DEPARTMENT OP THE INTEEIOB

OB1 THE

GEOLOGICAL ' SURYE3

ERRATA TO BULLETIN 50.

Ofp°a g6e343, latitude 31° 00' and 10' longitade, read for abscissa, 9.891 

" °4M «o w, read for meridional distance, 57.557 instead

L99, latitude 46° 50' and 10' longitude, read for abscissa, 16.687

of 11.687. 107, first column of table,'thirty-first argument, read 15 30 in0. first column of table, seventh argument, read 12 07 30 instead of 12 70 30. 16939 b 3 m

WASHINGTON

GOVERNMENT PRINTING OFFICE 

1889

DEPARTMENT OP THE INTEEIOE

BULLETIN

GEOLOGICAL -SURVEY

ISTo. 5

WASHINGTON

GOVERNMENT PRINTINGS OFFICE

1889

UNITED STATES GEOLOGICAL SURVEY

J. W. POWELL, DIRECTOR

FORMULAS AND TABLES

TO

FACILITATE THE CONSTRUCTION AND USE OF MAPS

EY

ROBERT SIMPSON WOODWARD

.WASHINGTON

GOVEENMENT FEINTING OFFICE

1889

CONTENTS

Pago.

Letter of transmittal........................................................ 7

A. Theory of the tables........ .............................................. 9

(1.) Adopted spheroid and constants thereof........................... 9

(2.) Principal radii of curvature....................................... 9

(3.) Lengths of arcs of meridian ....................................... 11

(4.) Lengths of arcs of parallels ..... .................................. 14

(5.) Co-ordinates for the polyconic projection of maps.................. 15

(6.) Areas of zones and quadrilaterals of the earth's surface ............ 18

B. Explanation of use of tables.............................................. 20

(7.) Table I........................................................... 20

(8.) Table II........................................................... 21

(9.) Table III......................................................... 21

(10.) Table IV ......................................................... 21

(11.) Tables V-XI..................................................... 22

(12.) Tables Xn-XV .................................................. 23

(13.) Table XVI....................................................... 23

Tables ...................._............................................ 25

Table I, logarithms of radius of curvature of meridian ................. 25

Table II, logarithms of radius of curvature of normal section .......... 28

Table III, lengths of arcs of meridian ............ ............ .......... 31

Table IV, lengths of arcs of parallels .................................. 32

Table V, co-ordinates for map projection on scale ^oWir- - -.--- -.---- 33

Table VI, co-ordinates for map projection on scale jTsVrTT .---.- - -- -- 36

Table VII, corordinates for map projection on scale -rrsWr -.- -..-- - 39

Table VIII, co-ordinates for map projection on scale nfav.............. 43

Table IX,-co-ordinates for map projection on scale roi<j 0 ----............ 47

Table X, co-ordinates for map projection on scale rr&TEr-----..--- ..-..- 53

Table XI, co-ordinates for map projection on scale 77-^7 - ----..--.-- - 78

Table XII, areas of quadrilaterals of the earth's surface of 1° extent in

latitude and longitude ..... ............................ ............ 103

Table XIII, areas of quadrilaterals of the earth's surface of 30' extent in

latitude and longitude .............................................. 105

Table XIV, areas of quadrilaterals of the earth's surface of 15' extent in

latitude and longitude ...... ............ ...... ...................... 109

Table XV, areas of quadrilaterals of the earth's surface of 10' extent in

latitude and longitude ..............................._:.......__ 117

Table XVI, actual intervals corresponding to 0.01 inch on maps of various \

scales.................. ............................................. . 123

Miscellaneous constants.........................................___.......... 124

(311)

LETTER OF. TRANSMITTAL.

DEPARTMENT OF THE INTERIOR,

UNITED STATES GEOLOGICAL, SURVEY,

Washington, D. C., January 9, 1889.

SIR : I have the honor to transmit herewith, through Mr. Henry Gannett, Geologist in charge of Geography, a series of mathematical formulas 

and tables designed to facilitate the construction and use of maps.

Manuscript copies of the tables were prepared for the Division of Geography in 1885-6. Constant use since then has demonstrated their utility. 

They have recently been revised and extended, and are here accompanied 

by an explanatory text.

The computations required in the preparation and revision of the tables 

were made chiefly by Mr. B. C. Washington, jr., and Mr. S. S. Gannett, 

who evinced a commendable zeal to render the work thoroughly accurate. 

Very respectfully, your obedient servant,

R-. S. WOODWARD, 

In charge of Mathematical Division. 

Hon, J. W. POWELL,

Director U. 8. Geological Survey.

(313)

FORMULAS AND TABLES TO FACILITATE THE CONSTRUCTION 

' AND USE OF MAPS.

BY E. S. WOODWARD.

A. THEORY OF THE TABLES.

ADOPTED SPHEROID AND CONSTANTS THEREOF.

(1.) The spheroid on which the data given in the following tables

depend is that whose elements were published by Clarke in 1866.* >This

spheroid undoubtedly represents very closely the true size and shape of 

the earth, and it is the one to which nearly all geodetic work in the 

United States is now referred.

The constants of the generating ellipse of this spheroid, whose numerical 

values are required in the ^computation of the tabular quantities, are 

denned as follows:

a = semi major axis, 

b = semi minor axis,

e = eccentricity = J ( I 2 \

 i

n = (1 - ]/ 1 - e2) (1 + T/ 1 - e2). 

The values of these constants and their logarithms are 

log.

a = 20926062 English feet, 7.3206875, 

6 = 20855121 " 7.3192127, 

e2 = 0.00676866, 7.8305030 - 10, 

n = 0.00169792, 7.2299162 10.

PRINCIPAL RADII OF CURVATURE.

(2.) Of the derived quantities essential to the present purposes the most 

important are the principal radii of curvature of. the adopted spheroid; 

and, as these radii and their reciprocals enter many of the formulas of

* Comparisons of Standards of Length, made at tLe Ordnance Survey Office, Southampton, England, by Capt. A. K. Clarke, R. E. Published by order of the Secretary 

of State for War, 1866.

9 

(316)
10 FORMULAS AND TABLES. [BULL. 50.

geodesy, it will be advantageous to give expressions from which their 

logarithms may be readily computed. At any point on the spheroid let

<p = the astronomical latitude, 

pm = the radius of curvature of the meridian section, 

pn = the radius of curvature of the section normal to the meridian. 

Then the values of the radii are 

P--"^ ^ ^ « 8m ?» N (1)

pn = a (1 e1 SIJT <p). *

The geometrical relations of the quantities just defined are shown in Fig. 1, 

which represents a meridian section of 

the spheroid. P is any point whose geographical latitude is (p. Both radii of 

curvature coincide in direction with the 

normal PQ. />n is that portion of the 

normal lying between P and the minor axis 

DE, or PQ; while pm = PO is always 

less than />n except when <p = ± 90°,

in which case the two radii are equal.

The logarithm of the radical which enters formulas (1) may be most

readily computed by the following formula, viz:

log (l o ea sin; = + log (1 + n)

 /m cos 2<p

 f ^ fJ-n2 cos 4<p

 J /m3 cos 6<p

(2)

in which n has the value defined above and // is the modulus of common 

logarithms. Introducing the values of the constants given above in formulas (1) and (2) there result 

Eadius of curvature of meridian section pm in feefe. 

log/>m = + 7.3199482

 [4.34482] cos 2<p (3) 

+ [1.274] cos 4<p

Radius of curvature of normal section pu in feet. 

log^n ^ -f 7.3214243

 [3.86770] cos 2p 

4- [0.797] cos 4(f

(4)

(316)
WOODWAED.] THEORY OF TABLES. 11

The numbers inclosed in brackets in these formulas are the logarithms 

of the coefficients of the trigonometrical factors for units of the seventh 

decimal place.

The formulas (3) and (4) will give log pm and log pn within one unit in 

the seventh place of decimals, or pm and pn within 1 /4000000 part (about 5 

feet), an accuracy about fifty times that of the semi axis a. The values of 

log pm and log |0n are given in Tables I and II respectively, for every 

minute of latitude from latitude 21° to latitude 50°.

LENGTHS OF AECS OF MERIDIAN.

(3.) For the computation of short meridional arcs lying between given 

parallels of latitude the following simple formulas suffice:

A<p = <f>2 ft,

V = 1 (ft + ft), (5) 

AM=pm A(p.

In these, ft and <p2 are the latitudes of the ends of the 'arc, AM is the 

required length, and pm is the meridian radius of curvature for the latitude (p of the middle point of the arc. The formula for AM implies that 

A<p is expressed in parts of the radius. If A<p is expressed in seconds, 

minutes, or degrees of arc, the formula becomes 

 Meridional' distance AM in feet.

AM seconds)

206264.8 ' 

_ pm A(p (in minutes) 

= 3437.747 '

_ pm A<p (in degrees). f .

~ 57.29578 ' W 

log (1/206264.8) = 4.6855749 10, 

log (1/3437.747) = 6.4637261 10, 

log (1/57.29578) = 8.2418774 10. 

(pi , <p2 = end latitudes of arc, Aq> = <p2 <pj, , pm = meridian radius of curvature for q> = £ (o> 2 + <PI) ; for log pm see Table I.

The relations (6) will answer most practical purposes when A<p does not 

exceed 5°. A comparison with the precise formula (7) below shows in 

fact that the error, of (6) is very nearly

. $ e2 A(pz cos 2</> . AM,

which vanishes for <p = 45°, and which for A<p = 5° is at most 

or about 11 feet.

Numerical example. Suppose 

<f>2 = 37° 297 48".17,

^ = 35° 48' 29".89.

(317)
12 FORMULAS AND TABLES. [BULL. 50.

Then '

? = *(?« + Pi) = 36° 39' 09".03,

dip = (f>2 (f>l= 1° 41' 18".28,

== 6078".28.

From the first of (6)

cons't. log 4.6855749 10

Table I, log pm 7.3193112

log Ay 3.7837807

AM = 614705 feet, log AM 5.7886668

The values of AM for intervals of 10", 20" . . . 60", and for 10', 

20' . . . 60' are given in Table III for each degree of latitude from 25° 

to 49°.

For precise computation of long meridional arcs the following formula 

is adequate : *

AM A0 A(p Al cos 2^ sin A<p

-J- A2 cos 4<p sin 2Ay>

 AB cos 6<p sin 3A<p (7) 

+ A cos 8( sin

In this, AM, <p, and Ay have the same meanings as above, and AQ) Al} 

. . are functions of a and e or of a and n. 

Thus, in terms of a and n,

4, = o(l + nf\l + in* + Jtn* + . . .), 

A, = 3o (1 + n} (n - ^ n3 . . . ),

^4 = ttf a (1 + n)n* - . . . ). 

Introducing the adopted values of a and n, these constants become 

log.

A0 = 20890606 feet, 7.3199510, 

Al = 106411 feet, 5.0269880, 

A2 = 113 feet, 2.0528, 

A3 = 0.1 5 feet, 9.174 10.

It appears, therefore, that the first three terms of (7) will give AM 

with an accuracy considerably surpassing that of the constant A0 . In

(318)
WOODWAED.] THEORY OF TABLES. 13

the use of (7) it will generally be most convenient to express J$ in degrees, and in this case A0 must be divided by the number of degrees in 

the radius, viz: 57.2957795 [1.7581226]. Applying this value and 

writing the logarithms of A0, A^ etc., in rectangular brackets in place of 

A0, Al} etc., (7) becomes

Meridional distance JM in feet.

AM = [5.5618284] A<p (in degrees)

 [5.0269880] cos 2y> sin 4<p (8) 

+ [2.0528] cos 4<p sin 2 A<p

2q> = q>% -f- q>i, A<p = cpi (Pi, tpi, <PZ = end latitudes of arc.

Formula (8) will suffice for the calculation of any portion or the whole 

of a quadrant. The length of a quadrant is the value of the first term of 

(8) when y> = 45° and A<p = 90°, since all of the remaining terms vanish.

Numerical examples. 1 °. Suppose

ft = 0° and (pz = 45°.

Then 2<p = 45°,

A<p = 45°.

log.

cons't 5.5618284 

45 1.6532125

1st term + 16407443 feet 1st term. 7.2150409

cos 2(f> 9.8494850 10

sin A<p 9.8494850 10

cons't 5.0269880

2dterm 53205.7 feet 2d term 4.7259580

The third term of the series vanishes by reason of the factor cos 4 <p = 

cos 90° = 0. The sum of the first two terms, or length of a meridional 

arc from the equator to the parallel of 45°, is 16354237 feet.

2°. Suppose ^ = 45° and <p2 = 90°. 

Then 2p = 135°,

A<p= 45°.

The numerical values of the terms will be the same as in the previous 

example, but the sign of the second term will be plus. Hence the length 

of the meridional arc between the parallel of 45° and the adjacent pole is 

16460649 feet. The sum of these two computed distances, or the length

of a quadrant, is 32814886 feet.

(319)
14 FORMULAS AND TABLES. [BULL. 50.

This agrees as it should with the length given by (8) when 2<p = 90° 

and A<p = 90°.*

LENGTHS OF ARCS OF PARALLEL.

(4.) The radius of any parallel of latitude is equal to the product of the 

radius of curvature of the normal section for the same latitude by the cosine 

of that latitude. That is, see FIG. 1, r being the radius of the parallel 

r = pn cos <p, 

and the entire length of the parallel is 

2 7i r = 2 TT pn cos (p.

Designate the portion of a parallel lying between meridians whose longitudes are ^ and ^2 by AP, and call the difference of longitude ^2 ^u AL

' Then 

Arc of parallel AP in feet.

,~ 2 re p cos <p ., ... , , 

AP = 1296000 M <m

2 7i a cos 

21600

2 7T />_ COS

(. (m

C> ,, ,. , x ^ (m degrees)-

log (2 7T/1296000) = 4.6855749 10, 

log (2 ^/21600) == 6.4637261 10, 

log (2 7T/360) = 8.2418774 10.

