43.

46

50

6.1253

logF 

diff.lO'=-0.7

7.869

7.867

7.866

7.864
260 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 41°.

Lat.

0 /

41 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

46

46

47

48

49

50

51

52

53

54

65

66

57

58

59

60

log A 

diff.l"=-0.07

8.509 0930

26

22

18

13

09

05

8. 509 0900

8. 509 0896

92

8.509 0888

83

79

75

71

67

62

58

54

49

8.6090845

41

37

32

28

24

20

15

11

07

8.609 0803

8. 609 0798

94

90

86

81

77

73

69

64

8.509 0760

56

52

47

43

39

35

30

26

22

8. 509 0718

13

09

05

8. 509 0700 .

8. 509 0696

92

'83 88

79

8. 509 0676

logB 

diff.l"=-0.21

8. 510 7755

42

30

17

8. 510 7704

8.510 7691

79

66

53

40

8. 510 7628

15

8. 510 7602

8. 510 7590

64

51

39

26

. 13

8.510 7500

8.510 7488

75

62

49

36

24

8. 510 7411

8. 510 7398

86

8. 510 7373

60

47

34

22

8. 510 7309

8. 510 72%

83

7058 '

8. 510 7245

32

19

8. 510 7207

8.510 7194

81

68

55

43

, 30

8.510 7117

8.510 7104

8.510 7091

79

66

53

40

27

15

8. 510 7002

8.510 6989

logC 

diff.l"=+0.42

1.34358

383

408

434

459

484

510

535

560

586

1.34611

636

662

687

712

738

763

788

814

839

1.34864

890

915

940

965

1. 34991

1.35016

041

066

092

1. 36117

142

168

193

218 .

243

269

294

319

345

1.35370

395

420

446

471

496

522

547

572

597

1.35623

648

673

698

723

749

774

799

 824

850

1.35875

logD 

diff.l"=+0.01

2.3882

82

82

83

83

83

84

84

84

85

2.3885

85.

86

86

87

87

" 87

88

88

88

2.3889

89

89

90

90

90

91

91

91

91

2.3892

92

92

93

93

93

94

94

94

95

2.3895

95

96

96

96

97

97

.97

97.

98

2.3898

98

98

99

99

2.3899

2.3900

00

00

00

2.3901

log E log F 

diff.l"=+0.06 diff.lO'=-0.8

6.1253 7.864

57

60

64

67

71

75

78

82

85

6. 1289

92

96

6. 1299

6. 1303

06

1014 

17

21

6.1324 7.863

28

31

35

38

42

46

49

53

56

6. 1360

63

67

70

74

78

81

85

88

92

6.1395 7.861

6.1399

6.1403

06

10

13

17

20

24

28

6. 143135 '

38

42

46

49

53

56

60

63

6.1467 7.860
GEOGRAPHIC TABLES AND FOEMULA8.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 42°.

261

Lat.

o / 

42 00

1

2

3

4

06

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

1 42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.07

8. 509 0675

71

66

62

58

54

49

45

41

36

8. 509 0632

28

24

19

15

11

07

8.5090602

8. 509 0598

94

8. 509 0590

86

81

77

72

68

64

60

55

51

8. 509 0547

43

38

34

30

25

21

17

13

08

8. 509 0504

8. 509 0500

8. 509 0496

91

87

83

78

74

70

66

8.509 0461

57

53

48

44

40

36

31

27

23

8. 609 0419

logB 

diff.l"=-0.21

8. 510 6989

76

64

51

38

25

12

8.510 6900

8. 510 6887

74

8.5106861

48

36

23

8.510 6810

8. 510 6797

84

72

59

46

8.510 6733

20

8.510 6707

8.610 6695

82

69

56

43

31

18

8.610 6605

8. 510 6592

79

66

54

41

28

15

8.510 6502

8. 510 6490

8. 510 6477

64

61

38

25

13

8. 610 6400

8.510 6387

74

61

8.510 6348

36

23

8. 510 6310

8. 510 6297

84

71

59

46

33

8.510 6220

logC 

diff.l"=+0.42

1.35875

900

925

951

1.35976

1.36001

026

052

077

102

1.36127

152

178

203

228

253

278

304

329

354

1. 36379

404

430

455

480

605

630

556

581

606

1.36631

656

682

707

732

757

782

808

833

858

1. 36883

908

934

959

1.36984

1.37009

034

059

085

110

1.37135

160

185

210

235

261

286

311

336

361

1.37386

logD 

diff.l"=+0.00

2. 3901

01

0101 

02

02

02

03

03

03

2. 3903

04

04

04

04

05

05

05

05

06

2.3906

06

06

07

07

07

07

08

08

08

2. 3908

08

09

09

09

09

10

10

1010 '

2. 3910

11

11

11

11

12

12

12

12

12

. 2.3913

13

13

13

13

14

14

14

14

14

2. 3914

logE 

diff.l"=+0.06

6. 1467

71

74

78

81

85

89

92

96

6. 1499

6. 1503

07

10

14

17

21

25

28

32

35

6. 1539

43

46

50

54

57

61

64

68

72

6. 1575

79

83

86

90

93

6. 1597

6.1601

04

08

6. 1612

15

19

22

26

30

33

37

41

44

6.1648

52

55

59

63

66

70

73

77

81

6.1684

logF 

did. 10'= -0.9

7.860

7.858

7.866

7.854
262 GEOGEAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 43°.

Lat.

0 /

43 00

1

2

3

4

05

6

7

8

9

10 "11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

64

55

56

57

58

59

60

log A 

diff.l"=-0.07

8. 509 0419

14

10

06

8.509 0401

8.5090397

93

89

84

80

8. 509 0376

71

67

63

59

54

50

46

41

37

8.509 0333

29

24

20

16

12

07

8.509 0303

8. 509 0299

94

8.509 0290

86

82

77

73

69

64

60

56

52

8. 509 0247

43

39

34

30

26

22

17

13

09

8. 509 0204

8. 509 0200

8.5090196

92

87

83

79

74

70

66

8.509 0162

logB 

diff.l"=-0.21

8. 510 6220

8.5106207

8. 510 6195

82

69

56

43

30

17

8.510 6105

8. 510 6092

79

66

53

40

' 28

15

8. 510 6002

8. 510 5989

76

8.51.0 5963

50

38

25

8.510 5912

8. 510 5899

86

73

60

48

8. 510 5835

22

8. 510 5809

8. 510 5796

83

71

58

45

32

v 19

8.510 5706

8. 510 5693

81

68

55

42

29

16

8. 510 5603

8. 510 5591

8. 510 5578

65

62

39

26

13

8. 510 5501

8. 510 5488

75

62

8. 510 5449

logC 

diff.l"=+0.42

1.37386

412

437

462

487

512

537

563

588

613

1. 37638

663

688

713

739

764

789

814

839

864

1.37889

915

940

965

1.37990

1. 38015

040

065

091

116

1.38141

166

191

216

241

266

292

317

342

367

1.38392

417

442

467

492

518

543

568

593

618

1.38643

668

693

719

744

769

794

819

844

869

1. 38894

logD 

diff.l"=+0.00

2. 3914

15

15

15

15

15

16

16

16

16

2. 3916

16

17

17

17

17

17

17

18

18

2. 3918

18

18

18

18

19

19

19

19

19

2. 3919

20

20

20

20

20

20

20

20

21

2. 3921

21

21

21

21

21

21

22

22

22

2. 3922

22

22

22

22

22

23

23

23

23

2. 3923

lOgE 

diff.l"=+0.06

6. 1684

88

92

95

6. 1699

6. 1703

06

10

14

17

6. 1721

25

28

32

36

39

43

47

50

54

C.1758

61

65

69

72

76

80

83

87

91

6. 1795

6. 1798

6.1802

06

09

13

17

20

24

28

6. 1831

35

39

42

46

50 

53

57

61

65

6. 1868

72

76

79

83

87

91

94

6. 1898

6.1902

6. 1905

logF 

diff.lO'=-1.0

7.854

7.852

7.850

7.848
GEOGEAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 44°.

263

Lat.

0 /

44 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

61

52

53

64

55

56

57

58

59

CO

log A 

diff. 1"=-0.07

8. 509 01C2

57

53

49

44

40

36

31

27

23

8. 509 0119

14

10

OC

8.5090102

8.509 0097

93

89

84

80

8.509 0076

72

67

63

59

54

50

46

42

37

8. 509 0033

29

24

20

16

= 11

07

8.509 0003

8. 508 9999

94

8.508 9990

86

81

77

73

69

64

60

56

51

8. 508 9947

43

39

34

30

26

21

17

13

09

8. 508 9904

log B log C 

cliff. 1"=-0.21 cliff. 1" = +0.42

8. 510 5449

36

23

8. 510 5411

8. 610 5398

85

72

69

46

33

8. 510 5320

8. 510 5307

8. 510 5295

82

69

56

43

30

18

8. 510 5205

8.5105192

79

66

53

40

28

15

8.510 5102

8. 510 5089

76

8. 510 5063

50

37

25

8. 510 5012

8.510 4999

86

73

60

47

8. 510 4935

22

'8.510 4909

8. 510 4896

83

70

57

44

32

19

8.5104806

8. 5lO 4793

80

67

54

41

. 29

16

8. 510 4703

8. 510 4690

8. 510 4677

1.38894

919

945

970

1. 38995

1.39020

045

070

095

120

1.39145

171

196

221

246

271

296

321

346

371

] . 39396

422

447

472

497

522

547

572

597

623

1. 39648

673

698

723

748

773

798

823

848

873

1. 39898

924

949

974

1.39999

1.40024

049

074

099

124

1.40149

174

200

225

250

275

300

325

350

375

1.40400

logD 

diff. 1"= +0.00

2. 3923

23

23

23

23

23

24

. 24

24

24

2. 3924

24

24

24

24

24

24

24

24

25

2. 3925

25

25

25

25

25

25

25

25

25

2. 3925

25

25

25

25

25

26

26

26

26

2.3926

26

26

26

26

26

26

26

26

26

2. 3926

26

26

26

26

26

26

26

26

26

2. 3926

. loRE 

diff. 1"= +0.06

6. 1905

09

13

17

20

24

28

31

35

39

6. 1943

46

50

54

58

61

65

69

72

76

6. 1980

84

87

91

95

6. 1999

6. 2002

06

10

14

6. 2017

21

25

29

32

36

40

44

47

51

6. 2055

59

62

66

70

74

77

81

85

89

6.2092

6.2096

6. 2100

04

08

11 '

15

19

23

27

6. 2130

logF 

cliff. 30' =1.2

7. 848

7.845

7.843

7.840
264 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 45°.

Lat.

o / 

45 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25 ' 26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

. 43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff. 1".= - 0.07

8. 508 9904

8. 508 9900

8. 508 9896

91

87

83

78

74

70

66

8. 508 9861

57

53

48

44

40

36

31

27

23

8.508 9818

34

10

06

8. 508 9801

8. 508 9797

93

88

84

80

8. 508 9776

71

67

6358 '

54

50

46

41

37

8. 508 9733

28

24

20

16

11

07

8.508 9703

8. 508 9698

94

8. 508 9689

85

81

77

72

' 68

64

60

55

51

8. 508 9647

logB 

diff.l"=-0.21

8. 510 4677

64

51

39

26

13

8. 510 4600

8. 510 4587

74

61

8.510 4548

36

23

8. 510 4510

8. 510 4497

84

71

59

46

33

8. 510 4420

8. 510 4407

8. 510 4394

81

68

56

43

3f

IV

8.510 4304

8. 510 4291

78

65

52

40

27

14

8. 510 4201

8.5104188

75

8.510 4162

49

37

24

8.510 4111

8.510 4098

85

72

60

47

8. 510 4034

21

8.510 4008

S. 510 3995

82

69

57

44

31

18

8. 510 3905

logC 

diff. 1"=+0.42

1. 40400

425

450

475

501

526

551

576

601

626

1.40651

676

701

727

752

777

802

827

852

877

1.40902

927

952

1. 40978

1. 41003

028

053

078

103

128

1.41153

178

203

229

254

279

304

329

354

379

1.41404

429

454

479

505

530

555

580

605

630

1.41655

680

705

.731

756

781

806

831

856

881

1.41906

logD 

diff. 1"= ±0.00 diff.

2. 3926

26

26

26

26

26

26

26

26

26

2. 3926

26

26

26

26

26

26

26

26

26

2. 3926

26

26

26

26

26

26

26

26

26

2.3926

26

26

26

26

26

25

25

25

25

2. 3925

25

25

25

25

25

25

25

25

25

2. 3925

25

25

25

24

24

24

24

24

24

2.3924

logE 

1"=+0.06

6. 2130

34

38

42

46

49

53

57

61

64

6. 2168

72

 76

80

83

. 87

91

95

6. 2199

6. 2202

6. 2206

10

14

18

21

25

29

33

37

40

6.2244

48

52

56

60

68

67

71

75

79

6. 2283

86

90

94

6. 2298

6. 2302

06

09

13

17

6. 2321

25

29

32

36

40

44

48

52

55

6.2359

logF 

diff.lO'=-1.3

7.840

7.838

7.835

7.832
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 46°.

265

Lat.

o /

46 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

. 50 51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.07

8. 508 9047

43

38

34

30

25

21

17

13

08

8. 508 9604

8. 508 9600

8. 508 9595

91

87

83

78

74

70

65

8. 508 9561

57

53

48

44

40

35

31

27

23

8. 508 9518

14

10

05

8. 508 9501

8. 508 9497

93

88

84

80

8. 508 9475

71 .

67

63

58

54

50

45

41 '37

8.508 9433

. 28

24

20

16

11

07

8. 508 9403

8. 508 9398

. 94

8. 508 9390

logB 

diff.l"=-0.21 d

8. 510 3905

8.510 3892

79

67

54

41

28

15

8. 510 3802

8.510 3789

8. 510 3776

64

51

38

25

8. 510 3712

8.5103699

86

74

61

8. 510 3648

35

22

8. 510 3609

8. 510 3596

84

71

58

45

32

8.5103519

8. 510 3506

8. 510 3494

81

68

55

42

29

17

8.510 3404

8. 610 3391

78

65

52

39

27

14

8. 510 3301

8. 510 3288

75

8. 510 3262

.49

37

24

8! 510 3211

8. 510 3198

85

72

60

47

8. 510 3134

logC 

iff. 1"= +0.4

1. 41906

931

957

1.41982

1.42007

032

057

082

107

132

1.42157

183

208

233

258

283

308

333

358

384

1.42409

434

459

484

509

534

559

584

610

635

1.42660

685

710

735

760

786

811

836

861

886

1.42911

936

961

1.42987

1.43012

037

062

087

112

137

1.43163

188

213

238

263

288

314

339

364

389

1. 43414

logD 

 i d iff. 1"= -0.00

2. 3924

24

24

24

24

24

23

23

23

23

2.3923

23

23

23

23

23

23

22

22

22

2.3922

22

22

22

22

22

21

21

21

21

2. 3921

21

21

21

20

20

20

20

20

20

2.3920

19

19

19

19

19

19

19

18

18

2. 3918

18

18

18

18

17

17

17

17

17

2. 3917

log E log F 

diff.l"=+0.06 diff.lO'=-1.4

6. 2359 7. 832

63

67

71

75

79

82

86

90

94

6.2398

6.2402

06

09

13

17

21

25

29

33

6. 2436 7. 830

40

44

48

52

56

60

64

67 .

71

6. 2475

79

83

87

91

95

6. 2499

6.2502

06

10

6. 2514 7. 827

18

22

. 26

30

34

38

41

45

49

6. 2553

57

61

65

69

73

77

81

84

88

6. 2592 7. 824
266 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 47°.

Lat.

O 1

47 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

difT. 1"=-0.07

8. 508 9390

86

81

77

73

68

64

60

56

51

8.508 9347

43

38

34

30

26

21

17

13

09

8. 508 9304

8. 508 9300

8. 508 9296

91

87

83

79

74

70

66

8. 508 926157 '

53

49

44

40

36

32

27

23

8. 508 9219

14

10

06

8.508 9202

8. 508 9197

93

89

84

80

8. 508 9176

72

6763 '

59

55

50

46

42

38

8. 508 9133

logB 

diff.l"=-0.21

8. 510 3134

21

8. 510 3108

8. 510 3095

82

70

57

44

31

18

8. 510 3005

8. 510 2993

80

67

54

41

28

16

8. 510 2903

8. 510 2890

8. 510 2877

64

51

39

26

13

8. 510 2800

8. 510 2787

74

62

8.5102749

36

23

8.510 2710

8. 510 2698

85

72

59

46

QO 00

8. 510 2621

8.510 2608

8.5102595

82

69

5744'

31

18

8.510 2505

8. 510 2493

80

67

54

41

28

16

8.510 2403

8. 510 2390

77

8. 510 2364

logC 

diff.l"=+0.42

1. 43414

439

465

490

515

540

565

590

615

641

1.43666

691

716

741

766

792

817

842

867

892

1.43917

943

968

1. 43993

1. 44018

043

069

094

119

144

1. 44169

195

220

245

270

295

321

346

371

396

1.44421

447

472

497

522

547

573

598

623

648

1.44673

699

724

749

774

800

825

850

875

900

1.44926

logD 

diff.l"=-0.00

2. 3917

16

16

16

16

16

16

15

15

15

2. 3915

15

14

14

14

14

14

13

13

13

2.3913

13

12

12

12

12

12

11

11

11

2. 3911

11

10

10

10

10

10

09

09

09

2.3909

08

08

08

08

07

07

07

07

07

2. 3906

06

06

06

05

05

05

05

04

04

2.3904

logE 

diff.l"=+0.07

6. 2592

6. 2596

6.2600

04

08

12

16

20

24

28

6. 2632

35

39

43

47

51

55

59

63

67

6. 2671

75

79

83

87

91

95

6. 2699

6. 2702

06

6. 2710

14

18

22

26

30

34

38

42

46

6. 2750

54

58

62

66

70

74

78

82

86

6.2790

94

6.2798

6. 2802

06

10

14

18

22

26

6. 2830

logF 

diff.lO' = -l.G

7. 824

^

7.821

7.817

7.814
GEO&KAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 48°.

267

Lat.

o /

48 00

1

2

3

4

05

G

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

61

52

53

54

55

56

57

58

69

60

log A 

diff.l"=-0.07

8.508 9133

29

25

20

16

12

08

8.5089103

8. 508 9099

95

8. 508 9091

8G

82

78

74

69

65

61

.57

52

8.508 9048

44

39

35

31

27

22

18

14

10

8. 508 9005

8. 508 9001

8. 508 8997

93

88

84

80

76

71

67

8. 508 8963

59

54

50

46

41

37

33

29

24

8.508 8920

16

12

08

8.508 8903

8. 508 8899

95

90

86

82

8. 508 8878

logB 

cliff. 1"= -0.21

8.510 2364

52

39

20

13

8. 510 2300

8. 510 2288

75

62

49

8. 510 2236

24

8. 510 2211

8.5102198

85

72

60

47

34

21,

8. 510 2108

8. 510 2096

83

70

57

45

32

19

8. 510 2000

8.510 1993

8.510 1981

68

55

42

30

17

8.510 1904

8.510 3891

78

60

8.510 1853

40

27

15

8.510 1802

8.510 1789

70

04

51

38

8. 510 1725

J3

8.510 1700

8.510 1687

74

62

49

36

23

8.510 1610

8.510 1598

logC 

cliff. 1"= +0.42

1. 44926

951

1.44970

1.45001

027

052

077

102

128

153

1.45178

203

229

254

279

304

330

355

380

406

1.45431

456

481

507

532

557

582

608

633

658

1.45683

709

734

759

785

810

835

861

886

911

1.45937

962

1.45987

1.46012

038

063

088

114

139

164

1.46190

215

240

266

291

316

342

367

392

418

1.46443

logD 

diff.l"=-0.00

2. 3904

04

03

03

03

02

02

02

02

01

2. 3901

01

01

00

00

2. 3900

2. 3899

99

99

99

2. 3898

98

98

97

97

97

97

96

96

96

2. 3895

95

95

95

94

94

94

93

93

93

2. 3892

92

92

91

91

91

90

90

90

89

2.3889

89

88

88

88

87

87

87

86

86

2.3886

log E log F 

diff.l"=+0.07 diff.lO'=-1.7

6. 2830 7. 814

34

38

42

46

50

54

58

62

66

G. 2870

74

78

82

86

90

94

6. 2898

6.2902

06

6.2910 7.811

14

18

22

26

30

34

38

42

46

6. 2950

54

58

62

66

70

74

78

82 86

6. 2990 7. 807

94

. 0. 2998

6. 3002

06

10

15

19

23

27

6. 3031

35

39

43

47

51

55

59

6367'

6.3071 7.804
268 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 49°.

Lat.

o / 

49 00

1

2

3

4

05

6

7

8

9

10

11

12.

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

67

58

59

60

log A 

diff. 1"= -0.07

8. 508 8878

73

69

65

61

57

52

48

44

39

8. 508 8835

31

27

23

18

14

10

06

8. 508 8801

8. 508 8797

8.508 8793

89

84

80

76

72

67

63

59

55

8. 508 8750

46

42

38

33

29

25

21

16

12

8. 60S 8708

04

8. 508 8700

8. 508 8695

91

87

83

78

74

8.508 8666

61

57

53

49

45

40

36

32

 28

8. 508 8623

lOgB 

diff. 1"= -0.21

8.510 1598

85

 72

59

47

'. 34

21

8.510 1508

8.510 1496

83

8.510 1470

58

45

 32

19

8.510 1407

8.510 1394

81

 68

56

8. 510 1343

30

17

8. 510 1305

8.510 1292

79

67

54

41

28

8.510 1216

8. 510 1203

8.510 1190

78

65

52

39

27

14

8.510 1101

8.510 1088

76

63

50

38

25

12

8.510 1000

8. 510 0987

74

8. 510 0962

49

36

23

8.510 0911

8.510 0898

85

73

60

48

8. 510 0835

logC 

diff. 1"= +0.42

1.46443

468

494

519

544

570

595

621

646

671

1.46696

722

747

773

 798

824

849

874

899

925

1. 46950

1.46976

1. 47001

026

052

077

103

128

153

179

1.47204

230

255

281

306

331

357

382

408

433

1.47459

484

509

535

560

586 .

611

637

662

688

1. 47713

738

764

789

815

840

866

891

917

942

1. 47968

logD 

diff. 1"= -0.01

2.3886

85

85

85

84

84

84

83

83

83

2.3882

82

81

81

81

80

80

80

79

79

2. 3878

78

78

77

77

77

76

76

75

75

2.3875

74

74

73

73

73

72

72

71

71

2. 3871

70

70

69

69

69

68

68

67

67

2.3866

66

66

65

65

64

64

63

63

63

2. 3862

log E log F 

diff.l"=+0.07 diff. 10'= -1.9

6.3071 7.804

75

79

84

88

 92

6. 3096

6.3100

04

08

6.3112

16

20

24

28

32

37

41

45

49

6. 3153 7. 800

57

61

65

69

73

78

82

86

90

6. 3194

6. 3198

6. 3202

06

10

15

19

23

27

31

6. 3235 7. 796

' 39

43

47

52

56

60

64

68

72

6. 3276

81

85

89

93

6. 3297

6. 3301

05

09

14

6. 3318 7. 792
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 50°.

269

Lat.

O 1

60 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

65

56

67

58

59

60

log A 

diff.l"=-0.07

8. 508 8623

19

15 * 11

06

8. 508 8602

8.508 8598

94

90

85

8.508 8581

77

73

68

64

60

56

52

47

43

8. 508 8539

35

30

26

22

18

14

09

05

8. 508 8601

8. 508 8497

93

88

84

80

76

71

67

63

59

8. 508 8455

50

46

42

38

34

29

25

21

17

8.508 8413

08

04

8. 508 8400

8. 508 8396

92

87

83

79

75

8. 508 8371

logB 

diff.l"=-0.21

8. 510 08352'2

8. 510 0809

8. 510 0797

84

71

59

46

33

21

8. 510 0708

8. 510 0695

83

70

67

45

32

19

8.510 0607

8. 510 0594

8.5100681

69

66

43

31

18

6. 510 0505

8. 510 0493

80

67

8. 510 0455

42

29

17

8. 510 0404

8. 510 0392

79

6654-

41

8 510 0328

16

8 510 0303

8. 510 0291

78

65

53

40

27

15

8. 510 0202

8.510 0190

77

64

52

39

27

14

8.510 0101

8. 510 0089

8. 510 0076

logC 

diff.l" = +0.43

1.47968

1.47993

1.48019

044

070

095

121

146

172

197

1.48223

248

274

299

325

350

376

401

427

452

1.48478

504

629

555

580

606

631

657

682

708

1.48734

759

785

810

836

861

887

913

938

964

1.48989

1.49015

041

066

092

117

143

169

194

220

1.49^46

>71

297

322

348

374

399

425

 451

476

1. 49502

logD 

difll"=-0.01

2. 3862

62

61

61

60

60

60

59

59

58

2. 3858

57

57

56

56

55

55

55

54

54

2.3863

53

52

52

51

51

60

50

49

49

2.3848

48

47

47

46

46

45

45

44

44

2. 3843

43

42

42

41

41

40

40

39

39

2. 3838

38

37

37

36

 36

36

35

34

34

. 2. 3833

log E log F 

diff.l"=+0.07 diff.lO'=-2.0

6. 3318

22

26

30

34

39

43

47

51

55

6.3359

63

68

72

76

80

84

88

93

6. 3397

6.3401

06

09

14

18

22

26

30

34

39

6. 3443

47

51

55

60

64

68

72

76

81

6. 3485

89

93

6.3497

6.3502

06

10

14

18

23

6.3527

31

35

40

44

48

52

56

61

65

6.3569 .

7.792

7.788

7.784

7.780
270 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 51°.

Lat.

0 '

51 00

1

2

3

4

. 05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

62

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.07

8. 508 8371

66

62

58

54

50

45

41

37

33

8.508 8329

24

20

16

VI

08

8. 508 8303

8. 508 8299

95

91

8. 508 8287

82

78

74

70

66

62

67

63

49

8. 508 8245

41

36

32

28

24

20

16

11

07

8. 508 8203

8. 508 8199

95

90

86

82

78

74

70

65

8. 508 8161

57

53

49

45

40

36

32

28

24

8. 508 8120

logB 

diff.l"=-0.21

8.510 0076

64

51

38

26

13

8.510 0001

8. 509 9988

75

63

8. 509 9950

38

25

13

8. 509 9900

8.509 9887

75

62

50

37

8. 509 9825

8. 509 9812

8.509 9799

87

74

62

49

37

24

8.509 9711

8. 509 9699

86

74

61

49

36

24

8.509 9611

8.509 9599

86

8. 509 9574

61

48

36

23

8. 509 9511

8.509 9498

86

73

61

8. 509 9448

36

23

8. 509 9411

8. 509 9398

86

73 61

48

36

8.509 9323

]ogC 

difl. 1»= +0.43

1. 49502

528

553

579

605

630

656

682

707

733

1.49759

785

810

836

862

887

913

939

965

1.49990

1. 60016

042

067

093

119

145

170

196

222

248

1.50273

299

325

351

376

402

428

454

480

505

3.50531

557

583

609

634

660

686

712

738

764

1.50789

815

841

867

893

919

944

970

1.50996

1.51022

.1.51048

logD 

diff.l"=-0.0l

2. 3833

33

32

32

31

31

30

29

29

28

2.3828

27

27

26

26

25

25

24

23

23

2.3822

22

21

21

20

20

19

18

18

17

2.3817

16

16

15

14

14

13

13

12 .

11

2. 3811

10

10

09

08

08

07

07

06

05

2.3805

04

04

03

02

02

01

01

2.3800

2.3799

2. 3799

logE 

diff.l" = +0.07

6. 3569

73

78 , 82 '

86

90

95

6. 3599

6. 3603

07

6. 3612

16

20

24

28

33

37

41

45

50

6.3654

58

63

67

71

75

80

84

88

92

6. 3697

6. 3701

05

10

14

18

22

27

31

35

6.3740

44

48

52

57

61

65

70

74

78

6. 3782 '

87

91

6. 3795

6.3800

04

08

13

17

21

6.3826

logF 

diff.lO'=-2.2

7.780

7.776

7.772

7.767
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 28. Geodetic position computations Continued.

LATITUDE 52°.

271

Lat.

o / 

52 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

. 32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

68

59

60

log A 

diff,l"=-0.07

8. 508 8120

15

11

07

8. 508 8103

8. 508 8099

95

90

86

82

8. 508 8078

74

70

65

61

57

53

49

45

41

8. 508 8036

32

28

24

20

16

11

07

8.5088003

8. 508 7999

8. 508 7995

91

87

82

78

74

70

66

62

58

8. 508 7953

49

45

41

37

33

29

24

20

16

8.508 7912

08

04

8.508 7900

8. 508 7895

91

87

83

79

75

8. 508 7871

logB 

diff.l"=-0.21

8.5099323

8.509 9311

8. 509 9298

86

73

61

48

36

23

8. 509 9211

8. 509 9198

86

73

61

48

36

23

8. 509 9111

8.509 9099

86

8. 509 9074

61

49

36

24

8. 509 9011

8. 509 8999

86

74

62

8. 509 8949

37

24

8. 509 8912

8. 509 8899

87

74

62

50

37

8.509 8825

12

8. 509 8800

8.509 8788

75

63

50

38

25

13

8. 509 8701

8. 509 8688

76

63

51

39

26

14

8. 509 8602

8. 509 8589

8.509 8577

logC 

diff.l"=+0.43

1. 51048

074

100

126

151

177

203

229

255

281

1. 51307

333

359

385

411

436

462

488

514

540

1. 51566

592

618

644

670

696

722

748

774

800

1.51826

852

878

904

930

956

1.51982

1.52008

034

060

1. 52086

112

138

164

190

216

242

268

294

320

1.52347

373

399

425

451

477

5C3

529

555

581

1. 52608

logD 

diff.l"=-0.01

2. 3799

98

97

97

96

96

95

94

94

93

2.3792

92

91

91

90

89

88

88

87

87

2. 3786

85

85

84

83

83

82

81

81

80

2. 3779

79

78

78

77

76

75

75

74

73

2.3773

72

71

71

70

69

68

68

67

66

2. 3766

65

64

64

63

62

61

61

60

59

2. 3759

log E log F 

diff.l"=+0.07 diff.lO' = -2.3

6. 3826 7. 767

30

34

39

43

47

52

56

60

65

6. 3869

73

78

82

86

91

95

6. 3899

6. 3904

08

6. 3912 7. 763

17

21

25

30

34

38

43

47

51

6.3956

60

65

69

73

78

82

86

91

6. 3995

6.4000 7.758

04

08

13

17

21

26

30

35

39

7.4043

48

52

67

.61

65

70

74

79

83

6.4088 7.753
272 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 53°.

Lat.

o / 

53 00

1

2

3

4

05

6

7

8

9 

10

11

12

1314-

15

16

17

18

19

20

21

22

23

24

25

1 26

27

28

: . 29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

' 46

! 47

48

49

50

51

52

53

54

55

56

57

68

59

60

log A 

diff.l"=-0.07

8.508 7871

67

62

58

54

50

46

42

38

34

8. 508 7829

25

21

17

13

09

05

8. 508 7801

8. 508 7797

92

8. 508 7788

84

80

76

72

68

64

60

55

51

8.508 7747

43

39

35

31

27

23

18

14

10

8.508 7706

8.508 7702

8.508 7698

94

90

86

82

77

73

69

8.508 7665

61

57

53

49

45

41

37

32

28

8.508 7624

logB 

diff.l"=-0.21

8. 509 8577

64

52

40

27

15

8. 509 8502

8.5098490

78

65

8. 509 8453

41

28

16

8. 509 8404

8. 509 8391

79

67

54

42

8. 509 8329

17

8. 609 8305

8.509 8292

80

68

55

43

31

18

8. 509 8206

8. 509 8194

82

69

57

45

32

20

8. 509 8108

8.5098095

8. 509 8083

71

58

46

34

22

8. 509 8009

8. 509 7997

85

72

8. 509 7960

48

36

23

8.509 7911

8. 509 7899

87

74

62

60

8.509 7838

logC 

diff.l"=+0.41

1.52608

634

660

686

712

738

764

790

817

843

1.52869

895

921

947

1. 52974

1.53000

026

052

078

105

1.53131

157

183

209

236

262

288

314

341

367

1.53393

419

446

472

498

524

551

577

603

630

1. 53656

682

709

735

761

788

814

840

867

893

1.53919

946

972

1.53998

1.54025

051 

077

104 '

130

157

1.54183

logD 

diff.l"=-0.01

2.3759

58

57 '

56

56

55

54

53

53

52

2. 3751

51

60

49

48

48

47

46

45

45

2. 3744

43

42

42

41

40

39

39

38

37

2.3736

36

 35

34

33

33

32

31

30

29

2. 3729

28

27

26

26

25

24

23

22

22

2. 3721

20

19

18

18

17

16

15

14

14

2. 3713

log E log F 

diff. 1"- +0.07 diff.lO'=-2.5

6. 4088 7. 753

92

6. 4096

6. 4101

05

10

14

18

2$

27

6. 4132

36

41

45

49

54

58

63

67

72

6. 4176 7. 748

80

85

89

94

6. 4198

6. 4203

07

12

16

6.4221

25

29 .

34

38

43

47

52

56

61

6. 4265 7. 743

70

74

79

83

88

92

6.4297

6.4301

06

6. 4310

15

19

24

28

33

37

42

46

51

6. 4355 7. 738
GEOGKAPHIC TABLES AND FOKMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 54°.

273

Lat.

0 1

54 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16.

17

18

19

20

21

22

23

.24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

60

61

52

53

64

55

66

67

58

59

60

log A 

diff. 1»= -0.07

8.508 7624

20

16

12

08

04

8. 508 7600

8. 508 7596

92

88

8. 508 7584

79

75

71

67

63

59

65

51

47

8.5087543

39

35

31

27

22

18

14

10

06

8.508 7502

8.508 7498

94

90

86

82 ' 78

74

70

66

8.508 7462

58

63

49

45

41

37

33

29

25

8.608 7421

17

13

09

05

8. 508 7401

8.508 7397

93

89

85

8.608 7381

logB 

diff. 1"=-0.20 difl

8.509 7838

25

13

8.509 7801

8.509 7789 

76

64

52

40

27

8. 509 7715

8. 509 7703

8.509 7691

78

66

54

42

30

17

8.509 7605

8.509 7593

81

69

56

44

32

20

8.509 7508

8. 509 7495

83

8.509 7471

59

 47

34

22

8.509 7410

8. 509 7398

86

74

61

8. 509 7349

37

25

13

8.509 7301

8. 509 7289

76

64

52

40

8. 509 7228

16

8.509 7204

8. 509 7191

79

67

55

43

31

19

8.509 7107

logC 

1"=+0.44

1.54183

209

236

262

288

315

341

368

394

421

1. 64447

474

600

527

553

580

606

633

659

686

1.54712

739

765

792

818

845

871

898

924

951

1.54977

1.55004

031

057

084

110

137

163

190

217

1. 55243

270

297

323

360

376

403

430

456

483

1.55510

536

563

590

616

643

670

696

723

760

1.55777

logD 

diff. 1"=-0.01

2.3713

12

11

10

09

09

08

07

06

05

2. 3705

04

03

02

01

00

0 2. 3700

2. 3699

98

97

2. 3696

95

94

94

93

92

91

90

89

88

2. 3688

 87

86

85

84

83

82

82

81

80

2. 3679

78

77

76

75

74

74

73

72

71

2. 3670

69

68

67

66

66

65

64

63

62

2. 3661

logE 

diff. 1"= +0.08

6.4355

60

64

69

73

78

82

87

91

6. 4396

6.4400

05

09

14

18

23

28

32

37

41

6. 4446

50

55

59

64

68

73

78

82

87

6. 4491

6. 4496

6.4500

06

09

14

19

23

28

32

6.4537

41

46

51

55

60

64

69

74

78

6. 4583

87

92

6.4597

6. 4601

06

10

16

20

24

6. 4629

logF 

diff. 10'= -2.6

7.738

7.733

7.728

7.723

41623° 16 18
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 55°.

Lat.

0 /

55 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

26

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

; 49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.07

8.508 7381

77

73

69

65

61

66

52

48

44

8. 508 7340

36

32

28

24

20

16

12

08

04

8.508 7300

8. 508 7296

92

88

84

80

76

72

68

64

8.508 7260

56

52

48

44

40

36

32

28

24

8.508 7220

16

12

08

04

8.508 7200

8. 508 7196

92

88

84

8. 508 7180

76

72

68

64

60

56

52

48

44

8. 508 7140 .

logB 

diff.l"=-0.20

. 8. 509 7107

8.509 7095

82

70

58

46

34

22

8.509 7010

8.509 6998

8. 509 6986

74

62

49

37

25

13

8. 509 6901

8.509 6889

77

8. 509 6865

53

41

29

17

8.509 6805

8. 509 6793

 81

69

57

' 8. 509 6745

33

21

8. 509 6709

8. 509 6696

84

72

60

48

36

8.509 6624

12

8.509 6600

8.509 6588

76

64

52

40

28

16

8. 509 6505

8. 509 6493

81

69

57

45

33

21

8. 509 6409

8. 509 6397

8. 509 6385

logC 

diff.l"=+0.

1.55777

803 

830

857

884

910

937

964

1.55991

1.56017

1.56044

071

098

125

151

178

* 205

232

259

286

1.56312

339

366

393

420

447

474

500

527

554

1.56581

608

635

662

689

716

743

770

797

823

I.,r 6850

877

904

931

958

1.56985

1.57012

039

066

093

1. 57120

147

174

201

229

256

283

310

337

364

1. 57391

logD 

:5 diff. i"=-0.02

2. 3661

60

59

58

- 57

56

56

55

54

53

2.3652

51

50

49

48

47

46

45

44

43

2. 3642

42

41

40

39

38

37

36

35

34

2. 3633

32

31

3029'

28

27

26

25 '

24

2. 3623

22

21

20

19

18

17

16

15

14

2. 613

12

11

10

09

08

07

06

05

04

2. 3603

logE 

diff. 1"- +0.08

6. 4629

33

38

43

47

52

57

61

66

70

6.4675

80

84

89

.94

6. 4698

6. 4703

08

12

17

6. 4721

26

31

35

40

45

49

54

59 

63

6. 476873'

77

 82

87

91

6.4796 '

6.4801

05

10

6. 4815

20

24

29

34

38

43

48

' 52

57

6.4862

66

71

76

81

85

90

6. 4895

6. 4900

04

6. 4909

logF 

diff. 10' =-2.8

7.723

'7. 717

'

7. 711

7.706
GEOGRAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 56°.

275

Lat.

0 /

56 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

! 27

28

; 29

30

31

32

33

34

: 35

I 36

' 37

38

r 39

40

41

1 42

43

! 44 i

i 45

46

: 47

; 48

: 49 i

50

 51

: 52

: 53

 54

: 55

56

57

58

59

60-

log A 

diff.l"=-0.07

8. 508 7140

36

32

28

24

20

16

12

08

04

8.5087100

8.508 7096

92

88

84

80

76

72

69

65

8. 508 7061

57

63

. 49

45

41

37

33

29

25

8. 508 7021

17

13

09

05

8. 508 7001

8. 508 6997

93

89

86

8.508 6982

78

74

70

66

62

58

54

50

46

8.508 6942

38

34

30

26

23

19

15

11

07

8.508 6903

logB 

diff.l"=-0.20

8.509 6385

73

61

49

37

25

13

8. 509 6301

8. 509 6289

77

8. 509 6266

54

42

30

18

8.509 6206

8. 609 6194

82

70

58

8.509 6147

'2335

8. 509 6111

8. 509 6099

87

75

63

51

40

8. 509 6028

16

8.509 6004

8.509 5992

80

68

57

45

33

21

8. 609 5909

8. 509 5897

86

74

62

60

38

27

15

8 509 5803

8. 509 5791

79

67

56

44

32

20

8. 509 5709

8. 509 5697

85

.8.509 5673

logC 

diff.l"=+0.45

1. 57391

418

445

472

499

526

554

581

608

635

1. 57662

689

717

744

771

798

825

852

880

907

1. 57934

961

1. 57989

1.58016

. 043

070

098

125

152

179

1. 58207

234

261

289

316

343

371

398

425

453

1.58480

507

535

562

589

617

644

672

699

726

1.58754

781

809

836

864

891

919

946

1.58974

1. 59001

1.59028

logD 

diff.l"=-0.02

2.3603

02

01

2.3600

2.3599

98

97

96

95

94

2. 3593

92

91

90

89

88

 87

86

85

84

2. 3583

82

81

80

78

77

76

75

74

73

2. 3572

71

70

69

68

67

66

65

64

62

2.3561

60

59

58

57

56

55

54

53

52

2. 3550

49

48

47

46

45

44

43

42

41

2. 3539

logE 

diff.l"=+0.08

6. 4909

14

18

23

28

33

37

42

47

52

6.4956

61

66

71

75

80

85

90

94 '

6.4999

6.5004

09

13

18

23

28

32

37

42

47

6.5052

56

61

66

71

75

80

85

90

95

6.5099

6. 510409 

14

19

24

28

33

38

43

6. 5148

52

57

62

67

72

77

81

86

91

6. 5196

logF 

diff.lO'=-3.0

7.706

0

7.700

7.694

7.688
276 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 57°.

Lat.

o / 

57 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

44

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56 57

58

59

60

log A 

diff.l"=-0.06

8.508 6903

8.508 6899

95

91

87

83

79

75

72

68

8.508 6864

CO

56

52

48

44

40

36

32

28

C. 508 6825

21

17

13

09

05

8. 508 6801

8.508 6797

93

90

8.508 6786

82

78

74

70

66

62

58

54

51

8.508 6747

43

39

35

31

27

23

20

16

12

8.508 6708

04

8. 508 6700

8.508 6696

92

89

85

81

77

73

8. 508 6669

logB 

diff.l"=-0.19

8. 509 5673

61

50

38

26

14

8. 509 5603

8. 509 5591

79

67

8.509 5556

44

32

20

8. 509 5509

8.509 5497

85

73

62

50

8. 509 5438

27

15

8. 509 5403

8. 509 5392

- 80

68

66

45

33

8. 509 5321

8.509 5310

8. 509 5298

86

75

63

51

40

28

16

8. 509 5205

8. 509 5193

81

70

58

46

35

23

12

8. 509 5100

8. 509 5088

77

65

54

42

30

19

8. 509 5007

8. 509 4996

84

 8.509 4972

logC 

diff.l"=+0.46

1.59028

056

083

111

139

166

194

221

249

276

1.59304

331

359

387

414

442

469

497

525

552

1.59580

608

635

663

691

718

746

774

801

829

1.59857

885

912

940

968

1.59996

1. 60023

051

079

107

1. 60134

162

190

218

246

274

301

329

357

385

1.60413

441

469

496

524

552

580

608 

636

664

1. 60692

logD 

diff.l"=-0.02

2. 3539

38

37

36

35

34

33

32

30

29

2. 3528

27

26

25

24

22

21

20

19

18

2. 3517

16

14

13

12

11

10

09

07

06

2. 3505

04

03

02

2.3500

2. 3499

98

97

96

95

2.3493

92

91

90

89

87

86

85

84

83

2.3481

80

79

78

76

75

74

73

72

70

2. 3469

logE 

diff.l"=+0.08

6. 5196

6. 5201

06

10

15

20

25

30

35

40

6.5244

49

54

59

64

69

74

79

83

88

6.5293

6. 5298

6. 5303

08

13

18

22

27

32

37

6. 5342

47

52

57

62

67

72

76 ' 81

86

6. 5391

6.5396

6. 5401

06

11

16

21

26

31

36

6.5441

46

50

55

60

65

70

75

80

85

6.6490

logF 

diff.lO'=-3.2

' 7. 688

7.682

7.676

7.f69
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 58°.

277

Lat.

0 /

58 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.06

8. 508 6669

65

62

58

54

50

46

42

38

35

8. 508 6631

27

23

19

15

11

08

04

8. 508 6600

8.508 6596

8. 508 6592

88

85

81

77

73

69

65

62

58

8. 508 6554

50

46

42

39

35

31

27

23

20

8. 508 6516

12

08

04

8.508 6500

8. 508 6497

93

89

85

81

8.508 6478

74

70

66

62

59

65

51

47

43

8. 508 6440

logB 

diff.l'r=-0.19

8. 509 4972

61

49

38

26

14

8, 509 4903

8. 509 4891

80

68

8. 509 4857

45

33

22

8.5094810

8.509 4799

87

76

64

53

8. 509 474130*

18

8.609 4707

8. 509 4695

84

72

61

49

38

8. 509 4626

15

8. 609 4603

8. 509 4592

80

69

57

46

35

23

8.5094512

8.509 4500

8. 509 4489

77

66

54

43

32

20

8.509 4409

8.509 4397

86

74

63

52

40

29

17

8. 509 4306

8. 509 4295

8. 509 4283

logC 

diff.l".= +0.47

1. 60692

720

748

776

804

832

860

888

916

944

1.60972

1. 61000

028

056

084

112

140

168

197

225

1.61253

281

309

337

365

393

422

450

478

606

1.61534

563

591

619

647

675

704

732

760

789

1. 61817

845

873

902

930

958

1.61987

1. 62015

043

072

1.62100

129

157

185

214

242

271

299

327

356

1.62384

logD 

diff.l»=-0.02

2. 3469

68

67

66

64

63

62

61

59

68

2.3457

56

64

53

52

51

49

48

47

46

2. 3444

43

42

41

39

38

3735'

34

33

2.3432

30

29

28

26

25

24

23

21

20

2.3419

17

16

15

14

12

11

10

08

07

2.3406

04

03

02

2.3400

2.3399

98

96

95

94

2.3392

logE 

diff.l"=+0.08

6.5490

6. 5495

6. 5500

05

10

15

20

25

30

35

6.5640

45

60

55

60

65

70

75

80

85

6.5590

6.5595

6.5600

05

10

15

20

25

30

35

6.5640

45

50

65

60

65

70

75

80

86

6. 5691

6. 5696

6. 5701

06

11

16

21

26

31

36

6. 5741

46

51

66

62

67

72

77

82

87

6. 5792

logF 

diff.lO'=-3.3

7.669

7. 662

7.666

7.649
278 GEOGEAPHIC TABLES AND FOBMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 59°.

Lat.

o / 

59 00

1

2

3

4

6

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

26

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

61

52

53

54

55

66

57

58

59

60

log A 

diff.l"=-0.06

8.508 6440

36

32

28

24

21

17

13

09

05

8. 508 6402

8. 508 6398

94

90

87

83

79

75

71

68

8. 508 6364

60

56

53

49

45

41

38

34

30

8. 508 6326

23 ' 19

15

11

"08

04

8. 508 6300

8. 508 6296

93

8.508 6289

85

81

78

74

70

66

63

59

55

8. 508 6251

48

44

40

36

33

29

25

22

18

8.508 6214

logB 

diff.l"=-0.19

8. 509 4283 .

72

61

49

38

26

15

8.509 4204

8. 609 4192

81

8.5094170

58

47

36

24

13

8. 509 4102

8. 509 4090

79

68

8. 509 4056

45

34

22

11

8. 509 4000

8. 509 3989

77

66

55

8. 509 3943

32

21

8. 509 3910

8. 509 3898

87

76

65

53

42

8. 509 3831

20

8.6093808

8.509 3797

86

75

63

52

41

30

8.509 3719

8. 509 3708

8. 509 3696

85

74

63

52

40

29

18

8. 50i» 4607

logC 

diff.l"=+(W8

1. 62384

413

441

470

498

527

555

584

612

641

1. 62669

698

727

755

784

812

841

870

898

927

1. 62955

1. 62984

1.63013

041

070

099

127

156

185

214

1.63242

271

300

329

357

386

415

444

473

501

1.63530

559

588

617

646

674

703

732

761

790

1. 63819

848

877

906

935

964

1.63993

1.64022

051

080

1. 64109

logD 

diff.l"=-0.02

2.3392

91

90

88

87

86

84

83

82

80

2. 3379

78

76

75

74

72

71

69

68

67

2. ' 336564

63

61

60

58

57

56

64

53

2. 3351

50

49

47

46

44

43

42

40

39.

2. 3337

36

35

33

32

30

29

28

26

25

2.3323

22

20

19

17

16

15

13

12

10

2. 3309

log E log F 

diff.l"=+0.09 diff.lO'=-3.5

6. 5792 7. 649

6.F97

6.5802

07

13

18 :

23- ' 28

33

38

6. 5843

48

54

59

64

69 :

74

79

84

89

6. 5895 7. 642

6. 5900

05 -

10

15

20

26

31

.36

41

6. 5946

51

57

62

67

72 ;

77

82

88

93

6. 5998 7. 635

6. 6003

08

14

19 '

24

29

34

40

45

6.6050

55

61

66

71

76

8187 :

92

6. 6097

6.6102 7.627
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 28. Geodetic position computations Continued.

LATITUDE 60°.

279

Lat.