AI, A2 end longitudes of arc, A A = A2 A, ,

pn = radius of curvature of normal section for latitude of parallel ; for log pn 

see Table II.

Numerical example. Suppose </> = 35°, and dX = 72°. Then from

the third of (9)

log.

cons't 8.2418774 10 

Table II, pa 7.3211716 ~

9.9133645 10 

1.8.573325

AP == 21564827 feet, AP 7.3337460

The values of 4Pfor intervals of 10", 20" . . . 60", and for 10', 20' 

... 60' are given in Table IV for each degree of latitude from 25° to 49°.

* The best formula for computing the entire length of a meridian curve is this:

TT (a + 6) (1 + i »* + -Jr n* + .'..'),

in which a, I, and « are the same as denned in section (1). For the values here 

adopted Jog>

(1 + i n2 + . . . ) 0.0000003

(a + ft) 7.6209807

Tt 0.4971499

length 8.1181309

The length of the perimeter of the generating ellipse, or the meridian circumference of the earth, is, therefore 

131259550 feet = 24859.76 miles.

(320)
WOODWARD.] THEORY OF TABLES. 15

CO-ORDINATES FOR THE POLYCONIC PROJECTION OF MAPS.

(5.) In the polyconic'system of map projection every parallel of latitude appears 

on the map as the developed circumference 

of the base of a right cone tangent to the 

spheroid along that parallel. Thus the 

parallel E F (FiG. 2) will appear in projection as the arc of a circle EOF (FiG. 

3) whose radius O G =7 is equal to the 

slant height of the tangent cone E F G, 

(FiG. 2). Evidently one meridian and J' 

only one will appear as a straight line. 

This meridian is generally made the central meridian of the area to be projected. 

The distances along this central meridian 

.between consecutive parallels are made

Fig.3.

equal (on the scale of 

the map) to the real distances along the surface of the spheroid. 

The circles in which 

the parallels are developed are not concentric, but their centers 

all lie on the central 

meridian. The meridians are concave toward the central meridian, and, except near 

the corners of maps showing large areas, they cross the parallels at angles 

differing little from right angles.

In the practical work of map making, the meridians and parallels are 

most advantageously defined by the co-ordinates of their points of intersection. These co-ordinates may be expressed in the following manner: 

For any parallel, as E O F (FiG. 3), take the origin O at the intersection 

with the central meridian, and let the rectangular axes of Y (O G) and X 

(O Q) be respectively coincident with and perpendicular to this meridian. 

Call the interval in longitude between the central meridian and the next 

adjacent one J^, and denote the angle at the center G subtended by the 

developed arc O P by a.

Then from FIG. 3 it appears that

x = I sina, 

y = 2 I sin2 |a. 

(321)
16 FORMULAS AND TABLES. [BULL. 50.

But from FIGS. 2 and 3,

I = /?n coty, 

la = r AX = |0n AX cosp,

whence

a = AX stop.

Hence, in terms of known quantities there result

x = pn cotp sin (AX stop),

y = 2 pn cot(f> sin2 J (JA stop).

Numerical example. Suppose p = 40° and AX = 25° = 90000".

Then

log 90000" = 4.9542425,

log sin 40° = 9.8080675 10,

log 57850".88 = 4.7623100.;

AX stop = 16° 04' 10".88,

J (AX stop) = 8° 02' 05".44.

log.

sin (AX stop) 9.4421760 10 

cotp 0.0761865 

pn, Table II 7.3212956

6.8396581 

x = 6912865 feet

log.

sin £ (AX stop) 9.1454305 10 

" " 9.1454305 10 

cot^ 0.0761865 

Pv Table II 7.3212956 

2 0.3010300 

y 5.9893731 

y = 975828 feet.

The equations (10) are exact expressions for the co-ordinates. But when 

AX is small, one may use the first terms in the expansions of sin (AX sm<p) 

and sin2 J (AX sin^>) and reach results of a much simpler form.

Thus,

sin (AX sinyj) = AX siny> $ (AX sin^)3 + 

sin2 1 (A<p sin^) = % (AX sin^)2 -fa (AX sin^) 

whence, to terms of the second order,

x = ,oa AX cosy [1 | (AX stop)2],

+ .

^ J

If the terms of the second order in these equations be neglected, the value 

of x will be too great by an amount somewhat less than |- (AX sinp)2 . x, 

and the value of y will be too great by an amount somewhat less than 

 ^ (AX sinp)2 . y. An idea of the magnitudes of these fractions of x and y 

may be gained from the following table, which gives the values of $ 

(AX sinp)2 for a few values of the arguments AX and <p.

(322)
WOODWAED.] THEORY OF TABLES. 

Values of $ (AX sirup}2.

17

M

o

12 

3

9

20°

1/168000 

1/42000 

1/18700

40°

1/47700 

1/11900 

1/5300

60°

1/26260 

1/6560 

1/2920

It appears from this table that the first terms of (11) will suffice in computing the co-ordinates for projection of all maps on ordinary scales, and 

of less extent in longitude than 2° from the middle meridian. For example, the value of x for M = 2° and <p = 40°, and for a scale of two 

miles to one inch (1/126720), is 53.063 inches less 1/11900 part, or 

about 0.004 inch, which may properly be regarded as a vanishing quantity 

in map construction. For the computation of the co-ordinates given in the 

following tables, where Ah does not exceed 1°, it is amply sufficient, therefore, to use

AX cos

- l ;

x =

In these formulas and in (11), if Ah is expressed in seconds, minutes, or 

degrees, it must be divided by the number of seconds, minutes, or degrees 

in the radius. The logarithms of the reciprocals of these numbers are 

given in equations (6) and (9) and also on the last page of this book. In 

the construction of tables like V to XI, it is most convenient, when 

English units are used, to express Ah in minutes and x and y in inches. 

For this purpose, supposing log p^ to be taken from Table II, if s be the 

scale of the map, or scale factor, equations (12) become 

Co-ordinates x and y in inches for scale 8.

12

A sin 2<p,

y (3437J47)2

AX in minutes;

log (12/3437.747) =7.54291 10,

log (3/(3437.747)2j = 3.4046 10.

(13)

Tables V-XI give the values of a; and y for various scales and for the 

zone of the earth's surface lying between 25° and 50°. 

Bull. 50 2

(323)
18 FORMULAS AND TABLES. [BULL. 60.

Numerical example. Suppose y> = 40° and Al = 15'; and let the 

scale of the map be one mile to the inch, or s = 1 / 63360. Then the 

calculation by (13) runs thus:

log. log. 

cons't 7.54291 10 cons't 3.4046 10 

^ 7.32130 pn 7.3213 

s 5.19818 10 s 5.1982 10 

15 1.17609 (15)2 2.3522 

cosy? 9.88425 10 sin 2^ 9.9934

x 1.12273 y 8.2697 10

In. In.

x= 13.266 9y = 0.01861.

These values of x and y, it will be observed, agree with those corresponding to the same arguments in Table Vlll, p. 45. 

. When many values for the same scale are to be computed log s should, 

of course, be combined with the constant logarithms of (13). Moreover, 

since in (13) x varies as ^A and y as (^/l)2> when several pairs of co-ordinates are to be computed for the same latitude, it will be most advantageous 

to compute the pair corresponding to the greatest common divisor of the 

several values of A~k and derive the other pairs by direct multiplication.

AREAS OF ZONES AND QUADRILATERALS OF THE EARTH'S SURFACE.

(6). An expression for the area of a zone of the earth's surface or of a 

quadrilateral bounded by meridians and parallels may be found in the following manner:

The area of an elementary zone dZ} whose middle latitude is <p and 

whose width is pm d<p, is (see FIG. 1),

dZ = 2 TT r pm d<p 

By means of the relations (1), this becomes

~\ fy _ o 2/1 2\ COS^ CL(D UtZt A TT a (I e ) o -. ^ ^5 

(1 e $\n tpY

< 14) 

_ f\ 2 *- ' ^ a \e s\n(pj

e (1 e2 sin2 <pf

The integral of this between limits corresponding to ^ and ^>2 > or the area 

of a zone bounded by parallels whose latitudes are <pv and <f>2 respectively, is

C ' e sin ^>2 e sin

~1 2 : 2 

-i o i e sin <£>9 I ____ /5* I / L

 

i i AT ' i (1 + e sin <£> ) (1 e sin tp,) I -f * JNap. log 4- -. Y2J. \^ ; 5LL' 

(1 e sm <p 2 ) (li+ e sin ^) J

(324)
WOODWARD.] THEORY OF TABLES. 19

To get the area of the entire surface of the spheroid, make ^ = £ K 

and <p2 = + £ TT in (1 5). The result is

Surface of spheriod = 2 TT a2 1~1 +' ^-=^- Nap. log (^-^-} 1 . (16) 

r L 2 e V.1 e/ J

For numerical applications it is most advantageous to express (16) in a 

 series of powers of e. Thus, by Maclaurin's theorem,

/ e2 64 g6 \ 

Surface of spheroid = 4 it a2 (1 ^- -y=- -^- . . . ) . (17)

For the calculation of areas of zones and quadrilaterals it is also most 

advantageous to expand (15) in a series of powers of e sin ^ and e sin <p2 

and express the result in terms of multiples of the half sum and half 

difference of ^ and <pz. Thus, (15) readily assumes the form

r 2 ~|

Z 2 /r a2 (1 e2) (sin <p2 sin ^) -f -5- e2 (sin3 <p2 sin3 ^) + . . .

From this, by substitution and reduction, there results

Z __'2 TT / ^i cos^ sm ^ ^¥ ^2 cos 3^? sin f Jy? 1

I + C3 cos 5^ sin | Jp . . )' 

wherein

^=1(^2 + Pl)l

A<?= y^ y^

(19)

If Q be the area of a quadrilateral bounded by the parallels whose lati 

tudes are ^ and <p2 and by meridians whose difference of longitude is ^,

Hence, using the English mile as unit of lengfeh, (18) and (19) give for 

the adopted spheroid 

Area of quadrilateral in square miles.

sin ' ~ c cos sin *

0 = AX (in degrees)

* 8 ; c3 cos ^ sn

logo* = 5.7375398, (20) 

log c2 = 2.79173, 

log c3 = 9.976 10.

& i (<P-2 + <Pi), Acp q> 2 <P!, 

-2 = latitudes of bounding parallels, 

A. = dift'erence of longitude of bounding meridians.

*d, Cj, c:; are obtained from Ci, C-i, C.\ respectively by dividing the latter by the 

number of decrees in the radius, viz: 57.29578.

(325)
20 FORMULAS AND TABLES. [BOIL. 50.

Numerical examples. 1°. Suppose <fl = 0, <f>2 = 90° and AX = 360°. 

Then (20) should give the area of a hemispheroid. The calculation runs 

thus:

log. log. log. 

Cl 5.7375398 c2 2.79173 c3 9.976 10 

cosy* 9.8494850 10 cos 3 ^ 9.84948n--10 cos 5 y 9.S49n 10 

sinf/ty 9.8494850 10 sin f Ay 9.84949 10 sin |- A<p 9.848n 10" 

360 2.5563025 360 2.55630 360 2.556

Sum 7.9928123 5.04700n 2.229

Hence 

1st term = + 98358591 

2d term =-f- 111429 

3d term = -f . 169

Q= sum= 98470189

Twice this is the area of the spheroidal surface of the earth; i. e. 

196940378 square miles.

1 2°. The last result may be checked by (17). Thus, 

(^ + fs + -^ = 0.00225928

\ O 4.0 y * X ' .

log fl ^ .. .^ = 9.9990177 

V t> s

log a2 . = 7.1961072 

log 4 ic . *= 1.0992099

log (196940407) = 8.2943348. 

This number agrees with the number derived above as closely as 7-place

logarithms will permit, the discrepancy between the two values being 

about -BTn^wo Part °^ ^e area* Hence, with a precision somewhat greater 

than the precision of the elements of the adopted spheroid warrants,

Area earth's surface = 196 940 400 square miles. 

The areas of quadrilaterals of the earth's surface bounded by meridians 

and parallels of 1°, 30', 15', and 10' extent respectively, in latitude and 

longitude, are given in Tables XII-XV.

B. EXPLANATION OF USE OF TABLES.

(7.) Table I gives the logarithms of the meridian radius of curvature 

of the earth for each minute "of latitude from 21° to 51°. The unit of 

length is the English foot. The method of computing these logarithms is 

explained in section. (2). Logarithms corresponding to arguments falling 

between the tabular arguments are derived by interpolation, this process

(326)
WOODWARD.] EXPLANATION OF TABLES. 21

being facilitated by the side tables of proportional parts. For example, 

log pm for latitude 27° 39' 42" is found thus :

log pm for 27° 39' 7.3186882 Tabular dif. 11.

tabular correction for 42", or ff X 11, + 8

log jOm for 27° 39' 42" 7.3186890

(8.) Table II gives the logarithms of the radius of curvature of the 

normal section. It is in all respects similar to Table I. Its derivation is 

explained in section (2).

(9.) Table III gives lengths of terrestrial arcs of meridians corresponding 

to latitude intervals of 10", 20" . . . 60" and 10', 20' . . . 60', 

or lengths corresponding to arcs less than one degree. The unit of length 

is the English foot. The derivation of this table is explained in section (3).

The length corresponding to any latitude interval is the distance along

the meridian between parallels whose latitudes are less and greater respectively than the given latitude by half the interval. Thus, for example, 

the length corresponding to the interval 30' and latitude 37° (182047.3 feet) 

is the distance along the meridian from latitude 36® 45' to latitude 37° 15'. 

By interpolation, we may get from this table the meridional distance 

corresponding to any interval falling between latitude 25° and latitude 50?. 