O '

60 00

1

2

3

4

05

6

1

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

. 44

45

46

47

48

49

50

51

52

53

54

55

56

67

58

59

60

log A 

diff. 1"=-0.06

8.508 6214

10

07

8. 5C8 6203

8.508 6199

96

92

88

84

81

8. 508' 6177

73

70

. 66

62

58

55

51

47

44

8.508 6140

36

33

29

.25

21

18

14

10

07

8. 508 6103

8.508 6099

96

92

88

85

81

77

74

70

8. 608 6066

63

59

55

52

48

44

41

37

33

8. 508 6030

26

22

19

15

11

08

04

8.508 6000

8.508 5997

8. 508 5993

logE 

diff. l"=-0.a

8.509 3607

8.509 3596

85

73

62

51

40

29

18

8.509 3507

8.509 3495

84

73

62

51

40

29

18

8.509 3407

8. 609 3395

8.509 3384

73

62

51

40

29

18

8.509 3307

8. 509 3296

85

8. 509 3274

63

52

40

29

18

8. 509 3207

8. 509 3196

85

74

8.609 3163

52

41

30

19

8. 509 3108

8.609 3097

86

75

64

8. 509 3053

42

31

20

8. 509 3010

8.509 2999

88

77

66

55

8.509 2944

logC 

G diff. 1"=+0.49

1.64109

138

167

196

225

254

283

312

341

370

1. 64400

429

458

487

516

545

574

604

633

662

1.64691

720

750

779

808

838

867

896 925

955

1.64984

1.65013

043

072

101

131

160

190

219

248

1.65278'

307

337

366

396

425

455

484

514

543

1.65573

602

632

661

691

721

750

780

809 '

839

1.65869

logD 

diff. 1"=-0.03

2. 3309

07

06

04

03

02

2.3300

2. 3299

97

96

2. 3294

93

91

90

88

87

85

84

82

81

2. 3279

78

76

75

73

72

70

69

67

66

2.3264

63

61

60

58

57

55

54

52

51

2. 3249

48

46

45

43

41

40

38

37

35

2. 3234

32

. 31

29

28

26

24

23

21

20

2. 3218

log E log F 

diff. 1"=+0.09 diff.lO'= -3.7

6. 6102 7. 627

08

13

18

23

29

34

39

44

50

6.6155

60

66

71

76

81

87

92

6. 6197

6. 6203

6.6208. 7.620

13

18

24.

29

34

40

45

50

56

6. 6261

66

72

77

82

87

93

6. 6298

6.6304

09

6. 6314 7. 613

20

25

30

36

41

46

52

57

62

6. 6368

73

79

84

89.

6. 6395

6.6400

05

11

16

6. 6422 7. 605
280 GEOGRAPHIC TABLES AND POBMULA&

TABLE 28. Geodetic position computations Continued.

LATITUDE 61°.

Lat.

O 1

61 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

66

67

58

59

60

log A 

diff.l"=-0.06

8. 508 5993

89

86

82

79

75

71

68

64

60

8. 508 5957

53

49

46

42

39

35

31

28

24

8. 508 5920

17

13

10

06

8. 508 5902

8. 508 5899

95

92

88

8. 508 6884

81

77

74

70

66

63

59

56

52

8. 608 5848

45

41

38

34

. 30

27

23

20

16

8. 508 5813

09

05

8.608 5802

8. 508 5798

95

. 91

88

84

80

8.508 5777

logB 

diff.l"=-0.18

8. 509 2944

33

22

11

5. 509 2900

8. 509 2889

78

67

56

40

8. 509 2835

24

13

S. 509 2802

8. 509 2791

80

69

58

48

37

8.509 2726

15

8. 509 2704

8. 509 2693

83

72

61

50

39

28

8. 509 2618

8.509 2607

8. 509 2596

85

,74

64

53

42

31

20

8.509 2510

8.5092499

88

77

67

56

 ' 45

34

24

IS

8. 509 2402

8. 509 2391

81

70

59

49

38

27

16

8. 509 2306

8. 509 2295

logC 

diff.l"=+0.50

1.65869

898

928

958

1. 65987

1.66017

047

076

106

136

1. 66166

195

225

255

285

315

344

374

404

434.

1.66464

494

524

553

583

613

643

673

703

733

1. 66763

793

823

853

883

913

943

1. 66973

1.67003

033

 1.67063

094

124

154

184

214

244

274

305

335

1. 67365

395

' 425

456

486

516

547

677

' 607

637

1. 67668

logD 

diff.l"=-0.03

2. 3218

17

15

13

. 12

10

09

07

06

04

2. 3202

2. 3201

2. 3199

98

96

94

93

91

90

88

2. 8186

85

83

81

80

78

77

75

73

72

2. 3170

68

67

65

64

52

60

5857'

55

2.3154

52

50

49

47

45

44

42

40

39

2. 3137

35

34

32

30

29

27

25

23

22

2.3120

logE 

diff.l"=+0.09

6.6422

27

32

38

43

48

54

59

65

70

6. 6476 '

81

87

92 .

6. 6497

6.6503

08

14

19

25

6. 6530

36

41

46

52

57

63

68

74

79

6. 6585

90

6.6596

6.6601

07

12

18

23

29

34

6. 6640

45

51

56

62

67

73

78

84

89

6. 6695

6. 6700

06

12

17

23

28

34

39

45

6.6750

logF 

diff.lO'=-4.0

7.605

7.597

O

7.589

7.681
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

281

LATITUDE 62°.

Lat.

0 /

62 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

. 15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

68

59

60

log A 

diff.l"=-0.06

8. 508 5777

73

70

66

63

59

55

52

48

45

8.508 5741

38

34

30

27

24

20

16

13 09

8.5085706

8. 508 5702

8. 508 5699

95

92

88

85

81

78

74

8.508 5671

67

64

60

56

53

49

46

42

39

8.508 5635 .

32

28

25

. 21

18

14

11

07

04

8.508 6600

8. 508 5597

93

90

86

83

80

76

73

69

8.508 5566

logB 

diff.l"=-0.18

8. 509 2295

84

74

63

52

42-

31

20

8.509 2210

8.509 2199

8. 509 2188

78

67

56

46

35

25

14

8.5092103

8.509 2093

8. 509 2082

71

61

50

40

29

19

8. 509 2008

8. 509 1997

87

8.509 1976

66

55

45

34

23

13

8.509 1902

8.509 3892

81

8.509 1871 .

60

50

39

29

18

8.509 1808

8.509 1797

87

76

8.509 1766

55

45

34

24

14

8.509 1703

8.509 1693

82

72

8.509 1661

logC 

diff.l»=+0.51

1. 67668

698

728

759

789

820

850

880

911

941

1.67972

1.68002

033

063

094

124

165

185

216

246

1.68277

307

338

369

399

430

461

491

522

553

1.68583

614

645

675.

706

737

768

799

829

860

1.68891

922

953

1. 68984

1. 69014

045

076

107

138

169

1. 69200

231

262

293

324

355

386

417

448

479

1.69510

lOgD 

diff.l"=-0.03

2. 3120

18

 17

15

13

 12

10

08

06

05

2.3103

01

2.3100

2.3098

96

94

93

91

89

87

2.3086

84

82

80

79

77

75

74

72

70

2. 3068

66

65

63

61

69

58

56

54

52

2.3050

49

47

45

43

42

40

38

36

34

2. 3033

31

29

27

25

23

22

20

18

16

2.3014 .

log E log F 

dlff.l"=+0.09 cliff. 10' = -4.2

6. 6750 7. 581

66

61

67

73

78

84

89

6. 6795

6. 6801

6. 6806

12

17

23

29

34

40

46

61

57

6.6862 7.573

68

73

79

85

90

6.6896

6.6902

07

13

6.6919

24

30

36

41

17

53

58

64

70

6. 6975 7. 564

81

87

92

6.6998

6.7004

09

15

21

26

6. 7032

38

44

49

55

61

67

72

78

84

6. 7089 7. 556
282 GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 28, Geodetic position computations Continued.

LATITUDE 63°.

Lat.

o / 

63 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff.l"=-0.06

8. 508 5566

62

59

55

52

48

45

41

38

34

8. 508 5531

27

24

20

17

14

10

07

03

8.5085500

8. 508 5496

93

89

86

83

79

76

72

69

65

8. 508 5462

58

55

52

48

45

41

38

34

31

8. 508 5428

24

21

17

14

11

07

04

8. 508 5400

8. 508 6397

8. 508 5394

90

87

83

80

77

73

70

66

63

8. 508 5360

logB 

diff.l"=-0.17

8. 509 1661

51

40

30

20

8.509 1609

8. 509 1599

88

78

68

8.5091557

47

36

26

16

8. 509 1505

8.509 1495

85

74

64

8. 509 1454

43

33

23

12

8. 509 1402

8.509 1392

81

71

61

8. 509 1350

40

30

19

8. 509 1309

8. 509 1299

89

78

68

58

8.509 1248

37

27

17

8.509 1207

8.509 1196

86

76

66

55

8. 509 1145

35

25

15

8.509 1104

8. 509 1094

84

74

64

54

8.509 1043

logC 

diff.l"=+0.52

1.69510

541

572

603

635

666

697

728 '

769

791

1.69822

853

884

915

947

1.69978

1.70009

041

072

 103

1. 70135

160

197

229

260

292

323

355

386

417

1.70449

480

512

544

575

607

638

670 701

733

1.70765

796

828

860

891

923

 955

1. 70986

1.71018

050

1.71082

114

145

177

209

241

273

305

337

368

1.71400

logD 

diff.l"=-0.03

2.3014

13

11

09

07

05

03

02

2.3000

2.2998

2.2996

94

92

90

89

87

85

83

81

79

2. 2977

75

74

72

70

 68

66

64

62

60

2.2958 ' 57 °

55

'51 53

49

47

45

43

41

2. 2939

37

36

34

32

30

28

26

24

22

2.2920

18

16

14

12

10

08 ' 06

04

02

2.2901

logE 

difl.l"=+0.10

6. 7089

6. 7095

6.7101

07

12

18

24

30

35

41

6. 7147

53

59

64

70

76

. 82

 88

93

6. 7199

6. 7205

11

17

22

28

34

40

46

51

57

6. 7263

69

75

81

86

92

6.7298

6.7304

10

16

6. 7322

28

33

 39

. 45

51

57

63

69

75

6.7381

86

92

6.7398

6.7404

10

16

22

28

34

6.7440

logF 

diff.lO'=-4.5

7.556

7.547

7.538

7.529
GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 64°.

283

Lat.

o /

64 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A log B 

diff. 1"=-0.06 cliff. 1"=-0.17

8. 508 5360

56

53

49

46

43

39

36

83

29

8. 508 5326

22

19

16

12

09

06

8.5085302

8.508 5299

96

8.5085292

89

85

82

79

75

72

69

65

62

8. 508 5259

55

52

49

45

42

39 ' 35

32

29

8. 508 5225

2219'

. 15

12

09

05

8. 508 5202

8.508 5199

95

8. 508 5192

89

86

82

79

76

. 72

69

66

62

8. 508 5159

8.509 1043

33

23

13

8.509 1003

8. 509 0993

82

72

62

62

8. 509 0942

32

22

12

8.5090902

8. 509 0891

81

71

61

51

8.509 084131 'J

21

11

8. 509 0801

8. 509 0791

81

71

61

51

8. 509 0741

31

21

11

8. 509 0701

8. 509 0691

81

71

61

51

8. 509 0641

31

21

11

8. 509 0601

8.509 0591

81

71

61

51

8. 509 0541

31

21

11

8. 509 0501

8. 509 0491

82

72

62

52

8.509 0442

logC 

diff. 1"=+0.54 diff

1. 71400

432

464

496

528

560

' 592

624

656

688

1.71720

752

785

817

 849

881

913

945

1.' 71977

1. 72010

1. 72042

074

106

139

171

203

235

268

300

332

1.72365

397

430

462

495

527

559

592

624

657

1.72689

722

755

787

820

852

885

918

950

1.72983

1. 73016

048

081

114

146

179

212

245

278

310

1.73343

logD 

1»=-0.03

'2.2901

2. 2899

97

95

93

91

89

87

85

83

2. 2881

79

77

75

73

71

69

67

65

63

2.2861

59

57

55

53

51

49

47

45

42

2. 2840

38

36

34

32

30

28

26

24

22

2.2820 ' 18

16

14

12

10

07

05

03

2.2801

2.2799

97

95

93

91

89

87

84

82

80

2.2778

log E 

diff. 1"=+0.10 diff

6. 7440

46

52

58

63

69

75

 81

87

93

6. 7499

6. 7505

11

17

23

29

35

41

47

53

6. 7559

65

71

77

83

89

6. 7595

6. 7601

07

13

6. 7619

25

31

37

43

49

56

62

68

74

6. 7680

 86

' 92

6. 7698

6.7704

10

16

22

28

35

0. 7741

47

53

59

66

71

77

84

90

6. 7796

6.7802

log F 

10'=-4.7

7.529

7.520 .

'

7.511

!

f

7.501
284 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 65°.

Lat.

0 /

65 00'

1

2

3

4

05

6

7

8

9

10

11

12

13

14

16

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

62

53

54

55

56

67

58

59

60

log A 

diff.l»=-0.05

8. 508 5159

56

52

49

46

43

39

36

33

30

8.508 5126

23

20

17

13

10

07

03

8. 508 5100

8. 508 5097

8.508 5094

90

87

84

81

77

74

71

68

64

8.508 5061

68

64

51

48

45

41

38

35

32

8.508 5029

25

22

19

16

13

09

06

03

8. 508 5000

8. 508 4996

93

90

87

84

80

 77

74

71

68

8. 508 4964

logB 

diff.l"=-0.16

8.5090442-

32

22

12

8. 509 0402

8.509 0393

83

73

63

53

8. 509 0344

34

24

14

8.509 0304

8. 609 0295

85

 75

65

56

8.509 0245

36

26

16

8.5090206

8.509 0197

87

77

67

67

8. 509 0148

38

28

18

8.509 0109

8. 509 0099

89

80

70

60

8. 509 0051

41

31

22

12

8.509 0002

8. 508 9993

83

73

64

8.508 9954

44

35

25

15

8. 508 9906

8. 508 9896

87

77

67

8.5089858

logC 

diff.l"=+0.56

1. 73343

376

409

442

475

508

541

574

607

640

1. 73673

706

739

772

806

838

871

904

937

1. 73970

. 1.74004

037

070

103

136

170

203

236

270

303

1. 74336

370

403

436

470

503

537

570

604

637

1. 74670

704

738

771

805

838

872

906

939

1.74973

1. 75007

040

074

108

142

175

209

243

277

311

1.75344

logD 

diff.l"=-0.04

2. 2778

76

74

72

70

68

65

63

61

. 59

2.2757

55

53

60

48

46

44

42

40

38

2.2735

33

31

29

27

24

22

20

18

16

2. 2714

11

09

07

05

03

2.2700

2. 2698

96

94

2.2692

89

87

85

83

80

78

76

74

72

2. 2669

67

65

63

60

58

56

53

51

49

' 2.2647

logE 

diff.l"=+0.10

6.7802

 08

14

20

27

33

39

45

51

57

6. 7864

70

76

82

88

6. 7896

6.7901

07

13

19

6. 7926

32

38

44

51

57

63

69

76

82

6. 7988 -

6. 7994

6.8001

07

13

19

26

32

38

44

6.8051

57

' 63

70.

76

82

89

6.8095

6.8101

07

6. 8114

20

27

33

39

46

62

58

65

71

6.8177

log? 

diff.lO' = -5.0

7.501

7.491

7.481

7.471
GEOGRAPHIC TABLES AND FORMULAE. 285

TABLE 2& Geodetic position computations Continued.

LATITUDE 66°.

Lat.

o

66

/

00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

16

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

63

54

55

56

57

58

59

60

log A 

diff.l"=-0.05

8. 508 4964

61

58

55 ..

52

48

45

42

39

36

8.508 4933

29

26

23

20

17

13

10

07

04

8.5084901

8.508 4898

95

91

88

85

82

79

76

73

8. 508 4869

66

63

60

57

'54

50

47

44

41

8. 508 4838

35

32

29

26

22

19

16

13

10

8. 508 4807

04

8. 508 4801

8. 508 4797

94

91

88

86

82

79

8.508 4776

logB 

diff.l"=-0.16

8.608 9868

48

39

29

20

10

8.608 9801

8. 508 9791

82

72

8. 508 9762

53

43

34

24

14

8. 508 9705

8. 508 9696

86

77

8.6089667

58

48

39

29

20

11

8.5089601

8. 508 9592

82

8.6089573

63

54

44

35

25

16

8. 508 9507

8. 508 9497

88

8. 508 9478

69

60

51

41

32

23

13

8.508 9404

8.608 9395

8. 508 9385

76

66

57

48

38

29

20

10

8. 508 9301

8. 508 9292

logC 

diff.l"=+0.57

1

1

1

1

1

1

1

.75344

378

412

446

480

514

548

582

616

650

.75684

718

752

786

820

854

889

923

957

.75991

76025

060

094

128

163

197

231

266

300

334

76369

403

438

472

507

541

576

610

645

679

76714

749

783

818

853

887

922

957

76991

logD 

diff.l"=-0.04

2

2

2

2

2647

4442 !

4038'

35

33

31

28

26

2624

22

19

17

16

12

10

08

05

03

2601

2598

96

94

91

89

87

84

82

80

2.2678

2

1. 77026

1. 77061

096

131

166

200

235

270

305

340

375

1. 77410

2

2.

75

73

70

68

66

63

61

59

56

2554

51

49

47

44

42

39

37

35

32

2530

27

25

23

20

18

15

13

11

08

2506

logE 

diff.l"=+0.11

6.8177

84

90

6. 8196

6.8203

09

16

22

28

35

6.8241

48

64

61

67

73

80

86

93

6.8299

6.8306

12

19

25

31

38

44

51

57

64

6.8370

77

83

90

6. 8396

6.8403

09

16

22

29

6.8436

42

49

55

62

68

75

81

88

6. 8496

6.8501

08

14

21

27

34

41

47

54

60

6.8567

IpgF 

diff. 10'=-5.3

7.471

7.461

7.450

7.440
286 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations^-Coniirmed. 

LATITUDE 67°.

Lat.

o / 

67 00

1

2

a

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

. 30

31

32

33

34

35

: 36

37

38

39

40

41

42

: 43

44

45

', 46

47

48

49

50

61

52

53

54

55

56

57

58

59

60

log A 

diff. 1"=^0.05

8. 508 '4776

73

70

66

63

60

57

54

51

48

8. 508 4745

42

39

36

33

30

26

23

,20

17

8. 508 4714

11

08

05

8. 508 4702

8. 508 4699

96

93

90

87

8.5084684

81

78

75

72

68

65

62

69

56

8.508 4653

50

 ,.47

44

41

38

35

32

29

26

8. 508 4623

20

17

14

11

08

05

8.5084602

8.508 4599

96

8. 508 4593

logB 

diff.l"=-0.15

8. 508 9292

83

73

64

55

46

36

27

18

8. 508 9208

8.508 9199

90

81

72

62

53

. 44

35

26

16

8.508 9107

8. 508 9098

89

80

71

62

52

43

34

25

8. 508 9016

8. 508 9007

8. 608 8998

88

79

70

61

52

43

34

8.508 8925

16

8.508 8907

8.5088898

89

80

71

62

53

44

8. 508 8834

' 25

16

8. 508 8807

8. 508 8798

89

80

71

62

54

8. 508 8745

logC 

diff. 1"= +0.59

1. 77410

445

480

515

550

585

620

656

691

726

1.77761

796

831

867

902

937

1. 77973

1.78008

043

079

1. 78114

149

185

220

256

291

327

362

398

433

1. 78469

506

540

576

612

647

683

719

755

790

1. 78826

862

898

934

1. 78970

1. 79006

042

078

114

150

1. 79186

222

258

294

330

366

402

438

474

511

1. 79547

logD 

diff. 1"= -0.04

2.2506

03

2.2501

2. 2498

96

93

. 91

89

86

84

2.2481

79

76

74

71

69

66

64

61

59

2.2456

54

61

49

46

44

41

39

36

34

2. 2431

29

26

24

21

11.

1614 '

11

09

2. 2406

03

2.2401

2. 2398

96

93

91

88

86

83

2.2380

78

75

73

70

67

65

62

60

57

2.2354

logE 

diff.l"=+0.11

6.8567

74

80

. 87

6.8594

6.8600

07

14

20

27

6.8634

40

47

64

60

. 67

74

80

87

6.8694

6.8700

07

14

20

27

34

41

47

54

61

6.8768

74

81

88

6. 8795

6.8802

08

15

22

29

6.8835

42

49

56

63

70

76

83

90

6.8897

6.8904

10

17

. 24

31

38

45

52

59

65

6. 8972

logF 

diff.lO'=-5.6

7.440

7.429

,7.418

i

7. 406
GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 68°.

287

Lat.

o / 

68 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

SCSI

52

53

54

55

66

67

58

59

GO

log A 

diff.l"=-0.05

8. 508 4593

90

87

84

81

78

76

73

70

67

8.5084564

61

58

55

52

49

. 46

43

40

37

8.508 4534

31

28

25

22

19

16 ' 13

10

07

8.508 4504

8.508 4501

8. 508 4499

96

93

90

87

84

81

78

8.608 4475

72

70

67

64

61

5855 

62

49

8. 508 4446

43

40

38

35

32

29

26

23

20

8. 508 4417

logB 

diff.l" = -0.15

8. 608 8745

36

27

18

09

8. 508 8700

8.508 8691

82

73

64

8.508 8656

47

38

29

20

11

8. 508 8602

8.5088593

84

75

8.5088566

58

49

40

31

22

13

8.508 8505

8,508 8496

87

8. 508 8478

69

60

' 52

43

34

26

17

8. 508 8408

8. 508 8399

8. 508 8390

82

73

64

56

47

38

30

21

12

8. 508 8303

8. 508 8295

86

77

68

60

51

43

34

25

8. 508 8217

logC 

diff.l"=+0.62

1. 79547

583

620

656

692

728

765

801

838

874

1. 79911

947

1. 79984

_ 1.80020

057

093

130

166

203

240

1. 80276

313

350

387

423

460

497

534

671

608

1.80645

682

719

766

793

830

867

904

' 941

1.80978

1. 81015

052

089

127

164

201

239

' 276

313

350

1. 81388

425

463

500

538

575

613

: 650

688

726

1.81763

logD difi.l"=-0.4

2.2354

52

49

47

44

41

39

36 

33

31

2.2328

26

. 23

20

18

15

12

10

07

04

2.2302

2.2299

96

94

91

88

85

83

80

77

2.2275

 72

69

67

64

"61

58

56

53

50

2.2248

45

42

39

36

34

31

28

26

23

2. 2220

17

14

12

09

06

03

2.2201

2. 2198

95

2. 2192

log E log F 

diff.l"=+0.12 cliff. 10'=- -5.9

6. 8972 7. 406

7986 

6.8993

6.9000

07

14

21

28

35

6.9042

48

55

62

69

76

83

90 

6.9097

6. 9104

6.9111 7.395

18

25

32

39

46

53

60

67

74

6. 9181

88

6. 9195

6. 9203

10

17

24

31

38

45

7.383

6. 9252

59

66

73

80

88

6. 9295

6. 9302

09

16

6.9323

30

37

45

52

69

66

73

80

88

6.9395 7.371
288 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 69°.

Lat.

0 /

69 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

. 41

42

43

44

45

46

47

48 .

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff. 1"=-0.05

8. 508 4417

14

12

09

06

03

8. 508 4400

8.508 4397

94

92

8.5084389

86

83

80

77

74

71

69

66

63

8.508 4360

67

55

52

49

46

43

40

37

35

8. 608 4332

29

26

23

21

18

15

12

09

06

8.508 4304

8. 508 4301

8. 508 4298

95

93

90

87

84

81

79

8. 508 4276

73

70

67

65

62

59

56

54

51

8. 508 4248

log B 

diff. 1"=-0.14

8.5088217

08

8. 508 8200

8. 508 8191

82

74

65

57

48

39

8. 508 8131

22

14

8.508 8105

8. 508 8096

88

79

71

62

54

8. 508 8045

37

28

20

11

8. 508 8003

8.508 7994

86

77

69

8.508 7960

52

43

35

26

18

09

8.508 7901

8.508 7893

84

8.508 7876

67

59

51

42

34

26

17

09

8.508 7801

8.508 7792

84

75

67

59

50

42

34

25

17

8. 508 7709

logC 

diff. 1"= +0.64

1.81763

801

838

876

914

952

1.81989

1.82027

065

103

1.82141

179

217

255

293

330

369

407

445

483

1. 82521

559

597

636

674

712

760

789

. 827

865

1.82904

942

1.82981

1. 83019

058

096

135

173

212

250

1. 83289

328

366

405

444

483

521

560

599

638

1.83677

716

755

794

833

872

911

950

1.83989

1. 84028

1.84068

log D 

diff. 1"= -0.05

2.2192

89

87

84

81

78

75

72

70

67

2.2164

61

58

55

53

50

47

44

41

38

2. 2136

33

30

27

24

21

18

15

12

10

2. 2107

04

2.2101

2. 2098

95

92

89

86

83

80

2. 2078

75

72

69

66

63

60

57

54

51

2. 2048

45

'42

39

36

33

30

27

24

21

2. 2018

log E log F 

diff.l"=+0.12 diff.lO'=-6.2

6. 9395 7. 371

6.9402

09

16

24

31

38

45

52

60

6. 9467

74

82

89

6.9496

6. 9503

11

18

25

32

6.9540 7.358

47

54

62

69

76

84

91

6. 9598

6.9606

6. 9613

20

28

35

 42

50

57

65

72

79

6. 9687 7. 346

6. 9694

6.9702

09

16

24

31

39

46

54

6. 9761

69

76

84

91

6.9799

6. 9806

14

21

29

6. 9836 7. 333
GEOGKAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued. 

LATITUDE 70°.

289

Lat.

o /

70 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33.

34

35

36

37

38

39

40

41 42

43

44

45

46

47

48

49

50

51

52

53

54

65

56

57

58

59

60

log A log B 

diff.l"=-0.04 diff. 1"=-0.14

8. 508 4248

45

43

40

37

34

32

29

26

23

8.5084221

18

15

12

10

07

04

8.508 4201

8. 508 4199

96

8. 508 4193

90

88

85

82

80

77

74

71

69

8. 508 4166

63

60

58

55

52 .

50

47

44

42

8. 508 4139

36

34

31

28

26

23

20

18

15

8.508 4112

10

07

04

8.508 4101

8. 508 4099

96

93

91

88

8. 508 4086

8. 508 7709

8. 508 7701

8. 508 7692

84

76

68

59 .

51

43

35

8. 508 7626

18

10

8.508 7602

8.5087594

86

78

69

61

52

8.5087644

36

28

20

12

8.508 7504

8.508 7495

87

79

71

8. 508 7462

64

46

38

30

22

14

8.508 7406

8. 508 7398

90

8. 508 7382

74

66

68

50

42

34

26

18

 10

8. 508 7302

8. 508 7294

86

77

69

61

53

45

38

30

8. 508 7222

logC 

diff. 1"= +0.67

1. 84068

107

146

185

225

264

303

343

382

421

1.84461

500

540

579

619

658

698

738

778

817

1.84857

897

937

1.84976

1.85016

056

096

136

176

216

o 1.85256-

296

336

376

416

456

497

537

577

618

1.85658

698

739

779

819

860

* 900

941

1. 85981

1. 86022

1. 86063

103

144

185

225

266

307

348

389

430

1. 86470

logD 

diff. 1"= -0.05

2. 2018

15

12

09

06 .

03

2.2000

2.1997

94

91

2. 1988

85

82

79

76

73

70

66

63

60

2.1957

54

51

48

45

42

39

36

33

29

2. 1926

23

20

17

14

11

08

04

2. 1901

2.1898

2. 1895

92

89

85

82

79

76

73

70

66

2. 1863

60

57

54

50

47

 44

41

38

34

2.1831

logE 

diff. 1"= +0.13

6. 9836

44

51

59

66

74

81

89

6. 9896

6.9904

6. 9912

19

27

34

42

50

57

65

73

80

6.9988

6.9995'

7.0003

11

18

26

34

41

49

57

7.0064

72

80

88

7.0095

7. 0103

11

19

26

34

7. 0142

50

57

65

73

81

88

7.0196

7. 0204

12

7.0220

27

35

43

51

59"

67

75

82

90

7. 0298

logF 

diff.lO'=-6.7

7.333

7.320

7.307

0

7.293

41623° 16
290 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 28. Geodetic position computations Continued.

LATITUDE 71°.

Lat.

0 '

71 00

1

2

3

4

05

6

7

8

9

10

11

12

13

14

15

16

17 ' 18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

log A 

diff. 1" = - 0.04

8. 508 4086

83

80

78

75

72

70

67

64

62

8.5084059

57

54

51

49

46

43

41

38

36

8. 508 4033

30

28

25

23

20

17

15

12

10

8. 508 4007

05

8. 508 4002

8. 508 3999

97

94

92

89

86

84

8. 508 3981

79

76

74

71

68

66

63

61

58

8. 508 3956

53

51

48

46

43

41

38

36

33

8. 508 3930

logB 

diff.l"=-0.13

8.5087222

14

8. 508 7206

8.508 7198

90

82

74

66

58

50

8.508 7142

34

27

19

11

8.508 7103

8. 508 7095

87

79

72

8,508 7064

56

48

40

33

25

17

09

8. 508 7002

8. 508 6994

8. 508 6986

78

71

63

55

47

40

32

24

16

8. 508 6908

8. 508 6901

8. 508 6893

85

78

70

62

55

47

40

8. 508 6832

24

17

09

8.508 6802

8. 508 6794

86

79

71

64

8.508 6756

logC 

diff.l"=+0.70

1.86470

511

552

593

634

675

717

758

799

840

1.86881

923

1. 86964

1.87005

046

088

129

171

212

254

1.87295

337

378

420

462

503

545

587

629

671

1/87712

754

796

838

880

922

. 1. 87964

1.88006

049

091

1.88133

175

217

260

302

344

387

429

472

514

1.88557

-599

642

685

727

770

813

855

898

941

1. 88984

logD 

diff.l"=-0.05 diff

2. 1831

28

25

21

18

15

12

08

05

2. 1802

2. 1799

95

92.

89

86

82

79

76

72

69

2. 1766

62

59

56

52

49

46

42

39

36

 2. 1732

29

26

22

19

16

12

09

06

2. 1702

2. 1699

95

92

89

85

. 82

78

75

72 * 68

2. 1665

61

58

54

51

48

44

41

37

34

2.1630 '

logE 

1"=+0.13

7.0298

7.0306

14

22

30

38

46

54

62

70

7. 0378

85

7.0393

7.0401

09

17

25

33

41

49

7.0457

65

73

82

90

7. 0498

7. 0506

14

22

30

v.0538

46

54

62

70

79

87

7.0595

7.0603

11.

7.0619

27

36

44

52

60

68

77

85

7. 0693

7. 0701

09

18

26

.34

42

51

59

67

75

7. 0784

logP 

diff. 10"= -7.2

7.293

7.279

7.265

7.250
GEOGRAPHIC TABLES AND FORMULAS. 

TABLE 29. Values of leg sec \

291

*

1011

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

log sec £

0. 000 000

1

1

1

1

1

1

1

1

2

2

2

2

2

3

3

3

3

*

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

log sec i

0. 000 004

4

. 4

4

5

5

5

6

6

6

7

7

7

8

S

8

9

9

*

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

log sec i

0. 000 010

10

11

11

11

12

12

13

13

14

14

15

15

16

16

17

18

18

*

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

log sec -J- 

(M

0. 000 019

19

.20

21

21

22

22

23

24

24

25

26

26

27

28

29

29

30

4,

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

log sec £

0. 000 031

32

32

33

34

35

36

36

37

38

39

40

41

41

42

43

44

45

To convert:

Meters to feet.

1

2

3.

4

5

6

7

8

9

= 3. 280 833

6.561 067

9. 842 500

13. 123 333

16. 404 166

19. 685 000

22.965833

26. 246 666

29.527 500

Feet to meters.

-i _

2

3

4

5

6

7

8

9

0.304 8006

0. 609 6012

0. 914 4018

1:219 2024

1. 524 0030

1. 828 8037

2. 133 6043

2.438 4049

2. 743 2055

To convert:

Kilometers tostat1

2

3

4

5

6

7

8

9

ute miles.

= 0.621 3699

1.242 7399

1. 864 1098

2. 485 4798

3.106 8497

3. 728 2196

4.349 5896

4. 970 9595

5. 592 3295

Statute miles to

1

2

3

4

5

6

7

8

9

kilometers.

= 1. 609 347

3. 218 694

4. 828 042

6.437 389

8.046 736

9. 656 083

11.265 430

12. 874 778

14.484 125
292 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 30. Corrections to longitude for difference in arc and sine.

logs(-)

3.876

4.026

4.114

4.177

4.225

4.265

4.298

4.327

4.353

4.376

4.396

4.415

4.433

4. 449

4.464

4.478

4.491

4.503

4.526

4.548

4. 570

4.591

4.612

4.631

 4.649

4.667

4.684

4.701

4.716

4.732

4.746

4.761

4.774

4.788

4.801

4.813

4.825

4.834

4.849

4.860

log difference.

0. 000 0001

02

03

04

05

06

07

08

09

10

11

12

13

14

15

16

17

18

20

23

25

27

30

33

36

39

42

45

48

52

56

59

, 63

67

71

75

80

84

89

94

logAA. ( + )

2.385

2.535

2.623

2.686

2. 734

2.774

2.807

2.836

2.862

2.885

2.905

2.924

2.942

2.958

2. 973

2.987

3.000

3.012

3.035

3.057

3.079

3.100

3.121

3.140

3.158

3.176

3.193

3.210

3.225

3.241

3.255

3.270

3.283

3.297

3.310

3.322

3.334

3.343

3.358

3.369

logs (-)

4.87l'

4.882

4.892

4.903

4.913

4.922

4.932

4.941

4.950

4.959

4.968

4.976

4.985

4.993

5.002

5.010

5.017

5.025

5.033

5. 040 .

5.047

5.054

5.062

5.068

5.075

5.082

5.088

5. 095

5.102

5.108

5.114

5.120

5.126

5.132

5.138

5.144

5.150

5.156

5.161

5.167

log difference.

0.000 0098

103

108

114

119

'124

130

136

142

147

153

160

166

172

179

' 186

192

199

206

213

221

228

236

243

251

259

267

275

284

292

300

309

318

327

336

345

354

364

373

383

logAA( + )

3.380

3. 391

3.401

3.412

3.422

3.431

3.441

3.450

3.459

3.468

3.477

3.485

3.494

3.502

3.611

3.519

3.526

3.534

3.542

3.549

3.556

3.563

3.571

3.577

3.584

3.591

3.597

3.604

3.611

3.617

3.623

3.629

3.635

3.641

3.647

3.653

3.659

3.665

3.670

3.676

'logs(-)

5.172

5.178

5.-183

5.188

5.193

5.199

5.204

5.209

5.214

5.219

5.223

5.228

5.233

5.238

5. 242

5.247

5.251

5.256

5.260

5.265

5.269

5.273

5.278

5.282

5.286

5.290

5.294

5.299

5. 303

5.307

5.311

5.315

5.319

5.323

5.327

5.331

5.335

5.339

5.343

5.347

log difference.

0. 000 0392

402

412

422

433

443

453

464

474

486

497

508

519

530

541

553

565

577

588

600

613

625

637

650

663

674

687

702

716

729

743

757

771

785

800

814

829

845

861

877

logAA.( + )

3.681

3. 687

3.692

3.697

3.702

3.708

3.713

3.718

3.723

3.728

3.732

3.737

' 3. 742

3.747

3.751

3.756

3.760

3.765

3.769

3.774

3.778

3.782

3.787

3. 791

3.795

3.799

3.803

3.808

3. 812

3.816

3.820

3.824

3.828

3.832

3.836

3.840

3.844

3.848

3.862

3.856

INVERSE SOLUTION.

HAVING LATITUDES AND LONGITUDES OF Two POINTS TO COMPUTE AZIMUTHS AND

DISTANCES.

The following example shows the method of performing the operation. The northernmost point should be used as the initial position, 

then all signs for (I), (II), and (III) are +, and for (IV) -. The 

value of A\. may be either -f- or , but this sign need only be used 

in determining in which quadrant the azimuth angle a falls, i. e., the 

sign of tan a (12). An inspection of a rough plat of the positions 

will also determine this. The correction to ^A. is found from a 

distance scaled off from the plat, and need not be very close. In 

(8) the term (I+1I)2 is the square of the difference of latitude d<p in 

seconds. Since (IV) is always small, log (I) in (8) may be taken as 

log of A(f> from (1). If cos OL is smaller than sin <*, find ? from 

log s cos a. in (11). As a check on the work compute the second
GEOGRAPHIC TABLES AND FORMULAS. 293

position, using distance and azimuth found as above. The order of 

solution is shown by figures in parentheses. The cosines of latitudes 

are proportional to the intercepted parallels.

Latitude = <j> =38° 23' 27" .00 Given. 

9 ' = 37 45 09 .30 Given.

A?) = 38' 17" .70

=2297" .70 (1) 

log A <p = 3.3612933 

log C = 1.303GO 

log S2 sin2a = 8.75770

log (II) 0.00130 (7)

(II) = 1" .152 

log D = 2.3812 

log (I + 11)2 = 6.722(1

log (III) 9.1038(8)

III = 0" .13

log E = 0.0711

log S2 sin^a = 8.7577

log I = 3.3613

log IV = 8.1901 (9) 

IV = -" .02

(II) = + 1.15"

(III) = + 0.13 

IV = - .02

Sum = + 1.26" (10) 

A? = 2297.70

(I) = 2296.44

Longitude = A 

\'

A A

= 104° 32' 48" .20 Given 

 104 49 05 .50 Given

16' 17" .30 + 

= 977" .30 + (2) 

log A A = 2.9900279

log A A correction = + 16 

log S (scaled distance) correction = 99

(apply with opposite sign) 83 (3) 

log A A' = 2.9900362 (4)

log A' = 8.5091750 (5) 

Sec 9' = 0.1020092

8.6111842 (+) 

log A A' = 2.9900362 (+)

log S sin a = 4.3788520 (+) (6)

log S cos a = 4.8500742 (+) (11)

sin a

 = tan a = 9.5287778 (12)

COS a

log (I) = 3.3610475 

log (B) = 8.5109733

log S cos a = 4.8500742 (11) 

Azimuth = a = 18° 40' 10" .8 (13) 

log S sin a = 4.3788520 

log sin a = 9.5053013

log distance = log S = 4.8735507 (14)
294 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 31. Log TO, for use in computing spherical excess. 

[Computed for the Clarke spheroid of 186C.]

Lat.

o /

 o oo

0 30

1 00

1 30

2 00

2 30

3 00

3 30

4 00

4 30

5 00

5 30

6 00

6 30

7 00

7 30

8 00

8 30

9 00

9 30

10 00

10 30

11 00

11 30

12 00

12 30

13 00

13 30

14 00

14 30

15 00

15 30

16 00

16 30

17 00

17 30

18 00

18 30

19 00

19 30

20 00

20 30

21 00

21 30

22 00

22 30

23 00

23 30

24 00

24 30

Login.

1. 40695

1, 40695

1. 40695

1. 40694

1. 40694

1. 40694

1. 40693

1. 40693

1. 40692

1. 40691

1. 40690

1. 40689

1. 40688

1. 40687

1.40686

1. 40685

1. 40683

1. 40682

1.40680

1.40679 '

1.40677

1. 40675

. 1. 40673

1. 40671

1. 40669

1. 40667

1. 40665

1. 40663

1. 40660

1. 40658

1. 40655

1. 40653

1. 40650

1. 40647

1. 40644

1. 40642

1.40639

1. 40636

1. 40632

1. 40629

1. 40626

1.40623

1. 40619

1. 40616

1. 40612

1. 40608

1. 40605

1. 40601

1. 40597

1. 40594

Lat.

0 /

25 00

25 30

26 00

26 30

27 00

27 30

28 00

28 30

29 00

29 30

30 00

30 30

31 00

31 30

32 00

32 30

33 00

33 30

34 00

34 30

35 00

35 30

36 00

36 30

37 00

37 30

38 00

38 30

39 00

39 30

40 00

40 30

41 00

41 30

42 00

42 30

43 00

43 30

44 00

44 30

45 00

45 30

46 00

46 30

47 00

47 30

48 00

48 .30

49 00

49 30

Log m.

1. 40590

1. 40586

1.40582

1. 40578

1. 40573

1. 40569

1. 40565

1. 40560

1. 40556

1. 40552

1. 40548

1. 40544

1. 40539

1. 40534

1. 40530

1. 40525

1.40520

'1. 40516

1. 40511

1. 40506

1. 40501

1. 40496

1. 40491

1. 40486

1.40482

1.40477

1. 40472

1. 40467

1. 40462

1. 40457

I. 40452

1. 40446

1. 40441

1. 40436

1. 40431

1. 40426

1. 40421

1. 40416

1. 40411

1. 40406

1. 40400

1. 40395

1. 40390

1. 40385

1. 40380

1. 40375

1. 40369

1. 40364

1. 40359

1. 40354

Lat.

o /

50 00

50 30

51 00

51 30

52 00

52 30

53 00

53 30

54 00

54 30

55 00

55 30

56 00

56 30

57 00

57 30

58 00

58 30

59 00

59 30

60 00

60 30

61 00

61 30

62 00

62 30

63 00

63 30

64 00

64 30

65 00

65 30

66 00

66 30

67 00

67 30

68 00

68 30

69 00

69 30

70 00

70 30

71 00

71 30

72 00

Log m.

1. 40349

1. 40344

1. 40339

1. 40334

1. 40329

1.40324

1. 40319

1.40314

 1.40309

1. 40304

1. 40299

1.40295

1. 40290

1. 40285

1.40280

1. 40276

1. 40271

1. 40266

1. 40262

1. 40257

1. 40253

1.40249

1.40244

1. 40240

1. 40235

1. 40231

1. 40227

1. 40223

1.40219

1.40215

1.40210

1. 40207

1.40203

1. 40199

1.40195

1.40192

1.40188

1. 40185

1. 40181

1. 40178

1. 40174

1.40171

1. 40168

1. 40164

1. 40161
GEOGRAPHIC TABLES AND FORMULAS. 295

TABLE 32. Logarithms and factors for converting latitudes and departures in feet to seconds of latitude and longitude for latitudes 0° 

to 72°.

[Prepared by D. H. BALDWIN.]

EXPLANATION OF TABLE.

This table has been prepared especially for use in computing primary traverses of the United States Geological Survey, in which 

sections each less than 2 miles in length are computed successively.

Logarithms of factors designated M and P are given for each 

minute of latitude from 0° to 72°. Logarithms of differences of 

seconds in latitude and longitude are found by adding tabular values 

of the M and P logarithms for a given latitude to the logarithms of 

the latitude and departure, respectively, of a section as computed in 

feet. If the adjusted azimuths of the courses be considered to define 

their directions with reference to the meridians through their centers, 

and if the courses comprising a section extend in one general direction, the mean latitude will then be the proper one to use in selecting 

log M and log P, but as the rate of change in log M is slight the known 

latitude at the beginning of a section of traverse can generally be used.

The factor M, for computation of seconds on the meridian, is 

Bx 0.3048006, or log M= log B +9.4840158. Similarly P, for computation of seconds on the parallel, is Ax0.3048006Xsec <£, or log 

P = log A + 9.4840158 + log sec 0, B and A being factors in the Coast 

and Geodetic Survey tables 1 for the computation of geodetic coordinates for use with metric measures, 0.3048006 the factor for 

reducing feet to meters, and 4> the mean latitude of the section.

In the margin of each page, for latitudes greater than 18°, there 

are given the differences of log P for multiples of 5" change in latitude,'for use in interpolation, none being required for log M nor for 

log P below 18°.

An error of one unit in the fifth place in log M is equivalent to 

about 0.002" for a distance of 10,000 feet for any latitude, and in log 

P for the same distance one unit in fifth place is equivalent to a value 

of 0.002" k> 0.007" for latitudes 0° to 72°, respectively, the value 

for 40° being 0.003". Examples of the use of tables are given below.

The position of station 50 is assumed to be latitude 49° 21' 26.54", 

the longitude 109° 46' 32.25", and the sum of the latitudes and the 

sum of the departures for the section to station 53, as previously 

determined, are 3,280 feet N. and 1,870 feet E., respectively. What 

is the position of station 53 ?

1 See Coast and Geod. Survey Special Pub. No. 8, Washington, 1911; also Table 28 of this bulletin.
296 GEOGRAPHIC TABLES AND FORMULAS.

Write quantities in the order of numbers in parentheses:

log 3280 =3.51587 (3) 

log M for lat. 49° 21^=7.99415 (5)

log seconds =1. 51002 (6) 

=32.36" (7)

Sta. 50 Lat. 49° 21' 26.54" (1) 

32.36" (7)

Sta. 53 Lat. 49° 2V 58. 90" (8)

log 1870 =3.27184 (4) 

log P for mean lat. 49° 21' 

43" =8.17913 (9)

log seconds =1.45097 (10) 

=28.25" (11) 

Long. 109° 46' 32. 25" (2) 

28. 25" (11)

Long. 109° 46' 04.00" (12)

The labor of computing may be lessened when a latitude or departure is expressed in simple numbers by using the marginal tables 

for 100M or 100P for the initial or for the mean latitude of section, 

respectively.

For example, suppose the latitude and departure of the next 

section to be 200 feet N. and 300 feet W., then 

49° 21' 58.90" 109° 46' 04.00" 

2 X 0.987 = 1.97" 3 X 1.511 = 4.53"

49° 22' 00.87" 109° 46' 08.53"

The longitudinal factor, 1.511 seconds for 100 feet, is found by 

interpolation between 1.510 for latitude 49° 20' and 1.515 for latitude 

49° 30' for the mean latitude 49° 22', or 0.2 times 0.005 the difference 

for 10 minutes, added to 1.510.

In -the computation for latitudes the initial latitude is used in 

finding M instead of the mean latitude, which should be used for a 

single course or for a section when the third term (D (A0) 2) of the 

Coast and Geodetic Survey formula is omitted. The maximum rate

of change in log M is only about two units in the sixth place Of decimals for 1 minute of latitude, and therefore the error introduced is 

generally inappreciable, but when increased accuracy is desired the 

approximate mean latitude can be estimated and used.

The error in longitude caused by including meridional and longitudinal courses in one section and using P for the mean latitude is 

greatest when half of the section is run continuously in one of these 

directions and the remainder in the other. At latitude 30° a section 

made up of courses first north 1 mile and then east 1 mile will 

terminate at a point 0.0087" east of a point located by running first 

east and then north, on account of convergence of meridians; and 

if the section is computed by using P for the mean latitude, the 

resulting longitude will be that of a point halfway between, being in 

error 0.0044". At latitude 50° the error will be twice as great.
GEOGBAPHIC TABLES AND FOEMULAS. 297

The following conversion logarithms are given for ready reference: 

Log feet = Log miles + 3.7226339. 

Log feet = Log chains (660 + 1.8195439. 

Log feet = Log meters + 0.5159842.
T"

298

Oc '0I23456789

10

ii

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

303 1

32

33

34

35

36

.37 38

39 

40

41

42

43

44

45

46

47

48

49

50

515 2

53

54

55

56

57

58

59

60

Log. M

7- 99669999999999

7- 99669999999999

7. 99669999999999

7- 9966999999999

9 

7- 99669999999999

7- 99669999999999

7- 99669

Log.P

7- 99374

74

74

74

74

74

74

74

74

74

. 7-99374

74

74

75

75

75

75

75

75

75

7- 99375

75

75

75

75

75

75

76

76

76

7- 99376

76

76

76

76

76

77

77

77

77 

7- 99377

77

77

78

78

78

78

78

78

79

7- 99379

79

79

79

80

80

80

80

80

81

7.99381

/oi23456789

10

ii

12

13

14

IS

16

i7

18

19

20

21

22

23

24

25

26

27

28

29

30

3i

32

33

34

35

36

3738

39

40

41

42

43

44

45

46

47

48

49

505 1

52

53

54

55

56

57

58

59

60

Log. M

7- 99669999999999

7- 99669999999"999

7- 99669999999999

7- 99669999999999

7- 99669999999999

7. 99669999999999

7- 99669

Log.P

7. 99381

81

81

81

82

82

82

82

83

83

7- 99383

83

84

84

84

85

85

85

85

86

7. 99386

86

87

87

87

87

88

88

88

89

7- 99389

89

90

90

909 1 9 1

91

9292

7- 99392

93

93

94

94

94

95

95

96

96

7- 99396

97

97

98

98

98

99

 99399

. 99400

oo

7. 99401

<£

0 /

o oo

I 00

10

20

30 

40

5°

2 OO

100 P

//

o. 9857

58

59 

60

60 

61 

62

63
CO

V

*

p<

s 1" " p.

s * ? § 2 o 2

0 N CO Tf

-e. -eco ^ *ovo 

V %

v Q OOO

O HI Cl C

O c^ 

CO ^" *O *ONO t"*» l^*OQ ON ON O H 04 W co ^" <^" *^VO l*^ r-» OO ON ON O M W W ro ^" 10 \O vO l"*»OQ ON O

cofOfOfOrOfOoOfOcoco^ ^ ^ Tj-Tj-^-^q-^-Tj-Ti-^ ^ ^ Tj-iomioioioioio u->ioio*ovn i^

O^ (^ O^ ON 

ON ON ON ON 

oocQcQoooooooocQoocQoo oooooooooooooooooooo oooooooooooooooooooo

\O VO vO vO 

\O VO VO vC 

ON. ON ' ON C 

ON ON ON C

O H o* ro ^ iovO t^oO ONO H W co ^t1 »J^vO t^-00 ONO w Ci co ^" iO\O t^-OO ONO

oooooo«^*>.

N 

N 

HI N co 'I" W>NO 

co co co co co c

V

s

}

M H HC« M coc'O^t'^w^io \OO t^- t^CO GOONONOO MMCjwcofO'^'^i-iOiOvOvO t^GO COO

O O MtHMMHMMMMMMMMMMMMMWaC

^^ ^ ^ 's^* 

ON ON ON ON 

ON ON ON ON 

f

ONONO^O^ONO^OkOkOvON ON CN ON ON ON ONOO CO OO OO OOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOO

\O vO vO 

\O vO \O 

ON ON ON 

O** " ON ON 

O w C1* co ^ »ovO t^-OO ONO H W co ^ iovO t^oO ONO M w co ^ i^ivo t-^QQ O\O H M co ^ >ONO 
II

8°

So

o- 2066 

86

Z6

t6

z6

68

*8

$8

?8

-o igg6 

//

dOOI

9 oo 

oS 

ot

o?

02

OI

S oo 

oS

ot

0?

OS

01

V oo 0 / 0

-Z 11966 

01

60

Zo

90

So

eo

ZO

10966 

66S66 

-Z g6S66 

Z6

96

t6

£6

26

16

68

88

*8

-Z 9gS66 

^8%

*8

18

6Z

8^

ZZZ 9

tz

-Z £ZS66 

eZ

iZ

oZ

899Z

999S9t

£g

-Z I9S66 

09

6S

8^

ZS

9S

ts

es

sS

!S

-Z oSS66 

6t

8^t9

st

tfr

et

2t

it

ot

-Z 6£S66 

d*3oi

-Z tgg66 ttttSSSS5

-Z 59966 5S55S55SS

-Z £9966 S5SSSSS5S

-Z 59966 S5S55SS55

-Z 59966 SSS599999

-Z 99966 999999999

-Z 99966 

nr3tvi

09

65

8?

ZS95

ss

frS

£5

25

iS

OS

6t

8*

Ztt9

St

ttft

2t

It

Of

6£

8?

ti

g£

se

te

££

z£

i£

6z^

8^

Lz

gz

Sz

ts

£s

zz

IZ

OZ

61

8i

Zi

9i

Si

tl

£i

21

II

OT68Z95t9zio/

-Z 6£S66 

8*e9

se

te

££

z£

i£

o£

62

-Z S66 Sg

Zs

92

52

Vz

£2

ss

IS

OS

8i

Zi566-Z

9i

Si

frl

£i

ZI

ii

01

60

8°

-Z ZoS66 

90

So

to

to

£o

ZO

IO

ooS66 

66t66 

-Z g6t66 

Z6

96

56

t6

£6

z6

16

06

68

-Z ggt66 

^8

^8

98

*8

^8

?8

^8

18

°8

-Z 6Zt66 

d'301

Z- 99966 999999999 Z- 99966 999999999

-Z 99966 999999999 Z- 99966 9ZZzzzzzz

-Z Z9966 Zzzzz'Zzzz

-Z Z9966 ZZZZzzzzz

-Z Zgg66 

IK'Soi

09

6S

8*

ZS

9?

SS

ts

£S

2S

iS

OS

6t

8*

Ztt9

St

tt

et

sfr it

Of

6£&

Li

g£

S£

te

££

z£

i£

0£

6z&

Lz

gz

Sz

ts

£z

zz

IZ

OK

611 8

Zi

9i

Si

ti

£i

ZI

ii

0168Z9S

fr£zi0/

008
£S

6>

Sfr

117

8?

t-f

o£

Lz

^z

oz

Li

171 . -o 1166 "

dOOI

g 00 

oS

ofr

o£

OS

01

i 00 

oS

ot

o£

OS

OI

9 oo 0 / #

S3

?S

'o £366 "

WOOI

8Z9o

*

-4 96466 

WJ

£6

16

68

98g2

°8

-4 64466 

44

S4W

s4

o4

89

49

S9

£9

'4 29466 

09

8S

4S

SS

£S

sS

oS&

LV

-4 Si'466 

£fr

z'v

ofr

8?

S£

££

s£

o£

-4 6s466 

Lz

Ss

t-3

25

IS

61

4i

91

ti

£i466-4

ii

60

80

90

So

£o

so

oo466 

66966 

-4 46966 

d*i

-4 19966 iiiiiiiii

-4 19966 iiiiiiiii

-4 19966 iiiizzzzz

-4 39966 3zzzzzzzz

-4 39966 zzzIzzzzz

'4 39966 3zzzz££££

-4 £9966 

K*l

09

6S

8$

4S

9S

SS

£S

sS

iS

09

6>

g*

9^

S^

Irt7 ft

sfr 'll7

Of

6£

8?

4££ 9

S£

t£

££

s£

i£

08

6ss 8

4s

93

Ss

tz

£s

33

IZ

02

61

gi

4i

91

Si

Vi

£i

SI

iiP0849S

fr£zio<

-4 46966 

S6

ttf

z6

16

68

00

oo

98

ss^

-4 S8966 

°8

64

44

9i

ti

£4

i4

o4

89

-4 49966 

So

"^O

£9

19

09

8S

4S

SS

frS

-4 sSg66 

iS

oS

ofr

4fc

Sfr

tt

it

Ofr

-4 8£966 

4£

?£

£?

i£

o£

6z

Lz

gz

-4 Ssg66 

£s

S3

IS

61

gl

91

Si

fa

£i

-4 11966 

"00^ d 

-4 £9966 ££££££££ ' £ 

-4 £9966 £££££££££

-4 £9966 ££££££££

fr

'L £9966 

 j?

fr

fr

fc

 f7*£

t>

'4 179966 *IV

fct

 fr t*

-4 179966 

 fr

t'

i?

17 >

 (7

|7

f7

17

-4 179966 

«*!

09

6S

g*

LS

9S

SS

1^5

£S

sS

iS

09

6fr

8^

41^

9^7 S1

 M7

£17

zV

ifr

Of

6£

8?

4£

g£

S£

1?£

££

z£

i£

08

6ss 8

Lz

gz

Ss

17S

ss

IZ

OK

61

ii1 9

Si

ti

£i

SI

ii

016849S

t-£zi0'

108
8°

-i £000 

86 

£6

88t'S

6Z

VL

oZ

999I

ZS

-o £566 "

dOOI

OI OO 

oS

o£

OZ

OI

6 oo 

oS

Ofr

o£

OZ

OI

8 oo 0 / . *' 

IZ

ZZ

o- zz66 "

wooi

0168o

#

-g S£ooo 

z£

o£2 8

92

IZ

61

Zi

Si

'8 £1000 

ii

8°

90

fro

zo

-g ooooo 

-Z g6666 

S6

£6

-Z 16666 

68

Sg

?g

13

gZz 9

frZ

zZ 

-Z oZ666 

89

99

^O

ZQ

09

ZS

SS

£S

iS

-Z 6fr666 

Zfr

$*

£fr

ifr 

6£

Z£

$£

££

i£

-Z 6z666 

Zc

Sz

£z

IZ

61

Zi

Si

£i

ii

-Z 60666 

d*l

66-Z9S999

9 999999

-Z 95966 9999 . Z ZZzz

-Z ZSg66 ZZzzzz-zzz

-Z ZSg66 ZZZZZZZ8'8

-Z 8S966 888888888

-Z 35966 888888888

-Z S5g66 

W30-I

09

65

8?

ZS

95

SS

frS £5

zS

iS

09

8*

gfr

Sfr

frfr

£fr

efr

ifr

Of

6£

g£

Z?e 9

fr£

££

z£

i£

08

6zs 8

Zz

9Z

Sz

frz

£z

ZZ

IZ

08

61

31

Zi

91

Si

frl

£i

ZI

ii

0168Z9S

fr£zio

/ 

-Z 60666 

Zo

So

£o

10666 

66366 

Z6

56

£6

16

-Z 63366 

ZsOJj 

J.O

18

6Z

ZZ

sz

£1

zL

-Z oZg66 

89

99

tQ9Z

09 - 95 

£5

-Z 5366 1 

6fr

Zfr

Sfr

£fr

ifr

ofr

8?£ 9

-Z z£866 

o£

8z

Lz

Sz

£z

IZ

61

31

91

*Z frig66 

ZI

OI

60

Zo

So

£o

IO

00366-

6Z66 8

-Z 96Z66 

d*l

-Z 66 958886666666

-Z 65966 666666666

-Z 65966 6666666

65966 

09966 

-Z 09966 0oo0ooooo

-Z 09966 ooooooooo

-Z 09966 oooooIIII

-Z 19966 

*iM

09

65

8S

ZS

95

55

frS

£S

zS

iS

09

8^

Zfr

fr9

Sfr

frfr

£fr

Zfr

ifr

Of

8?

Li

g£

$£

fr£

££

z£

i£

oe

6zZ 8

Lz

gz

Sz

frz

£z

ZZ

IZ

02

611 8

Zi

91

Si

fri

£i

ZI

ii

OT68Z9S

fr£zi0

'/
10

C 11' 303

/

. oI234

5-6789

10

ii

12

13

14J 5

16

17

18J9

20

21

22

23

24

25

262 7

2829

30

3i

32

33

34

35

36

37

38

39

40

4i

42

43

44

45

46

47-

48

49

50

5i

52

53

54

55

56

57

58

59

60

Log. M

7. 99656666666666

7- 99655555555555

7- -996555555S5555

7- 99655444444444

7- 99654444444444

7- 99654443333333

7- 99653

Log.P

8. 00035

37

39

4i

44

46

48

5°

52

55

8. 00057

59

61

64

66

68

71

73

75

77

8. 00080

82

84

87

89

9i

93

96

. 00098

. QOIOO

8. 00103

0507

IO

12

14

17

19

21

. . 24

8. 00126

293 1

33

36

38

40

43

45

48

8. 00150

52

55

57

60

62

64

67

69

72

8. 00174

/oi23456789

10

ii

12

*3

14

IS

16

17

18J9

20

21

22

23

24

25

26

27

2829

303 1 3 2

33

34

35

36

37

38

39

10

4i

42

43

44

45

46

47

48

49

50

Si

52

53

54

55

56

57

58

59

60

Log. M

7- 9965333333333

. . 3

7- 99653333222222

7- 99652222222222

7- 99652222IIIIII

7.99651IIII

7- 99651iio0oo

. o00

7- 9965°

Log.P

8. 00174

77

79

82

84

86

899 1

94

96

8. 00199

. OO20I

0406

. 09

II

14

16J 9

21

8. 00224

26

293 1

34

36

39

4i

44

47

8. 00249

 52

54

57

59

62

65

67

70

72

8. 00275

77

80

83

85

88

90

93

96

. 00298

8. 00301

04

06

09

12

14

17

19

222 5

8. 00327

0

o

10

II

12

100 M

//

0.9921 

20

20

<£

0 /

IO OO

IO

20

3°

40

So

II OO

IO

20

3° 

40

5°

12 OO

100 P

//

I. 0008

13

18

24

29

34

40

46' 5 2

57 

64

70

76
ZS

6t 

st

S£

8'

IZ

ti

8° 

'I 1010 

S6

88 8e

-i Zoo 9 

//

dOOI

ti oo 

oS

ot 

o£

OS

01

£i oo 

oS 

ot

0?

OS 

01

SI OO 0 / 

<t>

8i

61

-o os66 

//

WOOI

ti

£i

SIo

^

-g oo 9 SZ

sZ

69

99

£9

°9 . ZS 

£S

oS

Zt

-g oo 9 tt

it

8?

S£

z£

6s

gz

£z

OS

91

-g £1900 

OI. . Zo 

to

10900 

g6Soo 

S6

s6

68

98

-g £gSoo 

°8

ZZ

tz

iZ

89

$9

zg

6S

<£

-g £SSoo 

oS

Zt

tt

it

8?

S£

s£

6s

Zs

-g tsSoo 

IS

8i

Si

SI

60

90

£o

ooSoo 

Z6too 

-g t6too 

d'Soi

-Z £tg66 £tttttttt

-Z ttg66 ttttttttS

-Z 66 9 StSSSSSSsss

-Z Stg66 SSSSS9999

'Z 9tg66 999999999 Z- 9tg66 999ZZZZZZ

-Z 66 9 Zt

W^OT

09

6S

8S

ZS

9*

SS

ts

£S

sS

iS

.OS

6t&

Ztt9

St

tt

£t

st

it

Of

6£

8?

tf£ 9

S£

t£

££

s£

 i£

0£

6s

S^

Zs

gz

Sz

ts

£z

S5

IZ

02

61

8i

Zi

9i

Si

ti-

£i

ZI

ii

OT68Z9Steei0/

-g t6too 

s6

68

98

?8

°8

It

tz

iZ

89

-g 99too 

£9

09

ZSts

iS

6tt9

£t

ot

-g Z£too 

t£

z£

6z

gz

£z

oz

8i

Si

ZI

-g 6otoo 

9°

to

lotoo 

g6£oo 

S6

£6

06

^8

^8

-g sg£oo 

6ZZ 9

£Z

iZ

89

S9

zg

og

ZS

-g tS£oo 

sS

6tt9

tt

it

8?

S£

££

o£

-g Zs£oo 

d'3oi

-Z 66 9 ZtZZZZZZZZZ

-Z Ztg66 Z88888888 Zm gtp66 888888888

-Z 6tg66 666666666

-Z 66 9 6t666666

66 9 6t

66 9 oSo

-Z 66 9 oSo00obooo0

-Z oS966 

PI^OI

09

6S

8^

ZS

9S

SS

ts

£S

sS

iS

OS

6t

8^

Ztt9

St

tt

£t

st

it

Of

6£

8?K

g£

S£

t£

££

z£

i£

0£

6z

8^

Zss 9

Ss

ts

£s

SS

IS

02

611 8

Zi

9i

Si

ti

£i

SI

iiT2o8Z9St£sio/
15

C 305 'oi23456789

10

ii

12

13

14

15

16

17

18

19

20

21

2223

24

25

262 7

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

Si

52

53

54

55

56

57

58

59

60

Log. M

7- 99643333333333

7- 99643333322222

7- 996422222222

. 22

7- 99642IIIIIIIII

7. 99641IIIIIIO0o

7. 996400ooo0oooo

7. 99640

Log.P

8. 00675

78

81

85

88

91

94

. 00697

. 00700

04

8. 00707

10

13

16X9

23

26

29

32

35

8. 00739

42

45

48

51

55

58

61

64

68

8.00771

74

77

81

84

87

90

94

. 00797

. 00800

8. 00804

07

10

13

17

20232 7

30

33

8. 00837

40

43

47

50

53

57

60

63

67

8. 00870 '0I23456789

10

ii

12I3

14

15

16

17

18

19

20

21

22

23

24

25

262 7

283

313 2

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

,51

52

53

54

55

56

57

58

59

60

Log. M

7- 99640o

. 99640

. 99639999999

7- 996399999999

8.8

7- 99638888888888888777777

7- 99637777777766

7- 99636666666666

7. 99636

Log. P

8. 00870

73

77

80

83

87

90

94

. 00897

. 00900

8. 00904

07

ii

14Z 7

21

24

28

31

35

8. 00938

42

45

48

52

55

59

62

66

69 

8. 00973

76

80

83

87

90

94

. 00997

. OIOOI

04

8. 01008

ii

IS

18

22

25

293 2

36

40

8. 01043

47

50

54

57

61

65

687 2

75

8. 01079

. *

o

14

16

100 M

o. 9918

17

$

0 t

14 oo

10

20

30

40

50

15 oo

10

20

3°

4050

16 oo

100 P

//

1.0157

64

72

79 

87

95

I. 02O2

IO

182 7

35

43

52

41623° 16- -20
306 16

C 17C

/oi23456789

10

ii

12

*3

14

15

16

i7

18J 9

20

21

2223

24

25

26

27

2829

303 1

32

33

34

35

36

37

38

39

10

4i

42

43

44.

45

46

47

48

49

50

Si

52

53

54

55

56

57

58

59

GO

Log.M

7. 99636665555555

7- 99635555555544

7- 99634444444444

7- 9963443

3-333333

7- 99633333332222

7.99632222222222

7.99631-

Log.P

8. 01079

82

86

90

93

. 01097

. OIIOI

04

08

ii

8. 01115X 9

22

26

30

33

37

4i

44

48

8. 01152

55

59

63

66

70

74

78

81

85

8.0118992

. 01196

. 01200

04

07

II15J 9

22

8. 01226

30

34

37

4i

45

495 2

56

60

8. 01264

68

7i

75

79

83

879 1

94

. 01298

8. 01302 '0I23456789

10

ii

12

13

14

IS

16

17

18

19

20

21

22

23

24

25

26

27

28

29

303 1

32

33

34

35

36

3738

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Log. M

7.99631iiiiiiiii

7.99631iii0ooGO0

7- 99630ooo0oo

. 99630

. 996299

7- 99629999999999

7- 99629888888888

7. 99628888877777

7. 99627

Log.P

8. 01302

06

10

14

17

21

252 9

33

37

8. 01341

44

48

52

56

60

64

687 2

76

8. 01380

84

879 1

95

. 01399

.-01403

07

ii

15

8. 01419

23

273 1

35

39

43

475 1

55

8. 01459

63

67

71

75

79

83

87

. 91

95

8. 01499

 01503

07-

ii

IS

19

23

273 1

35

8. 01540

*

o

16

17

18

100 M

o. 9917

15

* '

0 /

16 oo

10

20 

30 

40

5°

17 oo

IO

20

30

.40

50

18 oo

100 P

i. 0252

60

69 

78 

86

95

i. 0304

142 3 3 2

425 1

61
18

C 19C 307

/0I23456789

10

ii

12

13

14

IS

16

17

18J 9

20

21

22

23

242 5

26

27

28

29

30

3i3 2

33

34

35

36

37

38

39

40

4i

42

43

44

45

46

47

48

49

50

5i

52

53

54

55

56

57

58

59

60

Log. M

7. 99627777777766

7. 99626666666666

7. 99626555555555

7- 99625555444444

7- 99624444444333

7.99623333333333

7. 99622

Log. P

8. 01540

44

48

52

56

. 60

64

68

72

76

8.01581

85

89

93

 01597

. 01601

°5

10

14

18

8. 01622

26

3°

34

39

43

47

5i

55

60

8. 01664

68

72

76

81

85

89

93

. 01698

. 01702

8. 01706

10

14

*923

27

32

36

40

44

8. 01749

53

57

6 1

66

70

74

79

83

87

8. 01792

/oi23456789

10

ii

12

13

14

15

16

i7

18J 9

20

21

2223

242 5

26

27

282 9

30

3i

32

33

34

35

36

37

38

39

40

4i

42

43

44

45

46

47

48

49

50

5i

52

53

54

55

56

57

58

59

60

Log. M

7. 99622222222222

7- 996222IIIIIIII

7- 99621III

' I00oo0

7. 996200oooo

. 99620

. 9961999

7- 99619999999998

7. 99618888888888

7. 99618

Log. P

8. 01792

. 01796

. 01800

°5

09

13

18

22

26

31

8. 01835

39

44

48

53

57

61

66

70

75

8. 01879

83

88

92

. 01897

. 01901

°5

10

14

19

8. 01923

28

32

37

4i

45

5°

54

59

63

8. 01968

?2

77

81

86

90

95

. 01999

. 02004

08

8. 02013

17

22

27

31

36

40

45

4954'

8. 02058 "5

IO

15

202 5

3°

35

40

45

5°

55

60

d. Log. P

°-3

0.7

I. O

i. 3

i. 7

2. 0

2-3

2-7

3- °

3-3

3-7

4.0

0.4

0.8

I. 2

i. 7

2. I

2-5 2.9

3-3

3-8

4.2

4.6

5-°

*

o

18

19

20

100 M

o. 9914

13

12

*

0 /

18 oo

IO

20

3°

40

5°

19 oo

IO

20

30 

40

5°

20 oo

100 P

i. 03617 1

819 1

i. 0401

ii

21

32

42

53 

64

74

85
308 20

C

21'

/oi23456789

10

ii

12

13

14

IS

16

i7

18

19

20

21

222 3

24

25

26

27

28

29

303 1

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

505 1 5 2

53

54

55

56

57

58

59

60

Log.M

7. 99618877777777

7- 996i7777666666

7. 9961666

6 . 665555

7- 996155 ' 55555444

7- 996i4444444443

7- 996i3333333333

7-.996 i3

Log.P

8. 02058

63

68

72

77

81

86

9i

. 02095

. O2IOO

8. 02 104

09

14

182327

32

37

4i

46

8. 02151

55

60

65

69

74

79

' 83

88

93

8. 02197

. O22O2

07

12

16

21

2630

35

40

8. 02245

49

54

59

64

68

73

78

83

o 8?

8. 02292

. 02297

. 02302

07

ii

16

21

263 r

35

8. 02340 '0"I23456789

10

ii

12

13

14

IS

16

17

18

19

20

21

22

23

24

25

26

27

282 9

303 1 3 2

33

34

35

36

37

38

39

40

41

42

'43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Log. M

7. 99613222222222

7. 9961222IIIIIII

7.99611IIIO0oooo

7. 99610oooo

. 99610

. 99609999

7- 99609999999888

7. 99608888888877

7- 99607

Log. P

8. 02340

45

So

55

60

64

69

74

79

84

8. 02389

93

. 02398

. 02403

08

13

18

23

28

33

8. 02437

42

47

52

57

62

67

72

77

82

8. 0248792

. 02497

. 02502

07

ii

16

21

26

31

8. 02536

41

46

51

56

61

66

71

76

81

8. 02586

92

 02597

. 02602

07

12

17

22

273 2

8. 02637

-5

10

15

20

25

30

35

40

45

So

55

60

d. Log. P

o-3

0.7

I. 0

i. 3

i. 7

2. 0

2-3 2.7

3-o

3-3

3-7

4.0

0.4

0.8

I. 2

i. 7

2. I

2-5

2.9

3-3

3-8

4.2

4.6

5-o

o-5

I. 0

i. 5

2. O

2.5

3-o

3-5

4.0

4-5

5-o

5-5

6.0

0

0

20

21

22

100 M

//

o. 9912 

ii

IO

*

0

20

21

22

,

OO

10 

20

30

40

50

OO

IO20 '

3° 

40

50

00

100P

1. 0485

96

I. 0508

193 1

42

54

65

77

89 

i. 0601

14

26
23

C 309

/oI23456789

10

ii

12J3

14

iS

16

17

18

19

20

21

22

23

24

25

262 7

28

29

303 1

32

33

34

35

36

37

38

39

40

4i

42

43

44

45

46

47

48

49

50

5i

52

53

5*

55

56

57

58

59

60

Log. M

7- 99607777777776

7. 99606666666666

7- 99605555555555

7. 99605

. 996044444444

'4

7- 99604433333333

7. 99603332222222

7- 99602

Log.P

8.02637

42

475 2

57

62

68

73

78

83

8. 02688

93

. 02698

 02703

08

14

*9

24

29

34

8. 02739

45

So

55

60

65

70

76

81

86

8. 02791

. 02796

. 02802

07

12

17

22

28

3338

8. 02843

49

54

59

64

 70

75

80

8691

8. 02896

. 02901

07

12

17

23

28

33

39

44

8. 02949

/OI23456789

10

ii

12J3

14

i5

16

17

18J 9

20

21

22

23

24

25

26

27

28

29

30

3i

32

33

34

35

36

37

38

39

40

4i

42

43

44

45

46

47

48

49

50

Si52

53

54

55

56

57

58

59

60

Log. M

7. 99602222IIIIII

7- 99601IIII00ooo

7. 99600oooo

. 99600

 99599999

7- 99599999998888

7- 99598888888777

7- 9959777 777766

 6

7- 99596

Log. P'

8. 02949

55.

60

65

?i

76

81

87

' 92

. 02997

8. 03003

08

13J 9

24

3°

35404651

8. 03057

62

68

73

78

84

89

 03095

. 03100

06

8. 03111

17

22

2733'

38

44

49

55

60

8. 03166

7i

77

82

88

93

.03199

 03205

10

16

8.03221

27

32

38

43

49

55

60

66

7i

8. 03277

//5

10

15

20

25

30

35

40

45

So

55

60

d. Log. P

0.4

0.8

I. 2

i-7

2. I

2-5 2.9

3-3

3-8

4.2

4-6

5-o

o-5

I. O

i-5

2. 0

2-5

3-o

3-5

4.0

 4-5

5-o

5-5

6.0

4>

o 

22

23

24

100 M

// 

o. 9910

o. 9909

07

*

0 /

22 OO

10

2C

3°

40

50

23 oo

10

2O

30 

40

50

24 oo

100P

tt

i. 0626

39

Si

64

77

9°

i. 0703

16

29

43 

56

70

84
310/0I23456789

10

ii

12

13

14

15

16

i?

18

19

20

21

222 3

24

25

26

27

2829

303 1

32

33

34

35

36

3738

39

10

4i

42

43

44

45

46

47

48

49

50

5i

52

53

54

55

56

57

58

59

GO

Log. M

7- 99596666666655

7- 99595555555544

7- 99594444444443

7- 995933333333

. 32

7- 995?222222222I

7- 99591iiiiiiii0

7- 99590

Log.P

8. 03277

82

88

94

. 03299

 03305

ii

16

22

27

8- 03333

39

44

50

56

61

67

73

78

84

8. 03390

 03395

 03401

07

12

18

24

30

35

4i

8. 03447

52

58

64

7o

75

81

87

93

 03498

8. 03504

10

16

21

*7

33

40

45

50

56

8. 03562

68

74

80

859 1

 03597

 03603

09

15

8. 03620

/oi23456

7-89

10

ii

12

13

14

IS

16

17

18

*9

20

21

22

23

24

25

26

27

28

29

30

3i

32

33

34

35

36

37 .38

39

10

41

42

43

44

45

46

47

48

49

50

5i

52

53

54

55

56

57

58

59

60

Log. M

7- 9959°o0o00ooo

 99590

7- 99589999999999

7- 99588888888888

7- 9958777

 7777777

7- 99586666666666

7- 99585555555555

7- 99584

Log.P

8. 03620

26

32

38

44

50

56

62

67

73

8. 03679

85

9i

. 03697

 03703

09

15

21

27

33

8. 03738

44

50

56

62

68

74

80

86

92

8. 03798

. 03804

10

16

22

28

34

40

4652

8. 03858

64

70

76

82

89

 03895

 03901

07

13

8. 03919

25

3i

37

43

49

55

62

68

74

8. 03980

//5

10

15

20

25

30

35

40

*5

50

55-

60

d. Log. P

0.4

0.8

I. 2

i-7

2. I

2-5

2.9

3-. 3

3-8

4.2

4.6

5-o

o-5

I. O

i-5

2. 0

2-5

3-o

3-5

4.0

4-5

5-o

5-5

6.0

0.6

I. 2

1.8 2 -3

2.9

3-5

4- i

4-7

5-2

5-8

6.4

7.0

»

o

2425

26

100 M

o. 9907

06

05

*

0 /

24 oo

IO

20

30

4050

25 oo

IO

20

3°

40

So

26 oo

100P

//

1. 0784

98

I. 0812

26

40

55

69

84

99

i. 0914

29

44

60
26

C 27

C 311

/oI23456789

10

ii

12

13

1415

16

17

18

19

20

21

2223

24

25

26

27

28

29

30

3i

32

33

34

35

36

37

38

39

40

4i

42

43

44

45

46

47

48

49

50

Si

52

53

54

55

56

57

58

59

60

Log. M

7- 99584444444443

7- 99583333333332

7- 9958222222222I

7- 9958iiiiiiiiio

7- 9958oo0o

! o

; o

: o

 9958o

 99579

: 9

7- 99579

' 999999988

7- 99578

Log.P

8. 03980

86

92

 03998

. 04004

ii

17

23

29

35

8. 04041

48

54

60

66

72

79

85

9i

. 04097

8. 04103

10

16

' 22

28

354i

47

53

60

8. 04166

72

78

' 85

9i

 04197

. 04204

10

16

22

8. 04229

35

4i

48

54

60

67

 73

79

86

8. 04292

. 04298

 04305

ii

, 18

24

3°

37

43

49

8. 04356

/

oi23456789

10

ii

12

13

14

IS

16

17

18

19

20

21

22

23

24

25

26

27

282 9

303 1 3 2

33

34

35

36

37

38

39

10

4i

42

43

44

45

46

47

48

49

50

5i

52

53

54

55

56

57

58

59

60

Log. M

7- 99578888888877

7- 99577777777666

7- 99576666666555

7- 995755555S4444

7- 99574444443333

7- 9957333

. 3322222

7- 99572

Log.P

8. 04356

62

69

75

81

88

. 04394

. 04401

07

14

8. 04420

27

33

39

46

52

59

65

72

78

8. 044859 1

. 04498

 04504

ii

17

24

30

37

o 43

8. 04550

57

63

70

76

83

89

. 04596

. 04602

09

8. 04616

22

29

35

42

49

55

62

68

75

8. 04682

88

 04695

. 04702

08

15

22

29

3542

8. 04748

//5

10

15

20

25

3°

35

40

45

50

55

60

d. Log. P

o-5

I. 0

i-5

2. O

2-5

3-°

3-5

4.0

4-5

5-o

5-5

6.0

0.6

I. 2

1.8

2-3

2.9

3-5

4- i

4-7

S2

5-8

6.4

7.0

.*

0 

26

27

28

100 M

o. 9905

03

02

*

0 /

26 oo

10

20

30 

40 

50

27 oo

10

20

30 

40

5°

28 oo

100 P

it

i. 0960

75

1. 1007 

23 

39

55

88

1. 1105

21 

38

55
sZ

es

*£

-i 91?! 

Z6

6Z

19

e>

Ss

-i goei 

06

ez

-i SSu 

//

dOOI

oe oo 

oS

ot

oe

OS

01

6s oo 

oS

ofr

oe

OS

OI

gs oo 0 / 0

-o 66g6 

oo

-o 2066 

'//

HOOT

oe

6s

8^o

*

o-g

e-z

^9

0-9

e-s

z-t

o-t

e-e

L-t

-z o 

e-i

Z-o

o-Z9 fg-s

s-S

z-t

-t i 

s-e

6-s

e-s

8'i

'I S 

9-0

0-9

s-s

o-S

S-fr

o-t

s-e

o-e

S-s

-z o 

S-i

-i o 

S-o

-p *3oi d 

09

SS

oS

Sf

ofr

se

oe

Ss

OS

Si

01S

//

-g tgSSo 

zz

oZ9e

SS

g*

it

te

gz

61

-g siSSo 

SoSSo 

g6tSo 

06

egz 9 96

zg

SS

Zt

-g ottSo 

ee

92

61

SI

totSo 

Z6eso 

06

egz 9

-g 6geSo 

29

SS

8^

ot

ee

gz

61

ZI

Soeso 

-g g6sSo 

16

ZZ

oZ9e

9?

st

se

-g gssSo . IS 

tl

Zo

oosSo 

'e6iSo 

98

6Z

zL

S9

-g gSiSo 

d*i

-Z 6SS66 6666

6SS66 

ogS66 ooo

-Z S66 9oooooIIIII

-Z 19^66 iiIszzzzz

-Z S66 9szzeeeeeee

-Z £gS66 ettttttt

-Z t9S66 tSSSSSSSs

-Z SgS66 

K*l

09

6S

gS

zs

9?

ts

es

sS

iS

09

gJ7

zt

9^

St

tt

et

st

it

Of

g£

Z£e 9

se

te

ee

z£

ie

oe

6s

8s

92

Ss

ts

es

zz

T.Z

02

61

Zi

91

Si

tl

ei

21

II?68Z9SteSIo'

-g gSiSo 

iS

tt

ze

oe

es

91

60

So soi 

S6oSo 

-g ggoSo 

ign

89

19

ts

Zt

ot

ee

92

-g 6ioSo 

ei

900^0 

666to 

s6

S8

iZ

S9

8?

y KL/ J 

ze

oe

ts

Zi

01 * eo6to - 96gto 

06

-g eggto z 99 6

£g

9S

ste 9

6z

zz

-g Sigto 

60

sogto 

S6Zto - 88 

sz

89

zg

SS

gtZto-g

d'*I

S66-Z9S999999999

-Z ZgS66 ZZzzzzzz8

-Z 89*66 8888 * 8 8866

-Z S66 96666666

69^66 

oZS66 o

-Z oZS66 oo0oooIII

-Z iZS66 iiiiizzzz

M66-1

'^K

09

6S

8*

ZS

9*

SSts

es

sS

iS

0$

6t

gt'Ztt9

St

tt

et

zV

it

Of

ee

§e

ze

g£

se

te

ee

se

ie

OS

6s

gs

Lz

gz

Ss

ts

£2

S2

IS

02

61

gi

Zi

91

Si

tl

ei

SI

ii

OT68Z9StezI0'

,85
30

C 313

/oI23456789

10

ii

12

13

14

IS

16

i?

18

*9

20

21

2223

24

25

26

27 '

28

29

30

3i

32

33

34

35

36

37

38

39

40

4i

42

43

44

55

56

47

48

49

50

Si52

53

54

55

56

57

58

59

60

Log. M

7- 99559999888888

7- 99558887777777

7- 99557766666666

7- 99556555555554

7- 99554444444433

7- 99553333

. 333222

7- 99552

Log.P

8. 05584.

92

 05599

. 05606

13

21

28

35

43

5°

8. 05657

65

72

79

86

 05694

. 05701

08

162 3

8-05731

38

45

53

60

67

75

82

90

 05797

8. 05804

12

192 7

34

4i

49

56

64

7i

8. 05879

86

.05894

. 05901

08

16

23

3i

38

46

8- 05953

61

68 76

83

9i

 05998

. 06006

14

21

8. 06029

/oI23456789

10

ii

12

13

14

IS

16

17

18

19

20

21

2223

24

25

26

27

28

29

30

3i

32

33

34

35

36

37

38

39

10

4i

42

43

44

45

46

37

48

49

50

Si

52

53

54

55

56

57

58

59

60

Log. M

7- 9955222222IIII

7- 9955ii"iiio0ooo

7- 995500o

 9955°

 9954999999

7- 99549988888888

7- 99548777777777

7- 99546666666655

7- 99545

Log.P

8. 06029

36

44

51

59

66

74

82

89

. 06097

8. 06104

12

2027

35

43

SO

58

65

73

8. 06181

88

. 06196

. 06204

ii

19

27

-34

42

So

8. 06257

65

73

81

88

. 06296

. 06304

12

19

27

8- 06335

43

So

58

66

74

81

89

 06397

. 06405

8. 06413

20

28

36

44

52

60

67

75

83

8. 06491

-5

10

15

20

25

30

35

40

45

5o

55

6o

d. Log. P

0.6

I. 2

1.8

2-3 2.9

3-5

4- i

4-7

5-2

5-8

6.4

7.0

0.7

i. 3

2. 0

2-7

3-3

4.0

4-7

5-3

6.0

6.7

7-3

8.0

*

0

3°

313 2

100 M

o. 9899

97

96

$

0 /

30 oo

IO

203040 50

31 oo

IO

20

3°

40

5°

32 oo

100 P

ff

i. 13729 1

1. 1411

30

5° 

69

89

1. 1509

29

So

709 1

1. 1612
' ZZ 

ts

ie

-i gogi 

98 i 9 e

it

-i 6iZi 

Z6 ! tS 

ee 

-i zigi "

dOOI

00

oS

ofr

oe

oz

OI

oo

oS

ofr

oe

OS

OI

oo/

te

ee

seo # ii e6 o- 0606 '"

HOOI

K

ee

seo

*

-Z o -g o 0-6 

-9 v -z e *'S o Ry -QZ «

-S z 0-9 

-fr z -s e 

-t- i t' Z 

-e s * o 

6-s e-e 

-z £ ~z Z 

-i g o-z 

z-i -i e 

9-0 -o Z 

'P *3oi d 

09

SS

oS

ofr

see O'Ss

OS

Si

01S

/x

imo-g

29

Sfr

ze

82

OS

SI

S6ezo 

-g 9gezo 

o£

.69

es

'H'

ge

Zs

61

ii

-g soezo 

98 U

69

P9

sS

t>t

se

Lz

-g 6isZo 

OI

zozLo 

fr6iZo 

98

ZZ 

69 

19

sS

tt

-g geiZo 

82

61-

ii

eoiZo 

S6oZo 

98

gZ

oZ

29

-g eSoZo 

ze

6z

IZ

ZI

t'ooZo 

96690 

88

°8

o-g9 iZ6

d*l

ieS66-Z IIzzzzzz

-Z seS66 zeeeeee

e 

 e

-Z KS66 . VV*V

t'^s

-Z SeS66 ssss999

-Z 9eS66 9999ZZz

 Zzzzz888888

eS66-Z8

H*I

09

6S

gS

ZSS 9

SSS7 1

es

sS

iS

OS

OK

8^

LV

gV

St^

tf

£V

zV

iV

Of

{.C

o Co O 3 00~-Je 9

se

 te

ee

se

ie

0£

6s5 8

.Zs

92

Ss

zz

IZ

OK

611 8

Zi

Si

ta

ei

SI

IIT68Z9SVesIo/

-g iZ69o 9e

SS

LV

6e

ie

£z

ti

90690 ' 89° 6 8

2Q

VL

99

8?

oS

i>

ee

Ss

Zi

10990 

zz96

19

es

Sfr

ze

IS

ei

SoZgo 

Z699O 

68 

18

ez

Sg

ZS

-g 6^990 

it'

ee

Sz

LI 

60

10990 

e6Sgo 

98

8^

-g oZSgo 

zg&

tf

o£

zz

bi

LoSgo 

66^90 

-g 16^90 

d*l

eS66-Z8866666666

-Z 6eS66 " OO Kju O oooooooo

I IIIIIIzzzzzz

z zeee

'Z e^S66 eeeeVbtV*

-Z W66 

t'

frSsssss

-Z SW66 

K*l

09

6S

gS

ZS

9S

SS

t'S

es

sS

iS

OS

OK&

LV

9^7 St

tfr

£V

zV

Of

/:<- 

r C00 

0CO e

9

se

te

ee

se

ie

08

6s

gs

Zs

92

Ss

SS

IS

02

61

Zi

Si

£1

£i

ZI

iiTS8Z9S>esIo/
oZW

'I 6lIS 

t6

69

'I OSOS 69

8^

Vz

'I Oo6l 

'I ZZgl "

dOOT

ge oo 

oS

ot

oe

OS

01

se oo 

oS

ot

oe

OS

01

te oo 0 / *

68

16

o- e6g6 "

MOOI

e9

se

t?o

<£

-g o '6 o oi - o 

-Z e -g s -6 s "-Q z -i, s o -Q w e 

0-9 -9 g -Z S 

-s e 0-9 -9 z 

-V Z -S s -S g 

-t o -t S -S o 

e-e -e g -v s z-s o-e e-e S- O "S S "S S 

-i e -i s -i z 

-o Z -o g -o g 

*p Jto'i <I 

09

SS

oS

st

ofr

se

oe

Ss

OS

Si

01S

/x

8. 8sSgo

gi

60

ooSgo 

i6tgo 

sg

ez

to

SS

zetgo-g

Zs

60

ootgo 

o 8 i6e

289t

SS

Kgo.-g 9

O Z?i* 

61

OI

ioego 

s6sgo 

£g

tz

Jg

Ssgo-g9

Zfr

ge

6s

OS

II

 sosgo 

e6igo 

"boz 9

-g igo 9Z

ot

SS

ei toigo 

S6ogo 

^8

-g gZogo 

69

09

iS

st

ee

Ss1 9

Zoogo 

g66Zo 

-g 6g6Zo 

d-301

-Z ZiS66 ZZZZZZ0o

-Z giS66 0o888666

6 6

-Z 6iS66 6

6 

6iS66-

osS66 oo0oo

-Z osS66 oii'ii

i iii

-Z ssS66 zzz

Z zzzee

-Z esS66 eeeeeettV

fsS66-Z

m*T

09

6S8'S

ZS

9S

SSS? t

es

sS

09

8^

Ztt9

St

tfr

et

zV

Of

Oc.

8?

zee 9

se

te

ee

z£

i£

6ss 8

Zs

92

Ss

es

SS

IS§gI

Zi

Si

ti

ei

SI

II

OT68Z9StesIo/

6Zo-g86

ig

sZ9?ts

St

ze

61

01

-g so6Zo 

e6oZo 

tg

SZ9Z

8?

ot

es

-g tigZo 

gogZo ' 88 

08

29ts

St

o£

-g 82^0 

61

OI

soZZo 

£6gLo 

Sg

Oi

Zop x 

6S

oS

-g stgZo 

ee

ts1 9

Z"og/o 

06"

ez

^9

-g gSSZo 

Zt

6e

oe

zz

ei

SoSZo-

'6tZo 9

88

6Z

iZWO'gu

d-sn

S66-iZ t.

i?t ' t SS55

-Z SsS66 5S99999

9 99

Z ZZzzzzz88888

8 866

-Z 6sS66 666

6 

6sS66 

oeS66 

o oo

-Z oeS66 ooooIIIII

ieS66-Z

K*I

.09

8?

ZS

9S

SSts

es

sS

iS

09

6t

gl7

IV

gV

St

tt

et

ll

Of6e

8?

9? se

te

ee

se

ie

6s

82

Zs

92

Ss

£z

zz

IS

02

611 8

Zi

Si

tl

SI

ii

OT689'SV

.esIo'
£6

-i 6rtz 

ig

ts

Zs

'I OOeS 

zt

'I IZZZ 

S6

-i oZis "

dOOI

ge oo 

oS 

ot

oe

OS

01

ze oo 

oS

OK 

O&

OS 

OI

ge oo 0 / . * 

98

88

-o 6gg6 ^

KOOI

8?

zee 90 *

-01 o 

s-6

s-z

o-S

 'v z e-e

S-s

-i Z 

g-o

0-6

s-g

s-z

'9 8 0-9

s-S

-t S 

'£ 8 

o-e

'Z S 

S-i

g-o

'p '001 d 

09

SS 

oS

St 

ot

se

oe

Ss

OS

Si

01S"

-g 6o 99S

SS

fr9

g£

gz

91

90960 

Z6S6o 

igU

-g LgS6o 

ZS

gt

8^ - - 1 8

6oS6o ° 6% 

°8

O

09

oS

It

IZ

ZI

Sot'60 

z6£6o 8?

-g eze6o 9e

tsw

te

Sz

Si

9o£6o 

6s6o 9

98

-g LLz6o 

Lg

gS

gt

ge

6z

61

OI

oos6o 

16160 

-g igi6o 

zL

zg

es

ft

te

ts

Si

Soi6o 

96060 

-g 9go6o 

'$°1 d 

-Z soS66 zzzzzeeee

-L eoS66 e eet17tt

-I toS66 vsSsssss

-Z 9oS66 9999999LL

-Z ZoS66 LL

L LL8888

-I goS66 8886

6.6666

-Z 6oS66 

«*i

09

6S

8?

ZS

9?

SSts

es

zS

iS

OS

gttz

Stt-t

si

it

Of6e

8^

se

te

ee

z£

i£

og

6s

gs

.Lz

gz

Ss

ts

£s

zz

IZ

03

61

gi

Li

9i

Si

 fri

ei

ZIa

OT68L9S

t?ezIo<

-g 9go6o 

LL

Lg

8S

6e

6z

oz

OI

10060 

-g s66go 

sg

ez9e

ts

St

ses 9

91

Zo6go 

'8 88° 68

88

6L

o£

09

iS

zV

z£

£z

ti

g- toggo 

S6Zgo 

98

gL

Lg

8?

6£

o£

IZ

siZgo-g

eoZgo 

go 9 e6

tg

SL

Sg

9S

Zt

8?

-g go 9 6i

01

loggo 

s6Sgo 

eg

ez

Vg

SS

gV

L£

'g gsSgo 

*3oi d 

-Z 6oS66 

6oS66 

oiS66 o0o0ooo

nS66-Z iiiiiiizz

-Z siS66 zzZZzzeee

-Z eiS66 eeee

17

t,VV

>iS66-Z ttsssssss

-Z SiS66 99999999Z

'Z ZiS66 

'BO'T Jff 

09

6S

8S

9^

SSts

es

sS

iS

OS

617

8^

Zt

9^

St

tt

et

et

it

Of6e

g£

IS

g£

se

te

ee

se

ie

0£

6z

gs

Zss 9

Ss

es

SS

IS

0?,

61

gi

Zi1 9

Si

ti

ei

SI

ii

OT68Z9StesI0'

918
38

C 39

C 317 'oI23456789

10

ii

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

.27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Log.M

7- 9950222IIIIIII

7- 995oioooooo0

 99500

 99499

7. 9949999999

. 9888

7- 994988888

. 77777

7- 99497776666666

7- 994965

. 55555554

7- 99494

Log.P

8. 09665

75

85

 09695

 09705

14

24

34

44

54

8. 09764

74

84

 09794

. 09803

13

23

33

43

53

8. 09863

73

83

 09893

 09903

13

23

33

43

53

8. 09963

73

83

 09993

. 10003

13

23

33

43

53

8. 10063

73

83

 10093

. 10103

14

24

34

44

54

8. 10164

74

84

 10195

. 10205

15

25

35

45

56

8. 10266 '0i23456789

10

ii

12

13

14

15

16

17

18

19

20

21

22

23

242 5

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

505 1

52

53

54

55

56

57

58

59

60

Log. M

7. 99494444444333

7- 99493333322222

7- 9949222IIIIIII

7- 99491

 9949°oooo00

 99490

 99489

7- 99489999999888

7- 99488888877777

7- 99487

Log.P

8. 10266

76

86

. 10296

. 10306

17

27

37

47

58

8. 10368

78

88

 10399

. 10409

19

29

40

So

60

8. 10471

81

. 10491

. 10502

12

22

33

43

53

64

8. 10574

84

 10595

. 10605

' 16

26

36

47

57

68

8. 10678

89

. 10699

. 10709

20

30

41

51

62

72

8. 10783

..- I0793

. 10804

142 5

35

46

56

67

77

8. 10888

"

5

IO

15

202 5

30

35

40

45

So

55

60

d. Log. P

0.8

i. 5

2. 2

3-o

3-8

4-5

S2

6.0

6.8

7-5

8.2

9-o

0.8

i. 7

2-5

3-3

4.2

5-o

5-8

6.7

7-5

8-3

9.2

IO. 0

0.9

1.8

2.8

3-7

4.6

5-5

6.4

7-3

8.2

9.2

10. I

II. O

<!>

o 

38

39

40

100 M

// 

0.9886

84

83

*

o /

38 oo

IO

20

30 

4050

39 oo

IO

20

3° 

40 

So

40 oo

100 P

i. 2493

i. 2521

So

79 

i. 2608

37

67

96

i. 2727

57 

87 

i. 2818

49
tt

-i 6ose 

SL

it

goie-i

?i

st

-i 6ooe z 9

tt

-i si6s 

18

-i 6tgs 

//

dOOI

oo

oS

ote O

OS

01

00

oS

ot

oe

OS

01

oo/

st

it

oto £

6Z.

HOOT

st

It

ot

-si o 

-ii o 

-oi o 

0-6

o-g

o-Z

0-9

o-S

o-t

o-e

-s o 

'I 0 

-ii o 

-01 I 

s-6

s-g

e-z9 ts-s

-t9

z-e

g-s

'I 8 

6-0.

-01 o 

s-6

£-8

s-z

Z-9

8'S

o-S

s-t

e-e

S-s

Z-i

g-o

'p 'Sol d 

09

ss

oS

St

ot

se

oe

Ss

OS

Si

01S

//

'g IOSSI 

o6isi 

8*'9Z

9$

tt

ee

zz

nisi 

66osi 

-g ggosi 

ZZ

$9

ts

et

se

IS

6oosi 

g66n 

*8

-g Z6ii 9

9t

£5

Z*

ie

OS

60611 

Z6gii 

98

SZ

-g gn 9t . es 

st

ie

OS ' 8°3" 

Z6Zii 

98

SZ9t

8- eszn 

st

ie

OS

6oZn 

n 9 g6

^8Z 9

$9

ts

-g ii 9 et

se

15

Oigil 

66Sii 

88

ZZ

99

SS

tt

-g eesn 

d'Soi

-Z iZt66 zzzzzzzze

-z ezt66 eeeeetttt

-Z tZt66 tt

frssssss

-Z SZt66 S . 9 99 ; 9 i 9 i 9 ' 9 9

-Z ZZt66 ZZ^Zzzz88

:Z gZt66 888886666

-Z 6Zt66 

K'Soi

09

6S

tf

zs

9?

SSts

es

sS

iS

09

6t

8>

Ztt9

St

tt

et

st

it.