The following example will illustrate this use: Required the length of the 

meridional arc between latitude 41° 28' 17".8 and latitude 41° 39' 53".4. 

The difference of these latitudes is 11' 35".6 and their mean is 41° 34' 

05".6. The computation runs thus :

Latitude 41°. Tabular difference. 

10' 60724.60 feet 10.70 feet 

V 6072.46 " 1.07 " 

30" 3036.23 " .54 " 

5" 506.04 " .09 " 

0".6 60.72 " .01 "

_

60 ______ Sura> 12-41 feetLength = 70407.10 feet.

When the degree of precision required is as great as that in the example 

just given it will be more convenient to use formula (6). Thus, in this

example 

log.

Jy> = 695".6 2.8423596 

<f> = 41° 34' 05".6, pm (Table 1) 7.3196820

cons't 4.6855749

Length = 70407.10 feet 4.8476165

(10.) Table IV gives lengths of terrestrial arcs of parallels corresponding 

to longitude intervals of 10", 20", . . , 60" and 10', 20', . . . 60', or

(327)
22 FORMULAS AND TABLES. [BULL. 50.

lengths corresponding to arcs less than one degree. Its derivation is explained in section (4). The unit is the English foot.

The method of using this table is similar to that applicable to Table III, 

explained above. For the precise computation of arcs along parallels 

intermediate to those of the table, direct application of formula (9) is less 

laborious than interpolation from the table.

(11.) Tables V to XI give the co-ordinates for the projection of maps 

according to the polyconic system explained in section (5) for the following 

scales respectively :

Scale Table V.

6S361T> 

62500?

V III.

The unit of length is the English inch.

The use of these tables and their application in the graphical construction of maps may be best explained by an example. Suppose it is required

S

U

H

50'

G

40'

R

30'

E M N

20

D

10

Fiy.4.

(328)
WOODWARD.] EXPLANATION OF TABLES. 23

to draw meridians and parallels for a map of an area of 1° extent in longitude, lying between the parallels of 34° and 35°. Let the scale of the map 

be one mile to the inch, or 1 / 63360, and let the meridians and parallels 

be 10' apart respectively. Draw on the projection paper an indefinite 

straight line A B, FIG. 4, to represent the middle meridian of the map. 

Take any convenient point, as C, on this line for the latitude 34°, and lay 

off from this point the meridional distances C D, C E, C F, . . .01 

given in the second column of Table VIII, p. 44.* Through the points 

D, E, F, -. . . . I thus found, draw indefinite straight lines perpendicular 

to A B. By means of these lines and the tabular co-ordinates, points 

on the developed parallels and meridians are readily found. Thus, for 

example, the abscissas for points ten minutes apart on the parallel 34° 20' 

are 9.53, 19.06, and 28.59 inches. These distances are to be laid off on 

N 1ST' in both directions from A B. At the points L, M, N, I/, M', F, 

so determined, erect perpendiculars to N N' equal in length, respectively, to 

the ordinates corresponding to the longitude intervals 10', 20', 30'. The 

carved line joining the extremities of these perpendiculars is the parallel 

required. It may be drawn by means of a flexible ruler. The other parallels are constructed in the same manner. They are all concave towards 

the north or south according as the map shows a portion of the northern 

or southern hemisphere. The meridians are drawn in a similar manner 

through the points (e. g., P, Q, M, R, S, T, U in FIG. 4) having the same 

longitude relative to the middle meridian. All meridians are concave 

towards the middle meridian.

A test of the graphical work which should always be applied is the 

approximation to equality of corresponding diagonals in the various quadrilaterals formed. Thus in FIG. 4, V X should be equal to W Y, C N* 

toCN', EVtoE W, etc.f

(12.) Tables XII to XV give the areas in square miles of quadrilaterals of the earth's surface of 1°, 30', 15' and 10' extent, respectively, in 

latitude and longitude. Their derivation is explained in section (6). The 

spheroid adopted in the computation of these tables is Clarke's (1866). 

See section (1). The arguments of the tables are the middle latitudes of 

the quadrilaterals. From the tabular values, by means of interpolation 

and summation, the area of any portion of the earth's surface bounded by 

meridians and parallels- may be found.

(13.) Table XVI shows the actual intervals or distances in feet corresponding to 0.01 inch on maps of different scales. It is derived in the following manner:

* The meridional distances and the abscissas of the points on the developed parallels 

in Fig. 4 are one-twentieth of the true or tabular values. The ordinates of points on 

the developed parallels are the tabular values.

t It should be noted that C N is not equal to E V, N and V referring here to points 

on the developed parallels.

(329)'
24 FORMULAS AND TABLES. [BULL, so.

Let I be the actual linear interval corresponding to the interval i on a 

map whose scale is s. Then

1 = _i

s

If in this we. make i = 0.01 inch and express I in feet, there results

T . , . 0.01 inch Jm feet = ^ . 

12 s

Making s successively 1 / 250000,1 /126720, etc., the values in the table 

are found.

(330)
WOODWARD.] RADIUS OF CURVATURE OF MERIDIAN. 25

TABLK I. Logarithms of meridian radius of curvature pm in English feet. 

[Derivation of table explained in section (2); use of table explained on p. 20.]

Lat,

0

1 

2 

3

4 

6 

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

51 

52 

53

54 

55 

56

57 

58 

69

60

21°

7.318

' 3045

3053 

30G2 

3070

3079 

3088 

3096

3105

3113

3122

3131

3139 

3148 

3157

3165 

3174 

3183

3191

3200 

3209

3217

3220 

3235 

3244

3252 

3261 

3270

3278

3287 

3296

3305

3313 

3322 

3331

3340 

3349 

3357

3366

3375 

3384

3393

3401 

3410 

3419

3428 

3437 

3446

3454

3463 

3472

3481

3490 

3499 

3508

3516 

3525 

3534

3543 

3552 

3561

3570

 22°

7.318

3570

3579 

3588 

3597

3605 

3614 

3623

3632

3641 

3R50

3659

3668 

3677 

3686

3695 

3704 

3713

3722

3731 

3740

'3749

3758 

3707 

3776

3785 

3794 

3804

' 3813

3822 

3831

3840

3849 

3S58 

3867

3876 

3885 

3894

3913 

3922

3931

3940 

31)49 

3958

3967 

3977 

3986

3995

4004 

4013

4022

4032 

4041 

4050

4059 

4068 

4078

4080 

4096 

4105

4115

23°

7.318

4115

4124 

4133 

4142

4152 

4161 

4170

4179

4189 

4198

4207

4216 

4220 

4235

4244 

4254 

4263

4272

4282 

4291

4300

4310 

4319 

4328

4338 

4347 

4356

4366

4375 

. 4384

4394

4403 

4413 

4422

4431 

4441 

4450

4469 

4479

4488

4498 

4507 

4516

4526 

4535 

4545

4554'

4504 

4573

4583

4592 

4602 

4611

4621 

4630 

4640

4649 

4659 

4668

4678

24°

7.318

4678

4088 

4097 

4707

4716 

4726 

4735

4745

4754 

4704

4774

4783 

4793 

4802

4812 

4822 

4831

4841

4851 

4800

4870

4879 

4889 

4899

4908 

4918 

4928

4937

4947 

4957

4960

4970 

4980 

4990

5005 

5015 

5025

5034

5044 

5054

5004

5073 

50S3 

5093

5103 

5112 

5122

5142 

5151

5161

5171 

5181 

5191

5200 

5210 

5220

5230 

5240 

5250

5259

25°

7.318

5259

5269 

5279 

5289

5299 

5309 

5319

5328

5338 

5348

5358

5368 

5378 

5388

5398 

5408 

5417

5427

5437 

5447

5457

5467 

5477 

5487

5497 

5507 

5517

5527

5537 

5547

5557

5567 

5577 

5587

5597 

5007 

5617

5037 

5647

5657

5667 

5677 

5687

5097 

5707 

5717

5727

5737 

5747

5757

5767 

5777 

5787

5798 

5808 

5818

5828 

5838 

5848

5858

26°

7.318

5858

5868 

5878 

5889

5899 

5909 

5919

5929

5939 

5949

5960

5970 

5980 

5990

6000 

6011 

6021

0031

6041 

G051

6062

6072 

6082 

6092

6102 

6113 

6123

6133

6143 

6154

6164

6174 

6185 

6195

6205 

0215 

6226

0246 

6256

6267

6277 

6287 

6298

6308 

6318 

6329

6339

6349 

6360

6370

6380 

6391 

6401

6411 

6422 

6432

6442 

6453 

6463

6474

27°

7.318

6474

0484 

6494 

6505

6515 

6526 

6536

6546

6557 

 6567

6578

0588 

6599 

6609

6620 

6630 

6640

6651

0661 

6672

6682

0693 

6703 

6714

6724 

6735 

6745

6758

676G 

6777

6787

6798 

6808 

6819

6829 

6840 

6851

6861

6872 

6882

6893

6903 

0914 

6924

6935 

6946 

,6956

6067

6977 

6988

6999

7009 

7020 

7030

7041 

7052 

7062

7073 

7084 

7094

7105

28°

7.318

7105

7116 

 7126 

7137

7148 

7158 

7169

7180

7190 

7201

7212

7222 

7233 

7244

7254 

7265 

7276

7287

7297 

7308

7319

7329 

7340 

7351

7362 

7372 

7383

7394

7405 

7416

7426

7437 

7448 

7459

7469 

7480 

7491

7cr\o

7513 

7523

7534

7545 

7556 

7567

7578 

7588 

7599

7610

7621 

7632

7643

7653 

 7664 

7675

7686 

7697 

7708

7719 

7729 

7740

7751

29°

7.318

7751

7762 

7773 

7784

7795 

7806 

7817

7828

7839 

7850

7860

7S71 

7882 

7893

7904

7915 

7926

7937

794S 

7959

7970

7981 

7992 

S003

8014

8025 

8036

8047

8058 

8069

8080

8091 

8102 

8113

8124 

8135 

8146

Q1R7

8168 

8179

8190

8201 

8212 

8223

8234 

8246 

8257

8268

8279 

8280

8301

8312 

8323 

8334

8345 

8356 

8368

8379 

8390 

8401

8412

30°

7.318

8412

8423 

8434 

8445

8457 

8408 

8479

8490

8501 

8512

8523

8535 

8546 

8557

8568 

8570 

8591

8602

8G13 

8624

8635

8647 

8658 

8669

8680 

8691 

8703

8714

8725 

8736

8747

8759 

8770 

8781

8792 

8804 

8815

QQOfi

8838 

8849.

8860

8871 

8883 

8894

8905 

8916 

8928

onqo

8950 

8962

8973

8984 

 8996 

9007

9018 

9030 

9041

9052 

9064 

9075

9086

P

10 

20

30

40

50 

60

10

30

40

50 

60

I

10

20

30 

40

50 

60

1

10 

20

30 

40

50 

60

1

10 

20

' 4030 

60 

60

. P.

8

1.3 

2.6

4.0 

5.3

6.7 

8.0

9

1.5

3 A

4.5 

6.0

7.5 

9.0

0

1.7

3

0

5.0 

G.7

8.3 

10.0

1

1.8 

3.7

5.5 

7.3

9.2 

11.0

2

2.0 

4.0

6.0 

8.0

10.0 

12.0

(331)
26 FORMULAS AND TABLES. [BULL 50.

TABLE I. Logarithms of meridian radius of curvature pm in English feet.

[Derivation of table explained in section (2); use of table explained on page 20.]

Lat.

/ 

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

11

45 

46

47 

48 

49

50

51 

52 

53

54 

55 

56

57 

58 

59

60

31°

7.318

9086

9098 

9109 

9120

9143 

9154

9166 

9177 

9189

9200-

9211 

9223 

9234

9245 

9257 

9268

9280 

9291 

9302

9314

9325 

9337 

9348

9360

9371 

9382

9393 

9405 

9417

9428

9440 

9451 

9463

9474 

9485 

9497

9508 

9520 

9531

9543

9554 

9566 

9577

9600 

9612

9623 

9635 

9646

9658

9669 

9681 

9692

9704 

9715 

9727

9739 

9750 

9762

9773

32°

7.318

9773

9785 

9796 

9807

9819

9831 

9843

9854 

9866 

9877

9889

9900 

9912 

9924

9935 

9947 

9958

9970 

9982 

9993

*0005

*0016 

*0028 

*0040

*0051

*0075

*0086 

*0098 

*0110

*0121

*0133 

*0144 

*0156

*0168 

*0179 

*0191

*0203 

*0214 

*0226

*0238

*0249 

*0261 

*0273

*0285

*029G 

*0308

*0320 

*0331 

*0343

*0355

*0366 

*0378 

*0390

*0402 

*0413 

*0425

*0437 

*0449 

*0460

*0472

33°

7.319

-0472

0484 

0495 

0507

0519

0531 

0542

0554 

0566 

0577

0590

0601 

0613 

0625

0637 

0648 

0660

0672 

0684 

0696

0707

0710 

0731 

0743

0755

0766 

0778

OWO 

0802 

0814

0826

0837 

. 0849 

0861

0873 

0885 

0897

0908 

0920 

0932

0944

0956 

0968 

0980

nnno

1003 

1015

1027 

1039 

1051

1063

1075 

1087 

1098

1110 

1122 

1134

1146 

1158 

1170

1182

34°

7.319

1182

1194 

1206 

1218

TOOA

1241 

'1253

1265 

1277 

1289

1301

1313 

1325 

1337

1349 

1361 

1373

1385 

1397 

1409

1421

1433 

1445 

1457

1469

1481 

1493

1505 

1517 

1529

1541

1553 

1565 

1577

1589 

1601 

1613

1625 

1637 

1649

1661

1673 

1685 

1697 

1709

1721 

1733

1745 

1757 

1769

1781

1793 

1805 

1817

1829 

1841 

1854

1866

1878 

1890

1902

35°

7.319

1902

1914 

1926 

1938

1950

1962 

1974

1986 

1999 

2011

2023

2035 

204-7 

2059

2071 

2083 

2095

2108 

2120 

2132

2144

2156 

2168 

2180

2192

2205 

2217

2229 

2241 

2253

2265

2278 

2290 

2302

2314 

2326 

2338

2351 

2363 

2375

. 2387

2399 

2411 

2424

2436

2448 

2460

2472 

2485 

2497

2509

2521 

2533 

2546

2558 

2570 

2582

2594 

2607 

2619

2631

36°

7.319

2631

2643 

2656 

2668

2680

2692 

2705

2717 

2729 

2741

2753

2766 

2778 

2790

2803 

2815

2827

2839

2852 

2864

2876

2888 

2901 

2913

2925

2938 

2950

2962 

2974 

2987

2999

3011 

3024 

3036

3048 

3060 

3073

3085 

3097 

3110

3122

3134 

3147 

3159

3171

3184 

3196

3208 

3221 

3233

3245

3258 

3270 

3282

3295 

3307 

3319

3332 

3344 

3356

3369

37°

7.319

3369

3381 

3394 

3406

3418

3431 

3443,

3455 

3468 

3480

3492

3505 

3517 

3530

3542 

3554 

3567

3579 

3592 

3604

3616

3629 

3641 

3654

3666

3678 

3691

3703 

3716 

3728

3741

3753 

3765 

3778

3790 

3803 

3815

3828 

3840 

3852

3865

3877 

3890 

3902

3927 

3939

3952 

3964 

3977

3989

4002 

4014 

4027

4039 

4052 

4064

4077 

4089 

4101

4114

38°

7.319

4114

4126 

4139 

4151

4164

4176 

4189

4201 

4214 

4226

4239

4251 

4264 

4276

4289 

4301 

4314

4326 

4339 

4351

4364

4376 

4389 

4401

4414

4439

4451 

4464 

4477

4489

4502 

4514 

4527

4539 

4552 

45G4

4577 

4589 

4602

4614

4627 

4640 

4652

4.n«c

4677 

4690

4702 

4715

4727

4740

4753 

4765 

4778

4790 

4803 

4815

4828 

4841 

4853

4866

39°

7.319

4866

4878 

4891 

4904

4916

4929 

4941

4954 

4966 

4979

4992

5004 

5017 

5029

5042 

5055 

5067

5080 

5092 

5105

5118

5130 

5143 

5156

5168

5181 

5193

5206 

5219 

5231

5244

5256 

5269 

5282

5294 

5307 

5320

5332 

5345 

5358

5370

5383 

5395 

5408

5421

5433 

5446

5459 

5471 

5484

5497

5509 

5522 

5535

5547 

5560 

5573

5585 

5598 

5611

5623

40°

7.319

5623

5636 

5649 

5661

5674

5687 

5699

5712 

5720 

5737

5750

5763 

5775 

5788

5801 

5813 

5826

5839 

5851 

5864

5877

5890 

5902 

5915

5928

5940 

5953

59C6 

5978 

5991

6004

6017 

6029 

6042

6055 

6067 

C080

G093 

6106 

6118

6131

6144 

6156 

6169

6182

6195 

6207

6220 

6233 

6245

6258

6271 

6284 

6296

6309 

6322 

6335

6347 

6360 

6373

6385

P. P.

11

10 1.8

20 3.7 

30 5.5 

40 7.3 

50 9.2

60 11. 0

?

12

10 2.0 

20 4.0 

30 6.0 

40 8. 0 

50 10. 0

60 12. 0

13

10 2.2 

20 4.3 

30 6.5 

40 8.7 

50 10. 8

\

(332)
WOODWAED.] RADIUS OF CURVATURE OF MERIDIAN. 27

TABLE I. Logarithms of meridian radius of curvature pm in English feet. 

[Derivation of table explained in section (2); use of table explained on page 20.]

Lat.

/ 

0

1

2 

3

4

5 

6

7 

8 

9

10

11

12 

13

. 14

15 

16

17 

18

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

41°

7.319

6385

6398 

6411 

6424

6436 

6449 

6462

6475 

6487 

6500

6513

6526

653S 

6551

6504 

6577 

6589

 6602 

C615

6628

6640

6653 

6666 

6679

6692 

6704 

6717

6730 

6743 

6755

6768

6781 

6794

6S06

6819 

6832 

6844

6858 

6870 

6S83

6896

6909 

6921 

6934

6947 

6960 

6973

6985 

6998 

7011

7024

7036 

7049 

7062

7075 

7088 

7100

7113 

7126 

7139

7152

42°

7.319

7152

7164 

7177 

7190

7203 

7216 

7228

7241 

7254 

7267

7280

7202

7318

7331 

7344 

7356

7369 

 7382 

7395

7408

7420 

7433 

7446

7459 

7472 

7485

7497 

7510

7523

7536

7549 

7561

7574

7587 

7600 

7613

7626 

7638 

7651

7664

7677 

7690 

7702

7715 

7728 

7741

7754 

7767 

7779

7792

7805 

7818 

7831

7844 

7856 

7869

7882 

7895 

7908

7921

43°

7.319

7921

7933 

7946 

7959

7972 

79S5 

7998

8010 

8023 

8036

8049

8062

8075 

8087

8100 

8113 

8126

8139 

8152

8165

8177

8190 

8203 

8216

8229 

8242 

8254

8267 

8280 

8293

8306

8319

8344

8357 

8370 

8383

8396 

8409 

8422

8434

8447 

8460 

8473

8486 

8499 

8512

8524 

8537 

8550

8563

8576 

8589 

8602

8614 

8627 

8640

8053 

8666 

8679

8092

44°

7.319

8692

8704 

8717 

8730

8743 

8756 

8769

8782 

8794 

8807

SS20

8833

8846 

8859

8872 

S884 

8897

8910 

8923

8949

8962 

8975 

8987

9000 

9013 

9026

9039 

9052 

9005

9077

9090

9116

9129 

9142 

9155

9168 

9180 

9193

9206

9219 

9232 

9245

9258 

9270 

9283

9296 

9309 

9322

9335

9348 

9361 

9373

9386 

9399 

9412

9425 

9438 

9451

9464

45°

7.319

9464

9476 

9489 

9502

9515

9528 

9541

9554 

9566 

9579

9592

9605

9631

9644 

 9657 

9669

9682 

9695

9721

9734 

9747 

9760

9772 

9785 

9798

9811

9824 

9837

9850

9862

9888

9901 

9914 

9927

9940 

9953 

9965

9978

9991 

*0004 

*0017

*0030 

*0043 

*0055

*0068 

*0081 

*0094

#0107

*0120 

*0133 

*0146

*0158 

*0171 

*0184

*0197 

*0210 

*0223

#0230

46°

7.320

0236

0248 

0261 

0274

0287 

0300 

0313

0326 

0338 

0351

0364

0377

0390 

0403

0416 

0429 

0441

0454 

. 0467

0480

0493

0506 

0519 

0531

0544 

0557 

0570

0583 

0596 

0009

0621

0034 

0047

0660

0673 

0686 

0699

0711 

0724 

0737

0750

0763 

0776 

0788

0801 

0814 

0827

0840 

0853 

0866

0878

0891 

0904 

0917

0930 

0943 

0955

'0968 

0981 

0994

1007

47°

7.320

1007

1020 

1033 

1045

1058 

1071 

1084

1097 

1110 

1122

1135

1148

1101 

1174

1187 

1199 

1212

1225 

1238

1264

1276 

1289 

1302

1315 

1328 

1341

1353 

1360 

1379

1392

1405 

1418

1430

1443 

1450 

1469

1482 

1494 

1507

1520

1533 

1546 

1559

1571 

1584 

1597

1610 

1623 

1635

1648

1661 

1674 

1087

1699 

1712

1725

1738 

1751 

1763

1776

48°

7.320

1776

1789 

1802 

1815

1827 

1840 

1853

1866 

1879 

1892

1904

1917

1930 

1943

1955 

1968 

1981

1994 

2007

2019

2032

2045 

2058 

2071

2033 

2096 

2109

2122 

2134 

2147

2160

2173 

2186

2198

2211 

2224 

2237

2249 

2262 

2275

2288

2301 

2313 

2326

2339 

2352 

2364

2377 

2390 

2403

2415

2428 

2441 

2454

2466 

2479 

2492

2505 

2517 

2530

2543

49°

7.320

2543

2550 

2569 

2581

2594 

2007 

2619

2632 

2045 

2058

2670

2683

2690 

2709

2721 

2734 

2747

2760 

2772

2785

2798

2811 

2823 

2836

2849 

2861 

2874

2887 

2900 

2912

2925

2938

2963

2976 

2989 

3001

3014 

3027 

3039

3052

3065 

3078 

3090

3103 

3116 

3128

3141

3154 

3106

3179

3192 

0205 

3217

3230 

3243 

3255

3268 

3281 

3293

3306

50°

7.320

3306

3319 

3331 

3344

3357 

3369 

3382

3395 

3407 

3420

3433

3445

3471

3483

3496 

3509

3521 

3534

3559

3572 

3585 

3597

3010 

3023 

3035

3648 

3661 

3673

3686

3099

3724

3736 

3749 

3762

3774 

3787 

3800

3812

3825 

3838 

3850

3803 

3875 

3888

3901 

3913 

3926

3938

3951 

3964 

3976

3989 

4002 

4014

4027 

4039 

4052

4005

P.P.

»

12

10 2.0 

20 4.0 

30 6.0 

40 S.O 

50 10. 0 

60 12. 0

13

10 2.2 

20 4.3 

30 6.5 

40 8.7 

50 10. 8 

60 13.0

(333)
28 FORMULAS AND TABLES. [BULL. 50.

TABLE II. Logarithms of radius of curvature of normal section pn in English feet. 

[Derivation of table explained in section (2); use of table explained on page 21.]

Lat.

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

21°

7.320

8763

8766

8769 

8772

8775 

8778 

8780

8784 

8786

o joy

8792

8795 

8798 

8800

8804 

8807 

8810

8812 

8815 

8818

8821

8824

8827 

8830

8833 

8830 

8839

8841 

8844

8S47

8850

8853 

8856 

8859

8862 

8S05 

88B8

8871 

8S74 

8877

8879

8882

8885 

8888

8891 

8894 

8897

8900 

8903

8909

8912 

8915 

8918

8921 

8924 

8927

893d 

8933 

8936

8939

22°

7.320

8939

8942

. 8945 

8948

8951 

8953 

8956

8959 

8962

8965

8968

8971 

8974 

8977

8980 

8983 

8986

8989 

8992 

8995

8998

9001

9004 

9007

9010 

9013 

9016

9020 

9023

9029

9032 

9035 

9038

9041 

9044 

9047

9050 

9053 

9056

9059

9062

9065 

' 9068

9071 

9074 

9077

9080 

9083

9089

9093 

9096 

9099

9102 

9105 

9108

9111 

9114 

9117

9120

23°

7.320

9120

9123

9126 

9129

9132 

9136 

9139

9142 

9145

9148

9151

9154

9157 

9160

9163 

9107 

9170

9173 

9176 

9179

9182

91.85

9188 

9191

9195 

9198 

9201

9204 

9207

9210

9213

9216 

9220 

9223

9226 

9229 

9232

9235 

9238 

9242

9245

9248

9251 

9254

9257 

9260 

9264

9207 

9270

9273

9276

9279 

9283 

9286

9289 

9292 

9295

9298 

9302 

9305

9308

24°

7.320

9308

9311

9314 

9318

9321 

9324 

9327

9330 

9333

9337

9340

9343 

9346 

9349

9353 

9356 

9359

9362 

9365 

9368

9372

9375

9378 

9381

9384 

9388 

9391

9394 

9398

9401

9404

9407 

9411 

9414

9417 

9420 

9424

9427 

9430 

9433

9437

9440

9443 

9446

9450 

9453 

9456

9459 

9463

9469

9472 

9476 

9479

9482 

9485 

9489

9492 

9495 

9498

9502

25°

7.320

9502

9505

9508 

9512

9515 

9518 

9521

9525 

9528

9531

9535

9538 

9541 

9545

9548 

9551 

9554

9558 

9561 

9564

9568

9571

9574 

9578

9581 

9584 

9588

9591 

9594

9598

9601

9604 

9608 

9611

9614 

9618 

9621

9624 

9G28 

9631

9034

9638

9641 

9644

9648 

9051 

9654

9658 

9061

9668

9671 

9674 

9678

9681 

9085 

9688

9691 

9695 

9698

9701

26°

7.320

9701

9705

9708 

9712

9715 

9718 

9722

9725 

9728

9732

9735

9739 

9742 

9745

9749 

9752 

9756

9759 

9762 

9766

9769

9773

9776 

9779

9783 

9786 

9790

9793 

9796

9803

9807 

9810 

9814

9817 

9820 

9824

9827 

98S1 

9834

9838

9841

9844 

9848

9851 

9855 

9858

9862 

9865

9872

9875- 

9879 

9882

9886 

9889 

9893

9896 

9900 

9903

9907

27°

7.320

0907

9910

9913 

9917

9920 

9924 

9927

9931 

9934

9941

9945 

9948 

9952

9955 

9959 

9962

9966 

9969 

9973

9976

99SO

9983 

9987

9990 

9994 

9997

*0001 

*0004

*0008

*0011

*0015 

*0018 

*0022

*0025 

*0029 

*0032

*0036 

*0039 

*0043

*0046

*0050

*0053 

*0057

*0060 

*0064 

. *0067

*0071 

*0074

*0078

*0082

*OOS5 

*0089 

*0092

*0096 

*0099 

*0103

*0106 

*0110 

*0113

*0117

28°

7.321

. 0117

0121

0124 

0128

0131 

0135 

0138

0142 

0145

0149.