Of

ee

8?

tt

g£

se

te

ee

se

ie

oe

6ss 8

Zs

gz

Ss

ts

es

zz

IS

0?,

61

8i

Zi

9i

Si

ti

ei

SI

II

OT68Z9StezIo/

8- eesn 

ss

II

ooSn 

6gtn 

8*9Z

9St9

se

-g tstn 

ei

sotn 

i6en 

°8

oZ

6S

8^

ze

gz

8- Sien 

Soen 

t6sii 

f8

sZ

19

iS

ot

6s

8i

-g gosn 

Z6in ' SZ 98

$9

ts

et

ee

zz

II

-g OOIII 

06011 

6Z

89

8S

Zte 9 s 9

Si

Soon 

-g t66oi 

?8

ez9S

iS

it

oe

OS

60601 

66goi 

-g 888°i 

d'Soi

-Z 6Zt66 6

6Zt66 

ogt66 oo' oooo

-Z ogt66 iiiiiiiiz

-Z sgt66 5ZZZzzeee

-Z egt66 eeeettttt

-Z tgt66 ttsssssss

-Z Sgt66 9999

9 99ZZ

-Z Zgt66 

W3<>1

09

6S

ss

ZS

9^

SS

ts

es

sS

iS

OS

6t

8^

Ztt9

St

tt

et

st

it

Of6e

8?

tt

g£

se

te

ee

se

ie

0£

6s

8s

Zss 9

Ss

ts

es

zz

IS

02!

61

8i

Zi

9i

Si

ti

ei

SI

IITS68Z9StezI0/

818
319 'oI23456789

10

ii 

12

13

14

15

16

17

18

19

30

21

22

23

24

25

26

27

282 9

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Log. M

7.99471iiiiiiioo

7. 99470o0

* o0

 9947°

 99469999

7- 99469999888888

7- -99468877777776

7- 99466666666555

7- 99465555544444

7- 99464

Log.P

8. I22OI

12

24

35465869

80

. 12292

 12303

8. 12315

26

37

49

60

72

83

 12395

. 12406

18

8. 12429

40

52

63

75

86

. 12498

 12509

21

32

8. 12544

56

67

79

 12590

. 12602

132 5

36

48

8. 12660

71

83

. 12694

. 12706

18

29

53

64

8. 12776

88

 12799

. 12811

23

34

. 46

58

70

81

8. 12893

 '

oi23456789

10

ii

12

13

14

15

16

17

18

19

20

21

22

23

242 5

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

GO

Log. M

7- 99464443333333

7- 994632222222II

7- 9946iiiiiioooo

7- 9946oo0

. 99460

 9945999999

7- 99459988888887

7- 99457777777666

7- 99456

Log.P

8. 12893

. 12905

17

28

40

52

64

75

87

. 12999

8. 13011

23

34

46

58

70

82

. 13094

 13105

17

8. 13129

41

53

65

77

. 13189

. 13201

12

24

36

8. 13248

60

72

 84

 13296

. 13308

203 2

44

56

8. 13368

80

 I3392

 13404

16

28

40

52

64

76

8. 13489

 I3501

13

25

37

49

61

73

85

 13598

8. 13610

//5

10

i5

20

25

30

35

40

45

5°

55

60

d. Log. P

0.9

1.8

2.8

3-7

4.6

5-5

6.4

7-3

8.2

9.2

10. I

II. 0

I. O

2. O

3-o

4.0

5-o

6.0

7.0

8.0

9.0

IO. O

II. O

12. 0

<£o

42

43 

44

100 M

//

o. 9879

77 

76

.*

o /

42 oo

IO

20

3°

40

So

43 oo

IO

20

3° 

40

5°

44 oo

100 P

1.3244

79

! 33I3

49

84

i. 3420

56

93

1-353° 

67 

i. 3604

42

80
-

!

H p)

HI CM

O O

HI CN

IO 

HI

O

cs co

CO *

0 0

co ^

in o

HI CN

"3- iovo t^«CO OO

0 

IOVO

0

10 vo

O 

1^00

O

t^.00

10 O m O

CN co co -^t

Os 

HI

O

O O

Os O

HI

H 

0

M

Os

to O 10 

Tf to to VO

O

HI

CN

O

M

CO

O

 e- 

*

.

§

^

O

9

-

3

CN to t^. O CO tOCO

iovo r^ Os O HI CN

CO CO ^t"

"fr * *

H HI HI

OO

O 

Os

Os I

HI CM co ^ tovo

O covO OO 

 ^- tovo 

M

^1

r^

00

Os

Os

^

r^oo OsO

H TfvO OS CS1 IO l~~ O CO to 

Os O HI CN ^ IOVO OO Os O

MM HI H

00

ON

Os

M N CO "^ to\O *-*-OO OsO

OO IH H-\O O\ CS tOOO 

w CO ^T IOVO OO O\ O

vO C^»

H H

vovo to 10 10 10 10 10

HI CM CO ^- tOVO t-»OO 

CNCNCNCMCNCMCNCN

O CO 

CM 

HI

^JCO

00

10^

Os

Os

CN 

OsO

W

vO Os CN ^f l~- O fo

 <* 10 r^CO Os M CN 

5;C§-

HI HI

HI CM CO ^ tOVO t-~

CO CO CO CO CO CO CO 

^ O CN 

CL H CN

" vo

" CO

O HI

1-^ od

Tl-VO OO HI CO to t~~ 

CO 't 10 t~-CO Os O

vo t^

CO CO

OS CM 

HI 

CO

CO

00

"^" vO OO HI co to 

^- tovo OO Os O

co 

r^oo

co

HI HI

vo vo VO vo vO to to to 10 to 10 10 10 ^J" ^" ^- ^" 

53 10 to 

^ ^t- *

. Os

h^ 

0

^*

v 0 M CM CO ^f IOVO t-^OO

Os

OsO HI (N CO <* IOVO

H M HI HI HI M

t~~ O csi <^- 

w co ^ to

00

HI

CO

to

00

^

Os

Os

t^OO OsO

HI HI M CM

(^ OS H Tj-SO OO 

VO t OS O HI CM

00 OS

CO CO

H CO 1000

 ^- tovo 

HI

CO

Os

t^

00

COCOCOCOCOCOCOCN CM 

 *

to 

CM 

HI CM CO "* IOVO 

CN CM PI CM CM CS)

Os

Os

t^OO OsO

CM CM CN M

Os O HI CM ^ IOVO 

Os O

CO *

HI HI

N CM CM CM CN HI M 

H CN CO * IOVO r-

CO CO CO CO CO CO C

CO
47° 321 'oI23456789

10

ii

12

13

14

15

16

17

18

19

20

21

2223

242 5

26

27

28

29

30

313 2

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

SiS 2

53

54

55

56

57

58

59

60

Log. M

7- 9944iioooooo

. 99440

 99439

7- 99439999999888

7- 99438888877777

7- 99437776666666

7- 99435555555544

7- 99434444443333

7- 99433

Log.P

8. 15121

34

47

60

73

86

 I5I99

. 152122 5

39

8. 15252

65

78

. 15291

 15394

17

31

44

57

70

8- 15383-

 15396

 1541023

36

49

63

76

 15489

 15502

8. 15516

29

42

55

69

82

 15595

. 15609

22

35

8. 15649

62

75

. 15689

 15702

IS

29

42

56

69

8. 15782

 15796

 158092 3

36

50

63

77

 15890

 15904

8. 15917 '0i23456789

10

ii

12

13

14

15

16

17

18

19

20

21

222 3

24

25

26

27

2829

303 1

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

Si

52

53

54

55

56

57

58

59

60

Log. M

7- 99433333222222

7- 994322IIIIIII0

7- 9943000ooo

 99430 9942999

7- 99429999988888

7. 99428887777777

7- 99427666666655

7-99425

Log.P

8.15917. 3 1

44

58

71

85

.15998

. 16012

25

39

8. 16053

66

80

 16093

. 16107

21

344862

75

8. 16189

. 16202

16

30

44

57

85

. 16298

. 16312

8. 16326

40

53

67

81

 16395

. 16408

22

36

50

8. 16464

78

. 16491

 16505

19

33

47

61

75

. 16588

8. 16602

16

30

44

58

72

. 16686

. 16700

14

28

8. 16742

//5

10

15

20

25

30

35

40

45

50

55

60

d. Log. P

1. 1

2. 2

3-2

4-3

5-4

6-5

7-6

8.7

9.8

10.8

11.9

13.0

I. 2

2-3

3-5

4-7

5-8

7.0

8.2

9-3

10.5

11.7

12.8

14.0

<t>

o

46

47 

48

100 M

//

o. 9872

70 

68

*

0 /

46 oo

IO

20

30 40 

50

47 oo

IO

20

30 

40 

50

48 oo

100 P

/,

1.4165

i. 4208

So

94 

i. 4338 

82

1.4427

72

i. 4517

63 

i. 4610

56

i- 4703

41623° 1C
322 48' '0I2T\J456789

10

ii

12

14 

15

16

17

18

19

20

21

222 3

24

25

26

27

28

29

30

32

33

34

35

36\J

3738

39

40

41

42

43

44

45

46

47

48

49

505 1 S 2

53

54

55

56

57

58

59

60

Log. M

7. I 9942 77 */<555554444

7- 994244

4 

4 

3 33333

7- 99423322222222

7.99421III

. III0oo

7- 99420ooo

. 99420

 994199 999

7- 99419

9 9888888

7. 99418

Log.P

8. 16742

56 

70

84

. 16798

. 16812

26

40

54

68

8. 16882

. 16896

. 16910 

24 

38 

53

67

81

 i6995

. 17009

8. 17023

37

52

66

80

 17094

. 17108

22

37

51

8. 17165 

79

. 17208

22

36

51

65

79

 17294

8. 17308

22

37

Si

65

80

 17394

. 17408

23

37

8. 17452

66 

80

 J 7495

24

38

53

67

82

8. 17596 '0i23456789

10

ii

12 

13 

14 

IS

16

18

19

20

21

22

23

24

25

26

27

282 9

303 2

33

34

35

36\j

3738

39

40

41

42

43

44

45

46

47

48

49

50

52

53

54

55

56

57

58

59

60

Log. M

7- 994*18777777776

7. 994166

6 

6 

6 66

'555

7-994I5555544444

7- 99414 443333333

7- 994122222222II

7. 99411IIIIIO0Oo 7.99410

Log.P

8. 17596

. 17611 

25

40

54

69

83

. 17698

. 17712

27

8. i774i

56«J

 17785 

. 17800

14

29

44

58

73

8. 17888

. 17902

17

32

46

61

76

 17990

. 18005

20

8. 18035

49 

64

79

. 18094

. 18108

23

38

53

68

8. 18183

. 18197

. 18212

27

42

57

72

. 18287

. 18302

16

8. 18331

46 

61

76

 18391

. 18406

21

36

51

66

8. 18481

" d. Log. P

5 I. 2 I. 2

10 2.3 2. 5

i5 3-5 3-8

20 4. 7 5. o

25 5. 8 6. 2

3° 7-o 7-5

35 8. 2 8. 8

40 9.3 10. o 

45 10. 5 n. 2 

50 ii. 7 12. 5 

55 12.8 13.8

60 14. o 15. o

0

0

48

49

50

100 M"

o. 9868 ' 67

65

<£

0 /

48 oo

IO

2030

40

5°

49 oo

IO

20 

3°

40

So

50 oo

100 P

f f

I- 4703

51

99

i. 4847

96

i. 4946

95

i. 5046

97 

1.5148

i. 5200

Si

i. \J\J «O4T^
00

<M

CO 

*

PH

co r 

M PI

O co t^ O

rt vovo OO

PI VOOO

M P)

vo 

M

O

O PI

CO rON O

vooo

co vovo t~-CQ

M

vo O vo

PI PI

O vo

CO CO rjO

M

O

O

O co

PI ro

M

r^

M VOOO

M PI CO

vo O vo 

 ^- vo vo

hO(

0

vo

O 

VO

-©-

8

VO CO PI

vo vO vO

v CO

V. 

0

ON

0 O M P. 

" vo VO vo

M

^

OH

.

X

3

OO *

ON M

ro <* 

ON ON

W M

co

O 

0\

ON

M

ON vo O vO PI r-» 

Pi ^-vo r-~ Ov O

Tj- 10

Ov Ov

M M

PI ro "* vovo t^

CO Ov ^1- 

PI CO 

Ov

VO

vo 

00

ON

ON

O

30 OvO

O vo M t~- rooO -* O vo M 

t-~CO O M ro ^vo CO ON M 

vovo vo I~» 

Ov ON ON ON

CO

ON

ON

o

M PI ro * vovo 1^-00 OvO

«-^ rooO * O vO 

PI -^ vo r^ ON O 

ON 

t--OO

ON

M M

O ON

ON Ov

ON Ov

M pi ro ^ vovo 

n PI M PI PI PI

PI r-- ro Ov vo M r^ rocO ^ 

PI ro vovo OO O M ro -^-vo O

OO OO ON 

Ov ON ON 

M M M 

CO

Ov

Ov

Ov

l^.OO OvO M PI ro ^t vovo 

«

^

(O

,

x

3

M VQ H O H VO M

CO ON H PI -3- vo t->

Tf ^ VO

CO OO OO

W M M

00

VO H

OO O

00 OO

H M

t-» PI

M ro

00

CO

O O O O Ov ON ON Ov ON ON O>

WHO O

ON ON ON

ON ON ON

O H PI CO * VOVO t^OO

ON

ON

CvO

i-l

t~- PI r-» PI t^ PI oo 

^ vo t^» ON O PI ro

vo t~~

CO 00

M M

CNCO CO 00 00 CO CO

M PI co * vovo f 

M M H M H M H

COCO ro OO Tf Ov T; 

vovo OO Ov H PI 1

CO CO CO

M MM

o

00

ON

ON

CO CNO M cvi ro ^

M M e>* PI PI PI P

 ON ^ O vo O vO

 vo i>* ON O PI co

co CO 00

MM M

Q.

00

ON

ON

t- vovo r^DO OvO

M vo M r^ PI i-. 

vovo OO Ov M pi 

OO Ov

M M

vovo vovo vovo 

M PI ro * vovo 

cococorororo
324 52

C

53C 'oI23456789

10

ii

12

13

14

IS

16

17

18

19

20

21

2223

24

25

26

27

282 9

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Log. M

7- 99395554444

. ' 444

7- 99394333333332

7- 99392222222III

7- 9939iiiii0o0oo

7- 993900

 99390

 99389999999

7- 993898888888

, 8)

7- 99387

Log.P

8. 20349

65

81

 20397

 204132 9

46

62

78

. 20494

8. 20510

27

43

59

75

 20592

. 20608

24

40

57

8. 20673

. 20689

. 20706

22

38

55

. 20788

. 20804

20

8. 20837

53

70

. 20886

. 20903

19

36

52

69

. 20985

8. 2 1 OO2

18

35

68

. 21084

. 2IIOI

17

34

51

8. 21167

. 21184

. 2I2OI

17

34

50

67

. 21284

. 21301

17

8. 21334

/oI23456789

10

ii

12

13

14

IS

16

17

18

19

20

21

222 3

24

25

26

27

28

29

303 1 3 2

33

34

35

36

3738

39

40

41

42

43

44

45

46

47

48

49

505 1 5 2

53

54

55

56

57

58

59

60

Log. M

7- 9938777777766

. 6

7. 99386666655555

7- 99385554444444

7- 99384433333333

7. 993822222222II

7- 9938iiiiiio0oo

7- 9938o

Log.P

8. 21334

5i

67

 21384

. 21401

18

35

5i

68

 21485

8. 21502J 9

35

52

69

. 21586

. 21603

20

37

54

8. 21670

. 21687

. 21704

21

38

55

72

. 21789

. 21806

23

8. 21840

 57

74

. 21891

. 21908

26

43

60

77

. 21994

8. 220II

28

45

63

80

. 22097

 22114

3i

49

66

8. 22183

. 222OO

18

35

52

69

. 22287

. 22304

21

39

8. 22356

"5

10

20 2 S

30

35

40

45

So

55

60

d. Log. P

2.7

4.0

5-3 

6.7

8.0

9-3

10.7

12. O

14.7

16. o

1.4

2.8

4.2

5-7

8-5

9-9

" 3

12.8

14.2 

15.6

17.0

3-o

4-5 

6.0

7-5

9.0

10.5

12. 0

r3-5 15.0 16.5

18. o

*

o

52

53

54

100 M

o. 9862

60

58

0

0 /

5 2 oo

IO

20

30

40

50

53 oo

IO

20

30

4050

54 oo

100 P

// 1

i- 5977

i. 6036

96

1.6157

i. 6219

81

i- 6343

i. 6407

70

I-6535

i. 6600

66

i. 6732
55

C 325

/0i23456789

10

ii

12

13

14

15

16

17

18J 9

20

21

22

23

24

25

26

27

282 9

30

3i

32

33

34

35

36

37

38

39

40

4i

42

43

44

45

46

47

48

49

50

5i

52

53

54

55

56

57

58

59 

60

Log. M

7. 993800o

. 99380

 9937999999

7-99379988888888

7- 99378777777776

7- 99376666666555

7- 99375555544444

7- 9937444333333

3 

7- 99373

Log.P

8. 22356

73

 22391

. 22408

25

43

60

78

 22495

 22513

8. 22530

47

. 65

. 22582

. 22600

17

3552

70

. 22687

8. 22705

23

40

58

75

 22793

. 22811

28

46

64

8. 22881

. 22899

. 22917

345 2

70

. 23987

 23005

23

4i

8. 23058

76

 23094

.23112

30

47

65

 23183

. 23201

*9

8. 23237

55

73

 23291

 23308

26

44

62

80

 23398 

8. 23416

/oi23456789

10

ii

12

*3

14

IS

16

17

18

*9

20

21

222 3

24

25

26

27

28

29

30

3i3 2

33

34

35

36

37

38

39

10

4i

42

43

44

45

46

47

48

49

50

5i

52

53

54

55

56

57

58

,0

Log. M

7- 99373322222222

7- 99371IIIIIIIOO

7. 99370Ooooo

 99370

 9936999

7- 9936999988888

7- 9936888

-1777777

7- 9936776666666

6 

7- 99365

Log.P

8. 23416

34

52

70

. 23488

 23506

24

43

61

79

8- 23597

 23615

33

5i

69

. 23688

. 23706

24

42

60

8. 23779

 23797

 23815

335 2

70

. 23888

. 23906

25

43

8. 23961

80

 23998

. 24016

35

53

72

. 24090

. 24108

27

8. 24145

64

. 24182

. 24201J 9

38

56

75

 24293

 243 12

8. 24331

49

68

. 24386

 24405

24

42

61

79

. 24498 

8. 24517

-5

10

2O

25

30

35

40

45

50

55

60

d. Log. P

1.4

2.8

4.2

5-7

&S

9-9

" 3

12.8

14.2 

15-6

17.0

3-o

4-5 

6.0

7-5

9.0

16.5

12. O

13-5 I 5.0 

I6.S

18. o

1.6 

S2

4.8 

6-3

7-9

9-5

ii. i

12.7

14.2

15-8 

17.4

19.0

<£ . 0

54

 55

56

100 M

// 

o. 9858

56

55

<£

0 /

54 oo

10

20

30

40

50

55 oo

10

20

30

40

50

5 6 oo

100 P

//

i. 6732

i. 6800

67

i. 6936

1.7005

75

i. 7146

1.7217

90

i. 7362

i. 7436 I -75"

i. 7586
320 57° 'oI23456789

10

ii

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

282 9

30

313 2

33

34

35

36

37

38

39

41

42

43

44

45

46

47

48

49

505 1

52

53

54

55

56

57

58

59

60

Log. M

7- 99365555555544

7- .99364444444333

7- 99363333322222

7- 99362222IIIIII

7. 99361IOoooo

. oo

 99360

7- 99359999999998

7- 99358

Log.P

8. 24517

36

54

73

 24592

. 24610

29

48

67

. 24686

8. 24704

23

42

61

80

. 24798

. 24817

36

55

74

8. 24893

. 24912

31

So

69

. 24988

 25007

26

45

64

8. 25083

. 25102

21

40

59

78

. 2.5216

36

55

8.25274

 25293

 253123 1 5 1

7o

 25389

. 25408

28

47

8. 25466

. 25486

 25505

24

43

63

 25582

. 25602

21

40

8. 25660 'oI23456789

10

ii

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

282 9

303 1 3 2

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

5152-

53

54

55

56

57

58

59

60

Log. M

7- 99358888888777

, 7-99357777776666

7- 99356666655555

7- 99355554444444

7- 9935443333

3.333

7- 9935222222222I

7- 99351

Log.P

8. 25660

79

 25699

 25718

37

57

76

.25796

 25815-

35

8. 25854

74

 25894

. 25913

335 2

72

 25992

. 26011

31

8. 26051

70

. 26090

. 26110

29

49

69

. 26188

. 26208

28

8. 26248

.68

. 26287

. 26307

27

47

67

. 26387

. 26407

26

8. 26446

66

. 26486

. 26506

26

46

66

. 26586

. 26606

26

8. 26646

66

. 26686

. 26706

26

47

67

 . 26787

. 26807

27

8. 26847

//5

10

15 

20

25

30

35

40

45 

So 

55

60

d. Log. P

i-5

3-o

4-5 

6.0

7-5

9.0

10.5

12. O

13-5 

15.0

16.5

18. o

1.6

3-2

4.8 

6-3

7-9

9-5

ii. i

12.7

14.2 

15.8 

17.4

19. o

i-7

3-3

5-o 

6.7

8-3

10. o

11.7 J 3-3

15.0 

16. 7 

18.3

20. o

</>

o

56

57

58

100 M

// 

0- 9855

53

52

$

0 /

56 oo

IO

20 

30

 40

50

57 oo

IO

20

30 

40 

5o

58 oo

100 P

//

i. 7586

i. 7662

i- 7739 

1.7817

95

i- 7975

i- 8055

i. 8136 

1.8218

i. 8301

85 

i. 8470

1-8555
58' 327

/

o.I23456789

10

ii

12J 3

14

15

16

17

18J 9

20

21

222 32 42 S

262 7

282 9

30

3i

32

33

34

35

36

37

38

39

40

4i

42

43

44

45

46

47

48

49

50

5i

52

53

54

55

56

57

58

59

60

Log. M

--7-99351iiiiiio0o

7- 993500ooo

 99350

 99349999

7- 99349999988888

7- 99348888777777

7- 99347766666666

7- 993465S5555555

7-99344

Log.P

8. 26847

67

. 26888

. 26908

28

48

69

. 26989

. 27009

29

8. 27050

70

. 27090

. 27111

3i

Si

72

 27192

.27213

33

8.27254

74

. 27294

 2 73I5

35

56

76

 27397

: 27417

38

8. 27459

 27479

 27500

20

41

62

.27582

. 27603

24

44

8. 27665

. 27686

. 27707

27

48

69

. 27790

. 278103 1

52

8. 27873

. 27894

 279I5

35

56

77

. 27998

. 28019

40

61

8. 28082

/oi23456789

10

ii

12

13

14

IS

16

i?

18J 9

20

21

222 3

242 5

26

27

28

29

30

3i

32

33

44

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

5i

52

53

54

55

56

57

58

59

60

Log. M

7- 99344444444443

7- 99343333333222

7- 9934222222IIII

7- 99341iiii0oo0o

7- 99340oo

 99340

 9933999999

7- 993399988888

. 88

7-993S8

- Log. P

8. 28082

. 28103

24

45

66

.28187

. 28208

29

50

7i

8. 28293

.28314

35

56.,

77

. 28398

. 28420

4i

62

. 28483

8. 28505

26

47

68

. 28590

.28611

32

54

75

. 28697

8. 28718

39

61

. 28782

. 28804

25

47

68

. 28890

. 28911

8. 28933

54

76

. 28997

. 29019

4i

62

. 29084

. 29106

27

8. 29149

7i

. 29192

. 29214

36

58

. 29279

 293012 3

45

8. 29367

-5

IO

15

20

25

30

35

40

45

So

55

60

d. Log. P

i-7

3-3

5-o

6.7

8-3

IO. O

11.7

13-3

15.0

!6.7 18.3

20. 0

1.8

3-5

5-2

7-o

8.8

10.5

12. 2

14. o

I5 .8

17-5

19. 2

21. 0

1.8

3-7

5- 5

7-3

9-2

II. O

12.8 14.7

t6.S

18.3

2O. 2

22. 0

$

o

58

59

60

100 M

//

o. 9852

So

49

<!>

0 /

58 oo

IO

20

30

40

50

59 oo

IO

20

30

4050

60 oo

100P

//

1.8555

i. 8642

i. 8730

i. 8819

. i. 8908

99

i. 9091

i. 9184

1.9277

i. 9372

 i. 9468

i- 9565

i. 9664
328 60

C 61

C

/oI234S6789

10

ii

12

13

14

IS

16

17

18

19

20

21

22

23

24

25

26

27

28

29

303 1

32

33

34

3536

3738

39

40

41

42

43

44

45

46

47

48

49

50

Si5 2

S3

54

55

56

57

58

59

60

Log. M

7- 99338877777777

7- 99337666666666

7- 993355SS5S5554

7- 99334444444433

7- 99333333333

2.22

7- 993322

.2222IIII

7- 9933i

Log.P

8. 29367

. 29389

8. 29410

32

54

76

. 29498

. 29520

42

64

8. 29586

. 29608

3°

52

74

. 29696

. 29718

40

62

. 29784

8. 29807

29

Si

73

 29895

.29917

40

62

. 29984

. 30006

8. 30029

Si

73

. 30096

.30118

40

63

.30185

. 30208

3°

8. 30252

75

. 30297

. 30320

42

65

 30387

 304io

32

55

8. 30478

.30500

23

45

68

 30591

. 30613

36

59

. 30682

8. 30704

/0i234

 56789

10

ii

12

13

14

15

16

i7

18r 9

20

21

222 3

24

25

26

27

282 9

303 1

32

33

34

35

36

3738

39

40

4i

42

43

44

45

46

47

48

49

50

Si

52

53

54

55

56

57

58

59

60

Log. M

7- 9933iiiiiooo0o

7- 99330o0

 99330 9932999999

7- 99329999888888

7- 99328887777177

7- 99327766666666

7- 99326555555555

7- 99325

Log.P

8. 30704

27

So

73

. 30796

. 30818

4i

64

. 30887

 3°910

8- 30933

56

 30979

. 31002

24

47

70

 31093

 3i"7

40

8.31163

.31186

.312093 2

55

.31278

 31301

25

48

7i

8. 31394

 3i4i7

4i

64

 31487

 31510

34

57 31581

 3 l6°4

8. 31627

5i

74

. 31698

.31721

44

68

 3I 79i

 31815

38

8.31862

. 31886

 3*909

33

56

.31980

.32004

275 1

75

8. 32098

//5

10

15

20

25

30

35

40

45

50

55

60

d. Log P

1.8

3-7

5-5

7-3

9.2

II. O

12.8 14.7 16.5 18.3

20. 2

22. O

1-9

3-8

5-8

7-7

9-6

" 5

i3-4

i5-3

17.2

19. 2

21. I

23.0

2. O

4.0

6.0

8.0

IO. O

12. O

14. o

16. o

18. o

20. 0

22. O

24. o

*

0

* 6o

61

62

100 M

o. 9849

47

46

<£

0 /

60 oo

IO

20

30

40

50

61 oo

10

20

30

40

So

62 oo

100 P

tt

i. 9664

i. 9763

i. 9864

i. 9966

2. 0069

2.0173

2. 0279

2. 0386

2. 0494

2. 0603

2.0714

2. 0827

2. 0940
62

C 63

C 329 'oI23456789

10

ii

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

282 9

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Log. M

7- 99325444444444

7- 99323333333333

7- 9932222222222I

7.99321IIIIIIIOO

7- 99320oo0ooo

 99320

 993199

7- 993199999"99988

7. 99318

Log. P

8. 32098

. 32122

46

70

 32193

.32217

41

. 65

. 32289

 32 3i3

8- 32336

60

.. 32384

. 324083 2

56

.32480

 32504

285 2

8. 32576

. 32600

24

49

73

. 32697

.32721

45

69

 32794

8. 32818

42

66

 32890

 329I5

39

63

. 32988

 33°12

37

8:33061

 33085

 33IIO

34

59

 33183

 332083 2

57

 33281

8. 33306

30

55

 3338o

 33404

29

54

 33478

 33503

28

8- 33553

* '0i23

 456789

10

ii

12

13

14

IS

16

17

18

19

20

21

22

23

24

25

26

27

28

29

303 1 3 2

33

34

35

36

37

38

39

40

4142

43

44

45

46

47

48

49

505 1 5 2

53

54

55

56

57

58

59

60

Log. M

888888777

7- 99317777777666

7- 993 l6666666555

7- 993 1 5

5 ' 55554444

7-993*4444443333

7- 993J3333332222

7. 99312

Log. P

8- 33553

 33577

 33602

27

52

 33677

 337O1

265 1

 33776

8. 33801

26

51

 33876

 33901

265 1

 33976

.34001'

26

8.34051

 34076

 34102

275 2

 34177

. 34202

28

 53

 342 78

8- 34303

29

54

 34379

 34405

30

56

 3448i

 345°63 2

8- 34557

 34583

. 34608

34

60

 34685

 347 11

36

62

. 34788

8. 34813

39

65

 34890

 349l6

42

68

 34993

 35019

45

8-35071

*

5

10

15

20

25

30

35

40

45

So

55

60

d. Log P

2. O

4.0

6.0

8.0

10. 0

12. O

14. o

1 6. o

18. o

20. 0

22. O

24. o

2. I

4.2

6.2

8-3

10. 4

12.5

14. 6

16.7

18. 8

20.8

22. 9 

25.0

2. 2

4-3

6-5

8-7

10.8

13.0

15.2

19. 5

21.7

23.8

26. o

*

o 

62

63

64

100M

o. 9846

44

43

</>

0 /

62 oo

IO

20

30

40

50

63 oo

10

20

3° 

40

50

64 oo

100 P

//

2. 0940

2- 1055

2. 1172

2. 1290

2. I4IO

2-I53I

2. 1654

2.1778

2. 1903

2. 2031 

2. 2l6o

2. 2291

2. 2424
330 65° 'oI23456789

10

ii

12

13

14

15

16

17

18

19

20

21

22

23

24

25

262 7

28

29

303 1 3 2

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59 

60

Log. M

7- 993 1222222IIII

7- 993"iiii0oooo

7- 993ioooo

.99310

 993099999

7- 99309999988888

7- 99308888877777

7- 9930777776666

6 

7- 993o6

Log.P

8- 35071

 35097

 35 I23

49

 35*75

27

. 53

 35279

 35305

8- 3 533 *

57

 35383

 35409

35

61

 35487

 35514

40

66

8. 35592

.356i8

45

 35697

 35724

So

.35776

 35803

29

8- 35856

 35882

 35909

35

62

 35988

 36015

41

68

 36095

8. 36121

48

 36175

. 36201

28

55

. 36282

 36308

35

62

8. 36389

 36416

43

69

 36496

 36523

So

 36577

. 366043 1 

8. 36658 '0i23456789

10

ii

12

13

14

.15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

303 1 3 2

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

5!S 2

53

54

55

56

57

58S

Log. M

7- 99306666665555

7- 9930555S5S4444

7- 99304444443333

7- 99303333332222

7- 99302222222III

7.99301IIIIIIOo

o 

7- 993oo

Log.P

8. 36658

 36685

.36712

40

 67

 36794

.36821

48

 36875

 36903

8- 3693°

57

' 36985

 37012

o 39

67

 37094

.37121

49

.37176

8:372043 1

59

 37286

 3733:4 41

69

 37397

 374245 2

8- 37479

 37507

35

62

 37590

.37618

46

 37674

.37702

30

8-37757

 37785

 37813

41

69

 37897

 37925

53

. 37981

. 38009

8. 38038

66

 38094

. 38122.

5°

.38178

 38207

35

63

 38292 

8. 38320

//

5

IOJ 5

20

25

30

35 40

45

50

55

60

d. Log P

2. 2

4-3 6.5 8.7

10.8.

13.0 

15.2 

17-3

*9-S

21. 7 23.8

26. o

2. 2

4-5 

6.8

9.0

II. 2

13-5 

15-8

18. o

2O. 2

22. 5

25.8

27. o

2-3

4-7 

7-o

9-3

11.7

14. o 

16.3 

18.7

21. O

23-3

25-7

28.0

C/>

O

6465

66

100 M

// 

o. 9843

4i

40

</>

0 /

64 oo

IO

2030

4050

65 oo

10

20

30 

40

50

66 oo

100 P

//

2. 2424

2. 2558 

2. 2694 

2. 2833

2. 2973 2 -3 II 5

2. 3258

2- 3405

2-3553

2. 3702 

. 2. 3854

2. 4009

2. 4166
67

C 881

f0i23456789

10

ii

12J 3H

15

16

17

18

19

20

21

222 3

24

25

26

27

28

29

30

3i

32

33

34

35

36

37

38

39

40

4i

42

43

44

45

46

47

48

49

505 1 5 2

53

54

55

56

57

58

59

60

Log. M

7. 99300oooo0

 99300

 9929999

7. 99299999999988

7. 99298888888887

7- 992977777777

 76

7- 99296666666666

7- 99295555555555

7- 99294

Log.P

8. 38320

48

 38377

 38495

33

62

 3849°

 38519

47

 38576

. 38604

33

62

. 38690

 38719

48

.38776

 38805

34

62

8. 38891

 38920

49

 38978

 39°°7

35

64

 39°93

.39122

Si

8. 39180

 39209

38

67

 39297

 39326

55

 39384

 39413

42

8. 39472

 395oi

30

60

. 39589

. 39618

48

 39677

 39706

36

8- 39765

 39795

 39824

54

. 39884

 399*3

43

 39972

. 40002

32

8. 40062

/oi23456789

10

ii

12

13

14

IS

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

3i

32

33

34

35

36

37

38

39

40

4i

42

43

44

45

46

47

48

49

505 1 5 2

S3

54

55

56

57

588

Log. M

7- 99294

 444444444

7- 99294333333333

7- 99293322222222

7- 9929222IIIIIII

7- 9929Jiii0o0o0o

7- 99290ooo

. 99290

.99289999

9 

7. 99289

Log.P

8. 40062

. 40091

. 40121

5i

. 40181

. 402 10

40

. 40270

 40300

30

8. 40360

 4039°

. 40420

So

. 40480

. 40510

, 40

 4057°

. 40601

3i

8. 40661

. 40691

. 40722

52

. 40782

. 40812

43

 40873

. 40904

34

8. 40964

 40995

.41025

56

. 41087

.41117

48

. 41178

.41209

40

8. 41270

 4i301

32

63

 41393

 41424

55

. 41486

 41517

48

8. 41579

. 41610

4i

.41672

 4i703

34

65

.41796

. 41828

59 

8. 41890

//5

10

i5

20

25

30

35

40

45

So

55

60

d. Log. P

2 -3

4- .7

7-o

9-3

11.7

14. o

16.3

18.7

21. O

23-3

25-7

28.0

2.4

4-8 7 .2

9-7

12. I

14-5

16. 9

J 9-3

21.8

24. 2

26.6

29.0

2.6

S2 7.8 10.3

12. 9

15-5

i8. i

20. 7

23.2

25.8

28.4

31.0

*

o 

66

67

68

100 M

o. 9840

39

38

$

0 /

66 oo

10

20 

30 

40 

50

67 oo

IO

20 

30 

40 

50

68 oo

100P

//

. 2. 4166

2- 4324 

2. 4486 

2. 4649 

2.4815 

2. 4983

2.5155

2- 5328

2- 5504 

2. 5683 

2. 5864 

2. 6049

2. 6236
332 68

C 'oI23456789

10

ii

12

13

14

15

16

18

19

20

21

2223

24

25

26

27

282 9

30

31

32

33

34

35

36

3738

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Log. M

7. 99289999998888

7. 99288888888877

7. 99287777777776

7. 99286666666666

7- 9928555555555

. 5

7- 99285544444444

7- 99284

Log. P

8. 41890

..419215 2

. 41984

 42015

46

. 42078

. 42 10941

.42172

8. 42204

35

67

. 42298

 4233°

62

 42393

 42425

57

. 42488

8. 42520

' 52

 42584

.42615

47

. 42679

.42711

43

 42775

. 42807

8. 42839

. 42871

 42903

35

. 42967

.43000

32

64

 43096

 43129

8.43161

 43193

. 43226

58

 4329°

 43323

55

 43388

 43420

53

8- 43485

 435i8

51

 43583

 43616

49

. 43682

 437*4

47

 4378o

8. 43813 'oi23456789

10

ii

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

2Q

30

31

32

33

34

35

36

3738

39

40

4i

42

43

44

45

46

47

48

49

50

515 2

53

54

55

56

57

58

59

60

Log. M

7- 99284

 443333333

7- 99283333322222

7. 99282222222III

7- 99281IIIIIIIIO

7- 99280Ooooo0ooo

7. 99280

 9927999999999

7- 99279

Log.P

8. 43813

46

 43879

.43912

45

 43978

. 44011

44-

.44077

. 44110

8. 44143

.44176

.44209

43

.44276

.44309

43

 44376

.44409

43

8. 44476

.44510

43

 44577

. 44610

44

.44678

.44711

45

 44779

8. 44812

46

.44880

.44914

48

.44982

 45015

49

 45083

. 45117

 8.45151

.45186

.45220

54

. 45288

. 45322

56

 45391

 45425

59

8. 45494

 45528

62

 45597

 45631

. 45666

. 45700

35

 45770

 45804

8. 45839

//5

10

15

20

25

30

35

40

45

So

55

60

d. Log. P

2-7

5-3

8.0

10. 7

13-3

16. o

18.7

21.3

24. o

26. 7

29-3

32.0

2.8

5-7

8-5

" 3

14.2

17.0

1.9.8

22. 7

22. 5

28.3

31.2

34-o

2-9

5-8

8.8

11.7

14. 6

17-5

20. 4

23-3

26. 2

29. 2

32. I

35-o

*

o

68

69

70

100 M

o. 9838

36

35

<£

0 /

68 oo

10

20

30

40 

5°

69 oo

IO

20

3° 

40 

50

70 oo

100P

//

2, 6236

2. 6427 

2. 662O

2. 68l6

2. 7015 

2. 7218

2. 7424

2. 7633 

2. 7846 

2. 8062 

2. 8282 

2. 8506

2- 8734
CO

CO 

CO 

-

0

 oi

AH

PI LOOO O

PI

COO

co

O 

HI 

coO

H

co LO c^oo

O

COO

O

to

COO

O

O 

M

P)

O O

O 

HI

PI

LO O

HI PI

UO t- O

O PI O

HI PI PI

O 0)

LO O PI

O O

PI

LO

LOCO

PI

HI 

O

PI

o

PI

CO

O 10 O

CO CO *

P) LOCO

O PJ LO

P) co co

uo

CO 

O

PI

^00

HI *3"

co co

o o

t~» O co 

PI co CO

LO O LO 

LO LO o

o

CO

O 

O

CO

od 

O

CO

o

o

-©-

r-t

§

Jq

LO ^~ CO

CO CO CO 

v OO

^ 

O

0

° a^ O!

^JO

&

KH

O

ti 

AH

V

0

oO LO PI CO LO c 

r HI LOOO' PI N£ O O O HI 

t-~oO 00 CO

00

 * <* "* "t co c 

O 

^

O

ON

PI

HI Pt CO ^ l

1 OO co O r~~

i O CO 1^ HI -tfHI PI P) CO CO

CO OO OO CO 

00

CO

O co co co co 

** 

0

O

co

ovO r~»oO ON^&

T}- HI oo LO P) o r-~ 

oo o LO o coo O 

co ^ rf LO LONO 

CO OQ_ CO OO OO CO

CO PO CO co co CO C«.

HI PI CO ^" LO\O t"^«

 * HI O

tj-CO HI

OO 

OO

OO

PJ PI 

^

ON

M

00 OO

NO co Hi OO O co HI OO "^ 

IO O POO O ^J"OO HI LO O 

r~00 00. 0 O O O 

OO OO OO CO 00 O 

^

o

0

CO

O

HI PI CO Tf LOO t^CO OO

Pi O r LO 

co t^ O *

O O ON

H M H H

H P| CO «* 

CO CO CO CO

CO HI O 

OO P) LO 

PI CO 

ON ON 

H H H 

CO co co 

V

s

^

o"

A,

O 'd-cO coco coco 

co i""* O ^" r^- H ^*o 

CO CO O O O

O

O 

oo

O HI P| CO ^j" LOO t

 q t-^ pi f^

) H HI

o

0

00

-^30 OO

1^

PI r^ Pi co coco coco 

pi LO o PI O O cO'O 

PI- Pi co co "^t* '<4'

HI PI co "^ LOO t"^CO

HiMHIHIHlHIhHHI

 * ON 

O CO

OO

O

ON 

PI 

we*

OO

^ O LO O ^O HI i--» 01 CO

«^ HI ^-OO HI LOCO PI LO

loo O t^« t^cO

HI PI CO * LOO t-^CQ O 

PIOJP1PIPIPIPIPIPJ

ON 

 *

CO

OO

3

o

o 

P)

PI O O co r O ^)-

O ON O O HI 

^- ^ Tj- .M- ^ 

HI PI CO -4' LOO I--

CO CO CO co CO CO CO 

to 
334 GEOGEAPHIO ' TABLES AND FOEMULAS. 

APPROXIMATE SPHERICAL EXCESS.

This may be obtained by dividing the ai'ea of the triangle in square 

miles by 75.5.

. TABLE 33. Mean refraction.

'S ai 

55 -g

«- 3

03 S 

ft +2

5P

0 1

00

10 

20 

30 

40 

50

10

10 

20 

30 

40 

50

20

10 

20 

30 

40 

50

30

10 

20 

30 

40 

50

40

10 

20 

30 

40 

50

50

10 

20 

30 

40 

50

60

^ 10 

20 

30 

40 

50

70

Refraction.

/ // 

34 54.1

32 49.2 

30 52.3 

29 3.5

27 22.7 

25 49.8

2424.6

23 6.7 

21 55.6 

20 50.9 

19 51.9 

18 58.0

18 8.6

17 23.0 

1640.7 

16 0.9 

15 23.4

14 47.8

14 14.6

13 43.7 

13 15.0 

12 48.3 

12 23.7 

12 0.7

11 38.9

11 18.3 

10 58.6 

10 39.6

10 21.2 

10 3.3

946.5

930.9 

916.0 

9 1.9 

848.4 

8 35.6

823.3

811.6 

8 0.3 

749.5 

739.2 

729.2

719.7

n 

124.9 

116.9 

108.8 

100.8 

92.9 

85.2 

77.9 

71.1 

64.7 

59.0 

53.9 

49.4 

45.6 

42.3 

39.8 

37.5 

35.6 

33.2 

30.9 

28.7 

26.7 

24.6 

23.0 

21.8 

20.6 

19.7 

19.0 

18.4 

17.9 

16.8 

15.6 

14.9 

14.1 

13.5 

12.8 

12.3 

11.7 

11.3 

10.8 

10.3 

10.0 

9.5

1-s

S P a-g -3 

<*PC 

o /

70

10 

20 

30 

40 

50

80

10 

20 

30 

40 

50

90

10 

20 

30 

40 

50

100

10 

20 

30 

40 

50

110

10 

20 

30 

40 

50

120

10 

20 

30 

40 

50

130

10 

20 

30 

40 

50

140

Refraction.

/ it 

7 19.7

710.5 

7 1.7» 

653.3 

645.1 

637.2

629.6

622.3 

615.2 

6 8.4 

6 1.8 

555.4

549.3

543.3 

537.6 

532.0 

526.5 

521.3

516.2

511.2 

5 6.4 

5 1.7 

457.2 

452.8

448.5

444.3 

440.2 

436.3 

432.4

428.7

425.0

421.4 

418.0 

414.6 

411.3 

4 8.1

4 4.9

4 1.8 

358.8 

355.9 

353.0 

350.2

347.4

n

9.2 

8.8 

8.4 

8.2 

7.9 

7.6 

7.3 

7.1 

6.8 

6.6 

6.4 

6.1 

6.0 

5.7 

5.6 

5.5 

5.2 

5.1 

5.0 

4.8 

4.7 

4.5 

4.4 

4.3 

4.2 

4.1 

3.9 

3.9 

3.7 

3.7 

3.6 

3.4 

3.4 

3.3 

3.2 

3.2 

3.1 

3.0 

2.9 

2.9 

2.8 

2.8

13

S 3 

03 S

OH -3 5f*

o /

140

20 

40

150

20 

40

160

20 

40

170

20 

40

180

20 

40

190

20 

40

200

20 

40

210

20 

40

220

20 

40

230

20 

40

240

20 

40

250

20 

40

260

20 

40

270

20 

40

280

Refraction.

i n 

347.4

342.1 

337.0

332.1

327.4 

322.9

318.6

3 14.5 

310.5

3 6.6

3 2.9 

259.3

255.8

252.5 

249.3

246.1

243.1 

240.2

237.3

234.5 

231.9

229.3

226.8 

224.3

221.9

219.6

217.4

2 15.2

213.0 

2 .1.0.9

2 8.9

2 7.0 

2 5.1

2 3.2

2 1.4 

159.6

157.8

156.1 

1 54.4

152.8

151.2 

149.7

148.2

n 

5.3 

5.1 

4.9 

4.7 

4.5 

4.3 

4.1 

4.0 

3.9 

3.7 

3.6 

3.5 

3.3 

3.2 

3.2 

3.0 

2.9 

2.9 

2.8 

2.6 

2.6 

2.5 

2.5 

2.4 

2.3 

2.2 

2.2 

2.2 

2.1 

2.0 

1.9 

1.9 

1.9 

1.8 

1.8 

1.8 

1.7 

1.7 

1.6 

1.6 

1.5 

1.5

Hi I* &

as $*

0 1

280

20 

40

290

20 

40

300

20 

40

310

20 

40

320

20 

40

330

20 

40

340

20 

40

350

20 

40

360

20 

40

370

20 

40

380

20 

40

390

20 

40

400

20 

40

410

20 

40

420

Refraction.

/ // 

148.2

146.7 

145.3

143.8

142.4 

141.0

139.7

138.4 

1 37.1

135.8

134.5 

133.3

132.1

130.9 

129.8

128.7

127.6 

126.5

125.4

124.3 

123.3

122.3

121.3 

120.3

1 19.3

118.3 

117.4

1 16.5

1 15.6 

1 14.7

113.8

1 12.9 

1 12.0

1 11.2

1 10.3 

1 9.5

1 8.7

1 7.9 

1 7.1

1 6.3

1 5.5

1 4.7

1 4.0

n 

1.5 

1.4 

1.5 

1.4 

1.4 

1.3 

1.3 

1.3 

1.3 

1.3 

1.2 

1.2 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

0.9

0.9 

0.9 

0.9 

0.9 

0.9 

0.9 

0.8 

0.9 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.8 

0.7

1-s §1B.E I*

o

42 

43

44 

45 

46

47 

48 

49 

 

"BT 

52 

53

54 

55 

56

57 

58 

59

60

61 

62 

63

64 

65 

66

67 

68 

69

70 

71

72 

73

74 

75 

76

77 

78 

79 

80 

81 

82 

86 

90

Refraction.

n 

64.0 

61.8

59.7 

57.7 

55.7

53.8 

51.9 

50.2 

48.4 

46.7^ 

45.1 

43.5

41.9 

40.4 

38.9

37.5 

36.1 

34.7

33.3 "sYo"

30.7 

29.4

28.2 

26.9 

25.7

24.5 

23.3

00 0 UTo" LL.L

19.9 

18.8 

17.7

16.6

15.5 

145

13.4 

12.3 

11.2 

10.2 

9.1 

8.1 

4.1 

0.0

n

2.2 

2.1 

2.0 

2.0 

1.9 

1.9 

1.7 

1.8 

1.7 

1.6 

1.6 

1.6 

1.5 

1.5 

1.4 

1.4 

1.4 

1.4 

1.3 

1.3 

1.3 

1.2 

1.3 

1.2 

1.2 

1.2 

1.1 

1.2 

1.1 

1.1 

1.1 

1.1 

1.1 

1.0 

1.1 

1.1 

1.1 

1.0 

1.1 

1.0 

4.0 

4.1
GEOGRAPHIC TABLES AND FORMULAS. . 335

TABLE 34. Corrections for curvature and refraction, infeet=0.574 (distance, miles} 2 . 

[Difference in feet between the apparent and true level at distances varying from i to 66 miles.]

Distance, 

miles. .

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

Difference in feet for 

Curvature.

0.7

2.7

6.0

10.7

16.7

24.0

32.7

42.7

54.0

66.7

80.7

96.1

112.8-

130.8

150.1

170. 8

- 192. 8

216.2

240.9

266.9

294.3

322.9

353.0

384.3 ;

417.0

451. 1

486.4

523.1

561. 2

600.5

641.2

683.3

726.6

Refraction.

0.1

0.4

0.8

1.5

2.3

3.4

4.6

6.0

7.6

9.3

11.3

13.4

15.8

18.3

21.0

23.9

27.0

30.3

33.7

37.4

41.2

45.2

49.4

53.8

58.4

63.1

68.1

73.2

78.6

84.1

89.8

95.7

101.7

Curvature 

and 

refraction.

0.6

- 2.3

5.2

9.2

14,4

20.6

28.1

36.7

46.4

57.4

69.4

82.7

97.0

112.5

129. 1

146.9

165. 8

185. 9

207.2

229.5

253.1

277.7

303.6

330.5

358.6.

388.0

418.3

449.9

482.6

516.4

551.4

587.6

624.9

Distance, 

miles.

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54 .

55

56

57

58

59

60

61

62

63

64

65

66

Difference in feet for 

Curvature.

771.3

817.4

864.8

913.5

963:5

1, 014. 9

1,067.6

1, 121. 7

1,177.0

1, 233. 7

1, 291. 8

1, 351. 2

1, 411. 9

1, 474. 6

1,537.3

1, 602. 0

1, 668. 1

1, 735. 5

1, 804. 2

1,874.3

1, 945. 7

2, 018. 4

2, 092. 5

2, 167. 9

2, 244. 6

2, 322. 7

2, 402. 1

2, 482. 8

2, 564. 9

2, 648. 3

2, 733. 0

2, 819. 1

2, 906. 5

Refraction.

108.0

114.4

121. 1

127. 9

134. 9

142.1

149.5

'157.0

164.8

172.7

180.8

189. 2

197.7

206.3

215 2

224.3

233. 5

243.0

252.6

262.4

272. 4

282.6

292. 9

303.5

314.2

325. 2

336. 3

347. 6

359. 1

370.8

382. 6

394. 7

406.9

Curvature 

and 

refraction.

663.3

703.0

743.7

785.6

828.6

872.8

918. 1

964.7

1, 012. 2

1,061.0

1, 111. 0

1, 162. 0

1,214.2

1, 267. 7

1, 322. 1

1, 377. 7

1, 434. 6

1, 492. 5

1, 551. 6

1,611.9

1, 673. 3

1, 735. 8

1, 799. 6

1, 864. 4

1 , 930. 4

1, 997. 5

2, 065. 8

2, 135. 2

2, 205. 8

2,277.5

2, 350. 4

2, 424. 4

2, 499. 6
336 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 35. FOR OBTAINING DIFFERENCES OF ALTITUDE FOR ANY MINUTE UP TO 15 

DEGREES, AND FOR ANY DISTANCE.

[Prepared by Arthur P. Davis.] 

EXPLANATION OF TABLE.

The left-hand column is the minutes of the vertical angle, the 

degrees being denoted by the large number at top of page. The boldface figures at top of column is the distance in miles. Numbers in the 

body of the table denote the difference of elevation corresponding to 

the angle on the left and the distance at top. The correction .for 

curvature, refraction, and height of instrument is always plus; it therefore increases the difference of level for angles of elevation, and is 

subtracted from the difference of level 'for angles of depression.

Example, Eequired the difference of altitude corresponding to a 

vertical angle of -f 9° 18' at a distance of 3.628 miles. On page 346 

the tabular number corresponding to 9° 18' and 

Feet. 

A. distance of 3 miles is ................................................... 2,594

For a distance of 6 miles is 5,188 for 0.6 is therefore ....................... 519

For a distance of 2 miles is 1,729 for 0.02 is therefore ...................... 17

For a distance of 8 miles ia 6,917 for 0.008 is therefore ...................... 7

Correction for curvature, refraction, and height of instrument for 3.6 miles is +. 12

Total difference of altitude..........................--.-..-..-.--.+ 3,149
GEOGRAPHIC TABLES AND FORMULAS. ' 337 

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

0°

1

2

3

4

5

6

7

8

9

10 11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

2829'

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

1

1.5

3.1

4.6

6.1

7.7

9.2

10.8

12. 3

13.8

15. 4

16.9

18.4

20.0

21.5

23.0

24.6

26.1

27.6

29.2

30.7

32.3

33.8

35.3

36.9

38.4

39.9

41.5

43.0

44.5

46.1

47.6

49.2

50.7

52.2

63.8

55.3

56.8

58.4

59.9

61.4

63.0

64.5

66.0'

67.6

69.1

70.6

72.2

73.7

75.3

76.8

78.3

79.9

81.4

82.9

84.5

86.0

87.5

89.1

90.6

92.2

2

3.1

6.1

9.2

12.3

15.4

18.4

21.5

24.6

27.6

30.7

33.8

36.9

39.9

43.0

46.1

49.1

52.2

55.3

58.4

61.4

64.5

67.6

70.7

73.7

76.8

79.9

82.9

86.0

89.1

92.2

95.2

98.3

101.4

104. 4

107.5

110. 6

113.7

116.7

119.8

122.9

125.9

129.0

132.1

135.2

138.2

141.3

144.4

147.5

150.5

153.6

156.7

159.7

162. 8

165.9

169.0

172.0

175.1

178.2

181.3

184.3

3

5

9

14

18

23

28

32

37

41

46

51

55

60

65

69

74

78

83

88

92

97

101

106

111

115

120

124

129

134

138

143

147

152

157

161

166

170

175

180

184

189

194

198

203

207

212

217

221

226

230

235

240

244

249

253

258

263

267

272

276

4

6

12

18

25

31

37

43

49

55

61

68

74

80

86

92

98

104

111

117

123

129

135

141

147

154

160

166

172

178

184

190

197

203

209

215

221

227

233

240

246

252

258

264

270

276

283

289

295

301

307

313

319

326

332

338

344

350

356

363

369

5

8

15

23

31

38

46

54

61

69

77

84

92

100

108

' 115

123

131

138

146

154

161

169

177

184

192

200

207

215

223

230

238

246

253

261

269

276

284

292

300

307

315

323

330

338

346

353

361

369

376

384

392

399

407

415

422

430

438

445

453

461

6

9

18

28

37

46

55

65

74

83

92

101

111

120

129

138

147

157

166

175

184

194

203

212

221

230

240

249

258

267

276

286

295

304

313

323

332

341

350

359

369

378

387

396

405

415

424

433

442

452

461

470

479

488

498

507

516

525

535

644

553

7

11

22

32

43

54

65

75

 86

97

108

118

129

140

151.

161

172

183

194

204

215

226

237

247

258

269

280

290

301

312

323

333

344

355

366

376

387

398

409

419

430

441

452

462

473

484

495

505

510

527

538

548

659

670

581

591

602

613

624

634

645

8

12

25

37

49

. 61

74

86

98

111.

123

135

147

160

172

184

197

209

221

233

246

258

270

. 283

295

307

319

332

344

356

369

381

393

405

418

430

442

456

467

479

492

504

516

528

541

553

565

578

590

602

614

627

039

651

664

670

688

700

713

725

737

9

14

28

41

55

69

83

97

111

124

138

152

166

180

194

207

221

235

249

263

276

290

304

318

332 '346

359

373

387

401

415

' 429

442

456

470

484

498

512

525

539

553

567

581

594

608

622

636

650

664

677

691

705

719

733

747

760

774

788

802

816

829

Corrections for curvature, refraction, and 

height of instrument.a

Miles.

1.6

2.1

2.5

2.8

3.1

3.4

3.6

3.8

4.1

4.3

4.5

4.7

4.8

5.0

5.2

5.4

6.5

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10.0

10.1

Feet.

6

 7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

60

61

62

63

Miles.

10.2

10.3

30.4

10.5

10.6

10.7

10.8

10.9

11.0

11.1

11.2

11.3

11.4

11.5

11.0

11.7

11.8

11.9

12.0

12.1

12. 2

12.3

12.4

12.5

12. 6

12.7

12.8

12.9

13.0

13.1

13.2

13.3

13.4

13.5

13. 6

13.7

13.8

13.9

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15.0

15.1

15.2

15.3

15.4

15.5

15. 6

15,7

15.8

15. 9

10.0

Feet.

04

05

07

68

69

70

71

73

74

75

77

78

79

80

82

83

84

86

87

89

90

91

93

94

96

97

99

100

102

103

105

106

108

109

111

112

114

115

117

119

120

122

124

125

127

129

130

132

134

135

137

139

141

142

144

146

148

160

151

« For all distances under 1.6 miles the correction may be taken as +5 feet. Height of instrument 

is assumed 4.5 feet.

41623° 1C 22
338 GEOGKAPHIC TABLES AND FOBMULAS.

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

1°

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

1

92.2

93.7

95.2

96.8

98.3

99.8

101.4

102.9

104.4

106.0

107. 5

109. 1

110. 6

112.1

113.7

115.2

116.7

118.3

119.8

121.4

122.9

124.4

126.0

127.5

129.0

130.6

132.1

133.6

135.2

136. 7

138.3

139.8

141. 3

142.9

144.4

146.0

147.5

149. 0

150.6

152.1

153.6

155.2

156. 7

158.2

159. 8

161. 3

162. 9

164.4

165.9

167.5

169.0

170.6

172.1

173.6

175.2

176.7

178.2

179.8

181.3

182. 8

184.4

2

184'. 3

187.4

190.5

193.5

196.6

199.7

202.8

205.8

208.9

212.0

215. 1

218.1

221.2

224.3

227.3

230.4

233.5

236.6

239.6

242.7

245.8

248.9

251.9

255. 0

258.1

261.2

264.2

267.3

270.4

273.5

276.5

279.6

282. 7

285.7

288.8

291.9

295.0

298.0

301.1

304.2

307.3

310.3

313.4

316.5

319.6

-322.6

325. 7

328.8

331.9

334.9

338.0

341.1

344.2

347.2

350.3

353.4

356.5

359.5

362.6

365.7

368.8

3

276

281

286

290

295

300

304

309

313

318

323

327

332

336

341

346

350

355

359

364

369

373

378

383

387

392

396

401

406

410

415

419

424

429

433

438

442

447

452

456

461

466

470

475

479

484

489

493

498

502

507

512

516

521

525-

530

535

539

544

549

553

4

369

375

381

387

393

399

406

412

418

424

430

436

442

449

455

461

467

473

479

485

492

498

504

510

516

522

528

535

541

547

553

559

565

571

578

584

590

596

602

608

615

621

427

633

639

645

651

658

664

670

676

682

688

694

701

707

713

719

725

731

738

5

461

468

476

484

492

499

507

515

622

530

538

545

553

561

568

576

584

591

599

607

614

622

630

638

645

653

661

668

676

684

691

699

707

714

722

730

737

745

753

760

768

776

784

791

799

807

814

822

830

837

845

853

860

868

876

883

891

899

907

914

922

(t

553

562

571

581

590

599

608

618

627

636

645

654

664

673

682

691

700

710

719

728

737

747

756

765

774

783

793

802

811

820

830

839

848

857

866

876

885

894

903

913

922

931

940

949

959

968

977

986

996

1,005

1,014

1,023

1,032

1,042

1,051

1,060

1,069

1,079

1,088

1,097

1,106

7

645

656

667

677

688

699

710

720

731

742

753

763

774

785

796

806

817

828

839

849

860

871

882

893

903

914

925

936

946

957

968

979

989

1,000

1,011

1,022

1,032

1,043

1,054

1, 065

1,075

1,086

1,097

1,108

1,118

1,129

1, 140

1,151

1, 162

1,172

1, 183

1,194

1,205

1, 215

1,226

1,237

1,248

1,258

1,269

1,280'

1,291

8

737

750

762

774

786

799

811

823

836

848

860

873

885

897

909

922

934

946

959

971

983

995

1,008

1,020

1,032

1,045

1, 057

1,069

1,082

1,094

1,106

1,118

1, 131

1,143

1,155

1,168

1,180

1,192

1,204

1,217

1,229

1,241

1,254

1,266

1, 278

1,291

1,303

1,315

1,327

1,340

1,352

1,364

1,377

1,381)

1,401

1,414

1, 426

1,438

1,450

1,465

1,475

9

829

843

857

871

885

899

912

926

940

954

968

982

995

1,009

1,023

1,037

1,051

1,065

1,078

1,092

1,106

1,120

1,134

1,148

1, 161

1,175

1,189

1,203

1,217

1,231

1,244

1,258

1,272

1,286

1,300

1,314

1,327

1, 341

1,355

1,369

1,383

1,397

1,410

1,424

1,438

1, 452

1,466

1,480

1,493

1,5(7

1, 521

1,535

1,549

1,563

1,576

1,590

1,604

1, 618

1,632

1,643

1,659

Corrections for curvature, refraction, and 

height of instruments

Miles.

16.1

16.2

16.3

16.4

16.5

16.6

16.7

16.8

16.9

17.0

17.1

17.2

17.3

17.4

17.5

17.6

17.7

17.8

17.9

18.0

18.1

18.2

18.3

18.4

18. 5

18.6

18.7

18.8

18.9

19.0

19.1

19.2

19.3

19.4

19.5

19.6

19.7

19.8

19.9

20.0

20.1

20.2

20.3

20.4

20.5

20.6

20.7

20.8

20.9

21.0

21.1

21.2

21.3

21. 4

21.5

21.6

21.7

21.8

21.9

22.0

Feet.

153

155

157

159

161

163

165

167

168

170

172

174

176

178

180

182

184

186

188

190

193

195

197

199

201

203

205

207

210

212

214

216

218

221

223

225

227

230

232

234

236

239

241

243

246

248

250

253

255

258

260

262

265

267

270

272

275

277

280

282

Miles.

22.1

22.2

22.3

22.4

22.5

22.6

22.7

22.8

22.9

23.0

23. 1

23. 2

23.3

23.4

23.5

23.6

23.7

23.8

23.9

24.0

24.1

24.2

24.3

24.4

24.5

24.6

24.7

24.8

24.9

25.0

25.1

25.2

25.3

25.4

25.5

25.6

25.7

 25.8

25.9

26.0

26.2

'26.4

26.6

26.8

27.0

27.2

27.4

27.6

27.8

28.0

28.2

28.4

28.6

28.8

29.0

29.2

29.4

; 29.6

29.8

30.0

Feet.

285

287

290

293

295

298

300

303

306

308

311

313

316

319

321

324

327

330

332

335

338

341

343

346

349

352

355

358

360

363

366

369

372

375

378

381

384

387

390

393

399

405

411

417

423

429

435

442

448

455

461

467

474

480

487

494

501

507

514

521

«For all distances under 1.6 miles the correction may be taken as +5 feet. Height of instrument 

ig assumed 4.5 feet.
GEOGEAPHIC TABLES AND FOKMULAS. 339

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

1

184.4

185.9

187. ft

189.0

190.5

192. .1.

193. 6

195. 1

196.7

198. 2

1 99. 8

201 . 3

202.8

204.4

205. 9

207. 5

209. 0

210.5

212. 1

213.6

215. 1

216. 7

218. 2

219. 8

221.3

222. 8

224. 4

225.9

227. 5

229. 0

230. 5

232. 1

233. 6

235. 1

236. 7

238. 2

239. 8

241.3

242.8

244.4

245. 9

247. 5

249.0

250. 5

252. 1

253. 6 '

255. 2

256. 7

258. 2

259. 8

261. 3

262. 9

264. 4

265.9

267. 5

269. 0

270. 6

272. 1

273. 6

275.2

276.7

2

368.8

371.8

374.9

378.0

381. 1

384. 1

387. 2

390. 3

393.4

396.4

399. 5

402. 6

405.7

408.8

411.8

414. 9

418. 0

421. 1

424. 1

427.2

430.3

433.4

436.4

439.5

442. 6

445.7

448. 7

451.8

454. 9

458. 0

401. 1

464.1

467. 2

470.3

473. 4

476.4

479.5

482.6

.485. 7

488.8

491. 8

494.9

497. 0

501 . 1

504. 2

507. 2

510. 3

513. 4

516. 5

519.5

522.6

525.7

528. 8

531.9

534.9

538. 0

541. 1

544. 2

547. 3

550. 3

553. 4

:$

553

658

562

567

572

576

581

585

590

595

599

604

609

613

618

622

627

632

630

(>41

646

650

655

659

664

669

673

678

682

687

692

696

701

705

711

715

719

 724

729

733

738

742

747

752

756

761

765

770

775

779

784

789

793

798

802

807

812

810

821

826

830

4

738

744

750

756

762

768

774

781

787

793

799

805

811

818

824

830

836

842

848

854

861

867

873

879

885

891

897

904

910

916

922

928

934

941

947

953

959

965

971

978

984

990

996

1,002

1,008

1,014

1,021

1,027

1, 033

1,039

1,045

1,051

1,058

1,064

1,070

1,076

1,082

1, 088

1,095

1, 101

1, 107

5

922

930

937

945

953

960

968

976

983

991

999

1, 006

1,014

1,022

1,030

1,037

1,045

1,053

1, 000

1,068

1, 076

1,083

1,091

1,099

1,106

1,114

1,122

1,130

1, 137

1,145

1,153

1, 160

1, 168

1, 176

1,183

1, 191

1, 199

1,207

1,214

1,222

1, 230

1,237

1 , 245

1,253

1,260

1,268

1,276

1,283

1, 291

1, 299

1, 307

1,314

1,322

1,330

1,337

1,345

1,353

1,360

1,368

1, 376

1,384

6

1,106

1,116

1,125

1, 134

1 , 1.43

1, 152

1, 162

.1,171

1,180

1,189

1,199

1,208

1, 217

1,226

1,235

1 , 245

1,254

1,263

1,272

1,282

1,291

1,300

1, 309

1,319

1,328

1,337

1,346

1,355

1,365

1,374

1,383

1,392

1, 402

1,411

1,420

1, 429

1,439

1,448

1,457

1,466

1, 476

1, 485

1,494

1,503

1,512

1, 522

1,531.

1,540

1, 549

1, 559

1, 508

1, 577

1,586

3,596

1,605

1,614

1, 623

1 , 633

1,642

1,651

1, 660

7

1, 291

1,301

1,312

1, 323

1, 334

1, 344

1, 355

1, 366

1,377

1, 388

1,398

1,409

1,420

1,431

1,441

1,452

1,463

1,474

1,484

1,495

1,506

1,517

1,528

1,538

1,549

1,560

1,571

1,581

1,592

1,603

1, 614

1,624

1,635

1,646

1,657

1,668

1, 678

1,689

1, 700

1,711

1, 721

1, 732

1,743

1,754

1,765

1 , 775

1, 786

1,797

1,808

1,818

1,829

1,840

1,851

1,862

1,872

1,883

1,894

1, 905

1,915

1,920

1, 937

8

1, 475

1,487

1,500

1,512

1,524

1, 537

1,549

1,561

1, 573

1,586

1,598

1,610

1, 623

1,635

1,647

1, 660

1,672

1,684

1,697

1,709

1,721

1, 733

1,746

1, 758

1, 770

1,783

1,795

1,807

1,820

1,832

1,844

1,857

1,869

1,881

1,893

1, 906

1,918

1,930

1,943

1,955

1, 967

1,980

1, 992

2,004

2, 017

2, 09.9

2,0<tl

2,054

2,066

2,078

2, 091

2,103

2,115

2, 127

2, 140

2,152

2, 164

2, 177

2, 189

2, 201

2,.214

9

1,659

1,673

1,687

1,701

1,715

1,729

1, 742

1, 756

1,770

1, 784

1, 798

1,812

1, 826

1,839

1,853

1,867

1,881

1, 895

1,909

1,932

1,936

1,950

1,964

1,978

1,992

2,006

2, 019

2, 033

2,047

2,061

2,075

2, 089

2, 102

2, 116

2,130

2, 144

2,158

2,172

2, 186

2,199

2,213

2,227

2, 241.

2,255

2, 269

2, 283

2, 296

2,310

2, 324

2,338

2,352

2, 366

2,380

2,393

2, 407

2, 421

2,435

2, 449

2,463

2,477

2,490

Corrections for curvature, refraction, and 

height of instrument."

Miles

1.0

2.1

2.5

2.8

3.1

3.4

3.6

3.8

4.1

4.3

4.5

4.7

4.8

5.0

5.2

5.4

5.5

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

.1.0.0

10.1

J'cet.

6

7

8

9

1.0

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

60

61

52

63

Miles

10.2

10.3

10. 4

10.5

10. 0

10.7

10.8

10. 9

11.0

11. 1

11.2

11. 3

11.4

11.5

11.0

11.7

11. 8

11. 9

12.0

12.1

12. 2

12.3

12.4

12. 5

12. 6

12.7

12.8

12.9

13. 0

13.1

13.2

13.3

13. 4

13.5

13.6

13.7

13.8

13.9

14.0

14. 1.

14.2

14.3

14. 4

14.5

14,6

14.7

14.8

14. 9

15.0

15.1

15.2

15.3

15.4

15. 5

15. 6

15. 7

15.8

15.9

16. 0

Fed. ' 64

65

67

68 ,

69

70

71

73 

. 74

75

77

78

79

.80 '

82 .'

83

84 '

86

87

89

90

91

93

94

96

97

99

100

102

103

105

106

108

109

1.11

112

114

11.5

117

119

120

122

124

125

127

129

130

132

134

135

137

139

141

142

144

146

148

150

151.

«For all distances under 1.6 miles the correction may be taken as -(-5 feet. Height of instrument 

is assumed 4.5 feet.
340 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 35. Fur obtaining differences of altitude for any minute, etc. Continued.

3°

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

1

276.7

278.3

279.8

281.3

282.9

284.4

286.0

287.5

289.0

290.6

292. 1

293.7

295.2

296.7

298.3

299.8

301.4

302.9

304.4

306.0

307.5

309.1

310.6

312.1

313.7

315.2

316.8

318.3

319.9

321. 4

322.9

324. 5

326.0

327.6

329.1

330.6

332. 2

333.7

335.3

336.8

338.4

339.9

34L4

343.0

344.5

346.1

347.6

349.2

350.7

352. 2

353.8

355.3

356.9

358.4

360.0

361. 5

363.0

364.6

366.1

367. 7

369.2

2

553.4

556.5

559.6

562.7

565.7

568.8

571.9

575.0

578. 1

581.2

584.2

587 3

590.4

593.5

596.6

599. 6

602.7

605.8

608.9

612.0

615.0

618.1

621.2

624.3

627.4

930.5

633.5

636.6

639.7

642.7

645. 9

649.0

652.0

655.1

658.2

661.3

664.4

667. 5

670.5

673.6

676.7

679.8

682. 9

686.0

689.1

692. 1

695.2

698.3

701.4

704.5

707.6

710.7

713.7

716. 8

719.9

723. 0

726. 1

729.2

732. 3

735.3

738.4

3

830

835

839

844

849

853

858

862

867

872

876

881

886

890

895

899

904

909

913

918

923

927

932

936

941

946

950

955

960

964

969

973

978

983

987

992

997

1, 001

1,006

1,010

1,015

1,020

3,024

1,029

1,034

1,038

1,043

1,047

1,052

1,057

1, 061

1,066

1,071

1,075

1,080

1,085

1,089

1,094

1,098

1,103

1,108

4

1,107

1,113

1,119

1,125

1,131

1,138

1,144

1,150

1,156

1,162

1, 168

1,175

1,181

1, 187

1 , 193

1,199

1,205

1,212

1,218

1,224

1,230

1,236

1,242

1,249

1,255

1,261

1,267

1,273

1,279

1,286

1, 292

1,298

1,304

1, 310

1, 316

1,323

1, 329

1,335

1,341

1,347

1, 353

1,360

1,366

1,372

1,378

1,384

1,390

1,397

1,403

1,409

1, 415

1,421

1, 427

1,434

1,440

1,446

1,452

1,458

1,465

1,471

1,477

5

1,384

1,391

1,399

1,407

1,414

1,422

1,430

1,437

1,445

1,453

1,461

1,468

1,576

1,484

1,491

1,499

1,507

1,515

1,522

1,530

1,538

1,545

1,553

1, 561

1,568

1,576

1,584

1,592

1,599

1,607

1,615

1, 622

1,630

1,638

1,646

1,653

1, 661 .

1,669

1,676

1, 684

1,692

1,700

1,707

1,715

1,723

1,730

1, 738

1,746

1,753

1,761

1, 769

1,777

1,784

1, 792

1,800

1,807

1, 815

1,823

1,831

1,838

1,846

(i

1,660

1, 670

1,679

1,688

1,697

1,706

1,716

1,725

1,734

1,743

1,753

1,762

1,771

1,780

1,790

. 1, 799

1,808

1,817

1,827

1,836

1,845

1,854

1,864

1,873

1,882

1,891

1,901

1,910

1,919

1,928

1,938

1,947

1,956

1,965

1,975

1,984

1,993

2,002

2,012

2,021

2,030

2,039

2,049

2, 058

2,067

2,076

2,086

2,095

2,104

2,113

2,123

2,132

2,141

2,150

2,160

2,169

2,178

2,188

2,197

2, 206

2,215

7

1,937

-1,948

1,959

1,969

1,980

1,991

2,002

2,012

2,023

2, 034

2,045

2,056

2,066

2, 077

2,088

2,099

2,110

2, 120

2,131

2,142

2,153

2,163

2, 174

2,185

2,196

2,207

2,217

2,228

2,240

2,250

2,261

2,271

2, 282

2, 293

2, 304

2,315

2,325

2,336

2,347

2,358

2,369

2,379

2,390

2, 401

2,412

2,422

2,433

2,444

2,455

2, 466

2,476

2,487

2,498

2,509

2,520

2,530

2,541

2, 552

2,563

2,574

2,584

8

2, 214

2,226

2,238

2,251

2,263

2,275

2,288

2,300

2,312

2,325

2,337

2, 349

2, 362

2,373

2,386

2,399

2,411

2,423

2,436

2,448

2,460

2, 473

2,485

2,497

2,510

2,522

2,534

2,547

2,559

2,571

2,584

2,596

2,608

'2,621

2,633

2,645

2,658

2,670

2,682

2,695

2,707

2,719

2,732

2,744

2,756

2,769

2, 781

2,793

2,806

2,818

2,830

2,843

2,855

2, 867

2,880

2,892

2,904

2, 917

2, 929

2,941

2,954

9

2,490

2,504

2,518

2,532

2,546

2,560

2,574

2,587

2,601

2,615

2,629

2,643

2,657

2,671

2, 685

2, 698

2,712

2,726

2,740

2,754

2,768

2,782

2,795

2,809

2,823

2,837

2,851

2,865

2,879

2,893

2,906

2,920

2,934

2,948

2, 962

2,976

2,990

3,004

3,017

3,031

3,045

3,059

3,073

3,087

3,101

3, 1 15

3,129

3,142

3,156

3,170

3,184

3,198

3, 212

3, 226

3,240

3,253

3,267

3, 281.

3, 295

3,309

3,323

Corrections for curvature, refraction, and 

heightof instrument.**

Miles.

10.1

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

11.2

11.4

11.6

11.8

12.0

12.2

12.4

12.6

12.8

13.0

13.2

13.4

13.6

13.8

14.0

14.2

14.4

14.6

14.8

15.0

15.2

15.4

15.6

15.8

16.0

16.2

16.4

16.6

16.8

17.0

17.2

17.4

17.6

17.8

18.0

18.2

18.4

18.6

18.8

19.0

19.2

19.4

39.6

19.8

20.0

21.0

22.0

23.0

24.0

25.0

Feet.

63

64

65

67

68

69

70

71

73

75

77

79

82

84

87

90

93

96

99

102

105

108

111

114

117

120

124

127

130

132

137

141

144

148

151

153

159

163

167

170

174

178

182

186

190

195

199

203

207

212

216

221

225

230

234

258

282

308

335

363

« For all distances under 1.6 miles the correction may be taken as +5 feet. Height of instrument 

is assumed 4.5 feet.
GEOQEAPHIO TABLES AND FOEMULA9. 341

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

40

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

20

27

28

29

30

31

32

33

34

35

36 ' 37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

eg

54

55

56

57

5869'

GO

1

369.2

370.8

372. 3

373. 8

375.4

376.9

378.5

380.0

381.6

383.1

384.7

386.2

387.7

389.3

390.8

392.4

393.9

395.5'

397.0

398.6

400.1

401.6

403.2

404.7

406.3

407.8

409.4

410.9

412.5

414.0

415.5

417. 1

418.6

420.2

421.7

423.3

424.8

426.4

427.9

.429. 5

431.0

432.5

434.1

435.6

437.2

438.7

440.3

441.8

443.4

444.9

446.5

448.0

449.6

451.1

452.7

454.2

455.8

457. 3

458.8

460.4

461.9

2

738

742

745

748

751

754

757

760

763

766

769

772

775

779

782

785

788

791

794

797

800

803

806

809

813

816

819

822

825

828

S31

834

837

840

843

847

850

853

856

859

862

865

868

871

874

877

881

884

887

890

893

896

899

902

905

908

912

915

918

921

924

3

1,108

1,112

1, 117

1,122

1,126

1,131

1,135

1,140

1,145

1,149

1,154

1,159

1,163

1,168

1,172

1,177

1,182

1,186

1,191

1,19.6

1,200

1,205

1,210

1,214

1,219

1,223

1,228

1,233

1,237

1,242-

1,247

1,251

1,256

1,261

1,265

1,270

1,274

1,279

1,284

1,288

1,293

1,298

1,302

1,307

1,312

1,316

1,321

1,325

1,330

1,335

1,339

1,344

1,349

1,353

1,358

1,363

1,367

1,372

1,377

1,381

1,386

4

1,477

1,483

1,489

1,495

1,502

1,508

1,514

1,520

1,526

1, 532

1,539

1,545

1,551

1,557

1,563

1,569

1,576

1,582

1,588

1,594

1,600

1,607

1,613

1,619

1,625

1,631

1,637

1,644

1,650

1,656

1,662

1,668

1, 675.

1,681

1,687

1,693

1,699

1, 705

1,712

1,718

1,724

1,730

1,736

1,743

1, 749

1,755

1,761

1,767

1,773

1,780

1,786

1,792

1,798

1,804

1,811

1,817

1,823

1,829

1,835

1,842

1,848

5

1,846

1,854

1,862

1,869

1,877

1,885

1,892

1,900

1,908

1,916

1,923

1,931

1,939

1,946

1,954

1,962

1,970

1,977

1,985

1,993

2,000

2,008

2,016

2,024

2,031

2,039

2,047

2,055

2,062

2,070

2,078

2,085

2,093

2,101

2, 109

2,116

2,124

2,132

2,140

2; 147

2,155

2,163

2,170

2,178

2,186

2, 194

2,201

2, 209

2,217

2, 225

2,232

2, 240

2,248

2,256

2,263

2,271

2, 279

2,286

2,294

2,302

2,310

G

2,215

2,225

2,234

2,243

2, 252

2,262

2,271

2,280

2,289

2, 299

2,308

2,317

2,326

2,336

2,345

2,354

2,363

2,373

2,382

2,391

2,401

2,410

2,419

2, 428

2,438

2,447

2,456

2,465

2, 475

2,484

2,493

2,503

2,512

2,521

2,530

2,540

2,549

2,558

2,567

2,577

2.586

2,595

2,605

2,614

2,623

2,632

2,642

2, 651

2,660

2,669

2,679

2,688

2, 697

2,707

2,716

2,725

2,735

2,744

2,753

2,762

2,772

7

2,584

2,595

2, 606

2,617

2,628

2, 639

2,649

2, 660

2, 671 '

2,682

2,693

2,703

2,714

2,725

2,736

2,747

2,757

2,768

2,779

2,790

2,801

2, 811

2,822

2, 833

2,844

2,855

2,866

2,876

2,887

2,898

2,909

2, 920

2, 930

2,941

2,952

2,963

2,974

2,985

2,995

3,006

3,017

3,028

3,039

3,049

3,060

3, 071

3,082

3,093

3,104

3,113

3,125

3, 136

3,147

3,158

3,] 69

3,179

3,190

3,201

3,212

3,223

3,234

8

2,954

2,966

2,978

2,991

3,003

3,015

3,028

3,040

3,053

3,065

3,077

3,090

3,102

3,114

3,127

3,139

3,151

3,164

3,176

3,188

3,201

3,213

3,225

3,238

3,250

3,263

3,275

.3,287

3,300

3, 312

3,324

3,337

3,349

3,361

3,374

3,386

3,399

3,411

3,423

3,436

3,448

3,460

3,473

3,485

3,498

3,510

3, 522

3,535

3,547

3,558

3,572

3, 584

3,596

3, 609

3,621

3,634

3,646

3,658

3,671

3,683

3,696

9

3,323

3,337

3,351

3,365

3,378

3,392

3, 406

3,420

3,434

3,448

3,462

3,476

3,490

3,504

3,517

3,531

3,545

3,559

3,573

3,587

3,601

3,615

3,629

3,643

3,656

3,670

3,684

3,698

3,712

3,726

3,740

3,754

3,768

3,782

3,796

3,809

3,823

3,837

3,851

3,865

3,879

3,893

3,907

3,921

3, 935

3,949

3,963

3, 976

3,990

4,003

4,018

4,032

4,046

4,060

4,074

4,088

4,102

4,116

4,130

4,144

4,157

Corrections for curvature, refraction, and 

height of instrument."

Sfttcs.

1.6

2.1

2.5

2.8

3.1

3.4

3.6

3.8

4.1

4.3

4.5

4.7

4.8

6.0

6.2

5.4

5.5

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10.0

10.1

Feet.

6

7

8

9

10

11

12

13

14

15

16

17

18

39

20

2L

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

60

61

62

63

Miles.

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

11.1

31.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

12.0

12.1

12.2

12.3

12.4

12.5

12.6

12.7

12.8

12.9

13.0

13. 1

13.2

13.3

13.4

13.5

13.6

33.7

13.8

13.9

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15.0

15. 1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16.0

Feet..

64

65

67

68

69

70

71

73

74

75

77

78

79

80

82

83

84

86

87

89

90

91

93

94

96

97

99

100

102

103

105

106

108

109

111

312

114

316

117

119

320

122

124

125

327

129

130

332

134

135

137

339

141

142

144

146

148

160

151

«For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument 

is assumed 4.6 feet.
342 GEOGBAPHIC TABLES AND FOEMULAS.

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

0

1

2

3

4

5

0

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

1

461.9

463.5

465.0

466.6

468.1

469.7

471.2

472.8

474.3

475.9

477.4

479.0

480.5

482.1

483.6

485.2

486.7

488.3

489.8

491.3

492.9

494.5

496.0

497.6

499.1

500. 7

502.2

503.8

505.3

506.9

508.4

510.0

511.5

513.0

514.6

516.2

517.7

519.3

520.8

522. 4

523.9

525.5

527. 0

528.6

530.1

531. 7

533. 2

534.8

536. 3

637.9

539.4

541. 0

542.5

544.1

545.6

547.2

548. 7

550,3

551.8

553.4

555.0

2

924

927

930

933

936

939

942

946

949

952

955

958

961

964

967

970

973

976

980

983

986

989

992

995

998

1,001

1,004

1,007

1,010

1,014

1,017

1,020

1,023

1,026

1,029

1,032

1,035

1,039

1,042

1,045

1,048

1,051

1,054

1,057

1,060

1, 063

1,066

1, 070

1,073

1,076

1,079

1, 082'

1, 085

1,088

1,091

1,094

1,097

1,101

1,104

1,107

1,110

3

1,386

1,390

1,395

1, 400

1,405

1,409

'1,414

1,419

1,423

1,428

1,432

1,437

1,442

 1,447

1,451

1,456

1,461

1,465

1,470

1,475

1,479

1,483

1,488

1,493

1,498

1,502

1,507

1,512

1,516

1,521

1, 525

1, 530

1,535

1,539

1,544

1,549

1.553

1,558

1,563

1,568

1,572

1,576

1,581

1,586

1,591

1,595

1,600

1,605

1,609

1,614

1,618

1,623

1,628

1,632

1,637

1,642

1,646

1,651

1,656

1,661

1,665

4

1,848

1,854

1,860

1, 866

1,873

1, 879

1,885

1,891

1,897

1,904

1,910

1,916

1,922

1,928

1,935

1,941

1,947

1,953

1,959

1,966

1,972

1,978

1, 984

1, 990

1, 996

2,003

2,009

2,015

2,021

2,027

2,034

2,040

2,046

2,052

2, 058

2, 065

2,071

2,077

2,083

2, 089

2,095

2,102

2, 108

2, 114

2, 121

2,127

2,133

2,139

2,145

2,154

2,158

2, 166

2,170

2,176

2,183

2,189

2,195

2,201

2,207

2,214

2,220

a

2,310

2,317

2,325

2,333

2,341

2,348

2,356

2,364

2,372

2,379

2,387

2,395

2,403

2,410

2,418

2,426

2,434

2,441

2,449

2,457

2,465

2,472

2,480

2,488

2,496

2,503

2, 511

2, 51.9

2,- 527

2,534

2, 542

2,550

2,558

2,565

2,573

2,581

2,589

2,596

2,604

2, 612

2,620

2, 627

2,635

2,643

2,651

2,658

2,666

2,674

2, 682

2,689

2,697

2,705

2,713

2,721

2,728

2,736

2,743

2,752

2,759

2,767

2,775

(i

2,772

2,781

2,790

2,800

2,809

2,818

2,827

2,837

2,846

2,855

2, 865

2,874

2,883

2,892

2, 902

2,911

2, 920

2,930

2, 939

2,948

2,958

2,967

2,976

2,985

2,995

3,004

3, 013

3,023

3, 032

3,041

3,050

3,060

3,069

3,078

3,088

3,097

3,106

3,116

3,125

3,134

3,144

3, 153

3,162

3,172

3,181

3, 190

3, 199

3,209

3,218

3,227

3,237

3,246

3,255

3,265

3,274

3,283

3, 292

3,302

3,311

3,320

3,330

7

3,234

3,244

3, 255

3,266

3,277

3, 288

3,299

3,309

3,320

3,331

3,342

3, 353

3, 364

3,375

3,385

3,396

3,407

3,418

3,429

3,440

3, 450

3,461

3,472

3, 483

3,494

3,505

3,515

3,526

3,537

3,548

3,559

3,570

3,581

3,591

3,602

3, 613

3, 624

3,635

3,646

3,657

3,667

3,678

3,689

3,700

3,711

3,722

3,733

3,743

3,754

3,765

3,776

3,787

3,798

3,809

3,819

3, 830

3,841

3,852

3,863

3,874

3,885

8

3,696

3, 708

3,720

3,733

3,745

3,757

3,770

3,782

3, 795

3,807

3, 819

3,832

3,844

3, 857

3,869

3,881

3,894

3,906

3,919

3,931

3,943

3, 956

3,968

3,981

3,993

.4,005

4,018

4,030

4,042

4,055

4,067

4,080

4, 092

4,105

4,117

4,129

4, 142

4,154

4,167

4, 179

4,191

4,204

4, 216

4, 229

4, 241 

4, 253

4, 266

4,278

4, 291

4,303

4,315

4,328

4,340

4,353

4,365

4,378

4,390

4,402

4,415

4,427

4,440

i)

4, 157

4,171

4,185

4,199

4,213

4,227

4,241

4,255

4,269

4,283

4,297

4,311

4,325

4,339

4,353

4,367

4,381

4,394

4,408

4, 422

4,436

4,450

4, 464

4,478

4,492

4,506

4,520

4, 534

4,548

4,562

4,576

4,590

4, 604

4,618

4,632

4,645

4,659

4,673

4,687

4,701

4,715

. 4, 729

4,743

4,757

4, 771

4,785

4,799

4,813

4,827

4,841

4,855

4,869

4,883

4,897

4,911

4,925

4,939

4,953

4,967

4,981

4,995

Corrections for curvature, refraction, and 

height of instrument."

Miles.

1.6

2.1

2.5

2.8

3.1

3.4

3.6

3.8

4.1

4.3

4.5

4.7

4.8

5.0

5.2

5.4

5.5

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.0

9.7

9.8

9.9

10.0

10.1

Feet.

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

60

61

62

63

Miles.

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

11.1

11.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

12.0

12.1

12.2

12.3

12.4

12.5

12.6

12.7

12.8

12.9

13.0

13.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9.

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15.0

15.1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16.0

Feet.

64

65

67

68

69

70

71

73

74

75

77

78

79

80

82

83

84

86

87

89

90

91

93

94

96

97

99

100

102

103

105

100

108

109

111

112

114

115

117

119

120

122

124

125

127

129

130

132

134

135

137

139

141

142

144 146'

148

150

151

a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument 

is assumed 4.5 feet.
GEOGRAPHIC TABLES AND FORMULAS. . 343

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

6°

0

1

2

3

4

5

0

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

20

27

28

29

30

31

32

33

34

35

30

37

38

39

40

41.

42

43

44

45

40

47

48

49

50

51

52

53

54

55

50

57

58

59

60

1

555.0

550.5

558.1

559.0

501.2

662. 7

564.3

565.8

567.4

508.9

570.5

572.0

573.0

575.2

576.7

578.3

579.8

581.4

582.9

584.5

586.0

587.6

589.1

590.7

692.2

593.8

595.4

596.9

598.5

600.0

601.0

603.1

604.7

600.3

007.8

009.4

610.9

612.5

614.0

615.5

617.2

618.7

020.3

021. 8

623.4

624.9

620. 5

628.0

629.6

631. 2

632.7

634.3

635.8

637.4

638.9

640.5

642.1

643.6

645.2

646.7

648.3

2

1,110

1, 113

1,116

1,119

1,122

1, 125

1,129

1,132

1, 135

1,138

1.141

1,144

1,147

1,150

1,153

1,157

1,160

1,163

1,160

1,169

1,172

1, 175

1,178

1, 181.

1,185

1,188

1,191

1,194

1,197

1,200

1,203

1, 206

1,209

1,213

1,216

1,219

1,222

1,225

1,228

1,231

1,234

1,237

1,241

1, 244

1,247

1,250

1,253

1,256

1,259

1,262

1,265

1,269

1,272

1,275

1,278

1,281

1,284

1,287

1,290

1,293

1,297

3

1,005

1,070

1,074

1, 679

1,084

1,088

1,093

1,097

1,702

1,707

1,711

1,716

1,721.

1,725

1,730

1,735

1,739

1,744

1,749

1,753

1,758

1,763

1,767

1,772

1,777

1,781

1,786

1,791

1,795

1,800

1,805

1,809

1,814

1,819

1,823

1,828

1,833

1,837

1,842

1,847

1,851

1,856

1,861

1,865

1,870

1,875

1,879

1,884

1,889

1,894-

1,898

1,903

1,908

1, 912

1,917

1,922

1,926

1,931

1,936

1,940

1,945

4

2,220

2,226

2, 232

2,238

2,245

2, 251

2,257

2, 263

2,270

2,276

2, 282

2,288

2,294

2, 301

2,307

2,313

2, 319

2,325

2,332

2,338

2, 344

2,350

2,357

2, 363

2,309

2,375

2,381

2,388

2,394

2, 400

2,400

2,413

2,419

2,425

2,431

2,437

2,444

2,450

2,450

2, 402

2,469

2,475

2,481

2,487

2,494

2,500

2,506

2, 512

2,518

2, 525

2,531.

2, 537

2,543

2,550

2,550

2,502

2, 568

2,575

2, 581

2,587

2,593

5

2,775

2,783

2,790

2,798

2,806

2,814

2,821

2, 829

2, 837

2,845

2,852

2, 860

2,868

2,876

2,884

2,891

2,899

2, 907

2,915

2,922

2,930

2,938

2,946

2, 953

2,901

2,969

2,977

2,985

2,992

3,000

3,008

3,016

3,023

3,031

3,039

3,047

3,055

3,062

3,070

3,078

3,080

3,094

3,101

3,109

3,117

3,125

3,132

3,140

3,148

3,156

3,164

3,171

3,179

3,187

3,195

3,203

3,210

3,218

3,226

3,234

3,242

6

3,330

3,339

3,348

3, 358

3,307

3,376

3,386

3,395

3,404

3,414

3,423

3, 432

3,442

3,451

3,460

3,470

3,479

3,488

3,498

3,507

3,516

3,526

3,535

3,544

3,554

3,563

3,572

3,581

3,591

3,600

3,009

3,019

3,628

3,637

3,647

3,050

3, 060

3,075

3, 684

3,694

3,703

3,712

3,722

3, 731

3,740

3,750

3,759

3, 768

3,778

3,787

3,796

3,806

3,815

3,824

3,834

3,843

3,852

3,862

3,871

3,880

3,890

7

3,885

3,890

3,906

3, 917

3,928

3,939

3,950

3,901

3,972

3,983

3,993

4,004

4,015

4,020

4,037

4,048

4,059

4,070

4,080

4,091

4,102

4,113

4,124

4,135

4,140

4,157

4,1.68

4,178

4,189

4,200

4,211

4,222

4,233

4, 244

4,255

4, 266

4,276

4,287

4,298

4,309

4,320

4,331

4,342

4,353

4,364

4,374

4,385

4,396

4,407

4,418

4,429

4,440

4,451

4,462

4,473

4,484

4,494

4,505

4,516

4,527

4,538

8

4,440

4,452

4,464

4,477

4,489

4, 502

4,514

4,527

4,539

4,551

4,604

4,576

4,589

4,601

4,614

4,626

4, 639

4,651

4,663

4,676

4,688

4,701

4,713

4,720

4,738

4,750

4,703

4,775

4,788

4,800

4,813

4,825

4,838

4,850

4,802

4,875

4,887

4,900

4,912

4,925

4,937

4,950

4,962

4,975

4,987

4,999

5,012

5,024

5,037-

5,049

5,062

5,074

5,087

5,099

5,112

5,124

5,130

5,149

6,101

5,174

5,186

9

4,995

5,009

6,023

5,037

5,050

5,064

5,078

5,092

5,106

5, 120

5,134

5,148

6,162

5,176

5,190

5,204

5,218

5,232

5,246

5,260

5,274

5,288

5,302

5, 316

5,330

5,344

5,358

5,372

6,386

5,400

5,414

5,428

5,442

5,456

5,470

5,484

5,498

6,512

5,526

5,540

5,554

5,508

5,582

5,590

5,610

6,624

5,038

5,053

5,007

5,681

5,695

5,709

6,723

5,737

5,751

5,765

5,779

5,793

5,807

5,821

5,835

Corrections for curvature, refraction and 

height of instrument."

Miles

1.6

2.1

2.5

2.8

3.1

3.4

3.6

3.8

4.1

4.3

4.5

4.7

4.8

5.0

5.2

5.4

5.5

5.7

5.8

6.0

0.1

6.3

0.4

6.5

6.7

6.8

6.9

. 7.0

7.2

7.3

7.4

7.5

7.0

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10.0

10.1

feet.

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

36

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

50

58

59

60

61

62

63

Miles

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

11.1

11.2'

11.3

11.4

11.5

11.0

11.7

11.8

11.9

12.0

12. 1.

12.2

12.3

12.4

12.5

12.6

12.7

12.8

12.9

13.0

13.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15.0

15.1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

10.0

Feet.

64

05

07

08

09

70

71

73

74

75

77

78

79

80

82

83

84

86

87

89

90

91

93

94

90

97

99

100

102

103

105

106

108

109

111

112

114

115

117

119

120

122

124

125

127

129

130

132

134

135

137

139

141

142

144

146

148

150

151

a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument 

Is assumed 4.5 feet.
344 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

7°

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

1

648.3

649.9

651.4

653.0

654.5

656.1

657.7

659.2

660.8

662.4

663.9

665.5

667.0

668.6

670.2

671.7

673.3

674.8

676.4

678.0

679.5

681.1

682.6

684.2

685.8

687.3

688.9

690.5

692.0

693.6

695.1

696.7

698.3

699.8

701.4

702.9

704.5

706.1

707.6

709.2

710.8

712.3

713.9

715. 5

717.0

718.6

720.2

721.7

723.3

724.8

726.4

728.0

729.5

731.1

732.7

734.2

735.8

737.4

738.9

740.5

742.1

2

1,297

1,300

1,303

1,306

1,309

1,312

1,315

1,318

1, 322 .

1,325

1,328

1,331

1,334

1,337

1,340

1,343

1,347

1,350

J.353

1,366

1,359

1,362

1,365

1, 368

1,372

1,375

1,378

1, 381

1,384

1,387

1,390

1,393

1,396

1,400

1,403

1,406

1,409

1,412

1,415

1,418

1,422

1,425

1,428

1,431

1,434

1,437

1,440

1,443

1,447

1,450

1,453

1,456

1,459

1,462

1,465

1,468

1,472

1,475

1,478

1,481

1,484

3

1,945

1,950

1,954

1,959

1,964

1, 968

1,973

1,978

1,982

1,987

1,992

1,996

2,001

2,006

2,010

2,015

2,020

2, 025

2,029

2,034

2,039

2,043

2,048

2,053

2,057

2,062

2,067

2,071

2,076

2,081

2,085

2,090

2,095

2, 099

2,104

2, 109

2, 114

2,118

2,123

2,128

2,132

2,137

2,142

2,146

2,151

2,156

2,160

2,165

2,170

2,175

2,179

2,184

2, 189

2,193

2,198

2,203

2,207

2,212

2,217

2,221

2,226

4

2,593

2,599

2,606

2, '612

2,618

2,624

2,631

2,637

2,643

2,649

,2, 656

2,662

2,668

2,674

2,681

2,687

2,693

2,699

2,706

2,712

2,718

2,724

2,731

2,737

2,743

2,749

2, 756

2,762

2,'768

2,774

2,781

2,787

2,793

2,799

2,806

2,812

2,818

2,824

2,831

2, 837

2,843

2,849

2,856

2,862

2,868

2,874

2,881

2,887

2,893

2,899

2,906

2,912

2, 918

2,924

2,931

2,937

2,943

2,949

2,956

2,962

2,968

5

3,242

3,249

3,257

3,265

3,273

3,281

3,288

3,296

3,304

3,312

3,320

3,327

3,335

3,343

3,351

3,359

3,366

3,374

3,382

3,390

3,398

3,405

3,413

3,421

3,429

3,437

3,444

3, 452

3,460

3,468

3,476

3,483

3,491

3,499

3,507

3,515

3,523

3,530

3,538

3,546

3,554

3,562

3,569

3,577

3,585

3,593

3,601

3,609

3,616

3,624

3,632

3,640

3,648

3,656

3,663

3,671

3,679

3,687

3,695

3,702

3,710

6

3,890

3,899

3,909

3,918

3,927

3,937

3,946

3,955

3,965

3,974

3, 983

3,993

4,002

4,012

4,021

4,030

4,040

4,049

4,058

4,068

4,077

4,087

4,096

4,105

4,115

4,124

4,133

4, 143

4,152

4,161

4,171

4,180

4,190

4,199

4,208

4,218

4,227

4,236

4,246

4,255

4,265

4,274

4,283

4,293

4,302

4,312

4, 321.