0153

0156 

0159 

0163

0167 

0170 

0174

 0177 

0181 

0185

0188

0192

0195 

0199

0203 

0206 

0210

0213 

0217

0224

0228 

0231 

0235

0238 

0242 

0246

0249 

0253 

0256

0260

0264

0267 

0271

0274 

0278 

0282

0285 

0289

0296

0300 

0303 

0307

0311 

0314 

0318

0322 

0325 

0329

0332

29°

7.321

0332

0336

0340 

0343

0347 

0351 

0354

0358 

0361

0365

0369

0372 

0376 

0380

0383 

0387 

0391

0394 

0398 

0402

0405

0409

0413 

0416

0420 

0424 

0427

0431 

0435

0442

0446 

0449 

0453

0457 

0460 

0464

04G8 

0471 

0475

0479

0482

0486 

0490

0493 

0497 

0501

05' 15 

0508

0516

0519 

0523 

0527

0530 

0534 

0538

0542 

0545 

0549

0553

30°

7.321

0553

0556

0560 

0564

0567 

0571 

0575

0579 

0582

0586

0590

0594 

0597 

0601

0605 

0608 

0612

0616 

0620 

0623

0627

0031

0635 

0038

0642 

0646 

0649

0653 

0657

0661

0604

0668 

0672 

0676

0679 

0683 

0687

0691 

0694 

0698

0702

0706

(>710 

0713

0717 

0721 

0725

0728 

0732

0736

0740

0743 

0747 

0751

0755 

0759 

0762

0766 

0770 

0774

0777

P. P.

2

10 .3 

20 .7 

30 1.0 

40 1.3 

50 1.7 

60 2.0

,

3

10 .5 

20 1. 0 

30 1.5 

40 2.0 

50 2.5 

60 3.0

4

10 .7 

20 1.3 

. 30 2. 0 

40 2.7 

50 3.3 

60 4.0

.

(334)
WOODWARD.] RADIUS CURVATURE OF NORMAL SECTION. 29

TABLE II. Logarithms of radius of curvature of normal section pu in English feet. 

[Derivation of table explained in section (2); use of table explained 011 page 21.]

Lat.

0

\ 

3

4

5 

6

7 

8 

9

10

11

12 

13

14 

15 

16

17 

18 

19

20

21 

22 

23

25 

26

27 

28 

29

30

31 

32 

33

34 

35 

30

37 

38 

39

40

41

42 

43

45 

46

47 

48 

49

50

51 

52 

53

54 

55 

56

57 

58 

59

CO

31°

7.321

0777

0781 

0785 

0789

0793

0790 

0800

0804 

0808 

OS11

0815

0819 

0823 

0827

0830 

0834 

OS38

0842 

0840 

0849

OS53

0857 

0861 

0865

0872 

0870

0880 

0884 

0888

OS91

0895 

0899 

0903

0907 

0910 

0914

0918 

0922 

0920

0930

0933 

0937 

0941

0949 

0953

0950 

0960 

0964

' 0968

0972 

0970 

0979

0983 

0987 

0991

0995 

0999 

1003

1006

32°

7.321

1000

10-10 

1014 

1018

1026 

1029

1033 

1037 

1041

1045

1049 

1053 

1057

1060 

1064 

1008

1072 

1076 

1080

1084

1087 

1091 

1095

1099

1103 

1107

1111 

1115 

1118

1122

1126 

1130 

1134

1138 

1142 

1140

1150 

1153 

1157

1161

1165 

1109 

1173

1177

1181 

1185

1189 

1192 

1196

1200

1204 

120"8 

1212

1216 

1220

1224

1228 

1231 

1235

1239

33°

7.321

1239

1243

1247 

. 1251

1255

1259 

1263

1207 

1271 

1275

1279

1282 

1286 

1290

1294 

1298 

1302

1306 

1310 

1314

1318

1322 

1326 

1330

1337 

1341

1345 

1349 

1353

1357

1361 

1365 

1309

1373 

1377 

1381

1385 

1389 

1393

1397

1401 

1405 

 1409

1412

1416 

1420

1424 

1428 

1432

1430

144& 

1444 

1448

1452 

1456 

1460

1464- 

1408 

1472

1476

34°

T.321

1476

1480 

1484 

1488

1492

1496 

1500

1504 

1508 

1512

1510

1520 

1524 

1528

1532 

1530 

1540

1544 

1548 

1552

1550

1560 

1564 

1568

T ^79

1576 

1580

1584 

1588 

1592

1596^

1600 

1004 

1008

1012 

1C16 

1620

1624 

1028 

. 1032

1030

1040 

1044 

1648

lGr.2

10JO 

1060

1664 

1668 

1672

1676

1080 

1084 

1088

1092 

1696 

1700

1704 

1708 

1712

1716

35°

7.321

1716

1720 

1724 

1728

1732

1730 

1740

1744 

1748 

1752

1756

1760 

1764 

1768

1772

1770 

1780

1784 

1789 

1793

1797

3801 

1805 

1809

1 Q1 £>

1817 

1821

1825 

- 1829 

1833

1837

1841 

1845 

1849

1853 

1857 

1861

1865 

1870 

1874

,1878

1882 

1880 

1S90

1898 

1902

1906 

1910 

1914

1918

1922 

1920 

1931

1935 

19:59 

1943

1947 

1951 

1955

1959

30°

7.321

1959

1903 

1907 

1971

1975

1979 

1983

1988 

1992 

1990

2000

2004 

2008 

2012

2816

2020 

2024

2028 

2033 

2037

2041

2045 

2049 

2053

2001 

2005

2009 

2073 

2077

2082

2086 

2090 

2094

2098 

2102 

2100

2110 

2114 

2119

2123

2127 

2131 

2135

2143 

2147

2151 

2150 

2100

2104

. 2168 

2172 

' 2176

2180 

2184 

2188

2193 

2197 

2201

2205

37°

7.321

2205

2209 

2213 

2217

9991

2226 

2230

2234 

2238 

2242

2240

2250 

2254 

2259

2263 

2267 

2271

2275 

2279 

2283

2287

2292 

22UG 

2300

noA/t

2308 

2312

2310 

2321 

2325

2329

2333 

2337 

2341

2345 

2350 

2354

2358 

2302 

2300

2370

2374 

- 2379 

2383

2391 

2395

2399 

2403 

2408

2412

2410 

2420 

2424

2428 

2433 

2437

2441

2445 

2449

2453

38°

7.321

2453

2457 

2402 

2400

94.7 A

2474 

2478

2482 

2487 

2491

2495

2499 

2503 

2507

2512 

2516 

2520

2524 

2528 

2532

2537

2541 

2545 

2549

2557 

2502

2500 

2570

2574

2578

2583 

2587 

2591

2595 

2599 

2603

2608 

2012 

2610

2020

2624 

2029 

2033

2041 

2045

2649 

2654 

2658

2062

2660 

2070 

2675

2679 

2683 

2687

2691 

2090 

2700

2704

39°

7.321

2704

2708 

2712 

2710

9791

2725 

2729

2733 

2737 

2742

2740

2750 

2754 

2758

2703 

2767 

2771

2775 

2779 

2784

2788

2792 

2790 

2800

2805

2809 

2813

2817 

2822 

2820

2830

2834 

2838 

2843

2847 

2851 

2835

2859 

2804 

2808

2872

2870 

2880 

2885

2893 

2897

2902 

2900 

2910

2914

2918 

2923 

2927

2931 

2935 

2940

2944 

2948 

2952

2956

40°

7.321

2950

2901 

2965 

2909

2978 

, 2982

2980 

2990 

2994

2999

3003 

3007 

3011

3010 

3020 

3024

3028 

3032 

3037

3041

3045 

3049 

3054

3058

3062 

3066

3071 

3075 

3079

3083

3087 

3092 

3090

3100 

3104 

3109

3113 

3' 17 

3121

3120

3130 

3134 

3138

3143

3147 

.3151

3155 

3160 

3104

3108

3172 

3177 

3181

3185 

3189 

3193

3198 

3202 

3206

3210

P. P.

3

10 .5 

20 1.0 

30 1.5 

40 2.0 

50 2.5

4

10 .7 

20 1.3 

30 2.0 

40 2.7 

50 3. 3

5

10 .8 

20 1.7 

30 2.5 

40 3. 3 

50 4.2 60 5.0

(335)
30 <> FORMULAS AND TABLES. [BULL. 60.

TABLE II. Logarithms of radius of curvature of normal section pn in English feet. 

[Derivation of table explained in section (2); use of table explained on page 21.]

Lat.

/ 

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

33

34 

35 

36

37 

38

OQ

40

41 

42 

43

44 

45 

46

47 

48 

49

50

51 

52 

53

54 

55 

56

57 

58 

59

60

41°

7.321

3210

3215 

3219

3223

3227 

3232 

323G

3240 

3244 

3249

3253

3257

3261 

3266

3270 

3274 

3278

3283 

3287

G«J-L

3295

3300 

3304 

3308

3312 

3317 

3321

3325 

3329 

3334

3338

3342

3351

3355 

3359 

3364

3368 

3372

3381

3385 

3389 

3393

3398 

3402 

3406

3410 

3415 

3419

3423

3427 

3432 

3436

3440 

3445 

3449

3453 

3457 

3462

3466

42°

7.321

3466

3470 

3474 

3479

3483 

3487 

3491

3496 

3500 

3504

3508

3513

3517 

3521

3526 

3530 

3534

3538 

3543

3547

3551

3555 

3560 

3564

3568 

3573 

3577

3581 

3585 

3590

3594

3598

OOU^i

3607

3611 

3615 

3620

3624 

3628

Of* 09

3637

3641 

3645 

3649

3654 

3658 

3662

3667 

3671 

3675

3679

3684 

3688 

'3692

3697 

3701 

3705

3709 

3714 

3718

3722

43°

7.321

3722

3726 

3731 

3735

3739 

3744 

3748

3752 

3756 

3761

3765

3769

3774 

3778

3782 

3786 

3791

3795 

3799

ooUo

3808

3812 

3816 

3821

" 3825 

3829 

3833

3838 

3842 

3846

3851

3855'

3863

3868 

3872 

3870

3881 

3885

OQQQ

3893

3898 

3902 

3906

3911 

3915 

3919

3923 

3928 

3932

3936

3941 

3945 

3949

3953 

3958 

3962

3966 

3971

3975

3979

44°

7.321

3979

3983 

3988 

3992

3996 

4001 

4005

4009 

4013 

4018

4022

4026

4031

4035

4039 

4043

4048

4052 

4056

u:UOi

4065

4069 

4073 

4078

4082 

4086 

4091

4095 

4099 

4104

4108

4112

4121

4125 

4129 

4134

4138 

4142 

4146

4151

4155 

4159 

4164

4168 

4172 

4176

4181 

4185 

4189

4194

4198 

4202 

4206

4211 

4215 

4219

4224 

4228 

4232

4236

45°

7.3211

4236

4241 

4245 

4249

4254 

4258 

4262

4267 

4271 

4275,

4279

4284

4288 

4292

4297 

4301 

4305

4309 

4314

 4318

4322

4327 

4331 

4335

4339 

4344 

4348

4352 

4357 

4361

4365

4369

4374 

4378

4382 

4387 

4391

4395 

4399

AA M

4408

4412 

4417 

4421

4425 

4430 

4434

4438 

4442 

4447

4451

4455 

4460 

4464

4468 

4472 

4477

4481 

4485 

4490

4494

46°

7.321

4494

4498 

4502 

4507

4511 

4515

4520

4524 

4528 

4532.

4537

4541

4545 

4550

4554 

4558 

4562

4567 

4571

^ty to

4580

4584 

4588 

4592

4597 

4601 

4605

4610 

4614 

4618

4622

4627

4631 

4635

4640 

4644 

4648

4652 

4657

4665

4670 

4674 

4678 

4682 

4687 

4691

4695 

4700 

4704

4708

4712- 

4717 

4721

4725 

4730 

4734

4738 

4742 

4747

4751

47° '

7.321

4751

4755 

4760 

4764

4768 

4772 

4777

4781 

4785 

4789

4794

4798

4802 

4807

4811 

4815 

4819

4824 

4828

4ooZ

4837

4841

4845 

4849

4854 

4858 

4862

4866 

4871 

4875

4879

48S4

4ooo

4892

4896 

4901 

4905

4909 

4913 

4918

4922

4926 

4931 

4935

4939 

4943 

4948

4952 

4956 

4960

4965

4969 

4973 

4978

4982 

4986 

4990

4995 

4999 

5003

5007

48°

7.321

5007

5012 

5016 

5020

5024 

5029 

5033

5037 

5042 

5046

5050

5054

5059 

5063

5067 

5071 

5076

5080 

5084

5088

5093

5097 

5101 

5105

5110 

5114 

5118

5123 

5127 

5131

5135

5140

5144 

5148

5152 

5157 

5161

5165 

5169 

5174

5178

5182 

5186 

5191

5195 

5199 

5203

5208 

5212 

5216

5220

5225 

5229 

5233

5237 

5242 

6246

5250 

5254 

v 5259

5263

49°

7.321

5263

5267 

5271 

5276

5280 

5284 

5288

5293 

5297 

5301

5305

5310

5314 

5318

5322 

5327 

5331

5335 

5339

5344

5348

5352 

5356 

5361

5365 

5309 

5373

5378 

5382 

5386

5390

5395

Uoou

5403

5407 

5412 

5416

5420 

5424

KAf)Q

5433

5437 

5441 

5445

5450 

5454 

5458

5462 

5467 

5471

5475

5479 

5484 

5488

5492 

5496 

5500

' 5505 

5509 

5513

5517

50°

7.321

5517

5522 

5526 

553d.