4,330

4,340

4,349

4,358

4,368

4,377

4,387

4,396

4,405

4,415

4,424

4,434

4,443

4,452

7

4,538

4,549

4,560

4,571

4,582

4,593

4,604

4,615

4,626

4,636

4,647

4,658

4,669

4,680

4,691

4,702

4,713

4,724

4,735

4,746

4,757

4,768

4,779

4,789

4,800

4,811

4,822

4,833

4,844

4,855

4,866

4,877

4,888'

4.899

4,910

4,921

4,932

4,943

4,953

4,964

4,975

4,986

4,997

5,008

5,019

5,030

5,041

6,052

5,063

5, 074

5,085

5,096

5,107

5,118

5,129

5,140

5,151

5,162

5,172

5,183

5,194

8

5,186

5,199

5,211

5,224

5,236

5,249

5, 261

5,274

5,286

5,299

5,311

5, 324

5, 336

5,349

5,361

5,374

5, 386

5,399

5,411

5,424

5,436

5,449

5,461

5,474

5,486

5,499

5,511

5,524

5,536

5, 549

5,561

5,574

5,586

5,599

5, 611

5,624

5,636

5,649

5,661

5,674

5,686

5,699

5, 711

5, 724

5,736

5,749

6,761

5,774

5,786

5,799

5,811

5,824

5,836

5,849

5,861

5,874

5,886

5,899

5,911

5,924

5,936

9

5,835

5,849

5, 863

5,877

5,891

5,905

5,919

5, 933

5,947

5,961

5,975

5, 989

6,003

6,017

6,031

6,045

6,060

6,074

6,088

6,102

6,116

6,130

6, 144

6, 158

6,172

6,186

6,200

6,214

6,228

6,242

6,256

6, 270

6,284

6, 298

6,312

6,327

6,341

6,355

6,369

6,383

6,397

6,411

6,425

6,439

6,453

6, 467

6,481

6,495

6, 510

6,524'

 6, 538

6,552

6,566

6,580

6,594

6,608

6,622

6,636

6,650

6,664

6,678

Corrections for curvature, refraction and 

height of instrument."

Miles.

1.6

2.1

2.5

2.8

3.1

3.4

3.6

3.8

4.1

4.3

4.6

4.7

4.8

5.0

5.2

6.4

5.5

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10.0

10.1

Feet.

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

4748-

49

50

51

52

53

54

55

56

58

59

60

61

62

63

Miles.

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

11.1

11.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

12.0

12.1

12.2

12.3

12.4

12.5

12.6

12.7

12.8

12.9

13.0

13.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15.0

15.1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16.0

Feet.

64

65

67

68

69

70

71

73

74

75

77

78

79

80

82

83

84

86

87

89

90

91

93

94

96

97

99

100

102

103

105

106

108

109

111

112

114

115

117

119

120

122

124

125

127

129

130

132

134

135

137

139

141

142

144

146

148

150

151

a For all distances under 1.6 miles the correction may be taken as + 6 feet. Height of instrument 

is assumed 4.5 feet.
GEOGRAPHIC TABLES AND FORMULAS. 345

TABLE 35. For obtaining differences of altitude fqr any minute, etc. Continued.

8° '

0

1

2

3

4

5

C

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

4G

47

48

49

60

51

52

53

64

55

56

57

58

59

60

1

742.1

743.0

745. 2

746.8

748.3

749.9

751.5

753.0

754.6

756.2

757.7

759.3

760.9

762. 4

764.0

765.6

767.1

768.7

770.3

771.8

773.4

775.0

776.6

778.1

779.7

781.3

782.8

784.4

786.0

787.5

789.1

790.7

792.2

793.8

795. 4

796. 9

798.5

800.1

801.7

803.2

804.8

806.4

808.0

809.5

811.1

812. 7

814.2

815. 8

817.4

819.0

820.5

822.1

823.7

825. 3

826.8

828.4

830.0

831. 5

833.1

834.7

836.3

2

1,484

1,487

1,490

1,494

1,497

1,500

1, 503

1,506

1,509

1,512

1,515

1,519

1,522

1,525

1,528

1,531

1,534

1,537

1,541

1,544

1,547

1,550

1,553

1,556

1,559

1, 562

1,566

1,569

1,572

1,575

1, 578

1,581

1,584

1,588

1..591

1,594

1,597

1,600

1,603

1,607

1,610

1,613

1, 616

1,619

1,622

1 , 625

1,628

1,632

1,635

1,638

1,641

1, 644

1,647

1;651

1,654

1,657

1,660

1,663

1,666

1,669

1,673

3

2,226

2,231

2, 236

2,240

2,245

2,250

2,254

2,259

2,264

2,269

2,273

2,278

2,283

2,287

2,292

2,297

2,301

2,306

2,311

2,316

2,320

2,325

2,330

2,334

2,339

2,344

2,348

2,353

2,358

2,363

2,367

2,372

2,377

2,381

2, 386

2, 391

2,396

2, 400

2,405

2,410

2,414

2,419

2,424

2, 429

2,433

2, 438

2,443

2,447

2, 452

2,457

2,462

2, 466

2, 471

2, 476

2,481

2,485

2, 490

2, 495

2,499

2,504

2,509

4

2,968

2,974

2, 981

2, 987

2, 993

3,000

3,006

3,012

3,018

3, 025

3,031

3,037

3,043

3, 050

3,056

3,062

3,069

3,075

3,081

3,087

3,094

3,100

3,106

3,112

3,119

3,125

3,131

3,138

3,144

3,150

3,156

3,163

3, 169

3,175

3,182

3,188

3,194

3,200

3,207

3,213

3,219

3,226

3,232

3,238

3,244

3, 251

3,257

3,263

3,270

3,276

3,282

3, 288

3,295

3,301

3,307

3,314

3,320

3,326

3,332

3,339

3,345

5

3, 710

3, 718

3,726

3,734

3,742

3, 749

3,757

3,765

3,773

3, 781

3,789

3,797

3,804

. 3, 812

3,820

3,828

3,836

3,844

3,851

3,859

3,867

3,875

3,883

3,891

3,898

3,906

3,914

3,922

3,930

3,938

3,945

3,953

3,961

3, 969

3,977

3,985

3,993

4,001

4,008

4,016

4,024

4,032

4,040

4,048

4,056

4,063

4,071

4,079

4,087

4,095

4,103

4, 111

4,118

4,126

4, 134

4,142

4, 150

4,158

4,166

4,173

4,181

G

4,452

4,462

4,471

4,481

4,490

4,499

4,509

4,518

4,528

4,537

4,546

4,556

4,565

4,575

4,584

4,593

4,603

4, 612

4,622

4,631

4,640

4,650

4,659

4,669

4,678

4,688

4,697

4,706

4, 716

4, 725

4,735

4,744

4, 753

4,763

4, 772

4,782

4,791

4,801

4, 810

4,820

4,829

4,838

4,848

4,857

4, 867

4,876

4,886

4,895

4,904

4,914

4,923

4,933.

4, 942

4,952

4,961

4,970

4,980

4,989

4,999

6,008

6,018

7

5,194

5,205

5, 216

5,227

5,238

5,249

5,260

5,271

5,282

5,293

5,304

5,315

5,326

5,337

5,348

5,359

5,-370

5,381

5,392

5,403

5,414

5, 425

5,436

5, 447

5,458

5,469

5,480

5, 491

5,502

5,513

5,524

5,535

5, 546

5,557

5,568

5,579

5,590

5,601

5, 612

5,623

5, 634

5, 645

5, 656

5,667

5,678

5,689

5,700

5, 711

5, 722

5,733

5, 744

5,755

5,766

5,777

5,788

5,799

5,810

5,821

5,832

5,843

5,854

8

5,936

5,949

5,962

5, 974

5,987

5,999

6,012

6, 02-i

6,037

6,049

6,062

6,074

6,087

6,100

6,112

6,125

6, 137

6,150

6,162

6,175

6,187

6,200

6, 212

6,225

6, 237

6, 250

6,263

6, 275

6,288

6, SOO

6,313

6,325

6,338

6,351

6,363

6,376

6,388

6,401

6,414

6,426

6, 439

6,451

6,464

6,476

6, 489

6,501

6,514

6,527

6, 539

6,552

6, 564

6,577

6,590

6,602

6,615

6,627

6,640

6, 652

6, 665

6,678

6, 690

9

6,678

6,693

6,707

6,721

6,735

6,749

6,763

6,777

6,791

6,806

6,820

6,834

6,848

6,862

6,876

6,890

6,904

6,918

6,933

6,947

6,961

6,975

6,989

7, 003

7,017

7,031

7,045

7, 060

7,074

7,088

7,102

7,116

7,130-

7,144

7, 159

7, 173

7,187

7,201

7,215

7, 229

7, 243

7,258

7,272

7,286

7,300

7,314

7,328

7,342

7,357

7,371

7,385

7,399

7,413

7,427

7,442

7,456

7,470

7,484

7,498

7,512

7,526

Corrections for curvature, refraction, and 

height of instrument."

Miles.

1.6

2.1

2.5

2.8

3.1

3.4

3.6

3.8

4.1

4.3

4.5

4.7

4.8

6.0

5.2

5.4

5.5

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10.0

10.1

Feet.

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

GO

61

62

63

Miles.

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

11.1

11.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

12.0

12. 1

12.2

12.3

12.4

12.5

12.6

12. 7

12.8

12.9

13.0

13.1

13.2

13.3

13.4

13.5

13. 6

13.7

13.8

13.9

14.0

14. 1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15.0

15.1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

16.9

16.0

Feet.

64

65

67

68

69

70

71

73

74

75

77

78

79

80

82

83

84

86

 87

89

90

91

93

94

96

97

99

100

102

103

105

106

108

109

111

112

114

115

117

119

120

122

124

125

127

129

130

132

134

335

137

139

. 141

142

144

146

148

150

151

a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument 

is assumed 4.5 feet.
346 GEOGBAPHIO TABLES AND FORMULAS.

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

9°

0

1

2

8

4

5

6

7

8

9

10

11

12

J.3

14

15

16

17

18

19

20-

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

1

836.3

837.8

839.4

841.0

842.6

844.2

845.7

847.3

848.9

850. 5

852.0

853.6

855.2

856.8

858.3

859.9

861.5

863.1

864.7

866.2

867.8

869.4

871.0

372.5

874.1

875.7

877.3

878.8

880.4

882.0

883.6

885.2

886.7

888.3

889.9

891. 5

893.1

894.6

896.2

897.8

899.4

901.0

902.5

904.1

905.7

907.3

908.9

910.5

912.0

913.6

915.2

916.8

918.4

919.9

921.5

923.1

924.7

926.3

927.8

929.4

931.0

._!

1,673

1, 676

1,'679

1,682

1,685

1,688

1,691

1,695

1,698

1,701

1,704

1,707

1,710

1,714

1,717

1,720

1, 723

1,726

1,729

1,732

1,736

1,739

1,742

1,745

1,748

1,751

1,755

1,758

1,761

1,764

1,767

1, 770

1,774

1,777

1,780

1,783

1,786

1,789

1,792

1,796

1,799

1,802

1,805

1,808

1,811

1,814

1,818

1,821

1,824

1,827

1,830

1,833

1,837

1,840

1,843

1,846

1,849

1,852

1,855

1,859

1,862

8

2,509

2,514

2,518

2,523

2,528

2,532

2,537

2,542

2,547

2,551

2,556

2,561

2,566

2,570

2,575

2,580

2,585

2,589

2,594

2, 599

2,603

2,608

2,613

2,618

2,622

2,627

2,032

2,637

2,641

2,646

2,651

2, 656

2, 660'

2,665

2,670

2,674

2,679

2,684

2,689

2,693

2,698

2,703

2,708

2,712

2,717

2,722

2,727

2,731

2,736

2,741

2,746

2,750

2,755

2, 760

2, 765

2,769

2,774

2,779

2,784

2,788

2, 793

4

3,345

3,351

3,358

3,364

3,370

3,377

3,383

3,389

3,396

3,402

3,408

3,414

3,421

3,427

3,433

3,440

3,446

3,452

3,459

3,465

3,471

3,478

3,484

3,490

3,496

3,503

3,509

3,515

3,522

3,528

3,534

3,541

3j547

3,553

3,560

3,566

3,572

3,579

3, 585

3,591

3,598

3,604

3,610

3,617

3,623

3,629

3,636

3,642

3,648

3,654

3,661

3,667

3,673

3,680

3,686

3,692

3,699

3,705

3,711

3,718

3, 724

5

4,181

4,189

4,197

4,205

4,213

4.221

4,229

4,237

4,244

4,252

4,260

4, 268

4,276

4,284

4,292

4,300

4,308

4,315

4,323

4, 331

4,339

4,347

4,355

4,363

4,371

4,379

4,386

4,394

4,402

4,410

4,418

4,426

4,434

4,442

4,450

4,457

4,465

4,473

4,481

4,489

4,497

4,505

4,513

4,521

4,529

4,537

4,544

4,552

4,560

4,568

4,576

4,584

4,592

4,600

4,608

4,616

4,623

4,631

4,639

4,647

4,655

0

5,018

5,027

5,037

5, 046

5,055

5, 065

5, 074

5,084

5,093

5,103

5,112

5, 122

5, 131

5,141

5,150

5, 160

5, 169

5, 179.

5,188

5, 197

5,207

5,216

5,226

5,235

5,245

5,254

5,264

5,273

5,283

5,292

5,302

5,311

5,320

5,330

5,339

5,349

5, 358

5,368

5,377

5,387

5,396

5,406

5,415

5,425

5,434

5,444

5,453

5,463

5,472

5,482

5,491

5,501.

5,510

5,520

5,529

5,539

5,548

5,558

5,567

5,577

5,586

7

5,854

5,865

5,876

5,887

5,898

5,909

5,920

5,931

5,942

5,953

5,964

5,975

5, 986

5, 997

6,008

6, 020

6,031

6,042

6,053

6,064

6,075

6,086

6,097

6,108

6,119

6,130

6,141

6, 152

6,163

6,174

6,185

6,196

6,207

6,218

6,229

6,240

6, 252

6,263

6, 274

6,285

6,296

6,307

6,318

6,329

6,340

6,351

6,362

6,373

6,384

6,395

6,406

6,417

6,429

6,440

6,451

6,462

6,473

6, 484

6,495

6,506

6,517

S

6,690

6,703

6,715

6,728

6,741

6,753

6,766

6,778

6,791

6,804

6,816

6,829

6,842

6,854

6,867

6,879

6,892

6,905

6,917

6,930

6,943

6, 955

6,968

6,980

6,993

7,006

7,018

7,031

7,043

7,056

7,068

7,081

7,094

7,107

7,119

7,132

7,145

7,157

7,170

7,183

7,195

7,208

7,220

7,233

7,246

7,258

7,271

7,284

7,296

7,309

7,322

7,334

7,347

7,360

7,372

7,385

7,397

7,410

7,423

7,435

7,448

!)

7,526

7, 541

7,555

7,569

7,583

7, 597

7,612

7,626

7,640

7,654

7,668

7, 683

7,697

7,711

7,725

7,739

'7, 754

7,768

7,782

7,796

7,810

7,825

7,839

7,853

7,867

7,881

7,896

7,910

7,924

7,938

7,952

7,967

7, 981

7,995

8,009

8,023

8,038

8,052

8,066

8,080

8,095

8,109

8,123

8,137

8, 151

8,166

8, 180

8,194

8,208

8,223

8,237

8,251

8,265

8,279

8,294

8,308

8,322

8,336

8,351

8,365

8,379

Corrections for curvature, refraction, and 

height of instruments

Miles.

1.6

2.1

2.5

2.8

3.1

3.4

3.6

3.8

4.1

4.3

4.5

4.7

4.8

5.0

5.2

5.4

5.5

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10.0

10.1

Feet.

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

60

61

62

63

Miles.

10.2

10.3

10.4

10.5

10.6

30.7

10.8

10.9

11.0

11.1

11.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

12.0

12.1

12.2

12.3

12.4

12.5

12.6

12.7

12.8

12.9

13.0

13.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15.0

15.1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16.0

Feet.

64

65

67

68

69

70

71

73

74

75

77

78

79

80

82

83

84

86

87

89

90

91

93

94

96

97

99

100

102

103

105

106

108

109

111

112

114

115

117

119

120

122

124

125

127

129

130

132

134

135

137

J39

141

. 142

144

146

148

150

151

a For all distances under 1.6 miles the correction may be taken as -f 5 feet. Height of instrument 

is assumed 4.5 feet.
GEOGRAPHIC TABLES AND FORMULAS. 347

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

10°

0

1

2

3

4

5

0

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51.

52

53

54

55

56

57

58

59

60

1

931.0

932.6

934.2

935. 8

937.4

938.9

940.5

942.1

943.7

945.3

946.9

948.5

950.0

951.6

QKQ <) yjd. L

954.8

956.4

958.0

959.6

961.1

962.7

964.3

965.9

967.5

969.1

970.7

'972. 2

973. 8

975.4

977.0

978.6

980.2

981.8

983.4

985.0

986.5

988.1

989. 7

99.1.8

992.9

994.5

996.1

997.7

999.3

1, 000. 9

1,002.5

1, 004. 0

3,005.6

1, 007. 2

1,008.8

1,010.4

1,012.0

1,013.6

1,015.2

1,016.8

1,018.4

1, 020. 0

1, 021. 5

1,023.1

1,024.7

1,026.3

2

1,862

1,865

1, 868

1,872

1,875

1,878

1,881

1,884

1,887

1,891

1,894

1,897

1,900

1,903

1,906

1,910

1,913

1, 916

1,919

1,922

1,926

1,929

1,932

1,935

1,938

1,941

1,944

1,948

1,951

1,954

1,957

1,960

1,964

1,967

1,970

1,973

1,976

1,980

1,983

1,986

1,989

1,992

1,995

1,999

2,002

2, 005

2,008

2,011

2,014

2,018

2,021

2, 024

2,027

2,030

2,034

2,037

2,040

2,043

2,046

2,049

2,053

3

2,793

2,798

2,803

2,807

2, 812

2,817

2,822

2,826

2, 831

2,836

2,841

2,845

2,850

2,855

2,860

2,864

2,869

2,874

2,879

2,883

2,888

2,893

2, 898 '

2,902

2,907

2,912

2,917

2,921

2,926

2,931

2, 936

2,941

2,945

2, 950

2,955

2, 960

2,964

2,969

2, 974

2, 979

2,984

2,988

2,993

2, 998

3,003

3,007

3,012

3,017

3,022

3, 026

3,031

3,036

3,041

3,046

3,050

3,055

3, 060

3,065

3,069

3,074

3,079

4

3,724

3,730

3,737

3,743

3,749

3, 756

3,762

3,768

3,775

3,781

3,787

3,794

3,800

3,807

3,813

3; 819

3,826

3,832

3,838

3,845

3,851

3,857

3,864

3,870

3, 876

3,883

3,889

3,895

3,902

3,908

3, 914

3,921

3,927

3,933

3,940

3,946

3,953

3, 959

3,965

3,972

3,978

3,984

3,991

3,997

4,003

4,010

4,016

4,023

4,029

4,035

4,042

4,048

4,054

4,061

4,067

4,073

4,080

4,086

4,093

4,099

4, 105 .

5

4,655

4,663

4,671

4,679

4,687

4,695

4,703

4,711

4,718

4, 726

4,734

4,742

4,750

4,758

4,766

4,774

4,782

4,790

4,798

4,806

4,814

4,822

4,830

4,837

4,845

4,853

4,861.

4,869

4 877

4,885

4,893

4,901

4,909

4,917

4,925

4,933

4,941

4,949

4,957

4,965

4,973

4,980

4,988

4,996

5,004

5,012

5,020

5,028

5,036

5,044

5,052

5,060

5,068

5, 076

5,084

5,092

5, 100

5,108

5,116

5,124

5,132

8

5,586

5,596

5,605

5,615

5,624

5,634

5,643

5,653

5,662

5, 672

5,681

5, 691

5,700

5,710

5,719

5,729

5,738

5,748

5,757

5,767

5,776

5,786

5,795

5,805

5,814

5,824

5,833

5,843

5,853

5, 862

5,872

5,881

5,891

5, 900

5,910

5, 919

5,929

5, 938

5,948

5, 957

5,967

5,977

5,986

5,996

6,005

0,015

6,024

6,034

6,043

6,053

6,002

6,072

6,082

6,091

6,101

6,110

6,120

6,129

6,139

6,148

6,158

7

6,517

6,528

6,539

0,550

6,561

6,573

6.5H4

6, 595

6,606

6,617

6, 628

6,639

6,650

6,661

0,672

6,684

6, 695

6,706

6,217

6,728

6,739

6,750

6,751

6,772

6,784

6,795

6,806

6,817

6,828

6,839

6,850

6,861

6,872

6,884

6, 895

6, 906

6,917

6,928

6,939

6,950

6,962

6,973

6,984

6,995

7,006

7,017

7,028

7,039

7,051

7,062

7,073

7,084

7,095

7,106

7,117

7,129

7,140

7,151

7,162

7,173

7,184

8

7,448

7,461

7,473

7,486

7, 499

7,512

7, 524

7,537

7, 550

7,562

7, 575

7,588

7,600

7,613

7,620

7,638

7, 651

7,664

7,676

7,689

7,702

7,715

7, 727

7,740

7,753

7,765

7,778

7,791

7,803

7,816

7,829

7,841

7,854

7,867

7,880

.7, 892

7,905

7,918

7,931

7,943

7,956

7, 969

7,981

7,994

8,007

8,020

8,032

8,045

8,058

8,071

8,083

8,096

8,109

8,121

8,134

8,147

8,160

8,172

8,185

8,198

8,211

0

8,379

8,393

8,408

8,422

8,436

8,450

8,465

8,479

8,493

8,508

8,522

8,536

8,550

8, 665

8,579

8,593

8,607

8,622

8,636

8,650

8,665

8,679

8,693

8,707

8,722

8,736

8,750

8,764

8,779

8,793

8,807

8,822

8,836

8,850

8,865

8,879

8,893

8,908

8,922

8,936

8,951

8,965

8,979

8,993

9,008

9,022

9,036

9,051

9,065

9,079

9,094

9,108

9,122

9,137

9, 151

9, 165

9,180

9, 194

9,208

9,223

9,237

Corrections for curvature, refraction and 

height of instrument.a

Miles.

1.6

2.1

2.5

2.8

3.1

3.4

3.6 3.8'

4.1

4.3

4.5

4.7

4.8

6.0

5.2

5.4

5.5

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.0

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10.0

10.1

Feet.

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

20

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

60

61

62

63

Miles.

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

11.1

11.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

12.0

12.1

12.2

12.3

12.4

12.5

12.6

12.7

12. 8 

12.9

13.0

13.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

1.4.0

14.1

14.2

14.4

14.3

14.5

14.6

14.7

14.8

14.9

15.0

15.1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16.0

Feet.

64

65

67

68

69

70

71

73

74

75

77

78

79

80

82

83

84

86

87

89

90

91

93

94

 96

97

99

100

102

103

105

106

108

109

111

112

11.4

115

117

119

120

122

124

125

127

129

130

132

134

135

137

139

141

142

144

146

148

150

151.

« For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument 

Is assumed 4.5 feet.
348 GEOGEAPHIO TABLES AND FORMULAS.

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

11°

1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

CO

1

1, 026. 3

1,027.9

1,029.5

1,031.1

1,032.7

1, 034. 3

1,036

1,038

1,039

1,041

1,042

1,044

1,045

1,047

1,049 .

1,050

1,052

1,053

1,055

1,057

1,058

1,060

1,061

1,063

1,065

1,066

1, 068

1,069

1,071

1,073

1,074

1,076

1,077

1,079

1,081

1,082

1,084

1,085

1,087

1,089

1,090

1,092

1,093

1,095

1,097

1, 098

1,100

1,101

1,103

l;105

1,106

1, 108

1,109

1,111

1, 113

1,114

1,116

1,117

1,119

1,121

1,122

2

2,053

2,056

2,059

2,062

2,065

2,069

2,072

2,075

2,078

2,081

2,085

2,088

2,091

2, 094

2, 097

2,101

2, 104

2,107

2,110

2,113

2,117

2,120

2,123

2,126

2,129

2,133

2,136

2,139

2,142

2,145

2,148

2,152

2,156

2, 158

2, 161

2,164

2,168

2,] 71

2,174

2, 177

2,181

2,184

2,187

2,190

2,f93

2, 197

2,200

2,203

2,206

2,209

2,213

2,216

2,219

2,222

2,225

2, 229

2,232

2,235

2,238

2,241

2,245

3

3,079

3,084

3,089

3,093

3,098

3,103

3,108

3,113

3, 117

3,122

3,127

3,132

3,136

3,141

3,146

3,151

3,156

3,160

3,165

3,170

3,175

3,180

3, 184

3,189

3,194

3,199

3,204

3,208

3,213

3,218

3,223

3,227

3,232

3,237

3,242

3,247

3,252

3,256

3,261

3,266

3,271

3,276

3,280

3,285

3,290

3,295

3,300

3,304

3,309

3, 314

3,319

3,324

3,328

3,333

3,338

3,343

3,348

3,352

3,357

3,362

3,367

4

4,105

4, 112

4,118

4,124

4,131

4,137

4,144

4,150

4,156

4,163

4,169

4,176

4, 182

4,188

4,195

4,201

4,208

4,214

4,220

4,227

4,233

4,239

4,246

4,252

4, 259

4,265

4,271

4, 278

4,284

4,291

4,297

4,303

4,310

4,316

4,323

4,329

4,335

4,342

4,348

4,355

4,361

4,367

4,374

4,380

4,387

4,393

4,399

4,406

4,412

4,419

4,425

4, 431

4,438

4,444

4,451

4,457

4,464

4,470

4,476

4,483

4,489

5

5,132

5,140

5,148

5,156

5,164

5,172

5,180

5,188

5,196

5,204

5,212

5,219

5, 227

5, 235

5,243

5,251

5,259

5,267

5,275

5,283

5,291

5,299

5,307

5,315

5,323

5,331

5,339

5,347

5, 355

5,363

5,371

5,379

5,387

5,395

5,403

5,411

5, 419

5,427

5,435

5,443

5,451

5,459

5,467

5,475

5,483

5,491

5,499

5,507

5,515

5,523

5,531

5,539

5,547

5,555

5,563

5,571

5,579

5,587

5, 595

5,603

5,611

6

6,158

6,168

6, 177

6,187

6, 196

6,206

6,215

6, 225

6,235

6,244

6,254

6,263

6,273

6,283

6,292

6,302

6,311

6,321

6,330

6,340

6,350

6,359

6,369

6, 378

6,388

6,398

6,407

6,417

6,426

6,436

6,445

6,455

6, 465

6,474

6,484

6,493

6,503

6,513

6,522

6,532

6,542

6, 551

6, 561

6,570

6,580

6,590

6,599

6,609

6, 618

6,628

6,638

6,647

6, 657

6,666

6,676

6,686

6,695

6,705

6, 715

6,724

6,734

7

7,184

7,195

7,207

7,218

7,229

7, 240

7,251

7,263

7,274

7,285

7,296

7,307

7,318

7,330

7,341

7,352

7,363

7,374

7,386

7,397

7,408

7,419

7,430

7,441

7,453

7,464

7,475

7,486

7,497

7,509

7,520

7,531

7,542

7,553

7,564

7,576

7.587

7,598

7,609

7,621

7,632

7,643

7,654

7,665

7,677

7,688

7,699

7,710

7, 721.

7,733

7,744

7,755

7,766

7,778

7,789

7,800

7,811

7,822

7,834

7,845

7,856

8

8,211

8,223

8,236

8, 249

8,262

8, 275

8,287

8,300

8,313

8,326

8,338

8,351

8,364

8,377

8,390

8,402

8,415

8,428

8,441

8,453

8,466

8,479

8,492

8,504

8,517

8,530

8,543

8,556

8,568

8,581

8,594

8,607

8,619

8,632

8,645

8,658

8,671

8,683

8,696

8,709

8,722

8, 735

8,748

8,760

8,773

8,786

8,799

8,812

8,825

8,837

8,850

8,863

8,876

8,889

8,901

8,914

8,927

8,940

8,953

8,966

8,978

9

-9, 237

9,251

9,266

9,280

9,294

9,309

9,323

9,338

9,352

9,366

9,381

9,395

9,409

9,424

9,438

9,453

9,467

8,481

9,496

9,510

9,524

9,539

9,553

9,568

9,582

9,596

9,611

9,625

9,639

9,654

9,668

9,682

9,697

9,711

9, 726

9,740

9,755

9,769

9,783

9,798

9/812

9,827

9,841

9,856

9,870

9,884

9,899

9,913

9,928

9,942

9,956

9,971

9,985

10, 000

10, 014

10,029

10, 043

10, 057

10,072

10, 086

10,101

Corrections for curvature, refraction, and 

height of instrument.a

Miles.

1.6

2.1

2.5

2.8

3.1

3.4

3.6

3.8.

4.1

4.3

4.5

4.7

4.8

5.0

5.2

5.4

5.5

5.7

. 5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7.

9.8

9.9

10.0

10.1

Feet.

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

60

61

62

63

Miles.

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

11.1

11.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

12.0

12.1

12. 2

12.3

12.4

12.5

12.6

12.7

12.8

12.9

13.0

33.1

J3.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

14.0

14.1

14. 2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15.0

15.1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16.0

Feet.

64

65

67

68

69

70

71

73

74

 75

77

78

79

80

82

83

84

86

87

89

90

91

93

94

96

97

99

100

102

103

105

106

108

109

111

112

114

115

117

119

120

122

124

125

127

129

130

132

134

135

137

139

141

142

144

146

148

150

151

a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument 

is assumed 4.5 feet.
GEOGRAPHIC TABLES AND FOKMULAS. 349 

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

12°

0

1

2

3

4

5

6

7

8

9

.10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25 ' 26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

. 46

47

48

49

'5150

52

 53

54

55

56

57

58

59

GO

1

1, 122

1,124

1, 126

1,127

1,129

1,130

1,132

1, 134

1, 135

1,137

1, 138

1,140

1, 142

1,143

1, 145

1, 140

1, 148

1,150

1,151

1,153

1,154

1,156

1,158

1,159

1,161

1,163

1,164

1,166

1, 167

1,169

1,171

1, 172

1,174

1,175

1,177

1,179

1,180

1,182

1,183

1,185

1,187

1, 188

1, 190

1, 192

1,193

1,195

1,196

1,198

1,200

1,201

1,203

1,204

1,206

1,208

1,209

1,211

1,213

1,214

1,216

1,217

* 1,219

2

2,245

2,248

2,251

2,254

2,257

2,261

2,264

2, 267

2,270

2, 274

2,277

2,280

2,283 2,28e

2,290

2, 293

2, 296

2, 299

2,302

2,306

2,309

2,312

2,315

2,319

2, 322

2,325

2,328

2,331

2,335

2,338

2,341

2,344

2,348

2,351

2,354

2,357

2,360

2,364

2,367

2,370

2,373

2,377

2,380

2,383

2,386

2,390

2,393

2,396

2,399

2, 402

2,406

2,409

2,412

2,415

2,419

2,422

2,425

2,428

2,431

2,435

2,438

3

3,367

3,372

3,377

3,381

3,386

3,391

3,396

3, 401

3, 405

3,410

3, 415

3,420

3,425

3,430

3,434

3, 439

3, 444

4

4,489

4,496

4, 502

4,508

4, 515

4,521

4, 528

4,534

4,541

4,547

4, 554

4, 560

4,566

4/573

4,579

4, 586

4,592

3,449 1 4,599

3,454

3,459

3,463

3,468

3,473

3, 478

3,483

3,487

3,492

3,497

3,502

3, 507

3,512

3,516

3,521

3,526

3, 531

3,536

3,541

3,546

3,550

3, 555

3,560

3, 565

3,570

3,575

3,579

3,584

3,589

3, 594

3,599

3,604

3,608

3, 613

3,618

3,623

3,628

3,633

3,638

3, 642

3,647

3,652

3,657

4,605

4,611

4,618

4, 624

4,631

4, 637

4,644

4,650

5

5, 612

5,620

5, 628

5,636

5, 644

5,652

5,660

5, 668

5, 676

5,684

5,692

5, 700

5,708

5,710

5, 724

5,732

5,740

5,748

5,756

5,764

5,772

5,780

5,788

5,796

5,804

5,812

4, 656 5, 821

4,663 6,829

4,669

4,676

4,682

4,689

4,695

4,702

4,708

4,714

4,721

4,727

4,734

4,740

4,747

4,753

4,760

4,766

4,773

4,779

4,785

4,792

4,798

4,805

4,811

4,818

4,824

4,831

4,837

4,844

4,850

4,857

4,863

4,869

4,876

5,837

5,845

5,853

5,861

5,869

5, 877

5,885

5,893

5,901

5,909

5,917

5,925

5,933

5,942

5,950

5,958

5,966

5,974

5,982

5,990

5,998

6,006

6, 014

6,022

6,030

6,038

6,046

6,055

6,063

e, on

6,079

6,087

6,095

(>

6, 734

6,743

6,753

6, 763

6,772

6, 782

6, 792

6, 801

6, 811

6, 821

6, 830

6,840

6,850

0,859

6,869

G, 879

6,888

6, 898

6,907

6, 917

6,927

6,936

6,946

6,956

6, 965

6,975

6,985

6, 994

7,004

7,014

7,023

7,033

7,043

7,052

7,062

7,072

7,081

7,091

7,101

7,110

7,120

7,130

7,140

7,149

7,159

7, 169

7,178

7,188

7,198

7, 207

7,217

7,227

7,236

7,246

7,256

7,265

7, 275

7,285

7,294

7,304

7,314

7

7,856

7,867

7,879

7,890

7,901

7,912

7,924

7,935

7,946

7,957

7, 969

7, 980

7,991

8,002

8,014

8,025

8, 036

8,047

8,059

8,070

8,081

8,092

8,104

8, 115

8,126

8,138

8,149

8,160

8,171

8,183

8,194

8,205

8,216

8,228

8,239

8,250

8, 262

8,273

8,284

8,296

8,307

8,318

8,329

8,341

8,352

8,363

8,375

8,386

8,397

8,409

8,420

8,431

8,442

8,454

8,465

8,476

8,488

8,499

8, 510

8,521

8,533

8

8,978

8, 991

9,004

9,017

9,030

9,043

9, 056

9,068

9,081

9,094

9,107

9, 120

9,133

9,140

9,158

9,171

9, 184

9,197

9,210

9,223

9,236

9,249

9,261

9,274

9,287

9,300

9,313

9,326

9,339

9,351

9,364

9,377

9,390

9,403

9,416

9,429

9,442

9,455

9,468

9,481

9,494

9,506

9,519

9,532

9,545

9,558

9, 571

9,584

9,597

9,610

9,623

9,636

9, 648

9,661

9,674

9, 687

9,700

9,713

9,726

9,739

9, 752

{)

10, 101

10,115

10, 130

10, 144

10,159

10, 173

10, 188

10,202

10, 216

10,231

10, 245

10,260

10, 274

10,289

10,303

10, 318

10,332

10, 347

10, 361

10, 376

10, 390

10,405

10,419

10, 434

10,448

10,463

10, 477

10, 491

10, 506

10, 520

10, 535

10,549

10,564

10, 579

10, 593

10, 608

' 10, 622

10, 637

10, 651

10, 666

10,680

10, 695

10, 709

10,724

10,738

10, 753

10, 767

10, 782

10, 796

10, 811

10, 825

10,840

10, 855

10, 869

10, 884

10, 898

10, 913

10, 927

10, 942

10, 956

10, 971

Corrections for curvature, refraction, and 

heightofinstrument.fi

Milan.

1.6

2.1

2.5

2.8

3.1

3.4

3.6

3.8

4.1

4.3

4.5

17

4.8

5.0

5.2

545*

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10.0

10.1

Feet.

6

7

8

9

10

11

12

13

14

15

16

17

1.8

19

20

21.

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

60

61

62

63

Miles.

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

11.1

11.2

11.3

11.4

11. 5

11. 6

11.7

11.8

11.9

12.0

12.1

12.2

12.3

12.4

12.5

12.6

12.7

12.8

12.9

13.0

13.1

13. 2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

14,0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15.0

15. 1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16.0

Feet.

64

65

67

68

69

70

71

73

74

75

77

78

79

so

h2s;i

84

80

87

89

90

91

93

94

96

97

99

100

102

103

105

106

108

109

111.

11.2

114

11.5

117

119

120

122

124

 125

127

129

130

132

134

135

137

139

141

142

144

1.46

148

150

151

a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument 

is assumed 4.5 feet.
350 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

13°

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

1

1,219

1,221

1,222

1,224

1,225

1,227

1,229

1,230

1,232

1,234

1,235

1,237

1,238

1, 240

1, 243

1,243

1,245

1,247

1,248

1,250

1,251

1,253

1,255

1,256

1,258

1,260

1,261

1, 263

1,264

1,266

1,268

1,269

1,271

1,273

1,274

1,276

1,277

1,279

1,281

1,282

1,284

1,286

1,287

1,289

1,290

1,292

1, 294

1,295

1,297

1,299

1,300

1,302

1,303

1,305

1,307

1,308

1,310

1,312

1,313

1,315

1,316

2

2,438

2, 441

2,444

2,448

2,451

2,454

2,457

2,461

2,464

2,467

2,470

2,474

2,477

2,480

2,483

2,487

2, 490

2,493

2,496

2,500

2,503

2,506

2,509

2,513

2,516

2, 519

2, 522

2,525

2,529

2,532

2,535

2,538

2,642

2,545

2,548

2,551

2,555

2,558

2,561

'2,565

2,568

2,571

2,574

2,578

2,581

2, 584

2,587

2,591

2,594

2,597

2,600

2,604

2,607

2,610

2,613

2,617

2, 620

2,623

2,626

2,630

2,633

8

3,657

3,662

3,667

3,672

3,676

3,681

3,686

3,691

3,696

3,701

3,706

3,710

3,715

3,720

3,725

3,730

3,735

3,740

3,744

3,749

3,764

3,759

3,764

3,769

3,774

3,779

3,783

3,788

3,793

3,798

3,803

3,808

3,813

3,817

3,822

3,827

3,832

3,837

3,842

3,847

3,852

3,857

3,861

3,866

3,871'

3,876

3,881

3,886

3,891

3,896

3.900

3)905

3,910

3,915

3,920

3,925

3,930

3,935

3,940

3,944

3,949

4

4,876

4,882

4,889

4,895

4,902

4,908

4,915

4,921

4,928

4,934

4,941

4,947

4,954

4,960

4,967

4,973

4,980

4,986

4,993

4,999

5,006

5,012

5,019

5,025

5,032

5,038

5,044

5,051

5,057

5,064

5,070

5,077

5,083

5,090

5,096

5,103

5,109

5,116

5,122

5,129

5,135

5,142

5,149

5,155

5,162

5,168

5,175

5,181

5,188

5,194

5,201

5,207

5,214

5,220

5,227

5,233

5,240

5,246

5,253

5,259

5,266

5

6,095

6,103

6,111

6,119

6,127

6,135

6,143

6,152

6,160

6,168

6,176

6,184

6,192

6,200

6,208

6,216

6,224

6,233

6, 241

6,249

6,257

6,265

6,273

6,281

6, 289

6,297

6,306

6,314

6,322

6,330

6,338

6,346

6,354

6,362

6,371

6,379

6,387

6,395

6,403

6,411

6,419

6,427

6,436

6,444

6,452

6,460

6,468

6,476

6,484

6,493

6,501

6,509

6,517

6,525

6,533

6,541

6,550

6,558

6,566

6,574

6,582

6

7,314

7,324

7,333

7,343

7,353

7,362

7,372

7,382

7,392

7,401

7, 411

7,421

7,430

7,440

7,450

7,460

7,469

7,479

7,489

7,499

7, 508

7,518

7,528

7, 537

7,547

7,557

7,567

7,576

7,586

7,596

7,606

7,615

7,625

7,635

7,645

7,654

7,664

7,674

7,684

7,693

7,703

7,713

7,723

7,732

7,742

7,752

7,762

7,771

7,781

7, 791

7,801

7,811

7,820

7,830

7,840

7,850

7,859

7,869

7,879

7,889

7,899

7

8,533

8,544

8,556

8,567

8,578

8,590

8,601

8,612

8,624

8,635

8,646

8,658

8,669

8,680

8,692

8,703

8,714

8,726

8,737

8,748

8,760

8,771

8, 782

8,794

8,805

8,816

8,828

8,839

8,851

8,862

8,873

8,885

8,896

8,907

8,919

"8,930

8,942

8,953

8,964

8,976

8,987

8,999

9,010

9,021

9,033

9,044

9,055

9,067

9,078

9,090

9,101

9,112

9,124

9,135

9,147

9,158

9,170

9,181

9,192

9, 204

9,215

8

9,752

9,765

9,778

9,791

9,804

9,817

9,830

9,843

9,855

9,868

9,881

9,894

9,907

9,920

9,933

9,946

9,959

9,972

9,985

9,998

10,011

10, 024

10, 037

10, 050

10,063

10,076

10, 089

10, 102

10, 115

10,128

10, 141

10,154

10, 167

10, 180

10, 193

10, 206

10, 219

10, 232

10, 245

10, 258

10, 271

10,284

10, 297

10,310

10, 323

10, 336

10, 349

10, 362

10, 375

10,388

10, 401

10,414

10, 427

10, 440

10,453

10,466

10, 479

10,492

10, 506

10,519

10, 532

10,971

10, 985

11,000

11,015

11,029

11, 044

11,058

11, 073

11, 087

11, 102

11, 117

11,131

11,146

11, 160

11,175

11,190

11, 204

11, 219

11, 233

11, 248

11,262

11,277

11, 292

11, 306

11, 321

11, 336

11,350

11, 365

11,379

11,394

11,409

11, 423

11,438

11, 452

11,467

11, 482

11, 496

11,511

11,526

11, 540

11,555

11, 569

11,584

11,599

11, 613

11,628

11, 643

11, 657

11,672

11,687

11,701

11,716

11, 731

11,745

11, 760

11,775

11, 789

11,804

11, 819

11,833

11,848

Corrections for curvature, refraction, and 

height of instruments

Miles.

1.6

2.1

2.5

2.8

3.1

3.4

3.6

3.8

4.1

4.3

4.5

4.7

4.8

5.0

5.2

5.4 -5.5

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

'9.7 9.6

9.8

9.9

10.0

10.1

Feet.

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

60

61

62

63

Miles.

10.2

10.3

10.4

10.5

10. 6

10.7

,10.8

10.9

11.0

11.1

11.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

12.0

12.1

12.2

12.3

12.4

12.5

12.6

12.7

12.8

12.9

13.0

13.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

14.0

14.1

14.2

14.3

14.4

14.5

14.6

.14.7

14.8

14.9

15.0

15.1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16.0

Feet.

64

65

67

68

69

70

71

73

74

76

77

78

79

80

82

83

84

86

87

89

90

91

93

94

96

97

99

100

102

103

105

106

108

109

111

112

114

115

117

119

120

122

124

125 127-

129

130

132

134

135

137

139

141

142

144

146

148

150

. 151

a For all distances under 1.6 miles the correction may be taken as + 5 feet. Height of instrument 

i§ assumed 4-5 feet.
GEOGRAPHIC TABLES AND FOKMULAS. 351

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

14°

1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

10

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

19

50

51

52

53

54

55

5C

57

58

59

60

1

1,316

1,318

1,320

1,321

1,323

1,325

1,326

1,328

1,330

1 , 331

1,333

1, 334

1, 336

1,338

1,339

1,341

1,343

1,344

1,346

1,348

1,349

1,351

1, 352

1,354

1, 356

1,357

1,359

1,361

1,362

1,364

1 , 306

1,367

1,369

1,370

1,372

1,374

1,375

1,377

1,379

1,380

1,382

1,384

1,385

1,387

1,388

1,390

1,392

1,393

1,395

1,397

1,398

1,400

1,402

1,403

1,405

1,407

1,408

1,410

1,411

1,413

1, 415

2

2,633

2,636

2,639

2,643

2,646

2,649

2,653

2,656

2, 659

2, 662

2,666

2,669

2,672

2,675

2,679

2,682

2,685

2,688

2,692

2,695

2,698

2,702

2,705

2,708

2, 711

2,715

2, 718

2,721

2,724

2,728

2,731

2,734

2,738

2,741

2, 744

2,747

2,751

2,754

2,757

2,761

2,764

2,767

2,770

2, 774

2, 777

2,780

2,784

2,787

2,790

2,793

2,797

2,800

2,803

2,807

2, 810

2,813

2,816

2,820

2,823

2, 826

2, 830

8

3,949

3,954

3,959

3,964

3,969

3,974

3, 979

3,984

3, 989

3,993

3,998

4,003

4,008

4,013

4,018

4, 023

4,028

4,033

4,038

4,042

4,047

4,052

4,057

4,062

4,067

4,072

4,077

4,082

4,087

4,092

4,097

4, 101

4,106

4,111

4,116

4,121

4,126

4, 131

4,136

4,141

4,146

4,151

4,156

4, 160

4,165

4,170

4,175

4,180

4,185

4,190

4,195

4,200

4,205

4,210

4, 215

4, 220

4,225

4,230

4,234

4,239

4,244

4

5,266

5, 272

5,279

5,285

5, 292

5,298

5, 305

5,312

5,318

5,325

5,331

5,338

5,344

5,351

5,357

5,364

5,370

5,377

5,383

5,390

5,397

5,403

5,410

5,416

5,423

5, 429

5,436

5,442

5,449

5,455

5,462

5,469

5,475

5,482

5,488

5,495

5, 501

5,508

5,514

5, 521

5,528

5,534

5,541

5,547

5,554

5,560

5, 567

5,574

5,580

5,587

5,593

5, 600

5, 606

5,613

5,020

6,626

5,633

5,639

5, 646

5, 653

5, 659

5

6,582

0,590

0,599

6,607

6,615

6,623

6,631.

6,639

6,648

6,056

6, 004

6,672

6,680

6,688

6,697

6, 705

6, 713

6,721

6,729

6,757

6,746

6,754

6,762

6,770

6,778

6,787

6,795

6,803

0,811

6,819

6,828

6,836

6,844.

6,852

6,860

6,868

6,877

6,885

6,893

0,901

6,910

6,918

6,926

6,934

6,942

6,951

6, 959

0,967

6,975

6,983

6,992

7,000

7,008

7,016

7,024

7,033

7,041

7,049

7,057

7,066

7,074

6

7,899

7,909

7,918

7,928

7,938

7,948

7,957

7,967

7,977

7,987

7,997

8,006

8,016

8,026

8,036

8,046

8,056

8, 065

8,075

8,085

8,095

8,105

8,114

8,124

8,134

8,144

8,154

8,164

8,173

8,183

8,193

8,203

8,213

8,223

8, 232

8,242

8,252

8, 262

8,272

8, 282

8,291

8,301

8,311

8, 321

8,331

8,341

8,351

8,360

8,370

8,380

8,390

8,400

8,410

8,420

8,429

8,439

8,449

8, 459

8,469

8,479

8,489

7

9,215

9, 227

9,238

9,249

9, 261

9,272

9,284

9, 295

9,307

9,318

9,329

9,341

9,352

9,364

9,375

9, 387

9,398

9, 410

9, 421

9,432

9,444

9,455

9.-4G7

9, 478

9, 490

9,501

9,513

9, 524

9,536

9,547

9,559

9,570

9,581

'9,593

9,604

9,616

9, 627

9,639

9, 050

9,662

9,073

9,085

9, 096

9,708

9.719

9; 731

9, 742

9,754

9, 765

9,777

9,788

9,800

9,811

9,823

9,834

9,846

9,857

9,869

9,880

9, 892

9,903

8

1.0, 532

10, 545

10, 558

10, 571

10,584

10, 597

10, 610

10, 623

10, 636

10, 649

1.0, 602

1.0, 675

10,688

10,701

10,715

10, 728

10, 741

10, 754

10, 767

10, 780

10,793

10, 800

10, 819

10, 832

10, 845

10, 859

10,872

10,885

10, 898

10, 911

10, 924

10, 937

10, 950

10, 963

10, 970

30,990

11,003

11,016

11, 029

11, 042

11, 055

11, 068

11, 081

11,095

11, 108

11,121

.11,134

11, 147

11, 160

11,173

11,187

11, 200

11, 213

11,226

11,239

11, 252

11,266

11,279

11, 292

11, 305

11, 318

9

11,848

11, 863

11, 877

11, 892

11,907

11, 923

11, 936

11, 951

11, 966

11,980

11,995

12, 010

12,024

12,039

12,054

12, 069

12, 083

12, 098

12, 113

12, 127

12,142

12,157

12, 172

12, 186

12. 201

12', 216

12, 231

12, 245

12, 260

12,275

12, 290

12, 304

12, 319

12, 334

12, 349

12, 363

12, 378

12, 393

12, 408

12,422

12, 437

12, 452

12, 467

12, 481

12, 496

12,511

12, 520

12,541

12,555

12, 570

12, 585

12, 000

12,015

12, 029

12, 644

12, 6f>9

12,674

12, 689

12, 703

12, 718

12, 733

Corrections for curvature, refraction, and 

heightofinstrnment.«

Miles.

1.6

2.1

2.5

2.8

3.1

3.4

3.0

3.8

4.1

4.3

4.5

4.7

4.8

5.0

5.2

5.4

5.5

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

0.8

0.9

7.0

7.2

7.3

7.4

7.5

7,6

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.0

9.7

9.8

9.9

10.0

10.1

Feel.

6

7

8

9

1.0

11

12

13

1.4

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

CO

61

62

63

MilCK.

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

11. 1

11. 2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

12.0

12.1

12.2

12.3

12.4

12.5

12. 6

12.7

12.8

12.9

13.0

13.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

1.4.0

14. 1

14.2

14. 3

14.4

14.5

14.0

1.4.7

.14.8

14.9

15.0

15.1.

15.2

15.3

15.4

15.5

15.0

15.7

1.5.8

15.9

10.0

Feel.

04

05

07

68

69

70

71

73

.74

76

77

78

79

80

82

83

84

86

87

89

90

91

93

94

96

97

99

100

102

103

105

1.06

108

109

111

112

114

115

117

119

120

122

124

.125

127

1.29

130

132

134

135

137

139

141

142

144

140

148

150

151.

a For all distances under 1.6 miles the correction may be taken as -(- 5 feet. Height of instrument 

is assumed 4.5 feet,
352 GEOGBAPHIC TABLES AND FORMULAS.

TABLE 35. For obtaining differences of altitude for any minute, etc. Continued.

15°

,

0

1

2

3

4

5

' 6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

1

1,415

1,416

1,418

1,420

1,421

1,423

1,425

1,426

1,428

1,430

1,431

1,433

1,435

1,436

1,438

1,439

1,441

1,443

1,444

1,446

1,448

1,449

1,451

1,453

1,454

1,456

1,458

1,459

1,461

1,463

1,464

1,466

1.468

1,469

1,471

1,473

1,474

1,476

1,478

1,479

1,481

1,482

1.484

1,486

1,487

1,489

1,491

1,492

1,494

1,496

1,497

1,499

1,501

1,502

1,504

1, 506

1,507

1,509

1,511

1,512

1,514

2

2,830

2,833

2,836

2,839

2,843

2,846

2,849

2,853

2,856

2,859

2,862

2, 866

2,869

2,872

2,876

2,879

2,882

2,886

2,889

2,892

2,896

2,899

2,902

2,905

2,909

2,912

2,915

2,919

2,922

2,925

2,928

2,932

2,935

2,938

2,942

2,945

2,948

2,952

2.955

2,958

2,962.

2,965

2,968

2,972

2,975

2,978

2,982

2,985

2,988

2,992

2,995

2,998

3,001

3,005

3,008

3,011

3,015

3,018

3,021

3,025

3,028

3

4,244

4,249

4,254

4.259

4,265

4,269

4,274

4,279

4,284

4,289

4,294

4,299

4,304

4,309

4,314

4,319

4,323

4,328

4,333

4,338

4,343

4,348

4,353

4,358

4,363

4,368

4,373

4,378

.4,383

4,388

4,393

4,398

4,403

4,408

4,413

4,418

4,423

4,428

4,432

4,438

4,442

4,447

4,452

4,457

4,462

4,467

4,472

4,477

4,482

4,487

4,492

4,497

4,502

4,507

4,512

4,517

4,522

4,527

4,532

4,537

4,542

4

5,659

5,666

5,672

5,679

5,685

5,692

5,699

5,705

5,712

5,718

5,725

5,732

5,738

5,745

5,751

5,758

5,765

5,771

5,778

5,784

5,791

5,798

5,804

5,811

5,817

5,824

5,831

5,837

5,844

5,850

5,857

5,864

5,870

5,877

5,884

5,890

5,897

5,903

5,910

5,917

5,923

5,930

5,937

5,943

5,950

5, 956

5,963

5,970

5,976

5,983

5,990

5,996

6,003

6,009

6,016

6,023

 6,029

6,036

6, 043

6,049

6,056

5

7,074

7,082

7,090

7,098

7,107

7,115

7,123

7,131

7,140

7,148

7.156

7,164

7,173

7, 181

7,189

7,197

7,206

7,214

7,222

7,231

7,239

7,247

7,255

7,263

7,272

7,280

7,288

7,296

7,305

7,313

7,321

7, 330

7,338

7,346

7,354

7,363

7,371

7,379

7,388

7,396

7,404

7,412

7,421

7, 429

7,437

7,446

7,454

7,462

7,470

7,479

7,487

7,495

7,504

7,512

7,520

7, 529

7,537

7,545

7,554

7,562

7,570

6

8,489

8,498

8,508

 8, 518

8,528

8,538

8,548

8,558

8,568

8,578

8,588

8,597

8,607

8,617

8,627

8,637

8,647

8,657

8,667

8,677

8,686

8,696

8,706

8,716

8,726

8,736

8,746

8,756

8,766

8,776

8,786

8,796

8,805

8,815

8,825

8,835

8,845

8,855

8,865

8,875

8,885

8,895

8,905

8,915

8,925

8,935

8,945

8,955

8,964

8,974

8,984

8,994

9,004

9,014

9,024

9,034

9,044

9,054

9,064

9,074

9,084

7

9,903

9,915

9,926

9,938

9,950

9,961

9,973

9,984

9,995

10, 007

10, 019

10,030

10, 042

10, 053

10, 065

10, 076

10,088

10, 100

10, 111

10, 123

10, 134

10, 146

10, 157

10, 169

10, 181

10, 192

10, 204

10,215

10, 227

10, 238

10, 250

10, 261

10,273

10,284

10, 296

10, 308

10, 319

10,331

10, 342

10,354

10, 366

10,377

10,389

10,401

10,412

10,424

10,435

10,447

10,459

10,470

10,482

10,493

10, 505

10. 517

10, 528

10, 540

10, 552

10, 563

10, 575

10, 586

10, 598

8

11,318

11,331

11,344

11, 358

11,371

11,384

11, 397

11,410

11,423

11, 437

11,450

11,463

11,476

11,490

11, 503

11,516

11, 529

11, 542

11,556

,11,569

li, 582

11,595

11,608

11, 622

11,635

11,648

11,661

11,674

11,688

11,701

11,714

11,727

11,741

11,754

11,767

11, 780

11,794

11, 807

11, 820

11,833

11,847

11,860

11,873

11,886

11,900

11,913

11,926

11, 939

11,953

11,966

11,979

11,992

12,006

12, 019

12,032

12,046

12,059

12,072

12,086

12,099

12, 112

9

12, 733

12, 748

12,762

12, 777

12,792

12,807

12, 822

12,837

12,851

12,866

12,881

12, 896

12,911

12, 926

12,941

12,955

12,970

12,985

13,000

13,015

13, 030

13,044

13,059

13,074

13,089

13, 104

13, 119

13, 134

13, 149

13,163

13, 178

13, 193

13,208

13,223

13,238

13, 253

13,268

13,283

13, 298

13,313

13, 327

13,342

13,357

13,372

13, 387

13,402

13,417

13,432

13,447

13,462

13,477

13,491

13, 506

13,521

13, 537

13,551

13, 566

13, 581

13, 596

13,611

13,626

Corrections for curvaature refraction, and 

height of instruments

Miles.

1.6

2.1

2.5

2.8

3.1

3.4

3.6

3.8

4.1

4.3

4.5

4.7

4.8

5.0

5..2

5.4

5.5

5.7

5.8

6.0

6.1

6.3

6.4

6.5

6.7

6.8

6.9

7.0

7.2

7.3

7.4

7.5

7.6

7.8

7.9

8.0

8.1

0. 8 9ii

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10.0

10.1

Feet.

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

 32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

58

59

60

61

62

. 63

Miles.

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

11.1

11.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

12.0

12.1

12.2

12.3

12.4

12.5

12.6

12.7

12:8

12.9

13.0

13.1

13.2

13.3

13.4

13.5

13.6

13.7

13.8

13.9

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15.0

15.1

15.2

15.3

15.4

15.5

15.6

15.7

15.8

15.9

16.0

Feet.

64

65

67

68

69

70

71

73

74

75

77

78

79

80

82

83

84

86

87

89

90

91

93

94

96

97

99

100

102

103

105

106

108

109

111

112

114

115

117

119

120

122

124

125

127

129

130

132

134

135

137

139

141

142

144

146

148

150

151

a For all distances under 1.6 mjles the correction may be taken as + 5 feet. Height of instrument is 

assumed 4.5 feet,
GEOGKAPHIO TABLES AND FORMULAS. 353

TABLE 36. HORIZONTAL DISTANCES AND ELEVATIONS FROM STADIA READINGS.

This is a most generally useful stadia table for rods reading 1 foot to 

the 100 feet and with angles up to 30°. The values of other measures 

than those given in the table are obtained by multiplying the quantities under the proper vertical angle by stadia readings in hundreds of 

units. The quantity representing the focal distance is very small and 

is given at the bottom of each page for focal lengths between threefourths and li feet and is represented as a constant equal to c. 

For ordinary work it is not necessary to take the latter into account. 

The direct use of the table involves a'. multiplication for each result 

obtained.

Example. Let rod intercept be 3.25 feet, and the angle of inclination be 5° 35'. Then the distance on the horizontal would be

d=325 feet.

If we accept the focal distance f-\-c as 1.25 feet, we have from the 

tables

^'=3.25 feetx 99.05+1.24=323.15 feet, 

and

A=3.25 feetx9.68+0.11=31.57 feet.

41623° 16 23
354 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 36. Horizontal distances and elevations from stadia readings.

Minutes.

0

2

4

6

8

10

-12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

c=0. 75

c=1.00

c=1.25

0°.

Horizontal distance.

100. 00

100. 00

100. 00

100. 00

100. 00

100. 00

100. 00

100. 00

100. 00

100. 00

100. 00

100. 00

100. 00

99.99

99.99

99.99

99.99

99.99

99.99

99.99

99.99

99.99

99.98

. 99. 98

99.98

99.98

99.98

99.98

99.97

99.97

99.97

0.75

1.00

1.25

Difference

of elevation.

0.00

0.06

0.12

0.17

0.23,

0.29

0.35

0.41

0.47

0.52

0.58

0.64

0.70

0.76

0.81

0.87

0.93

0.99

1.05

1.11

1.16

L22

1.28

1.34

1.40

1.45

1.51

1.57

1.63

1.69

1.74

'0.01

0.01

0.02

l°.

Horizontal distance.

99.97

99.97

99.97

99.96

99.96

99.96

99.96

99.95

99.95

99:95

99.95

99.94

99.94

99.94

99.93

99.93

99.93

99.93

99.92

99.92

99.92

99.91

99.91

99.90

90.90

99.90

99.89

99.89

99.89

99.88

99.88

0.75

1.00

1.25

Difference

of elevation.

1.74

1.80

1.86

1.92

1.98

2.04

2.09

2.15

2.21

2.27

2.33

2.38

2.44

2.50

2.56

2.62

2.67

2.73

2.79

2.85

2.91

2.97

3.02

3.08

3.14

3.20

3.26

3.31

3.37

3.43

3.49

0.02

0.03

0.03

2°.

Horizontal distance.

99.88

99.87

99.87

99.87

99.86

99.86

99.85

99.85

99.84

99.84

99.83

99.83

99.82

99.82

99.81

99.81

99.80

99.80

99.79

99.79

99.78

99.78

0 99.77

99.77

99.76

99.76

99.75

99.74

99.74

99.73

99.73

0.75

1.00

1.25

Difference

of elevation.

3.49

3.55

3.60

3.66

3.72

3.78

3.84

3.90

3.95

4.01

4.07

4.13

4.18

4.24

4.30

4.36

4.42

4.48

4.53

4r 59

4.65

4.71

4.76

4.82

4.88

4.94

4.99

5.05

5.11

5.17

5.23

0.03

0.04

0.05

3°.

Horizontal distance.

99.73

99.72

99.71

99. 71

99.70

99.69

99.69

99.68

99.68

99.67

99.66

99.66

99.65

99.64

99.63

99.63

99.62

99.62

99.61

99.60

99.59

99.59

99.58

99.57

99.56

99.56

99.55

99.54

99.53

99.52

99.51

0.75

1.00

1.25

Difference

of elevation.

5.23

5.28

5.34

5.40

5.46

5.52

5.57

5.63

5.69

5.75

5.80

5.86

5.92

5.98

6.04

6.09

6.15

6.21

6.27

6.33

6.38

6.44

6.50

6.56

6.61

6.67

6.73

6.78

6.84

9.90

6.96

0.05

0.06

0.08
GEOGRAPHIC TABLES AND FORMULAS. 355

TABLE 36. Horizontal distances and elevations from stadia readings Continued.

Minutes.

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

c=0. 75

c=l. 00

c=1.25

4°.

Horizontal distances.

99. 51

99.51

99.50

99.49

99.48

99.47

99. 46'

99.46

99.45

99.44

99.43

99.42

99. 41

99.40

99. 39

99.38

99.33

99.37

99.36

99.35

99. 34

99.33

99.32

99.31

99.30

99.29

99.28

99.27

99.26

99.25

99.24

0.75

1.00

1.25

Difference

of elevation.

6.96

7.02

7.07

7.13

7.19

7.25

7.30

7.36

7.42

7.48

7.53

7.59

7.65

7.71

7.76

7.82

7.88

7.94

7.99

8.05

8.11

8.17

. 8.22.

8.28

8.34

8.40

8.45

8.51

8.57

8.63

8.68

0.06

0.08

0.10

5°.

Horizontal distances.

99.24

99.23

99.22

99.21

99.20

99.19

99.18

99.17

99.16

99.15

99.14

99.13

99.11

99.10

99.09

99.08

99.07

99.06

99.05

99.04

99.03

99.01

99.00

98.99

98.98

98.97

98.96

98.94

98.93

98.92

98.91

0.75

0.99

1.24

Difference

of elevation.

8.68

8.74

8.80

8.85

8.91

8.97

9.03

9.08

9.14

9.20

9.25

9.31

9.37

9.43

9.48

9.54

9.60

9.65

9.71

9.77

9.83

9.88

9.94

10.00

10.05

10.11

10.17

10.22

10.28

10.34

10.40

0.07

0.09'

0.11

6°.

Horizontal distances.

98.91

98.90

98.88

98.87

98.86

98.85

98.83

98.82

98.81

98.80

98.78

98.77

98.76

98.74

98.73

98.72

98. 71

98.69

98.68

98.67

98.65

98.64

98.63

98.61

98.60

98.58

98.57

98.56

98.54

98.53

98.51

0.75

0.'99

1.24

Difference

of elevation.

10.40

10. 45

10. 51

10.57

10.62

10.68

10.74

10.79

10.85

10. 91

10.96

11.02

11.08

11. 13

11. 19

11.25

11.30

11.36

11. 42

11.47

11.53

11.59

11.64

11.70

11.76

11.81

11.87

11.93

11.98

12.04

12.10

0.08

0.11

0.14

7°.

Horizontal distances.

98.51

98.50

98.48

98.47

98.46

98.44

98.43

98.41

98.40

98.39

98.37

98.36

98.34

98.33

98.31

98.29

98.28

98.27

98.25

98.24

98.22

98.20

0 98.19

98.17

98.16

98.14

98. 13

98. 11

98.10

98.08

98.06

0.74

0.99

1.24

Difference

of elevation.

12.10

12. 15

12.21

12.26

12. 32

12.38

12.43

12.49

. 12. 55

12. 60

12.66

12.72

12.77

12.83

12.88

12.94

13.00

13.05

13.11

13.17

13.22

13.28

13.33

13.39

13.45

13.50

13.56

13.61

1.3. 67

13.73

13.78

0.10

0.13

0.16
356 GEOGRAPHIC TABLES . AND FOBMULAS.

TABLE 36. Horizontal distances and elevations from stadia readings Continued.

Minutes.

0

2

4

6

8

10

12

14

16

18

20

2224-

26

28

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

c=0. 75

c=1.00

c=1.25

8°.

Horizontal distances.

98.06

98.05

98.03

98.01

98.00

97.98

97.97

97. 95

97. 93

97.92

97.90

97.88

97.87

97.85

97.83

97.82

97.80

97.78

97.76

97.75

9.7. 73

97.71

97. 69'

97.68

97.66

97.64

97.62

97.61

97.59

97.57

97.55

0.74

0.99

1.23

Difference

of elevation.

13.78

13.84

13.89

13.95

14.01

14.06

14.12

14.17

14.23

14.28

14.34

14.40

14.45

14.51

14.56

14.62

14.67

14. 73

14.79

14.84

14.90

14.95

15.01

15.06

15.12

15.17

15.23

15.28

15.34

15.40

15.45

0.11

0.15

0.18

9°.

Horizontal distances.

97.55

97.53

97. 52

97. 50

97.48

97.46

97.44

97.43

97.41

97.39

97.37

97.35

97.33

97.31

97.29

97.28

97.26

97.24

97.22

97.20

97.18

97.16

97.14

97.12

97.10

97.08

97.06

97.04

97.02

97.00

96.98

0.74

0.99

1.23

Difference

of elevation.

15.45

15.51

15.56

15.62

15.67

15.73

15.78

15.84

15.89

15.95

16.00

16.06

16. 11

16.17

16.22

16.28

16.33

16.39

16.44

16.50

16.55

16.61

16.66

16.72

16.77

16.83

16.88

16.94

16.99

17.05

17.10

0.12

0.16

0.21

10°.

Horizontal distances.

96.98

96.96

96.94

96.92

96.90

96.88

96.86

96.84

96.82

96.80

96.78

96.76

96.74

96.72

96. 70

96.68

96.66

96.64

96.62

96.60

96.57

96.55

96.53

96.51

96.49

96.47

96.45

96.42

96.40

96.38

96.36

0.74

0.98

1.23

Difference

of elevation.

17.10

17.16

17.21

17.26

17.32

17.37

17.43

17.48

17.54

' 17. 59

17.65

17.70

17.76

17.81

17.86

17.92

17.97

18.03

18.08

18.14

18.19

18.24

18.30

18.35

18.41

18.46

18.51

18.57

18.62

18.68

18.73

0.14

0.18

0.23

ll°.

Horizontal distances.

96.36

96.34

96.32

96.29

96.27

96.25

96.23

96.21

96.18

96.16

96.14

96.12

96.09

96.07

96.05

96.03

96.00

95.98

95.96

95.93

95.91

95.89

95.86

95.84

95.82

95.79

95.77

95.75

95.72

95.70

95.68

0.73

0.98

1.22

Difference

of elevation.

18.73

18.78

18.84

18.89

18.95

19.00

19.05

19.11

19. 16

19.21

19.27

19.32

19.38

19.43

19.48

19.54

19.59

19.64

19.' 70

19.75

19.80

19.86

19.91

19.96

20.02

20.07

20.12

20.18

20.23

20.28

20.34

0.15

0.20

0.25
GEOGRAPHIC TABLES AND FORMULAS. 357

TABLE 36. Horizontal distances and elevations from stadia readings Continued.

Minutes.

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

c=0. 75

c=1.00

c=1.25

12°.

Horizontal distances.

95.68

95.65

95. 63

95. 61

95.58

95.56

95.53

95. 51.

95.49

95.46

95.44

95.41

95.39

95.36

95.34

95.32

95.29

95.27

95.24

95.22

95.19

95.17

95.14

95.12

95.09

95.07

95.04

95.02

94.99

94.97

94.94

0.73

0.98

1.22

Difference

of elevation.

20.34

20.39

20.44

20.50

20.55

20.60

20.66

20. 71

20.76

20.81

20.87

20.92

20.97

21.03

21.08

21.13

21.18

21.24

21.29

21.34

21.39

21.45

21.50

21.55

21.60

21.66

21.71

21.76

21.81

21.87

21.92

0.16

0.22

0.27

13°.

Horizontal distances.

94.94

94.91

94.89

94.86

94.84

94. 81

94.79

94.76

94. 73

94.71

94.68

94.66

94.63

94.60

94. 58

94.55

94.52

94.50

94.47

94.44

94.42

94.39

94.36

94.34

94.31

94.28

94.26

94.23

94.20

94.17

94.15

0.73

0.97

1.21

Difference

of elevation.

21.92

21.97

22.02

22.08

22. 13

, 22.18

22.23

22.28

22.34

22.39

22.44

22.49

22.54

22.60

22.65

22.70

22.75

22.80

22.85

22.91

22.96

23.01

23.06

23.11

23. 16

23.22

23.27

23.32

23. 37

23. 42

23.47

0.17

0.23

0.29

14°.

Horizontal distances.

94.15

94.12

94.09

94.07

94.04

94.01

93.98

93.95

93.93

93.90

93.87

93.84

93.81

93.79

93.76

93.73

93.70

93.67

93.65

93.62

93. 59

93.56

93.53

93.50

93.47

93.45

93.42

93.39

93.36

93.33

93.30

0.73

0.97

1.21

Difference

of elevation.

23.47

23.52

23.58

23.63

23.68

23.73

23.78

23. 83

23.88

23.93

OQ qq u<J, VU

24.04

24.09

24.14

24.19

24.24

24.29

24.34

24.39

24.44

24.49

24.55

24.60

24.65

24.70

24.75

24.80

24.85

24.90

24.95

25.00

0.19

0.25

0.31

15°.

Horizontal distances.

93.30

93.27

93.24

93.21

93.18

93. 16

93.13

93.10

93.07

93.04

93.01

92.98

92.95

92.92

92.89

92.86

92.83

92.80

92.77

92.74

92.71

92.68

92.65

92.62

92.59

92.56

92.53

92.49

92.46-

92.43

92.40

0.72

0.96

1.20

Difference

of elevation.

25.00

25.05

25.10

25.15

25.20

25.25

25. 30

25.35

25.40

25.45

25.50

25.55

25.60

25.65

25.70

25.75

25.80

25.85

25.90

25.95

26.00

26.05

26.10

26. 15

26.20

26.25

26.30

26.35

26.40

26.45

26.50

0.20

0.27

0.34
358 GEOGRAPHIC TABLES AND FOBMDLAS.

TABLE 36. Horizontal distances and elevations from stadia readings Continued.

Minutes.

0

2

4

6

8

10

12

14

16

18

20

 22

24

26

28

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

c=0. 75

c=1.00

c=l. 25

16°.

Horizontal distances.

92.40

92.37

92.34

92.31

92.28

92.25

92.22

92.19

92.15

92.12

92.09

92.06

92.03

92.00

91.97

91.93

91.90

91.87

91.84

91. 81

91.77

91.74

91.71

91.68

91.65

91.61

91.58

91.55

91.52

91.48

91.45

0.72

0.86

1.20

Difference

of elevation.

26.50

26.55

26.59

26.64

26.69

26.74

26.79

26.84

26.89

26.94

26.99

27.04

27.09

27.13

27.18

27.23

27.28

27.33

27.38

27.43

27.48

27.52

27.57

27.62

27.67

27.72

27.77

27.81

07 QC //. 00

27.91

27.96

0.21

0.28

0.35

17°.

Horizontal distances.

91.45

91.42

91.39

91.35

91.32

91.29

91.26

91.22

91.19

91.16

91.12

91. 09

91.06

91.02

90.99

90.96

90'92

90.89

90.86

90.82

90.79

90.76

90.72

90.69

90.66

90.62

90.59

90.55

90.52

90.48

90.45

0.72

0.95

1.19

Difference

of elevation.

27.96

28.01

28.06

28.10

28.15

28.20

28.25

28.30

28.34

28.39

28.44

28.49

28.54

28.58

28.63

28.68

28.73

28.77

28.82

28.87

28.92

28.96

29.01

29.06

29.11

29.15

29.20

29.25

29.30

29.34

29.39

0.23

0.30

0.38

18°.

Horizontal distances.

90.45

90.42

90.38

90.35

90.31

90.28

90.24

90.21

90.18

90.14

90.11

90.07

90.04

90.00

89.97

89.93

89.90

89.86

89.83

89.79

89.76

89.72

89.69

89.65

89.61

89.58

89.54

89.51

89.47

89.44

89.40

0.71

0.95

1.19

Difference

of elevation.

29.39

29.44

29.48

29.53

29.58

29.62

29.67

29.72

29.76

29. 81

29.86

29.90

29.95

30.00

30.04

30.09

30.14

30.19

30.23

30.28

30. 32

30.37

30.41

30.46

30.51

30.55

30.60

30.65

30.69

30.74

. 30.78

0.24

0.32

0.40

19°.

Horizontal distances.

89.40

89.36

89.33

89.29

89.26

89.22

89. 18

89.15

89.11

89.08

89.04

89.00

88.96

88.93

88.89

88. 86

88.82

88.78

88.75

88.71

88.67

88.64

88.60

88.56

88.53

88.49

88.45

88.41

88.38

88.34

88.30

0.71

0.94

1.18

Difference

of elevation.

30.78

30.83

30.87

30.92

30.97

31.01

31.06

31.10

31.15

31. 19

31.24

31.28

31.33

31.38

31.42

31.47

31.51

31.56

' 31.60

31.65

31.69

31.74

31.78

31.83

31.87

31.92

31.96

32.01

32.05

32.09

32.14

0.25

0.33

0.42
GEOGKAPHIC TABLES AND FOKMULAS. 359

TABLE 36. Horizontal distances and elevations from stadia readings Continued.

Minutes.

0

2

4

6

8

10

12

14

16

18

20

22

' 24

26

28

30

32

34

36

38 

40

42

44

46

48

50

52

54

56

58

60

c=0. 75

c=1.00

c=1.25

20°.

Horizontal distances.

88.30

88.26

88.23

88.19

88.15

88.11

88.08

88.04

88.00

87.96

87.93

87.89

87.85

87.81

87.77

87.74

87.70

87.66

87.62

87.58

87.54

87.51

87.47

87.43

87.39

87.35

87.31

87.27

87.24

87.20

87.16

0.70

0.94

1.17

Difference

of elevation.

32.14

32.18

32.23

32.27

32.32

32. 36

32.41

32.45

32.49

32.54

32. 58

32.63

32.67

32.72

32.76

32.80

32.85

32.89

32.93

32.98

33.02

33.07

33.11

33.15

33.20

33.24

33.28

33.33

33.37

33.41

33.46

0.26

0.35

0.44

21°.

Horizontal distances.

87.16

87. 12

' 87.08

87.04

87.00

86.96

86.92

86.88

86.84

86.80

86.77

86.73

86.69

86.65

86.61

86.57

86.53

86.49

86.45

86.41

86.37

86.33

86.29

86.25

86.21

86.17

86.13

86.09

86.05

86. 01.

85.97

0.70

0.93

1.16

Difference

of elevation.

33.46

33.50

33.54

33.59

33.63

33.67

33.72

33.76

33.80

33. 84

33.89

33.93

33.97

34.01

34.06

34.10

34.14

34.18

34.23

34.27

34.31

34.35

34.40

34.44

34.48

34.52

34.57

34. 61

34.65

34.69

34. 73

0.27

0.37

0.46

22°.

Horizontal distances.

85.97

85.93

85.89

85.85

85.80

85.76

85.72

85.68

85.64

85.60

85.56

85.52

85.48

85.44

85.40

85.36

85.31

85.27

85.23

85.19

85.15

85.11

85.07

85.02

84.98

84.94

84.90

84.86

84.82

84.77

84.73

0.69

0.92

1.15

Difference

of elevation.

34.73

34.77

34.82

34.86

34.90

34.94

34.98

35.02

35. 07

35.11

35.15

35.19

35.23

35.27

35.31

35.36

35.40

35.44

35.48

35.52

35.56

35.60

35.64

35.68

35.72

35.76

35.80

35.85

35.89

35.93

35.97

0.29

0.38

0.48

23°.

Horizontal distances.

84.73

84.69

84.65

84. 61

84.57

84.52

84.48

84. 44 . 84.40

84.35

84.31

84.27

84.23

84.18

84.14

84.10

84.06

84.01

83.97

83.93

83.89

83.84

83.80

83.76

83.72

83.67

83.63

83.59

83.54

83.50

83.46

0.69

0.92

1.15

Difference

of elevation.

35.97

36.01

36.05

36.09

36.13

36.17

36.21

36.25

36.29

36.33

36.37

36.41

36.45

36.49

36.53

36.57

36.61

36.65

36.69

36.73

36.77

36.80

36.84

36.88

36.92

36.96

37.00

' 37. 04

37.08

37.12

37. 16

0.30

0.40

0.50
360 GEOGBAPHIC TABLES AND FORMULAS.

TABLE 36. Horizontal distances and elevations from stadia readings Continued.

Minutes.

0

2

4

6

8

10

12

14

16

18

20

22

24

26.

28

30

32

34

36

38

40

4244 '

46

48

50

52 .

54

56

58

60

c=0. 75

c=1.00

c=1.25

24°.

Horizontal distances.

83.46

83.41

83.37

83.33

83.28

83.24

83.20

83.15

83.11

83.07

83.02

82.98

82.93

82.89

82.85

82.80

82.76

82.72

82.67

82.63

82.58

82.54

82.49

82.45

82.41

82.36

82.32

82.27

89 9q 04. 4O

82.18

82.14

0.68

0.91

1.14

Difference

of elevation.

37.16

37.20

37.23

37.27

37.31

37.35

37.39

37.43

37.47

37.51

37.54

,37. 58

' 37. 62

37.66

37.70

37.74

37.77

37.81

37.85

37.89

37.93

37.96

38.00

38.04

38.08

38. 11

38.15

38.19

OO. Qfi iiO9Q

38.26

38.30

0.31

0.41

0.52

25°.

Horizontal distances.

82.14

82.09

82.05

82.01

81.96

81.92

81.87

81.83

81.78

81.74

81.69

81.65

81.60

81.56

81.51

81.47

81.42

81.38

81.33

81.28

81.24

81.19

81.15

81.10

81.06

81.01

80.97

80.92

80.87

80.83

80.78

0.68

0.90.

1.13

Difference

of elevation.

38.30

38.34

38.38

38.41

38.45

38.49

38.53

38.56

38.60

38.64

38.67

38.71

38.75

38.78

38.62

38.86

38.89

38.93

38.97

39.00

39.04

39.08

39.11

39.15

39.18

39.22

39.26

39.29

U<7. qq OOqq

39.36

39.40

0.32

0.43

0.54

26°.

Horizontal distances.

80.78

80.74

80.69

80.65

80.60

80.55

80.51

80.46

80.41

80.37

80.32

80.28

80.23

80.18

80.14

80.09

80.04

80.00

79.95

79.90

79.86

79.81

79.76

79.72

79.67

79.62

79.58

79.53

79.48

79.44

79.39

0.67

0.89

1.12

Difference

of elevation.

39.40

39.44

39.47

39.51

39.54

39.58

39.61

39.65

39.69

39.72

39.76

39.79

39,83

39.86

39.90

39.93

39.97

40.00

40.04

40.07

40. 11

40.14

40.18

40.21

40.24

40.28

40.31

40.35

40.38

40.42

40.45

0.33

0.45

0.56

27°.

Horizontal distances.

79.39

79.34

79.30

79.25

79.20

79.15

79.11

79.06

79.01

78.96

78.92

78.87

78.82

78.77

78.73

78.68

78.63

78.58

78.54

78.49

78.44

78.39

78.34

78.30

78.25

78.20

78.15

78.10

78.06

78.01

77.96

0.66

0.89

1.11

Difference

of elevation.

40.45

40.49

40.52

40.55

40.59

40.62

40.66

40.69

40.72

40.76

40.79

40. 82.

40.86

40.89

40.92

40.96

40.99

41.02

41.06

41.09

41.12

41.16

41.19

41.22

41.26

41.29

41.32

41.35

41.39

41.42

41. 45

0.35

0.46

0.58
GEOGRAPHIC TABLES AND FORMULAS. 361

TABLE 36. Horizontal distances and elevations from stadia readings Continued.

Minutes.

0

2

. 4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

c=0. 75

c=l. 00

c=l. 25

28°.

Horizontal distances.

77.96

77.91

77.86

77.81

77.77

77.72

77.67

77.62

77.57

77.52

77.48

77.42

77.38

77.33

77.28

77.23

77.18

77.13

77.09

77.04

76.99

76.94

76.89

76.84

76.79

76.74

76.69

76.64

76.59

76.55

76.50

0.66

0.88

1.10

Difference

of elevations.

41. 45

41.48

41.52

41.55

41.58

41.61

41.65

41.68

41.71

41.74

41.77

41.81

41.84

41.87

41.90

41.93

41.97

42.00

42.03

42.06

42.09

42.12

42.15

42.19

42.22

42.25

42.28

42.31

42.34

42.37

42.40

0.36

0.48

0.60

29°.

Horizontal distances.

76.50

76.45

76.40

76.35

76.30

76.25

76.20

76.15

76.10

76.05

76.00

75.95

75.90

75.85

75.80

75.75

75.70

75.65

75.60

75.55

75.50

75.45

75.40

73.35

75.30

75.25

75.20

75.15

75.10

75.05

75.00

0.65

0.87

1.09

Difference

of eleva- tions.

42.40

42.43

42.46

42.49

42.53

42.56

42.59

42.62

42.65

42.68

42.71

42.74

42.77

42.80

42.83

42.86

42.89

42.92

42.95

42.98

43.01

43. 04

43.07

43.10

43.13

43.16

43.18

43.21

43.24

43.27

43.30

0.37

0.49

0.62

30°.

Horizontal distances.

75.00

74.95

74. 90

74.85

74.80

74.75

74.70

74.65

74.60

74.55

74.49

74.44

74.39

74.34

74.29

74,24

74.19

74.14

74.09

74.04

73.99

73.93

73.88

73.83

73.78

73.73

73.68

73.63

73.58

73.52

73.47

0.65

0.86

1.08

Difference

of elevations.

43.30

43.33

43.36

43.39

43.42

43.45

43.47

 43. 50

43.53

43.56

43.59

43.62

43.65

43.67

43. 70 . 43.73

43.76

43.79

43.82

43.84

43.87

43.90

43.93

43.95

43.98

44.01

44.04

44.07

44.09

44.12

44.15

0.38

0.51

0.64
362 GEOGEAPHIC TABLES AND FOEMULAS.

TABLE 37. For converting metric into United States measures.

LINEAR,

Meters. Inches.

1 39. 3700

2 78. 7400

3 118. 1100

4 157. 4800

5 196. 8500

6 236. 2200

7 275.5900

8 314. 9600

9 354. 3300

Meters. Feet.

1 3. 280833

2 6. 561667

3 9. 842500

4 13. 123333

5 16. 404166

6 19. 685000

7 22. 965833

8 26.246666

9 29. 527500

Meters. Yards.

1 1. 093611

2 2. 187222

3 3. 280833

4 4. 374444

5 5. 468056 '

6 6.561667

7 7. 655278

8 8. 748889

9 9. 842500

Kilo- Mjl meters. Mlles'

1 0. 62137

2 1. 24274

3 1 . 86411

 4 2. 48548

5 3. 10685

6 3, 72822

7 ' 4. 34959

8 4. 97096

9 5. 59233

SQUARE.

«gSg? S(*uare

Srs. mches "

1 0. 1550

2 0. 3100

3 0. 4650

4 0. 6200

5 0. 7750

6 0. 9300

7 1. 0850

8 1. 2400

9 1.3950

Square Square 

meters. feet.

1 10. 764

2 21. 528

3 32. 292

4 43. 055

5 53. 819

6 64. 583

7 75. 347

8 86. Ill

9 96. 875

Square Square 

meters. yards.

1 1. 196

2 2. 392

3 3. 588

4 4. 784

5 5. 980

6 7. 176

7 8. 372

8 9. 568

9 10. 764

Set Acres1 2.471

2 4. 942

3 7. 413

4 9. 884

5 12. 355

6 14. 826

7 17. 297

8 19. 768

9 22. 239
GEOGEAPHIO TABLES AND FOEMULAS.

TABLE 38. For converting United States measures into metric. 

LINEAR.

363

"«"- SL

I 25. 4001

2 50. 8001

3 76. 2002

4 101. 6002

5 127. 0003

6 152. 4003

7 * 177.8004

8 203. 2004

9 228. 6005

Feet. Meters.

1 0.304801

2 0. 609601

3 0.914402

4 1. 219202

5 1.524003

6 1.828804

7 2. 133604

8 2. 438405

9 2. 743205

Yards. Meters.

1 0. 914402

2 ] . 828804

3 2. 743205

4 3. 657607

5 4.572009

6 5. 486411

7 6.400813

8 . 7. 315215

9 8. 229616

Miles- nSrs.

1 1. 60935

2 3. 21869

3 4. 82804

4 6. 43739

5 8. 04674

6 9. 65608

7 11. 26543

8 12. 87478

9 14. 48412

 *>

SQUARE.

Square *£*?> 

inches. meters

N

1 °6.452

2 12. 903

3 19. 355

4 25. 807

5 32. 258

6 38.710

7 45. 161

8 51. 613

9 58. 065

s?S'e *£"

Ieci;- meters.

1 9. 290

2 18. 581

3 27. 871

4 37. 161

5 46.452

6 55. 742

7 65. 032

8 74. 323

9 83. 613

Square Square 

yards. meters.

1 0.836

2 1. 672

3 2. 508

4 3.344

5 4. 181

6 5. 017

7 5. 853

8 6. 689

9 7. 525

Acres Hec- Acres. tareg

1 0. 4047

2 0. 8094

3 1. 2141

4 1. 6187

5 2. 0234

6 2. 4281

7 2. 8328

8 . 3. 2375

9 3. 6422
364 GEOGRAPHIC TABLES AtfD FORMULAS.

TABLE 39. FOR INTERCONVERSION OP MILES AND LOGARITHMS OP METERS, FOR DISTANCES FROM 10 TO 100 MILES.

The value adopted for the meter is 39.3700 inches. Distances 

between triangulation stations are given in logarithms of meters, but 

for general use distances in miles are most frequently desired.

The following examples illustrate use of the table:

To find the number of miles corresponding to log. distance in meters ...... 4. 56857

Next lower log. in table is for 23.00 miles ................................ 4.56838

Difference ...............................

Corresponding to tabular difference for 0.01 mile. 

Hence distance required is 23.01 miles.

19

For distances less than 10 miles proceed as above; first adding 1 to 

the characteristic of the given logarithm and afterwards dividing the 

corresponding number of miles by 10. Example:

Having given the log. 3.84062, which is less than any given in 

the table, and therefore for a distance less than 10 miles, adding 

1 to the characteristic of the logarithm gives 4.84062, which corresponds to a distance of 43.05 miles. Hence the distance sought is

43.05 =4.305 miles.

To change (Add.)

Log. of miles to log. of meters..................................... 3.2066498

Log. of yards to log. of meters .................................... 9. 9611371

Log. of feet to log. of meters ...................................... 9.4840158

Log. of inches to log. of meters.................................... 8. 4048346

Log. of meters to log. of miles..................................... 6. 7933502

Log. of meters to log. of yards ..............................._.... 0.0388629

Log. of meters to log. of feet ...................................... 0.5159842

Log. of meters to log. of inches.................................... 1.5951654

TABLE 39. For interconversion of miles and logarithms of meters. 

[Prepared by S. S. Gannett.]

Miles.

10.00

.05

.10

.15

.20

.25

.30

.35

.40

. .45

Log. meters.

4. 20665

4. 20882

4. 21097

4. 21312

4. 21525

4. 21737

4. 21949

4. 22159

4. 22368

4. 22577

Diff.log. 

.01 mile.

43

42

41

Miles.

10.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

4. 22784

4. 22990

4. 23196

4. 23400

4. 23603

4. 23806

4. 24007

4. 24208

4. 24408

4. 24606

Diff. log. 

.01 mile.

41

40

Miles.

11.00

.05

.10

.15 .20 V

.25

.30

.35

.40

.45

Log. meters.

4. 24804

4. 25001

4. 25197

4. 25393

4. 25587

4. 25780

4. 25973

4. 26165

4. 26355

4. 26545

Biff. log. 

.01 mile.

39

38
GEOGRAPHIC TABLES AND FORMULAS. 365

TABLE 39. For interconversion of miles and logarithms of meters Continued.

Miles.

11.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

12.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

13.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

4. 26735

4. 26923

4. 27111

4. 27298

4. 27484

4. 27669

4. 27853

4. 28037

4. 28220

4. 28402

4. 28583

4. 28764

4. 28944

4. 29123

4. 29301

4. 29479

4. 29656

4. 29832

4. 30007

4. 30182

4. 30356

4. 30529

4. 30702

4. 30874

4. 31046

4. 31216

4. 31386

4. 31555

4. 31724

4. 31892

4. 32059

4. 32226

4. 32392

4. 32558

4. 32722

4. 32887

4. 33050

4. 33213

4.33375

4. 33537

4. 33698

4. 33859

4. 34019

4. 34178

4. 34337

4. 34495

4. 34653

4. 34810

4. 34966

4. 35122

Diff. log. 

.01 mile.

38

37

36

35

34

,

33

32

31

Miles.

14.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.6P

.65

.70

.75 .80'

.85

.90

.95

15.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

16.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

4. 35278

4. 35433

4. 35587

4. 35741

4. 35894

4. 36047

4. 36199

4. 36350

4. 36501

4. 36652

4. 36802

4. 36951

4. 37100

4. 37249

4. 37397

4. 37544

4. 37691

4. 37838

4. 37984

4. 38129

4. 38274

4. 38419

4. 38563

4. 38706

4. 38849

4. 38992

4. 39134.

4. 39276

4. 39417

4. 39558

4. 39698

4. 39838

4. 39977

4. 40116

4. 40255

4. 40393

4. 40531

4. 40668

4. 40805

4. 40941

4. 41077

4. 41213

4. 41348

4. 41482

4. 41616

4. 41750

4. 41884

4. 42017

4. 42149

4. 42282

Difl. log. 

.01 mile.

31

30

29

28

27

26

Miles.

16.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

17.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

, .95

18.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

4. 42413

4. 42545

4. 42676

4. 42806

4. 42937

4. 43067

4. 43196

4. 43325

4. 43454

4. 43582

4. 43710

4. 43837

4. 43964

4. 44091

4. 44218

4. 44344

4. 44470

4. 44595

4. 44720

4. 44845

4. 44969

4. 45093

4. 45216

4. 45339

4. 45462

4. 45585

4. 45707

4. 45829

4. 45950

4. 46071

4. 46192

4. 46313

4. 46433

4. 46553

4. 46672

4. 46791

4. 46910

4. 47029

4. 47147

4. 47265

4. 47382

4. 47499

4. 47616

4. 47733

4. 47849

4. 47965

4.48081

4. 48196

4. 48311

4. 48426

Diff. log. 

.01 mile.

26

 25

24

23
366 GKEOGKAPHIC TABLES ATCD FOEMULAS.

TABLE 39. For interconversion of miles and logarithms of meters Continued.

Miles.

19.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

T50

.55

.60

.65

.70

.75

.80

.85

.90

.95

20.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

21.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

4. 48540

4. 48654

4.48768

4. 48882

4. 48995

4. 49108

4. 49221

4. 49333

4. 49445

4. 49557

4. 49669

4. 49780

4. 49891

4. 50001

4. 50112

4. 50222

4. 50332

4. 50441

4.50550

4. 50659

4. 50768

4. 50876

4. 50985

4. 51093

4. 51200

4. 51308

4. 51415

4. 51521

4. 51628

4. 51734

4.51840

4. 51946

4. 52052

4. 52157

4. 52262

4. 52367

4. 52471

4. 52576

4. 52680

4. 52783

4. 52887

4. 52990

4. 53093

4. 53196

4. 53299

4. 53401

4. 53503

4. 53605

4. 53706

4. 53808

Diff. log. 

.01 mile.

. 23

22

21

20

Miles.

21.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

22.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

00 flfi /O. UU

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

4. 53909

4. 54010

4. 54110

4. 54211

4. 54311

4. 54411

4. 54511

4. 54610

4. 54709

4. 54808

4. 54907

4. 55006

4. 55104

4. 55202

4. 55300

4. 55398

4. 55495.

4. 55593

4. 55690'

4. 55787

4. 55883

4. 55980

4. 56076

4. 56172

4. 56268

4. 56363

4. 56459

4. 56554

4. 56649

4. 56743

4. 56838

4. 56932

4. 57026

4. 57120

4. 57214

4. 57307

4. 57401

4. 57494

4. 57587

4. 57679

4. 57772

4. 57864

4. 57956

4. 58048

4. 58140

4. 58231

4. 58323

4. 58414

4. 58505

4. 58596

Diff. log 

.01 mile

20

19

18

Miles.

24.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

25.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

26.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

L6g. meters.

4. 58686

4. 58777

4. 58867

4. 58957

4. 59047 v

4. 59136

4.59226

4. 59315

4. 59404

4. 59493

4. 59582

4. 59670

4. 59759

4. 59847

4. 59935

4. 60023

4. 60110

4. 60198

4. 60285

4. 60372

4. 60459

4. 60546

4. 60632

4. 60719

4. 60805

4. 60801

4. 60977

4. 61063

4. 61148

4. 61234

4. 61319

4. 61404

4. 61489

4. 61574

4. 61658

4. 61743

4. 61827

4. 61911

4. 61995

4. 62079

4. 62162

4. 62246

4. 62329

4. 62412

4. 62495

4. 62578

4. 62661

4. 62743

4. 62825

4. 62908

Diff. log. 

.01 mile.

. 18

17

16
GEOGEAPHIC TABLES AND FOEMULAS. 367

TABLE 39. For interconversion of miles and logarithms of meters Continued.

Miles.

26.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

27.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

28.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85 :9o

.95

Log. meters.

4. 62990

4. 63071

4. 63153

4. 63235

4. 63316

4. 63397

4. 63479

4. 63559

4. 63640

4. 63721

4. 63801

4. 63882

4. 63962

4. 64042

4. 64122

4. 64202

4. 64281

4. 64361

4. 64440

4. 64519

4. 64598

4. 64677

4. 64756

4. 64835

4. 64913

4.64991'

4. 65069

4. 65147

4. 65225

4. 65303

4. 65381

4. 65458

4. 65536

4. 65613

4. 65690

4. 65767

4. 65844

4. 65920

4. 65997

4. 66073

4. 66149

4. 66226

4. 66302

4. 66377

4. 66453

4. 66529

4. 66604

4. 66680

4.66755

4. 66830

Difl.log 

.01 mile

16

15

Miles.

29.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

30.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

31.00

.05 .'10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

4. 66905

4. 66980

4. 67054

4. 67129

4. 67203

4. 67278

4. 67352

4. 67426

4. 67500

4. 67573

4. 67647

4. 67721

4. 67794

4. 67867

4. 67941

4. 68014

4. 68087

4. 68159

4. 68232

4. 68305

4. 68377

4. 68449

4. 68522

4. 68594

4. 68666

4. 68737

4. 68809

4. 68881

4. 68952

4. 69024

4. 69095

4. 69166

4. 69237

4. 69308

4. 69379

4. 69449

4. 69520

 4.69590

4. 69661

4. 69731

4. 69801

4. 69871

4. 69941

4. 70011

4. 70081

4. 70150

4. 70219

4. 70289

4. 70358

4. 70427

Difl. log. 

.01 mile.

15

14

Miles.

31.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

32.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

33.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

4. 70496

4. 70565

4. 70634

4. 70702

4. 70771

4. 70839

4. 70908

4. 70976

4. 71044

4. 71112

4. 71180

4. 71248

4. 71315

4. 71383

4. 71451

4. 71518

4. 71585

4. 71652

4. 71719

4. 71787

4. 71853

4. 71920

4. 71987

4. 72053

4. 72120

4. 72186

4. 72252

4. 72319

4. 72385

4. 72451

4. 72516

4. 72582

4.72648

4. 72713

4. 72779

4. 72844

4. 72909

4. 72975

4. 73040

4. 73105

4. 73169

4. 73234

4. 73299

4. 73363

4. 73428

4. 73492

4. 73557

4. 73621

4. 73685

4. 73749

Difl.log. 

.01 mile.

14

.

13
368 GEOGKAPHIC TABLES AND FOKMULA8.

TABLE 39. For interconversion of miles and logarithms of meters Continued.

Miles.