5534 

5538 

5543

5547 

5551 

5555

5560

5564

5568 

5572

5576 

5581 

5585

5589 

5593

ooyo

5602

5606 

5610 

5614

5619 

' 5623 

5627

5631 

5636 

5640

5644

5648

5657

5661 

5665 

5669

5673 

5678

KftQO

5686

5690 

5694 

5699

5703 

5707 

5711

5716 

5720 

5724

5728

5732 

5737 

5741

5745 

5749 

5753

5758 

5762 

5766

5770

P.P.

4

10 .7 

20 1.3 

30 2.0 

40 2.7 

50 3.3 

60 4.0

5

10 .8 

20 1.7 

30 2.5 

40 3.3 

50 4.2 

60 5.0

-

(336)
WOODWABD.] ARCS OF MERIDIAN. 31

TABLE III. Lengths of Terrestrial Arcs of Meridian.

[Derivation of table explained in section (3); use of table explained on page 21.]

Latitude

Interval.

n

10

20

30

40

50

60

10

20

30

40

50

CO

10

20

30

40

60

60

10

20

30

40

50

60

10

20

30

40

50

60

10

20

30

40

50

60

10

20

30

40

50

60

10

20

30

40

60

60

n 

10

20

30

40

50

60

 10

20

30

40

50

60

Latitude

25°

Feet.

1009. 49

2018. 97

3028. 46

4037.95

5047. 44

0056. 92

G0569. 2

121138. 5

181707. 7

242276. 9

302846. 1

363415.4

30°

1010. 22

2020.44

3030. GO

 4040.88

5051.10

6061.32

60613. 2

121220.4

181839. 7

242452. 9

303066. 1

363679. 3

35°

1011. 03

2022. 06

3033. 10

4044. 13

5055. 16

COCO. 19

60661. 9

121323. 9

181985. 8

242647. 8

303309. 7

303971. 7

40°

1011.90

2023. SO

3035. 70

4047. 60

5059. 50

6071. 39

60713. 9

121427. 9

182141. 8

242855. 8

303569. 7

364283. 7

45°

1012. 79

2025.59

3038. 38

4051. 18

5063. 97

0076. 77

60767. 7

121535. 3

182303. 0

243070. 6

303838. 3

364606. 0

Latitude 26°

Feet.

1009. 63

2019. 25

3028. 88

4038. 51

5048.13

6057. 76

60577. 6

121155. 2

181732. 7

242310. 3

302887. 9

363465. 5

31°

1010. 38

2020. 75

3031. 13

4041.51

5051.89

6062. 26

G0622. 6

121245. 3

181867. 9

242490. 5

303113. 2

363735. 8

30°

1011.20

2022. 40

3033. 61

4044. 81

5056. 01

6067. 21

60672. 1

121344. 3

182016. 4

242688. 5

303300. G

3C4032. 8

41°

1012. 08

2024. 15

3030. 23

4048. 31

5060. 38

0072. 4G

60724. G

121449. 2

182173. 8

242898.4

303623. 0

304347. 0

40°

1012. 97

2025. 95

3038. 92*

4051.90

5064. 87

6077. 85

60778. 5

121556. 9

182335. 4

243113. 9

303892. 4

364670. 8

Latitude

27°

Feet.

1009. 77

2019.54

3029.31

4039.08

5048. 85

6058. 62

60586. 2

121172. 3

181758. 5

242344. 7

302930. 9

363517. 1

32°

1010.54

2021.07

3031. 61

4042.15

5052. 68

6063. 22

GOG32. 2

121264. 4

181896. 6

242528. 8

303161. 1

363793. 3

37°

1011.37

2022. 75

3034. 12

4045. 50

5050. 87

0008. 24

GOGS2.4

' 121364.9

182047.3

242729. 7

303412. 2

364094. 0

42°

1012. 25

2024. 51

3030. 77

4049/02

5061. 28

6073. 53

60735. 3

121470. 6

182206. 0

242941.3

303676. 6

364411. 9

47°

1013. 15

2026. 31

3039. 46

4052. 62

5005. 77

6078. 93

60789. 3

121578. 5

182367. 8

243157. 0

303946. 3

364735. 5

Latitude

28°

Feel.

1009.92

2019.83

3029. 75

4039. 67

5049. 58

6059. 50

60595.0

121190. 0

181785.0

242379. 9

302974. 9

363509. 9

33°

1010. 70

2021. 40

3032. 10

4042.80

5053. 50

6004. 20

GOG42. 0

121283. 9

181925. 9

2425G7. 9

303209. 9

363851.8

38°

1011.55

2023. 09

3034. 64

4046. 19

5057. 74

6069.29

GOG92. 9

121385. 7

182078. 6

242771.4

303404. 3

304157. 1

43°

1012. 43

2024. 87

3037. 30

4049. 74

5002. 17

6074. 61

60746. 1

121492. 2

182238. 2

242984. 3

303730. 4

364476.5 ,

48°

1013. 33

2026. 67

3040. 00

4053. 34

5066. 67

6080. 00

60800. 0

121000. 1

182400. 1

243200. 1

304000. 1

364800. 2

Latitude 29°

Feet.

1010.07

2020. 13

3030. 20

4040. 27

5050. 33

6060. 40

60604. 0

121208. 0

181812.0

242416. 0

303019. 9

303023. 9

34°

1010. 86

2021. 73

3032. 59

4043.46

5054. 32

6065.19

60651.9

121303. 8

181955. 7

242607. 6

303259. 4

363911. 3

39°

1011.72

2023.44

3035. 17

4046. 89

5058. 01

6070. 34

60703. 4

121400. 7

182110. 1

242813. 4

303516. 8

364220. 2

'14°

1.012. 01

2025. 23

3037. 84

4050. 4.0.

5003. 07

0075. 69

00750. 9

121513. 7

182270. G

243027. 4

303784. 3

364541.2

4:9°

1013. 51

2027.02

3040. 54

4054. 05

5067. 56

6081. 08

60810. 8

121621.5

182432. 3

243243. 0

304053. 8

364864. 5

(337;
FORMULAS AND TABLES. [BULL. 50.

TABLE IV. Lengths of Terrestrial Arcs of Parallel. 

[Derivation of table explained in section (4); use of table explained on page 21.]

Longitude

Interval.

"

10

20

30

40

50

60

10

20

30

40

50

60

n 

10

20

30

40

50

60

10

20

30

40

50

60

10

20

30

40

50

60

10

20

30

40

50

60

10

20

30

40

50

60

10

20

30

40

50

60

n 

10

20

30

40

50

60

10

20

30

40

50

60

Latitude

25°

Feet.

920. 03

1840. 05

2760. 08

3680. 11

4600. 14

5520. 17

55201. 7

110403. 3

165605. 0

220806. 0

276008. 3

331209. 9

30°

879. 35

1758. 70

2638. 04

3517.39

4396:74

5276. 09

52760.9 '

105521. 8

158282. 6

211043. 5

263804.4

310565. 3

35°

831. 98

1663. 95

2495.93

3327. 91

4159.88

4991. 86

49918. 6

99837. 2

149755. 8

199674. 3

249592. 9

299511.5

40°

778. 26

1556.52

2334. 78

3113. 04

3891.30

4669. 56

46695. 6

93391. 2

140086. 7

186782. 3

233477. 9

280173. 5

45°

718.59

1437.19

2155.78

2874. 38

3592. 97

4311. 56

43115. 6

86231.3

129346. 9

172402. 5

215578. 2

258693. 8

Latitude

26°

Feet.

912.44

1824. 88

2737.33

3649. 77

4562. 21

5474. 65

54746. 5

109493. 0

104239. 5

218986. 1

273732. 6

328479. 1

31°

870. 40

1740. 80

2611. 20

3481. 59

4351. 99

5222. 39

52223. 9

104447. 8

156671. 8

208895. 7

261119. 6

313843.5

36°

821.73

1643. 4.6

2465. 19

3286. 91

4108. 64

4930. 37

49303. 7

98007. 4

147911. 2

197214. 9

246518. 6

295822. 3

41°

706. 79

1533. 58

2300. 37

3067. 16

3833. 94

4600. 73

46007. 3

92014. 7

138022. 0

184029.3

230036. 7

276044. 0

40°

705. 99

1411. 97

2117. 96

2823. 94

3529. 93

4235.91

42359. 1

84718.2

127077.3

169436. 5

211795. 6

254154. 7

Latitude

27°

Feet.

904.58

1809. 16

2713. 74

3618.32

4522. 89

5427.47

54274. 7

108549. 5

162824. 2

217099. 0

271373. 7

325648.4

32°

861.18

1722. 37

2583. 55

3444. 74

4305. 92

5167. 10

51671. 0

103342. 1

155013. 1

206684. 2

258355. 2

310020. 3

37°

811. 23

1622. 46

2433. 69

3244. 92

4056. 15

4867.38

48673. 8

97347. 6

146021.4

194695. 2

243369. 0

292042. 8

42°

755. 08

1510. 17

2265. 25

3020. 33

3775.42

4530. 50

45305.0 '

90610. 0

135915. 0

181220. 0

226525. 0

271830. 1

47°

693. 16

1386. 32

2079. 48

2772. 64

3465. 80

4158. 96

41589. 6

83179. 2

124768. 7

166358. 3

207947. 9

249537. 5

Latitude

26°

Feel.

896.44

1792. 88

2689. 32

3585. 76

448'^. 20

5378. 04

53786. 4

107572. 9

161359. 3

215145. 7

268932. 2

322718. 6

33°

851.71

1703.41

2555. 12.

3406. 83

4258. 53

5110. 24

51102. 4

102204. 8

153307. 3

204409. 7

255512. 1

300614. 5

38°

800. 48

1600. 97

2401. 45

3201. 93

4002. 42

4802. 90

48029. 0

96058. 0

144087.0

192116. 0

240145. 0

288174. 0

43° ,

743. 15

1486. 29

2229. 44

2972.59

3715. 73

4458. 88

44588. 8

89177. 6

133766.4

178355. 2

222944. 0

267532. 8

48°

680. 12

1360. 24

2040. 36

2720. 49

3400. 61

4080. 73

40807. 3

81614. 6

122421.9

163229. 2

204036. 4

244843. 7

Latitude 29°

Feel.

888. 03

1776. 06

2664. 09

3552. 12

4440.15

5328. 18

53281. 8

106563. 5

159845. 3

213127. 1

266408. 8

319690. 6

34°

841. 97

1683. 94

2525.91

3367. 88

4209. 85

5051. 82

50518. 2

101036. 4

151554. 6

202072. 8

252591. 0

303109. 2

39°

789.49

1578. 98

2368. 48

3157. 97

3947.46

4736. 95

47369. 5

94739. 1

142108. 6

189478. 2

2§ 6847. 7

284217.2

44°

730. 98

1461.96

2192.95

2923. 93

3654. 91

4385. 89

43858. 9

87717.9

131570.8

175435. 8

219294. 7

263153.6

49°

666. 87

1333.75

2000. 62

2667. 50

3334. 37

4001. 2.5

40012. 5

80024. 9

120037.4

160049. 9

200062.3

240074, 8

(338)
WOODWAKU.] MAP CO-ORDINATES.

TABLE V. Co-ordinates for projection of maps. Scale

[Derivation of table explained in section (5); use of table explained on page 22.]

&P.

*§_.

 c^

>3

O /

25 00

15

30

45

26 00

15

30

45

2700

15

30

45

28 00

15

30

45

29 00

15 ' 30

45

30 00

15

30

45

31 00

15

30

45

32 00

15

30

45

33 00

15

30

45

34 00

15

30

45

35 00

jj a mT3 > 'o

 ® 

ail o£ S,

'C § to %~* <u <s o

Inches.

4, 301

8. 722

13. 083

17. 444

4.302

8.723

13.085

17.440

4.302

8.724

13. 087

17.449

4. 363

8. 720

13.0SS

17.451

4.363

8.727

13. 091

17.454

4. 364

8. 728

13. 092

17.457

4.305

8.730

13. 095

17. 400

4.306

8.731

13. 097

17.402

4.360

8.733

13. 099

17.405

4. 307

' 8. 734

13. 101

17. 408

Co-ordinates of developed parallel for 

15' longitude.

X

Inches.

3.974

3. 906

3. 958

. 3.950

3.942

3.933

3.925

3.916

3.908

3. 899

3.890

3.881

3. 873

3. 863

3. 854

3.845

3.836

3.827

3. 817

3.808

3.799

3.789

3.779

3.770

3.760

3.750

3. 740

3. 730

3.720

3.710

3.700

3.690

3.679

3.669

3.658

3.648

3.037

3.020

3. 616

8.605

3.594

y

Inches

.004

.004

.004

.004

.004

.004

. 004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.001

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

.004

30' longitude.

X

Inches.

7.949

7. 933

7.!) 10

7. 900

7. 883

7.800

7. 849

7.833

7.816

7.798

7.780

7.703

7.745

7.727

7.709

7.091

7.073

7. 004

7.635

7. 010

7.598

7.578

7.559

7.540

7.520

7.500

7.480

7.400

7.441

7.420

7.400

7.379

7.359

7.338

7.317

7.290

7.275

7.253

7.231

7.210

7.188

y

fnches

.015

.015

.015

.015

.015

.015

.015

.015

.015

.016

.016

.010

.010

.010

.010

.010

.016

.010

.016

.010

.017

.017

.017

.017

.017

.017

.017

.017

.017

.017

.017

.017

.017

.018

.018

.018

.018

.018

.018

.018

.018

45' longitude.

X

Inches.