34.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

35.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

36.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

4. 73813

4. 73877

4. 73940

4. 74004

4. 74068

4. 74131

4. 74194

4. 74258

4. 74321

4. 74384

4. 74447

4. 74510

4. 74573

4. 74635

4. 74698

4. 74761

4. 74823

4. 74885

4. 74947

4. 75010

4. 75072

4. 75134

4. 75196

4. 75257

4. 75319

4. 75381

4. 75443

4. 75504

4. 75565

4. 75627

4. 75688

4. 75749

4. 75810

4. 75871

4. 75932

4. 75993

4. 76053

4. 76114

4. 76174

4. 76235

4. 76295

4. 76355

4. 76416

4. 76476

4. 76536

4. 76596

4. 76656

4. 76715

4. 76775

4. 76835

Diff. log. 

.01 mile.

13

12

Miles.

36.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

37.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

38.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

4. 76894

4. 76954

4. 77013

4. 77072

4. 77132

4. 77191

4. 77250

4. 77309

4. 77368

4. 77426

4. 77485

4. 77544

4. 77602

4. 77661

4. 77719

4. 77778

4. 77836

4. 77894

4. 77952

4. 78010

4. 78068

4. 78126

4. 78184

4. 78241

4. 78299

4. 78357

4. 78414

4. 78472

4. 78529

4. 78586

4. 78643

4. 78701

4. 78758

4. 78815

4. 78871

4. 78928

4. 78985

4. 79041

4. 79098

4. 79155

4. 79211

4. 79267

4. 79324

4. 79380

4. 79436

4. 79492

4. 79548

4. 79604

4. 79660

4. 79716

Diff. log. 

.01 mile.

12

11

Miles.

39.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

40.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

41.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

4. 79771

4. 79827

4. 79883

4. 79938

4. 79994

4. 80049

4. 80104

4. 80159

4. 80215

4. 80270

4. 80325

4. 80380

4. 80435

4. 80480

4. 80544

4. 80599

4. 80653

4. 80708

4. 80762

4. 80817

4. 80871

4. 80925

4. 80979

4. 81034

4. 81088

4. 81142

4. 81195

4. 81249

4. 81303

4. 81357

4. 81411

4. 81464

4. 81518

4. 81571

4. 81624

4. 81677

4. 81731

4. 81784

4. 81837

4. 81890

4. 81943

4. 81996

4. 82049

4. 82102

4. 82155

4. 82207

4. 82260

4. 82313

4. 82365

4. 82417

Diff. log. 

.01 mile.

11

10
GEOGRAPHIC TABLES AND FORMULAS. 369

39. For interconversion of miles and logarithms of meters Continued.

Miles.

41.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

42.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

43.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

4. 82470

4. 82522

4. 82574

4. 82627

4. 82679

4. 82731

4. 82783

4. 82835

4. 82886

4. 82938

4. 82990

4. 83042

4. 83093

4. 83145

4. 83196

4. 83248

4. 83299

4. 83350

4. 83402

4. 83453

4. 83504

4. 83555

4. 83606

4. 83657

4. 83708

4. 83759

4. 83809

4. 83860

4. 83911

4. 83961

4. 84012

4. 84062

4. 84113

4. 84163

4. 84213

4. 84264

4. 84314

4. 84364

4. 84414

4. 84464

4. 84514

4. 84564

4. 84614

4. 84663

4. 84713

4. 84763

4. 84812

4. 84862

4. 84911

4. 84961

Diff. log. 

.01 mile.

10

Miles.

44.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

45.00

.05

.10

.15

.20

.25

.30

.35

.40

' .45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

46.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

4. 85010

4. 85060

4. 85109

4. 85158

4. 85207

4. 85256

4. 85305

4. 85354

4. 85403

4. 85452

4. 85501

4. 85550

4. 85599

4. 85647

4. 85696

4. 85744

4. 85793

4. 85841

4. 85890

4. 85938

4. 85986

4. 86035

4. 86083

4. 86131

4. 86179

4. 86227

4. 86275

4. 86323

4. 86371

4. 86418

4. 86466

4. 86514

4. 86561

4. 86609

4. 86657

4. 86704

4. 86751

4. 86799

4. 86846

4. 86894

4. 86941

4. 86988

4. 87035

4. 87082

4. 87129

4. 87176

4. 87223

4. 87270

4. 87317

4. 87364

Diff. log. 

.01 mile.

10

9

Miles.

46.50

.55

.60

.65

. .70

.75

.80

.85

.90

.95

47.00

.05

,10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

48.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

4. 87410

4. 87457

4. 87504

4. 87550

4. 87597

4. 87643

4. 87690

4. 87736

4. 87782

4. 87829

4. 87875

4. 87921

4. 87967

4. 88013

4. 88059

4. 88105

4. 88151

4. 88197

4. 88243

4. 88289

4. 88334

4. 88380

4. 88326

4. 88471

4. 88517

4. 88562

4. 88608

4. 88653

4. 88699

4. 88744

4. 88789

4. 88834

4. 88879

4. 88925

4. 88970

4. 89015

4. 89060

4. 89105

4. 89149

4. 89194

4. 89239

4. 89284

4. 89329

4. 89373

4. 89418

4. 89462

4. 89507

4. 89551

4. 89596

4. 89640

Diff. log. 

.01 mile.

9

41623° 16 24
370 GEOGKAPH1C TABLES AND FORMULAS.

TABLE 39. For interconversion of miles and logarithms of meters Continued.

Miles.

49.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

50.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

 .70

.75

.80

.85

.90

.95

51.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

4. 89685

4. 89729

4. 89773

4. 89817

4. 89861

4. 89906

4. 89950

4. 89994

4. 90038

4. 90082

4. 90125

4. 90169

4. 90213

4. 90257

4. 90301

4. 90344

4. 90388

4. 90431

4. 90475

4. 90519

4.90562

4. 90605

4. 90649

4. 90692

4. 90735

4. 90779

4. 90822

4. 90865

4. 90908

4. 90951

4.90994

4. 91037

4. 91080

4. 91123

4. 91166

4. 91209

4. 91251

4. 91294

4. 91337

4. 91379

4. 91422

4. 91465

4. 91507

4. 91550

4. 91592

4. 91634

4. 91677

4. 91719

4. 91761

4. 91803

Diff.log. 

.01 mile.

9

8

Miles.

51. 50

.55

.60

.65

..70

.75

.80

.85

.90

.95

52.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

53.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

4. 91846

4. 91888

4. 91930

4. 91972

4. 92014

4. 92056

4. 92098

4. 92140

4. 92182

4. 92224

4. 92265

4. 92307

4. 92349

4. 92390

4. 92432

4. 92474

4. 92515

4. 92557

4. 92598

4. 92639

4. 92681

4. 92722

4. 92764

4. 92805

4. 92846

4. 92887

4. 92928

4. 92969

4. 93011

4. 93052

4.93093

4. 93133

4. 93175

4. 93215

4. 93256

4. 93297

4. 93338

4. 93378

4. 93419

4. 93460

4. 93500

4. 93541

4. 93581

4. 93622

4. 93662

4. 93703

4. 93743

4. 93784

4. 93824

4. 93864

Diff. log. 

.01 mile.

8

Miles.

54.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

55.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

56.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

4. 93904

4. 93945

4. 93985

4. 94025

4. 94065

4. 94105

4. 94145

4. 94185

4. 94225

4. 94265

4. 94305

4. 94345

4. 94384

4. 94424

4. 94464

4. 94503

4. 94543

4. 94583

4. 94622

4. 94662

4. 94701

4. 94741

4. 94780

4. 94820

4. 94859

4. 94898

4. 94937

4. 94977

4. 95016

4. 95055

4.95094

4. 95133

4. 95172

4. 95212

4. 95251

4. 95289

4. 95328

4. 95367

4.95406

4. 95445

4. 95484

4. 95523

4. 95561

4. 95600

4. 95639

4. 95677

4. 95716

4. 95754

4. 95793

4. 95831

Diff. log. 

.01 mile.

8
GEOGBAPHIO TABLES AND FOBMULAS. 371

TABLE 39. -For interconversion of miles and logarithms of meters Continued.

Miles.

56.50

.55

.60

.65

.70

.75

.80

.85

.90

' .95

57.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

58.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

4. 95870

4. 95908

4. 95947

4. 95985

4. 96023

4. 96062

4. 96100

4. 96138

4.96176

4. 96214

4. 96253

4. 96291

4. 96329

4. 96367

4. 96405

4. 96443

4. 96481

4. 96518

4. 96556

4..96S94

4. 96632

4. 96669

4. 96707

4. 96745

4. 96783

4. 96820

4. 96858

4. 96895

4. 96933

4. 96970

4. 97008

4. 97045

4. 97083

4. 97120

4. 97157

4. 97195

4. 97232

4. 97269

4. 97306

4. 97343

4. 97381

4. 97418

4. 97455

4. 97492

4. 97529

4. 97566

4. 97603

4. 97640

4. 97677

4; 97713

Diff. log. 

.01 mile.

8

7

Miles.

59.00

.05

 .10

.15

.20

.25

.30

.35

.40

.45

.50

.55 .60'

.65

.70

.75

.80

.85

.90

.95

60.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

 .60

.65

.70

.75

.80

.85

.90

.95

61.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

4. 97750

4. 97787

4. 97824

4. 97861

4. 97897

4. 97934

4. 97971

4. 98007

4. 98044

4. 98080

4. 98117

4. 98153

4. 98190

4. 98226

4. 98262

4. 98299

4.98335

4. 98371

4. 98408

4. 98444

4. 98480

4. 98516

4. 98552

4. 98589

4. 98625

4. 98661

4. 98697

4. 98733

4. 98769

4. 98805

4. 98841

4. 98876

4. 98912

4. 98948

4. 98984

4. 99020

4. 99055

4. 99091

4. 99127

4. 99162

4. 99198

4. 99234

4. 99269

4. 99305

4. 99340

4. 99376

4. 99411

4. 99447

4. 99482

4. 99517

Diff. log 

.01 mile

7

Miles.

61.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

62.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

63.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters

4. 99553

4. 99588

4. 99623

4. 99658

4. 99693

4. 99729

4. 99764

4. 99799

4. 99834

4. 99869

4. 99904

4. 99939

4. 99974

5. 00009

5. 00044

5. 00079

5. 00114

5.00149

5. 00183

5. 00218

5. 00253

5. 00288

5. 00322

5. 00357

5. 00392

5. 00426

5. 00461

5. 00495

5. 00530

5. 00565

5. 00599

5. 00633

5. 00668

5. 00702

5. 00737

5. 00771

5. 00805

5. 00840

5. 00874

5. 00908

5. 00942

5. 00977

5. 01011

5.01045

5. 01079

5. 01113

5. 01147

5. 01181

5. 01215

5. 01249

Diff. log. 

.01 mile.

7
372 GEOGBAPHIC TABLES AND FOKMULAS.

TABLE 39. For interconversion of miles and logarithms of meters Continued.

Miles.

64.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

' .65

.70

.75

.80

.85

.90

.95

65.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

66.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

5. 01283

5. 01317

5. 01351

5. 01385

5. 01419

5. 01452

5. 01486

5. 01520

5. 01554

5. 01587

5. 01621

5. 01655

5. 01688

5. 01722

5. 01755

5. 01789

5. 01823

5. 01856

5. 01889

5. 01923

5. 01956

5. 01990

5. 02023

5. 02056

5. 02090

5. 02123

5. 02156

5. 02190

5. 02223

5. 02256

5. 02289

5. 02322

5. 02355

5. 02389

5. 02421

5. 02455

5. 02488

5. 02521

5. 02554

5. 02587

5. 02619

5. 02652

5. 02685

5. 02718

5. 02751

5. 02784

5. 02816

5. 02849

5. 02882

5. 02915

Diff.log. 

01 mile.

7

Miles.

66.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

67.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

68.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

5. 02947

5. 02980

5. 03012

5. 03045

5. 03078

5. 03110

5. 03143

5. 03175

5. 03208

5. 03241

5. 03273

5. 03305

5. 03337

5. 03370

5. 03402

5. 03434

5. 03467

5. 03499

5. 03531

5. 03563

5. 03595

5. 03627

5. 03660

5. 03692

5. 03724

5. 03756

5. 03788

5. 03820

5. 03852

5. 03884

5. 03916

5. 03948

5. 03980

5. 04012

5. 04043

5. 04075

5. 04107

5. 04139

5. 04171

5. 04202

5. 04234

5. 04266

5. 04297

5. 04329

5. 04361

5. 04392

5. 04424

5. 04455

5. 04487

5. 04518

Diff.log. 

01 mile.

7

6

Miles.

69.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

70.00

.05

 .-10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

71.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

5. 04550

5. 04581

5. 04613

5. 04644

5. 04676

5. 04707

5. 04738

5. 04770

5. 04801

5. 04832

5. 04863

5. 04895

5. 04926

5. 04957

5. 04988

5. 05019

5. 05051

5. 05082

5. 05113

5. 05144

5. 05175

5. 05206

5. 05237

5. 05268

5. 05299

5. 05330

5. 05361

5. 05391

5. 05422

5. 05453

5. 05484

5. 05515

5. 05545

5. 05576

5. 05607

5.05538

5. 05668

5. 05699

5. 05730

5. 05760

5. 05791

5. 05821

5. 05852

5. 05883

5. 05913

5. 05943

5. 05974

5. 06004

5. 06035

5. 06065

Diff. log. 

.01 mile.

6
GEOGKAPHIO TABLES AND FOBMULAS. 373

TABLE 39. For interconversion of miles and logarithms of meters Continued.

Miles.

71.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

72.00

.05

.10

.15

.20

. .25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

73.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

5. 06096

5. 06126

5. 06156

5. 06187

5. 06217

5. 06247

5. 06277

5. 06308

5. 06338

. 5. 06368

5. 06398

5. 06428

5. 06459

5.06489

5. 06519

5. 06549

5. 06579

5. 06609

5. 06639

5. 06669

5. 06699

5. 06729

5. 06759

5. 06789

5. 06818

5. 06848

5. 06878

 5. 06908

5. 06938

5. 06967

5. 06997

5. 07027

5. 07057

5. 07086

5. 07116

5. 07146

5. 07175

5. 07205

5. 07235

5. 07264

5. 07294

5. 07323

5. 07353

5. 07382

5. 07412

5. 07441

5. 07471

5. 07500

5. 07529

5. 07559

Diff.log. 

.01 mile.

6'

Miles.

74.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

-.75

.80

.85

.90

.95

75.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

76.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

5. 07588

5. 07617

5. 07647

5. 07676

5. 07705

5. 07735

5. 07764

5. 07793

5. 07822

5. 07851

5. 07881

5. 07910

5. 07939

5. 07968

5. 07997

5. 08026

5. 08055

5. 08084

5.08113

5. 08142

5. 08171

5. 08200

5. 08229

5. 08258

5. 08287

5. 08316

5. 08345

5. 08373

5. 08402

5. 08431

5. 08460

5. 08488 

5. 08517

5. 08546

5. 08575

5. 08603

5. 08632

5.08661

5. 08689

5. 08718

5. 08746

5. 08775

5. 08803

5. 08832

5. 08861

5. 08889

5. 08917

5. 08946

5. 08974

5. 09003

Diff. log. 

.01 mile.

6

,

Miles.

76.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

77.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

. .90

.95

78.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

5. 09031

5. 09059

5. 09088

5. 09117

5. 09145

5. 09173

5. 09201

5. 09229

5. 09258

5. 09286

5. 09314

5. 09342

5. 09370

5. 09399

5. 09427

5. 09455

5. 09483

5. 09511

5. 09539

5. 09567

5. 09595

5. 09623

5. 09651

5. 09679

5. 09707

5. 09735

5. 09763

5. 09791

5. 09819

5. 09847

5. 09875

5.09902

5. 09930

5. 09958

5. 09986

5. 10013

5. 10041

5. 10069

5. 10097

5. 10124

5. 10152

5. 10180

5. 10207

5. 10235

5. 10263

5. 10290

5. 10318

5. 10345

5. 10373

5. 10400

Diff. log. 

.01 mile.

6

,
374 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 39. For interconversion of miles and logarithms of meters Continued.

Miles.

79.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

80.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

81.00

.05

.10

.15

.20

.25

.30

.35

.40

,45

Log. meters.

5.10428

5. 10455

5. 10483

5. 10510

5. 10537

5. 10565

5. 10592

5. 10620

5. 10647

5. 10674

5. 10702

5. 10729

5. 10756

5. 10784

5. 10811

5. 10838

5. 10865

5. 10893

5. 10920

5. 10947

5. 10974

5. 11001

5. 11028

5. 11055

5. 11082

5. 11109

5. 11137

5. 11164

5. 11191

5. 11218

5. 11245

5. 11272

5. 11299

5. 11325

5. 11352

5. 11379

5. 11406

5. 11433

5. 11460

5. 11487

5. 11513

5. 11540

5. 11567

5. 11594

5. 11621

5. 11647

5. 11674

5. 11701

6. 11727

6, 11754

Diff. log. 

.01 mile.

5

Miles.

81.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

82.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

83.00

.05-

.10

.15

.20

.25

.30

.35

.40

.45

/ .50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

5. 11781

5. 11807

5. 11834

5. 11861

5. 11887

5. 11913

5. 11940

5. 11967

5. 11993

5. 12020

5. 12046

5. 12073

5. 12099

5. 12126

5. 12152

5. 12179

5. 12205

5. 12231

5. 12258

5. 12284

5. 12310

5. 12337

5. 12363

5. 12389

5. 12416

5. 12442

5. 12468

5. 12494

5. 12521

5. 12547

5. 12573

5. 12599

5. 12625

5. 12651

5. 12677

5. 12703

5. 12729

5. 12756

5. 12782

5. 12808

5. 12834

5. 12860

5. 12886

5. 12912

5. 12937

5. 12963

5. 12989

5. 13015

5. 13041

5, 13067

Diff. log. 

.01 mile.

5

Miles.

84.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

85.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

86.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

Log. meters.

5. 13093

5. 13119

5. 13145

5. 13170

5. 13196

5. 13222

5. 13248

5. 13273

5. 13299

5. 13325

5. 13351

5. 13376

5. 13402

5. 13428

5. 13453

5. 13479

5. 13505

5. 13530

5. 13556

5. 13581

5. 13607

5. 13632

5. 13658

5. 13683

5. 13709

5. 13734

5. 13760

5. 13785

5. 13811

5. 13836

5. 13862

5. 13887

5. 13912

5. 13938

5. 13963

5. 13988

5. 14014

5. 14039

5. 14064

5. 14090

5. 14115

5. 14140

5. 14165

5. 14191

5. 14216

5. 14241

5. 14266

5. 14291

5, 14316

5, 14341

Diff. log. 

.01 mile.

5
GEOGRAPHIC TABLES AND FORMULAS. 375

TABLE 39. For interconversion of miles and logarithms of meters Continued.

Miles.

86.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

87.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

 .50

.55

.60

.65

.70

.75

.80

.85

.90

.95

88.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

5. 14367

5, 14392

5. 14417

5. 14442

5. 14467

5. 14492

5. 14517

5. 14542

5. 14567

5. 14592

5. 14617

5. 14642

5. 14667

5. 14692

5. 14717

5. 14741

5. 14766

5. 14791

5. 14816

5. 14841

5. 14866

5. 14891

5. 14915

5. 14940

5. 14965

5. 14990

5. 15014

5. 15039

5. 15064

5. 15089

5. 15113

5. 15138

5. 15163

5. 15187

5. 15212

5. 15237

5. 15261

5. 15286

5. 15310

5. 15335

5. 15359

5. 15384

5. 15408

5. 15433

5. 15457

5. 15482

5. 15506

5. 15531

5. 15555

5.15580

Diff. log. 

.01 mile.

5

Miles.

89.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

90.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

91.00

.05

.10

.15

.20

.25

.30

.35

.40

,45

Log. meters.

5. 15604

5. 15628

5. 15653

5. 15677

5. 15701

5. 15726

5. 15750

5. 15775

5. 15799

5. 15823

5.15847.

5. 15872

5. 15896

5. 15920

5. 15944

5. 15968

5. 15993

5. 16017

5. 16041

5. 16065

5. 16089

5. 16113

5. 16137

5. 16162

5. 16186

5. 16210

5. 16234

5. 16258

5. 16282

5. 16306

5. 16330

5. 16354

5. 16378

5. 16402

5. 16426

5. 16450

5. 16474

5. 16497

5. 16521

5. 16545

5. 16569

5. 16593

5. 16617

5. 16641

5. 16665

5. 16688

5. 16712

5. 16736

5. 16760

5. 16783

Diff. log. 

.01 mile.

5

Miles.

91.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

92.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

93.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

5. 16807

5. 16831

5. 16855

5. 16878

5. 16902

5. 16926

5. 16949

5. 16973

5. 16997

5. 17020

 5. 17044

5. 17067

5. 17091

5.17115

5. 17138

5. 17162

5. 17285

5. 17209

5. 17232

5. 17256

5. 17279

5. 17303

5. 17326

5. 17349

5. 17373

5. 17396

5. 17420

5. 17443

5. 17467

5. 17490

5. 17513

5. 17537

5. 17560

5. 17583

5. 17607

5. 17630

5. 17653

5. 17676

5. 17700

5. 17723

5. 17746

5. 17769

5. 17793

5. 17816

5. 17839

5. 17862

5. 17885

5. 17908

5. 17932

6. 17955

Diff.log. 

.01 mile.

5
376 GBOGEAPHIC TABLES AND FOKMULAS.

TABLE 39. For interconversion of miles and logarithms of meters Continued.

Miles.

94.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

95.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95.

Log.meters.

5. 17978

5. 18001

5. 18024

5. 18047

5. 18170

5. 18193

5. 18116

5. 18139

5. 18162

5. 18185

5. 18208

5. 18231

5. 18254

5. 18277

5. 18300

5. 18323

5. 18346

5. 18369

5. 18392

5. 18415

5. 18437

5. 18460

5. 18483

5. 18506

5. 18529

5. 18551

5. 18574

5. 18597

5. 18620

5. 18643

5. 18665

5. 18688

5. 18711

5. 18733

5. 18756

5. 18779

5. 18802

5. 18824

5. 18847

5. 18869

Diff.log. 

.01 mile.

5

Miles.

96.00

.05

.10

.15.

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

97.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

5. 18892

5. 18915

5. 18937

5. 18960

5. 18983

5. 19005

5. 19028

5. 19050

5. 19073

5. 19095

5. 19118

5. 19140

5. 19163

5. 19185

5. 19208

5. 19230

5. 19253

5. 19275

5. 19297

5. 19320

5. 19342

5. 19365

5. 19387

5. 19409

5. 19432

5. 19454

5. 19476

5. 19499

5. 19521

5. 19543

5. 19565

5. 19588

5. 19610

5. 19632

5. 19655

5. 19677

5. 19699

5. 19721

5. 19743

5. 19765

Diflf. log. 

.01 mile.

5

4

Miles.

98.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

99.00

.05

.10

.15

.20

.25

.30

.35

.40

.45

.50

.55

.60

.65

.70

.75

.80

.85

.90

.95

Log. meters.

5. 19788

5. 19810

5. 19832

5. 19854

5. 19876

5. 19898

5. 19920

5. 19942

5. 19965

5. 19987

5. 20009

5. 20031

5. 20053

5. 20075

5. 20097

5. 20119

5. 20141

5. 20163

5. 20185

5. 20207

5. 20229

5. 20250

5. 20272

5. 20294

5. 20316

5. 20338

5. 20360

5. 20382

. 5. 20404

5. 20425

5. 20447

5. 20469

5. 20491

5. 20513

5. 20535

5. 20556

5. 20578

5. 20600

5. 20621

5. 20643

Difl. log! 

.01 mile.

4

1 acre =209 feet square, nearly.

1 acre = 43,560 square feet = 4,840 square yards.

1 statute mile = 1,760 yards = 5,280 feet = 63,360 inches.

1 cubic foot = 7.48 gallons = 0.804 bushel.

1 cubic foot of water weighs 62.4 pounds.

1 wine gallon = 8.34 pounds water.

1 wine gallon = 231 cubic inches.

1 avoirdupois pound = 7,000 grains.

1 troy pound = 5,760 grains,
GEOGEAPHIC-TABLES AND FOEMULAS. 377

1 meter = 39.37 inches. Log. 1.5951654.

1 meter = '3.28083 feet. Log. 0.5159842.

1 meter = 1.093611 yards. Log. 0.0388629.

1 meter = 0.00062137 mile. Log. 6.7933502.

1 kilometer = 3,281 feet = five-eighths mile, nearly.

1 cubic meter = 35.314 cubic feet = 1.308 yards.

1 liter = 1.0567 quarts.

1 gram = 15.43 grains.

1 kilogram = 2.2046 avoirdupois pounds.

1 tonneau (metric ton) = 2,204.6 pounds.

1 cubic meter per minute = 0.5886 second-foot.

1 second-foot = 50 California miner's inches.

1 second-foot = 40 Arizona miner's inches.

1 second-foot = 449 gallons per minute.

1 second-foot for one day = 1.9835 acre-feet.

1 second-foot for one day = 646,272 United States gallons.

1 second-foot = about one acre-inch per hour.

1 acre-foot = 325,850 gallons.

1,000,000 gallons = 3.07 acre-feet.

1,000,000 cubic feet = 22.95 acre-feet.

1,000,000 gallons per 24 hours = L55 second-feet.

1 horse power = 550 foot-pounds per second.

1 horse power = 76 kilogrammeters per second.

1 horse power = 746 watts.

1 horse power = 1 second-foot water falling 8.8 feet.

1 second-foot falling 10 feet = 1.135 horse power.

1 foot per second =1.077 kilometers per hour.

1 foot per second = 0.68 miles per hour.

1 inch = 2.54 centimeters.

1 foot = 0.3048 meters.

1 yard = 0.9144 meters.

1 mile = 1.60935 kilometers.

1 square yard = 0.836 square meters.

1 acre = 0.4047 hectares.

1 square mile = 259 hectares.

1 square mile = 2.59 square kilometers.

1 cubic foot = 0.0283 cubic meters.

1 cubic yard = 0.7646 cubic meters.

1 gallon = 3.7854 liters.

1 pound = 0.4536 kilograms.

f 15 pounds per square inch. 

1 atmosphere = about -I 1 ton per square foot.

I 1 kilo per square centimeter. 

Acceleration of gravity = 32.16 feet per second. 

To change miles to inches on map:

Scale 1:125000, 1 mile = 0.50688 inches. Log. = 9.7049052.

Scale 1:90000, 1 mile = 0.70400 inches. Log. = 9.8475727.

Scale 1:62500, 1 mile = 1.01376 inches. Log. = 0.0059352.

Scale 1:45000, 1 mile = 1.40800 inches. Log. = 0.1486027. 

To change log. of meters to log. of inches on map:

Scale 1:125000 add 6.4982552.

Scale 1:90000 add 6.6409228.

Scale 1:62500 add 6.7992853.

Scale 1:45000 add 6.9419528.
378 GEOGRAPHIC TABLES AND FORMULAS.

TABLE 40. Ratios for customary map scales and the logarithm of each.

Scale Ito 

600

1,200

2,400

2,500

4,800

5,280

10,000

12,000

15,000

21, 120

31,680

45,000

48,000

62,500

63,360

90,000

96,000

125,000

126,720

192,000

250,000

253,440

380, 160

500,000

506,880

1,000,000

Decimal.

0. 00166667 

7.2185

0.00083333 

6.92082

0.00041667 

6.61979

0.00040000 

6. 60206

0.00020833 

6.31876

0.00018940 

6.27737

0. 00010000 

6.00000

0.00008333 

5.92082

0.00006667 

5.82391

0.00004735 

5. 67531

0.00003157 

5.49921

0.00002222 

5.34679

0.00002083 

5.31876

0.00001600 

5.20412

0.00001578 

5. 19818

0.00001111 

5.04576

0.00001042 

5.01773

0.00000800 

4.90309

0.00000789 

4.89715

0.00000521 

4.71670

0. 00000400 

4. 60206

0.00000395 

4. 59612

0.00000263 

4.42003

0.00000200 

4. 30103

0.00000197 

4. 29510

0.00000100 

4.00000

Inches 

per 

mile.

105.60 

2.02366

52.80 

1.72263

26.40 

1.42160

25.344 

1.40388

13.20 

1. 12057

12.000 

1. 07918

6.336 

0.80182

5.280 

0. 72263

' 4.224 

0.62572

3.000 

0.47712

2.000 

0. 30103

1.408 

0. 14860

1.320 

0. 12057

1.014 

0. 00594

1.000 

0.00000

0. 7040 

9. 84757

0. 6600 

9. 81954

0. 5069 

9. 70491

0. 5000 

9.69897

0.3300 

9.51851

0.2534 

9.40388

0.2500 

9. 39794

0. 1667 

9. 22185

0. 1267 

9. 10285

0. 1250 

9. 09691

0.06336 

8.80182

Inches 

per 1,000 

feet.

20.000 

1.30103

10.000 

1.00000

5.000 

0. 69897

4.800 

0. 68124

2.500 

0. 39794

2.°273 

0.35655

1.200 

0.07918

1.000 

1.00000

0.800 

9.90309

0.5682 

9.75449

0.3788 

9. 57839

0. 2667 

9.42597

0.2500 

9.39794

0. 1920 

9. 28330

0. 1894 

9.27737

0. 1333 

9. 12494

0. 1250 

9.09691

0.0960 

8.98227

0.0947 

8. 97634

0.0625 

8.79588

0. 0480 

8. 68124

0.0473 

8. 67531

0.0316 

8. 49921

0.0240 

8. 38021

0.02368 

8. 37428

0.0120 

8.07918

Miles 

per 

inch.

0.00947 

7. 97634

0.01894 

8. 27737

0.03788 

8. 57840

0.03946 

8.59612

0.07576 

8. 87943

0. 08333 

8.92082

0. 15783 

9. 19818

0. 18939 

9. 27737

0.23674 

9. 37428

0.33333 

9.52288

0. 50000 

9. 69897

0. 71023 

9. 85140

0.75758 

9. 87943

0. 98643 

9. 99406

1.00000 

0.00000

1.4205 

0. 15243

1. 5152 

0. 18046

1.9729 

0.29509

2.0000 

0.30103

3.0303 

0.48149

3.9457 

0. 59612

4.000 

0.60206

6.000 

0.77815

7.8914 

0. 89715

8.0000 

0.90309

15.783 

1.19818

Feet 

per 

inch.

50

1.69897

100 

2.00000

200 

2.30103

208.3 

2. 31876

400 

2.60206

440 

2. 64345

833.3 

2.92082

1,000 

3.00000

1,250 

3.09691

1.760 

3.24551

2,640 

3.42160

3,750 

8. 57403

4,000 

3.60206

5,208.3 

3.71670

5,280 

3.72263

7, 500 

3.87506

8,000 

3.90309

10,416.7 

4. 01773

10,560 

4. 02366

16,000 

4.20412

20,833.3 

4.31876

21,120.0 

4. 32469

31,680.0 

4.50079

41,666.7 

4. 61979

42,240 

4.62572

83,333.3 

4.92082

Meters 

. per 

inch.

15.24 

1. 18299

30.48 

1.48402

60.96 

1.78505

63.50 

1.80277

121.9 

2.08608

134.1 

2. 12747

254.0 

2.40484

304.8 

1.48402

381.0 

2.58093

436.4 

2.72953

804.7 

2.90562

1,143.0 

3.05805

1,219.2 

3.08608

1, 587. 5 

3.20071

1/609.3 

3. 20665

2,286.0 

3. 35908

2,438.4 

3.38711

3,175.0 

3.50174

3,218.7 

3.50768

4,876.9 

3.68814

6,350.0 

3. 80277

6,437.4 

3. 80871

9,656.1 

3.98480

12,700 

4, 103. 80

12,875 

4. 10974

25,400 

4. 40583

Feet 

per 

Tkinch.

1.0

2.0

4.0

4.2

8.0

8.8

16.7

20.0

25.0

35.2

52.8

75.0

80.0

104.2

105.6

150.0

160.0

208.3

211.2

320.0

416.7

422.4

633.6

833.3

844.8

1,666.7

In the formulas given below for each column, N represents the number in the lefthand column.

The logarithms for the six central columns of the table are in all cases written 

below the corresponding numbers.

N 1

N

63,360

NN

12,000

NN

N

63,360

N 

12

N

39.37

N

600
GEOGRAPHIC TABLES AND FORMULAS. 379

BASE LINE COMPUTATIONS FOR STEEL TAPE 

MEASURES.

Correction for sag, always negative; .let

n=number of sections into which each tape length is divided

by its supports.

1=length of each section; ordinarily this should be 50 feet. 

w=weight of tape per unit of length; found by dividing the

weight of whole tape in pounds by the length in feet. 

t = tension, which should be 20 pounds for Geological Survey 

lines

then the correction for each tape length = ^ X ^-7-^

^4r Tf

Correction for slope, always negative; let

Ji = difference in height between the ends of a long tape or

between the ends of a line having a uniform slope 

Z=length of the line or tape

^2 _____

then the correction = ^, or the corrected length == ^V ~h?

Reduction to sea level, always negative; let 

L = length of line

H = average height above sea level,

R = radius of curvature of the earth for the mean latitude and 

azimuth of the line

then the correction = -=0-

An average value of log R in meters for the United States and for a 

base measured along a meridian line would be 6.80357, and for a line 

measured along a parallel 6.80530.

An exact value for log R for meridional lines can be derived from 

the B geodetic coordinate factor; thus,

log R = B log sin I"

For east and west lines the fourth place of decimals of the log 

found should be increased by about one-third the colatitude in 

degrees.

See Coast and Geodetic Survey report for 1876 (p. 386), for log of 

R in meters for various latitudes and azimuths.
380 GEOGRAPHIC TABLES AND FORMULAS.

ERRORS IN ELEVATIONS WHICH RESULT FROM INACCURATE DETERMINATIONS OF DISTANCES ON STEEP 

SLOPES.

[The assumed error in distance is taken as 0.001 mile or 5.28 feet.]

Vertical 

angle.

0 /

1 5

10 43

20 45

29 36

37 09

43 26

45

Error.

Feet.

0.1

1

2

3

4

5

5.28

ERRORS IN LEVELING.

The errors in platted directions, or in horizontal angles measured 

with a transit, due to faulty leveling of the instrument, are as follows:

Error in 

leveling.

1

2

3

4

5

10

Maximum error 

in horizontal 

angle.

0 16

1 03

2 21

4 12

6 33

26 19

ERRORS IN PLUMBING RODS.

A 12-foot leveling rod inclined 44 minutes from the vertical is 1.86 

inches out of plumb and the resulting error in reading is 0.001 foot.
GEOGRAPHIC TABLES AND FORMULAS. 

Comparison of Centigrade and Fahrenheit degrees.

(1) °F.=-g-°C.+32. (2) °C.=5( °F9~32) .

381

c

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

F.

32.0

33.8

35.6

37.4

39.2

41.0

42.8

44.6

46.4

48.2

50.0

51.8

53.6

55.4

57.2

59.0

60.8

62.6

64.4

66.2

68.0

69.8

71.6

73.4

75.2

77.0

78.8

80.6

82.4

84.2

86.0

87.8

89.6

91.4

93.2

95.0

96.8

98.6

C,

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

F.

100.4

102.2

104.0

105.8

107.6

109.4

111.2

113.0

114.8

116.6

118.4

120.2

122.0

123.8

125.6

127.5

129.2

131.0

132.8

134.6

136.4

138.2

140.0

141.8

143.6

145.4

147.2

149.0

150.8

152.6

154.4

156.2

158.0

159.8

161.6

163.4

' 165. 2

167.0

C,

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

F.

168:8

170.6

172.4

174.2

176.0

177.8

179.6

181.4

183.2

185.0

186.8

188.6

190.4

192.2

194.0

195.8

197.6

199.4

201.2

203.0

204.8

206.6

208.4

210.2

212.0

213.8

215.6

217.4

219.2

221.0

222.8

224.6

226.4

228.2

230.0

231.8

233.6

235.4

C

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

F.

237.2

239.0

240.8

242.6

244.4

246.2

248.0

249.8

251.6

253.4

255.2

257.0

258.8

260.6

262.4

264.2

266.0

267.8

. 269.6

271.4

273.2

275.0

276.8

278.6

280.4

282.2

284.0

285.8

287.6

289.4

291.2

293.0

294.8

296.6

298.4

300.2

302.0

303.8

C

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

F.

305.6

307.4

309.2

311.0

312.8

314.6

316.4

318.2

320.0

321.8

323.6

325.4

327.2

329.0

330.8

332.6

334.4

336.2

338.0

339.8

341.6

343.4

345.2

347.0

348.8

350.6

352.4

354.2

356.0

357.8

359.6

361.4

363.2

365.0

366.8

368.6

370.4

372.2

0

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

220

230

240

250

260

270

280

290

300

350

400

450

500

550

600

650

700

F.

374.0

375.8

377.6

379.4

381.2

' 383. 0

384.8

386.6

388.4

390.2

392.0

393.8

395.6

397.4

399.2

401.0

402.8

404.6

406.4

408.2

410.0

428.0

446.0

464.0

482.0

500.0

518.0

536.0

554.0

572.0

662.0

752.0

842.0

932.0

1,022.0

1,112.0

1,202.0

1,292.0
382 GEOGRAPHIC TABLES AND FORMULAS.

CONSTANTS.

	Log. 

Basis of natural logarithms.................... e=2.7182818285 0.4342944819

Modulus of Briggs's logarithms.............. m=0.4342944819 9.6377843113 10

Radius of the circle in seconds................r= 206264. 8062 5.3144251332

Radius of the circle in minutes............. jc= 3437.74677 3.5362738828

Radius of the circle in degrees................r= 57.2957795 1.7581226324

Circumference of the circle in seconds........... 1296000 6.1126050015 .

Circumference of the circle in minutes........... 21600 4.3344537512

Circumference of the circle in degrees............ 360 2.5563025008

Circumference of the circle for the diameter.... = 1 0.0000000000

=3.1415926536 0.4971498727

ASTRONOMICAL CONSTANTS (HARKNESS).

Sidereal year=365.256 357 8 mean solar days. 

Sidereal day=23h 56m 4. 8 100 mean solar time. 

Mean solar day=24h 3m 56." 546 sidereal time. 

Mean distance of the earth from the sun=92 800 000 miles.

PHYSICAL CONSTANTS.

Velocity of light (Harkness)=186 337 miles per second=299 878 km. per second. 

Velocity of sound through dry air=1090Vl+0.00367 t° C. feet per second.

LINEAR EXPANSIONS OF PRINCIPAL METALS IN 

MICRONS PER METER (OR MILLIONTHS PER UNIT 

LENGTH).

Name of metal.

Brass. .............................................

Copper ...........................................

Glass. ............................................

Gold..............................................

Nickel-steel. .......................................

Silver. ...........................................

Steel, hard. .......................................

Steel, soft. ........................................

Tin. .............................................

Zinc. .............................................

Expansion 

. per 

degree C.

20

19

17

9

15

11

12

28

0

9

8.7

19

12

11

19

29

Expansion 

per 

degree F.

11.1

10.5

9.4

5 0

8.3

6.1

6.7

15.5

0.0

5.0

4.8

10.5

6.7

6.1

10.5

16.1
^^.^rf^wcowcocowtofcototototot'

WC^<I l OtOrf».OiOOOMOi*4CO»-'WCnMOtsD*-O>OOOfcOCn-^eO»-

§

OiWO*4COO"^I^l-**^^l-'OOCJil--OOOifcOCOCnfcOCOOabOcOOiW 

CO-'-lCJ>Wi 'COOi^fcOOOQO^^H^cOMCnWh^OOJ^tO a OQC5**H

50 O 

b ^ 

£ 1 i I 

S M 

s I? 

St, *3 

^> JO 

13-.

$

05

saiavi a^tv 888
tOtOtOtObOtOtOtOtOtOf *! «t iMMMt »MI 'H*

! i( * 1 ! ') 'H- 4 COfcOtOfcOtOtOtCbOtObOl 'I 'I 'I 'h-

* O 

0«

& £t 

pa

ON

_§g

S

rfiiciiSt^.i^cowcocococototototototoi-'i-ii-'i-iMi-' 

OOO5>^COt-'SO^JC>>&.bO^-'tO~lCnkb.MppO^IO<COjN3ppOO>CnWH'

OO^COcOC^tOCOOlbOOOOItOOOCni iQO^w) >*<]^M*<l^O*^]COOOdCO

»

u

3D

?ff.

0

c

CD

sanavx
i "

r

SALARY TABLES Continued. 

Payments by the month, or fractions thereof Contin

Month of 30 days.

[Use the 30-day month table only for computing official salaries for part of a month if the compe

Days. 

1.... ......

2..........

3..........

4..... ..

5..........

6..........

7..........

8..........

9..........

10..........

11........ .

12..........

13..........

14........ .

15........ .

16..........

17..........

IS..........

19........ .

20..........

21..........

22..........

23..........

24........ .

25. .........

26..........

27..........

28..........

29..........

30..........

S15

0.50

1.00

1.50

2.00

2.50

3 nn

3.50'

4 00

4.50

5.00

5.50

6.50

7.00

7 <tf1

8.00

8.50

9.00

Q V>

10.00

10.50

11.00

11.50

19 nn

12.50

13.00

13.50

14.00

14.50

15.00

,816

0.53

1.07

1 60

2.13

2.67

4.27

4 SO

5.33

5.87

6.93

7.47

8.00

 8.53

9.07

9.60

10.13

10.67

11.20

11.73

12.27

19 on

10 qo

13.87

14.40

H QO

-15. 47

16.00

817

0.57

1 11

1.70

2

co"

3.40

3 Q7

4.53

5.10

6

00

6 

on

7 17

7.93

S

en

9

/17

9

fiO

10.20

10.77

n qq

n on

12.47

13.03

13.60

14 70

15.30

1 e 07

16.43

17.00

sis

1 20

1 oft

2 4ft

3 

Aft

S fift

4 20

4 

Of)

5.40

6.00

6.60

7 on

9

AA

10.20

10.80

19 nft

12.60

13.20

13.80

15.00

15.60

16.80

17.40

IS. 00

S19.

0.63

1 27

1 Qft

2 53

3 1 7

3 

QA

4 43

5.70

6.33

6 Q7

O Oq

8

07

9 50

10.13

10.77

19 fY*

12.67

iq OA

10 no

15.20

1 C 00

16.47

17.10

17 73

1 Q "37

19 00

S20

O il'7

1 33

2 f\{\

3

00

4 00

4.67

6

00

6.00

7 H

8 nft

9

00

10.00

10.67

n qq

12.00

10 00

14.00

14.67

15 33

16.00

1 7 H

i s n.n

in qq

20.00

S25

O QQ

2

CA

3

OO

5.00

5

00

6.67

7 50

8

00

9 17

10.00

10.83

11.67

 to cn

10 00

1 c QQ

17 50

i ft qq

1Q 1 7

9ft ftq

21.67

99 K/l

OO. qq

25.00

$30

1 00

2

AA

3 ftft

4.00

5.00

6.00

7 OQ

8.00

9 00

10.00

11.00

13.00

14.00

15.00

17.00

19.00

20.00

91 on

no nn

94 nn

9^ nn

26.00

27. 00

835

2

00

3 

erv

4.67

5

QO

7 00

fi 1 7

9

00

10.50

19 ftq

14.00

15.17

16.33

17 50

1Q QQ

91 nn

99 1 7

00 00

24.50

25.67

26.83

OQ fiA

on i 7

30 33

31.50

oo go

35.00

S40

1 °.°.

4 00

5.33

6.67

8

AA

9

00

10.67

12 00

10 00

14. 67

1700

18.67

20.00

21 33

24.00

OC 00

OQ AT)

OQ 00

30.67

0.0 nn

n wi

34.67

36.00

07 oo

38.67

40 00
386 GEOGRAPHIC TABLES AND FORMULAS.

I

gp

00

o

p

so a

OOi O1O3 000 IN IMIMi-H-H i

( r-l i-H ^H (M C^I W <N O1 CO CO CO CO C

' i-! I-H cq IN c to i> t> 06 od o> o> o c> I-H i-< ci c4 co co 
INDEX.

,-r

Alidades, micrometer, determination of constant and value of division...... 12-13

Altitude, differences of.................... 336-352

Arc for each statute mile on the parallel, latitudes 0°to 70°.................. 27-28

Arc into time, conversion of................. 124

Arcs of the parallel, in meters............... 38

Areas of quadrilaterals of 1° extent in latitudes and longitude........... 108-109

of 30' extent in latitude and longitude. 110-112 

of 15' extent in latitude and longitude. 113-118 

of 10' extent in latitude and longitude. 119-123 

Azimuth and apparent altitude of Polaris at

different hour angles............ 17-26

Azimuth of Polaris at elongation............ 16

Azimuths and distances, method of computing, when latitudes and longitudes are given................ 292-293

Baseline computations for steel tape measures ............................. 379

Center, reduction to......................... 6-7

reduction to, graphic.................... 8

Centigrade and Fahrenheit degrees, comparison of....................... 381

Chains into feet, conversion of............... 129

Circular functions, five-place logarithms of. 171-215 

Constants................................... 382

Convergence of meridians, latitudes 0° to

70° ............................. 27-28

Coordinates of curvature.................... 39-47

Cosines, natural........................... 162-170

Curvature, coordinates of.................... 39-47

Curvature and refraction, corrections for..... 335

Degrees of the meridian, lengths of.......... 36

Degrees of the parallel, lengths of............ 37

Elevations, errors in, from errors in distances

on steep slopes.................. 380

Elevations and horizontal distances from

stadia readings................ 353-361

Equivalents, convenient.................. 376-377

Fahrenheit and Centigrade degrees, comparison of....................... 381

Feet and decimals of a mile, interconversion

of............................... 128

Feet and meters, interconversion of.......... 291

Feet into chains, conversion of.............. 129

Geodetic coordinates, computation of, examples of...................... 217-218

Geodetic position computations........... 216-290

constants and formulas for............... 216

Kilometers and statute miles, interconversion

of............................... 291

Latitudes and departures, conversion of, 

from feet to seconds of latitude ' 

and longitude................. 295-334

Leveling, errors in............................ 380

Log. sec. J (A v)> values of.................. 291

Logarithms of natural numbers, five-place. 140-160 

Longitude, corrections to, for difference in

arc and sine..................... 292

Map scales, ratios for, and the logarithm of

each............................. 378

Maps, scale 1:125,000, projection of, coordinates for ........................ 48-57

scale 1:63,360, projection of, coordinates

for.............................. 58-69

scale 1:62,500, projection of, coordinates

for.............................. 70-75

scale 1 :48,000, projection of, coordinates

for.............................. 76-89

scale 1:24,000, projection of, coordinates

for.............................. 90-98

scale 1:12,000, projection of, coordinates

for............................. 99-107

Maps of large areas, projection of............ 36-47

Meridian, fixing, at any time by hour angle.. 14-15 

Meridians, convergence of, latitudes 0° to

70°.............................. 27-28

Metals, linear expansion of.................. 382

Meters and feet, interconyersion of........... 291

Metric into United States measures, conversion of........................... 362

Micrometer alidades, determination of constant and value of division....... 12-13

Mile, decimals of, and feet, interconversion

of............................... 128

statute, arc for, on the parallel, latitudes

0° to 70°......................... 27-28

Miles and logarithms of meters, interconversion of......................... 364-376

Numbers, natural, five-place logarithms of. 140-160 

Offsets from the secant to the parallel......... 32

computation of.......................... 32-33

Polaris, azimuth of, at elongation............ 16

azimuth and apparent altitude of, at different hour angles............... 17-26

Projection of maps, scale 1 :125,000, coordinates for......................... 48-57

scale 1 :63,360, coordinates for .......... 58-69

scale 1: 62,500, coordinates for........... 70-75

scale 1 :48,000, coordinates for........... 76-89

scale 1 : 24,000, coordinates for........... 90-98

scale 1 :12,000, coordinates for.......... 99-107

Projection of maps of large areas............. 36-47

Projection tables, example of use of.......... 34-35

Reduction to center......................... 6-7

graphic.................................. 8

Refraction, mean............................ 334

Refraction and curvature, corrections for.... 335

Rods, errors in plumbing.................... 380

387
388 INDEX.

S and T, formula for using................... 161

Salary, monthly, portions of, for fractions of a

month......................... 383-386

Seconds of latitude and longitude, values of,

in feet.....:..................... 29-31

Sines, natural............................. 162-170

Slopes, steep, errors in elevations on......... 380

Spherical excess, log m for computing......... 294

Stadia readings, horizontal distances and 

-, elevations from................ 353-361

Statute miles and kilometers, interconversion

of............................... 291

Tangents to a parallel, offsets and azimuths.. 33

Tape measures, base-line computations for .. 379 

Three-point problem........................ 9-10

graphic solution of....................... 11-12

Time, mean, into sidereal time, conversion of. 126

sidereal, into mean time, conversion of... 127

Time into arc, conversion of.................. 125

Triangle, finding the angles of, when three

sides are given................... 11

Triangles, solution of........................ 5,8-9

United States into metric measures, conversion of........................... 363-

Wheel revolutions into hundredths of a mile,

conversion of.................. 130-139

o

tr