11. 923

11.899

11.874

11.850

11.825

11. 800

11.774

11. 749

11.723

11. 697

11.671

11. 044

11. 618

11.591

11.563

11.530

11.509

11.481

11.453

11.425

11.396

11.367

11.338

11. 309

11.280

11.250

11. 221

11. 191

11. 161

11. 130

11. 100

11. 069

11. 038

11.007

10. 975

10. 943

10. 912

10. 879

10. 847

10. 815

10. 782

y

Inches

.033

.033

.033

.034

.034

.034

.034

.035

.035

.035

. 035

-.036

.036

.036

.036

.036

.036

.037

.037

.037

.037

.037

.038

.038

.038

.038

.038

.038

.039

.039

.039

.039

.039

.039

.040

.040

.040

.040

.040

.040

.040

1° longitude.

X

Inches.

15. 898

15. 865

15. 832

15. 800

15. 767

15. 733

15. 699

15. 665

15.G31

10. 596

10. 501

15. 526

15. 490

15. 454

15.418

15.382

15.345

10. 308

15. 270

15. 233

15. 195

15. 156

15. 118

15. 079

15.040

15. 001 . 14. 961

14. 921

14. 881

14. 840

14. 799

14. 758

14. 718

14. 676

14. 033

14. 591

14. 549

14.506

14.463

14.420

14.376

y

Liclies.

. 009

.059

. 059

.000

.060

.001

.001

.061

.002

.002

.003 iocs

.004

.064

.064

.065

.065

.065

.066

.066

.066

.067

.067

.067

.068

.068

.068

.068

.069

.069

.069

.070

.070

.070

.070

.071

.071

.071

.071

.072

.072

Bull. 50 3

(339)
34 FORMULAS AND TABLES. [BULL. 50.

TABLE V. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on p. 22.]

a 

s

-U9

1

o / 

35 00 

15 

30 

45

36 00

15 

30 

45

37 00

15 

30 

45

38 00

15 

30 

45

39 00

15 

30 

45

40 00

15 

30 

45

41 00

. 15 

30 

45

4200

15 

30 

45

43 00

15 

30 

45

44 00

15 

30 

45

45 00

Meridional distances fromeven degree parallels.

Inches.

4.368 

8.735 

13. 103

17.471

4.368 

8.736 

13. 105

17. 473

4.369 

8.738 

13. 108

17.477

4. 370 

8.740 

13. 110

17.480

4.371 

8.741 

13.112

17.483

4.371 

8.743 

13. 114

17. 486

4.372 

8.744 

13. 117

17.489

4.373 

8.746 

13. 119

'17.492

4.374 

8.747 

13.121

17.495

4.375 

8.749 

13. 124

17. 498

Co-ordinates of developed parallel for 

15' longitude.

X

Inches.

3.594 

3.583 

3.572 

3.561

3.550

3.539 

3. 527 

3.516

3.504

3.493 

3.481 

3.470

3.458

3.446 

3. 434 

3.422

3.411

3.398 

3.386 

3.374

3.362

3.350 

3.337 

3.325

3.312

3.300 

3.287 

3.275

3 0RO 

. 604

3.249 

3.236 

3.223

3.210

3.197 

3. 184 

3.170

3.158

3.144 

3.131 

3.118

3.104

y

Inches

.004 

.004 

.004 

.005

.005

.005 

.005 

.005

.005

.005 

.005 

.005

.005

.005 

.005 

.005

.005

.005 

.005

.005

.005 

.005 

.005

.005

.005 

.005 

.005

.005

.005 

.006 

.005

.005

.005 

.005 

.005

.005

.005 

.005 

.005

.005

30' longitude.

X

Inches.

7.188 

' 7.166 

7.144 

7.122

7.100

7.077 

7.054 

7.032

7.009

6.986 

6.963 

6.939

6.916

6.892 

6.869 

6. 845

6.821

6.797 

6. 773 

6.748

6.724

6.699 

6.675 

6.650

6.625

6.600 

6.575 

6.549

6.524

6.498 

6.472 

6.447

6.421

6.394 

6.368 

6.342

6.316

6.289 

6.262 

6.235

6.209

y

Inches

.018 

.018 

.018 

.018

.018

.018 

.018 

.018

.018

.018 

.018 

.018

.019

.019 

.019 

.019

.019

.019 

.019 

.019

.019

.019 

.019 

.019

.019

.019 

.019 

.019

.019

.019 

.019 

.019

.019

.019 

.019 

.019

.019

.019 

.019 

.019

.019

45' longitude.

X

Inches.

10. 782 

10. 749 

10. 716 

10. 683

10. 650

 10. 616 

10. 582 

10. 547

10. 513

10. 479 

10.444 

10.409

10.374

10. 339 

10. 303 

10.267

10. 232

10. 195 

10. 159 

10. 123

10. 086

10.049 

10. 012 

9.975

9.937

9.900 

9.862 

9.824

9.786

9.747 

9.709 

9.670

9.631

9.592 

9.552 

9.513

9.473

9.433 

9.393 

9.353

9.313

y

Inches

.040 

.041 

.041 

.041

.041

.041 

.041 

.041

.041

.041 

.042 

.042

.042

.042 

.042 

.042

.042

.042 

.042 

.042

.042

.042 

.043 

.043

.043

.043 

.043 

.043

.043

.043 

.043 

.043

.043

.043 

.043 

.043

.043

.043 

.043 

.043

.043

1° longitude.

X

Inches.

14. 376 

14. 332 

14. 288 

14. 244

14. 200

14. 154 

14. 109 

14.063

14. 018

13. 972 

13. 925 

13. 879

13. 832

13. 785 

13. 737 

13. 690

13. 642

13. 594 

13.545 

13.497

13.448

13. 399 

13.349 

13. 300

13. 250

13.200 

13. 149 

13.098

13.048

12. 996 

12.945 

12. 893

12.842

12. 789 

12. 736 

12. 684

12. 631

12. 578 

12. 524 

12. 471

12.417

y

Inches.

.072 

.072 

.072 

.073

.073

.073 

.073 

.073

.074

.074 

.074 

.074

.074

.074 

.075 

.075

.075

.075 

.075 

.075

.075

.075 

.076 

.076

.076

.076 

.076 

.076

.076

.076 

.076 

.076

.076

.076 

.076 

.076

.077

.077 

.077 

.077

.077

(340)
WOODWARD.] MAP CO-ORDINATES. 35

TABLE V. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

1

^-4

OS

T> 0! 

&

3

o / 

45 00 

15 

30 

45

46 00

15 

30

45

4700

15 

30 

45

48 00

15 

30 

45

49 00

15 

30 

45

6000

Meridional disfrom tanceseven degree parallels.

 Inches.

'4.375 

8.751 

13. 126

17. 501

4.376 

8.752 

13. 128

17.504

4. 377 

8.754 

13. 131

17. 508

4.378 

8.755 

13. 133

17. 511

4.378 

8.757 

13. 135

17.514

Co-ordinates of developed paralle*! for 

15' longitude.

X

Inches.

3.104 

3.091 

3.077 

3.063

3.050

3.036 

3.022 

3.008

2.994

* 2.980 

 2. 966 

2. 952

2.938

2.924 

2.909 

2.895

2 QQ1 

. Ool

2.866 

2.852 

2.837

2.823

y

Inches.

.005 

.005 

.005 

.005

.005

.005 

.005 

.005

.005

.005 

.005 

.005

.005

.005 

.005 

.005

.005

.005 

.005 

.005

.005

30' longitude.

X

Inches.

6.209 

6.181 

6.154 

6.127

6.100

6.072 

6.044 

6.017

5.989

5.961 

5.933 

5.904

5.876

5.848 

5.819 

5.790

5.762

5.733 

5.704 

5.675

5.646

y

Inches.

.019 

.019 

.019 

.019

.019

.019 

.019 

.019

.019

.019 

.019 

.019

.019

.019 

.019 

.019

.019

.019 

.019 

.019

.019

45' longitude.

X

Inches.

9.313 

9.272 

9.231 

9.190

9.150

9.108 

9.067 

9.025

8.983

8.941 

8.899 

8.857

8.814

8.771 

8.728 

8.686

8.643

8.599 

8.555 

8.512

8.468

y

Inches.

.043 

.043 

.043 

.043

.043

.043 

.043 

.043

.043

.043 

.043 

.043

.043

.043 

.043 

.043

.043

.043 

.043 

.042

.042

1° longitude.

X

Inches.

12.417 

12. 363 

12.308 

12.254

12. 200

12. 144 

12. 089 

12. 033

11.978

11. 922 

11. 865 

11. 809

11. 752

11. 695 

11. 638 

11. 581

11.524

11.465 

11.407 

11.349

11.291

y

Inches.

.077 

.077 

.077 

.077

.077

.077 

.077 

.077

.076

.076 

.076 

.076

.076

.076 

.076 

.076

.076

.076 

.076 

.076

.076

(341)
36 FORMULAS AND TABLES. [BULL. 50.

TABLE VI. Co-ordinates for projection of maps. Scale -r

[Derivation of table explained in section (5). Use of table explained on page 22.]

£&

"g .

2

F Is

cs

Hi

O /

25 00

15

30

45

26 00

15

30

45

27 00

15

30

45

28 00

15

30

45

29 00

15

30

45

30 00

15

30

45

31 00

15

30

45

32 00

15

30

45

33 00

15

30

.45

34 00

15

30

45

36 00

! S 4

las a 3 os

"3 § §

0 ^ <? a* 1 *

Inches.

8.604

17. 207

25. 811

34.415

8.605

17.210

25.814

34. 419

8.606

17. 212

25. 818

34. 424

8.607

17. 215

25. 822

34.430

8.609

17.217

25. 826

34.435

8.610

17.220

25. 830

34.440

8.611

17. 223

25. 834

34.446

8.613

17.225

25. 838

34. 451

8.614

17. 228

25. 842

34.456

8.615

17.231

25. 846

34.462

Co-ordinates of developed parallel for 

15' longitude.

X

Inches.

7.841

7.825

7.809

7.793

7.776

7.760

7.743

7.726

7.709

7.692

7.675

7.657

7.640

7.622

7.604

7.586

7.568

7.550

7.531

7.513

7. 494

7.475

7.456

7.437

7.418

7.398

7.379

7.359

7.340

7.319

7.299

7.279

7.259

7.238

7.217

7. 197

7.176

7.154

7.133

7.112

7.091

y

Inches.

.007

.007

.007

.007

.007

.007

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.008

.009

.009

.009

.009

.009

.009

.009

.009

.009

.009

.009

30' longitude.

X

Inches.

15. 682

15. 060

15. 617

15.585

15. 553

15.519

15.486

15.452

15.419

15. 384

15. 350

15. 315

15. 280

15.244

15. 208

15. 173

15. 137

15. 100

15.063

15. 026

14. 989

14. 951

14. 913

14. 874

14.836

14. 797

14. 758

14. 718

14. 679

14. 639

14. 598

14. 558

14. 518

14.476

14. 435

14.393

14. 352

14. 309

14. 266

14. 224

14. 181

y

Inches.

.029

.029

. 029

.030

.030

.030

.030

.030

.031

.031

.031

.031

.031

.031

.032

.032

.032

. 032

.032

. 033

.033

.033

. 033

.033

.033

.033

.034

.034

.034

.034

.034

.034

.034

.035

.035

.035

.035

.035

.035

.035

.035

45' longitude.

X

Inches.

23. 523

23.475

23.426

23. 378

23.329

23. 279

23. 229

23. 179

23. 128

23. 076

23. 024

22. 972

22. 920

22. 866

22. 813

22. 759

22. 705

22. 650

22. 594

22. 539

22. 483

22. 426

22. 369

22.312

22.254

22. 195

- 22. 137

22. 078

22. 019

21. 958

21.898

21.837

21.777

21. 714

21. 652

21.590

21. 527

21.464

23,400

2f.'336

21.272

y

Inches.

.065

.065

.066

.067

.067

.007

.068

.068

.069

\069

.070

.070

.070

.071

.071

.072

.072

.072

.073

.073

.074

.074

.074

.075

.075

.075

.076

.076

.076

.077

.077

.077

.078

.078

.078

.078

.079

.079

.079

.080

.080

1° longitude.

X

Inches.

31.364

31.3UO

31.235

31.170

31. 100

31. 039

30. 972

30. 905

30. 838

30. 769

30. 099

30. 630

30. 560

30.489

30.417

30. 345

30. 274

30. 200

30. 125

30.051

29. 978

29. 902

29. 825

. 29. 749

29. 672

29.594

29. 515

29.437

29.358

29.278

29. 197

29. 116

29. 036

28. 953

28. 869

28. 786

28. 703

28. 618

28. 533

28.448

28. 362

y

Inches.

.116

.117

.117

.118

.119

.120

.121

.121

.122

.123

.124

.124

.125

.126

.127

.127

.128

.129

.130

.130

.131

.131

.132

.133

.133

.134

.135

.135

.136

.136

.137

.137

.138

.138

.139

.139

.140

.141

.141

.142

.142

(342)
 WOODWABD.] MAP CO-ORDINATES. 37

TABLE VI. Co-ordinates for projection of maps.

[Derivation of table explained in section (o); use of table explained on page 22.]

1

&

0 1

35 00 

15 

30 

45

36 00

15 

30 

45

37 00

15 

30 

45

38 00

15 

30 

45

39 00

15 

30 

45

4000

15 

30 

45

41 00

15 

30 

45

4200

15 

30 

45

43 00

15 

30 

45

44 00

15 

30 

45

4500

Meridional dis>- 

from tances even parallels. degree 

Inches.

8. 617 

17.234

25. 851

34.468

8.618 

17. 237

25. 855

34.474

S.620 

17.240 

25. 860

34.480

8.621 

17. 243 

25.864

34.485

8.623 

17. 246

25.868

34.491

8.624 

17.249 

25.873

34.497

8.625 

17. 250 

25.875

34.500

8.627 

17. 255 

25. 882

34.510

8.629 

17. 257 

25. 886

34.515

8. 630 

17. 261 

25. 891

34.522

Co-ordinates of developed parallel for 

15' longitude.

X

Inches.

7.091 

7.069 

7.047 

7.025

7.003

6.981 

6.959 

6.936

6.914

6.891 

6.868 

6.845

6.822

6.799

6.775 

6.752

6.729

6.705 

6.681 

6.657

6.633

6.608 

6.584 

6.560

6.535

6.510 

6. 485 

6.460

6.435

6.410 

6.385 

6.359

6.334

6.308 

6.282 

6.256

6.230

6.203 

6.177 

6.151

6.124

y

ladies.

.009 

.009 

.009 

.009

.009

.009 

.009 

.009

.009

.009 

.009 

.009

.009

.009 

.009 

.009

.009

.009 

.009 

.009

.009

.009 

.009 

.009

.009

.009 

.009 

.009

.009

.009 

.009 

.009

.009

.009 

.009 

.009

.009

.009 

.009 

.009

.009

30' longitude.

X

Indies.

14.181 

14. 138 

14. 094 

14.050

14.007

13. 962 

13. 917 

13. 873

13.828

13.782 

13.736, 

13. 690

13.645

13. 598 

13.551 

13. 504

13.457

13.409 

13. 361 

13.314

13.266

13. 217 

13. 168 

13. 119

13.070

13. 020 

12.970 

12. 920

12. 871

12.8,20 

12. 769 

12. 718

12. 667

12.615 

12. 563 

12.512

12.460

12. 407- 

12.354 

12.301

12. 249

y

Inches.

.035 

.036 

.036 

.036

.036

.036 

.036 

.036

.036

.036 

.036 

.037

<\ 

.037

.037 

.037 

.037

.037

.037 

.037 

.037

.037

.037 

.037 

.037

.037

.037 

.037 

.037

.037

.037 

.038 

.038

.038

.038 

.038 

.038

.038

.038 

.038 

.038

.038

45' longitude.

X

Indies.

21. 272 

21. 207 

21. 141 

21.076

21.010

20.943 

20. 876 

20.809

20.742

30. 673 

20. 604 

20.536

20.467

20. 397 

20.326 

20.256

20.186

20.114 

20. 042 

19. 970

19.899

19. 825 

19. 752 

19. 679

19.605

19. 530 

19.456 

19.381

19.306

19. 230 

19. 154 

19. 077

19.001

18.'923 

18. 845 

18.767

18.689

18.610 

18. 531 

18.452

18.373

y

Inches.

.080 

.080 

.080 

.080

.081

.081 

.081 

.081

.082

.082 

.082 

.082

.082

.083 

.083 

.083

.083

.083 

.083 

.084

.084

.884 

.084 

.084

.084

.084 

.084 

.084

.085

.085 

.085 

.085

.085

.085 

.035 

.085

.085

.085 

.085 

.085

.085

1° longitude.

X

laches.

28.362 

28. 275 

28. 188 

28.101

28.014

27. 924 

27. 835 

27. 745

27.655

27. 564 

27. 472 

27.381

27.289

27.196 

27. 102 

27. 008

26. 914

26. 819 

26. 723 

26.627

26. 532

26. 434 

26. 336 

26. 238

26. 140

26.041 

25. 941 

25. 841

25.741

25. 640 

25. 538 

25.436

25.335

25. 231 

25. 127 

25.023

24. 919

24.814 

24. 708 

24. 603

24.497

y

Indies.

.142 

.142 

.143 

.143

.144

.144 

.144 

.145

.145

.145 

.146 

.146

.147

.147 

.147 

.147

.148

.148 

.148 

.148

.149

.149 

.149 

.149

.150

.150 

.150 

.150

.150

.150 

.151 

.151

.151

.151 

.151 

.151

.151

.151 

.151 

.151

.151

(343)
38 FORMULAS AND TABLES. [BULL. 60.

TABLE VI. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

a

"3

CDS

r i

O '

45 00 

15 

30 

45

46 00

15 

30 

45

47 00

15 

30 

45

48 00

15

30

45

49 00.

15 

30

45

60 00

Meridional disfrom tanceseven degree parallels.

Inches.

8.632 

17.264 

25.896

- 34. 528

8. 633 

17. 267 

25. 901

34.534

8.635 

17. 270 

25. 905

34.540

8. 637 

17. 273 

25.9.10

34. 546

8.638 

17.276 

25.914

34.552

Co-ordinates of developed parallel for 

15' longitude.

X

Inches.

6.124 

6.097 

6.071 

6.044

6.017

5.990 

5.962 

5.935

5.908

5.880 

5.852 

5.824

5.796

5.768 

5.740 

5.712

5.684

5.655 

5.626 

5.598

5.569

y

Inches.

.009 

.009 

.009 

.009

.009

.009 

.009 

.009

.009

.009 

.009 

.009

.009

.009 

.009 

.009

.009

.009 

.009 

.009

.009

30' longitude.

X

Inches.

12. 249 

12. 195 

12. 141 

12. 088

12. 034

11.979 

11. 925 

11. 870

11. 815

11. 760 

11. 704 

11.648

11. 593

11.536 

11.480 

11. 424

11.367

11. 310 

11.253 

11. 195

11. 138

y

Inches.

.038 

.038 

.038 

.038

.038

.038 

.038 

.038

.038

.038 

.038 

.038

.038

.038 

.038 

.037

.037

.037 

.037 

.037

.037

45' longitude.

X

Inches.

18. 373 

18. 292 

18. 212 

18. 131

18.051

17. 969 

17. 887 

17. 805

17. 723

17. 640 

17. 556 

17.473

17.389

17. 305 

17. 220 

17.135

17. 051

16. 965 

16. 879 

16. 793

16.707

y

Inches.

.085 

.085 

.085 

.085

.085

.085 

.085

.085

.085

.085 

.085 

.085

.085

.085 

.084 

.084

.084

.084 

.084 

.084

.084

1° longitude.

X

Inches.

24.497 

24. 390 

24. 283 

24. 175

24. 068

23. 959 

23. 849 

23. 740

23. 631

23.520 

23.408 

23. 297

23. 186

23. 073 

22. 960 

22. 847

22.734

22. 620 

22.505 

22. 391

22.276

y

Inches.

.151 

.151 

.151 

.151

.151

.151 

.151 

.151

.151

.151 

.151 

.151

.150

.150 

.150 

.150

.150

.150 

.150 

.150

.150

(344)
 WOODWARD.] MAP CO-ORDINATES. 39

TABLE VII. Co-ordinates for projection of maps. Scale .., ,.

[Derivation of table explained in section (5); use of taljle explained on page 22.]

Latitude of

parallel.

o / 

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 

60

31 00

Meridional distances fromdegreeven parallels.

Inches.

5.815 

11. 629 

17.444 

23. 259 

29. 074

5.816 

11. 031 

17.446 

23. 262 

29. 077

5.816 

11. G33 

17.449 

23. 265 

29. 082

5.817 

11. 634 

17.461 

23.268 

29.086

5.818 

11.C36 

17. 464 

23. 272 

29.090

6.819 

11.638 

17.457 

23.276 

29.094

Abscissas of developed parallel.

5' longitude.

Inches.

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. f.Ol 

, 2. 597 

2.593 

2.589 

2.586

2.582 

2.578 

2.574 

2.570 

2.566 

. 2. 562

2.658 

2. 553 

2.549 

2.545 

2.641 

2.537

2.533 

2.528 

2.624 

2.520 

2.515 

2.611

2.507

10' longitude.

Inches.

5.299 

5.292 

5.285 

5.278 

5. 270 

5.263

5.256 

5.248 

5.240 

5.233 

5.225 

6.218

5.210 

6.203 

5.195 

5. 187 

5.179 

5.171

5.163 

5.155 

5.147 

5.139 

5.131 

5.123

5.115 

5.107 

6.098 

6.090 

5.082 

5.073

5.065 

5.056 

6.048 

. 5.039 

5.031 

5.022

6.014

15' longitude.

Inches.

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 

7.672 

7.559 

7.646 

7.533

7.520

20' longitnde.

Inches.

10. 599 

10. 584 

10. 570 

10. 555 

10. 540 

10.626

10. 511 

10. 496 

10. 481 

10. 466 

10. 461 

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

25' longitude.

Inches.

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 

12.698 

12. 577 

12.655

12.534

30' longitude.

Inches.

15. 898 

16.877 

15. 854 

15. 833 

16. 811 

15. 788

15. 767 

15.744 

15. 721 

15. 698 

15. 676 

15.654

15.631 

15. 608 

15.584 

15. 660 

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 

16. 143 

15. 118 

15. 092 

15.066

15.040

Ordinates of developed parallel.

Longitude interyal.

/ 

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

25°

Inches. 

0.001 

.003 

.007 

.013 

.020 

.029

27°

0.001 

.003 

.008 

.014 

.022 

.031

26°

Inches. 

0.001 

.003 

.008 

.013 

.021 

.030

28°

0.001 

.004 

.008 

.014 

.022 

.032

Longitude interval. __

i 

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

26 

30

28°

Inches. 

0.001 

.004 

.008 

.014 

.022 

.032

30°

0.001 

.004 

.008 

.015 

.023 

.033

29°

Inches. 

0.001 

.004 

.008 

.014 

.023 

.032

31°

0.001 

.004 

.008 

.015 

.023 

.034

(345)
40 FORMULAS AND TABLES. [BULL. 50.

TABLE VII. Co-ordinates for projection of maps. Scale T^sWrr- 

[Derivation of table explained in section (5); use of table explained on page 22.]

of Latitude parallel.

o' / 

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 

60

35 00 

10 

20 

30 

40 

50

36 00 

10 

20 

30 

40 

50

37 00

Meridional from distances degreeven parallels.

Incites.

5. 820 

11.640 

17. 160 

23. 280 

29. 100

5.821 

11. 642 

17. 462 

23. 2S3 

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

Abscissas of developed parallel.

'5' longitude.

Inches.

2.507 

2.502 

2.498 

2.493 

2.489 

2.485

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

10' longitude.

Inches.

5.014 

5.005 

4.996 

4.987 

4.978 

4.969

4.960 

4.951 

4.942 

4.933 

c 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

15' longitude.

Inches.

7. 520 

7.507 

7.494 

7.480 

7.467 

7.454

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. OS5 

7.070 

7.055 

7.039 

7.024

7.009

20' longitude.

Inches.

10.027 

10.009 

9.992 

9.974 

9.956 

9. 938

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

25' longitude.

Inches.

12.534 

12. 512 

12.490 

12.467 

12.445 

12.423

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

30' longitude.

Inches. '

15.040 

15.014 

14. 987 

14. 960 

14. 934 

14. 908

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. 402 

 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

Ordinates of developed parallel.

Longitude ^interval.

5 

10 

15 

20 

25 

30

5 

10 

15 20' 

25 

30

31°

Inches. 

0.001 

.004 

.008 

.015 

.023 

.034

33°

0.001 

.004 

.009 

.016 

.024 

.035

32°

Inches. 

0.001 

.004 

.009 

.015 

.024 

.034

34°

0.001 

.004 

.009 

.016 

.025 

.036

Longitude interval.

/ 

5 

10 

15 

20 

25 

30

, 5 

10 

15 

20 

25 

30

34°

Inches. 

0.001 

.004 

.009 

.016 

.025 

.036

36°

0.001 

.004 

.009 

.016 

.025 

.036

35°

Inches. 

0.001 

.004 

.009 

.016 

.025 

.036

37°

0.001 

.004 

.009 

.016 

.026 

.037

(346)
WOODWARD.] MAP CO-ORDINATES. 41

TABLE VIL Co-ordinates for projection of maps.

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

O '

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 

10 

20 

30 

40 

50

43 00

Meridional from distances degreeven parallels.

Inches.

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

5.829 

11.657 

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

Abscissas of developed parallel.

5' longitude.

Inches.

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 

2.236 

2.230 

2.225 

2.219 

2.214

2.2C8 

2.203 

2.197 

2.192 

2.186 

2.180

2.176 

2.169 

2.163 

2.157 

2.152 

2.146

2.140

10' longitude.

Inches.

4.673 

4.662 

4.652 

4.642 

4.631 

4.621

4.611 

4.600 

4.590 

4.579 

4.568 

4.558

1548 

4.537 

4.526 

4.515 

4.504 

4.493

4.483 

4.472 

4.461 

4.450 

4.439 

4.428

4.417 

4.408 

4.394 

4.383 

4.372 

4.360

4.349 

4.338 

4.326 

4.315 

4.303 

4.292

4.281

15' longitude.

Inches.

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 

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

20' longitude.

Inches.

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 

8.943 

8.921 

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

25' longitude.

Inches.

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 

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

3<y longitude.

Inches.

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 

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 

12.870

12. 842

Ordinates of developed parallel.

Longitude interval.

/ 

5 

10 

15 

20 

25 

30

5 

10 

15 

20

25

30

37°

Inches. 

0.001 

.004 

.009 

.016 

.026 

.037

39°

0.001 

.004 

.009 

.017

.026

.037

38°

Inches. 

0.001 

.004 

.009 

.017 

.026 

.037

40°

0.001 

.004 

.009 

.017

.026

.038

Longitude interval.

/ 

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

41°

Inches. 

0.001 

.004 

.009 

.017 

.026 

.038

43°

0. 001 

.004 

.010 

.017 

.027 

.038

(347)
42 FORMULAS AND TABLES. [BULL. 60.

TABLE VII. Co-ordinates for projection of maps. Scale -nrsWo-

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o ' 

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

Meridional distances from degree even parallels.

Inches.

5.832 

11.663 

17. 495 

23. 327 

29. 159

6. 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

5.837 

11. 674 

17. 511 

(23.348 

29. 185

5.838 

11.676 

17. 514 

23.352 

29. 190

Abscissas of developed parallel.

5' longitude.

Inches.

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 

1.952 

1.946 

1.940 

1.933 

1.927

1.921 

1.914 

1.908 

1.901 

1.895 

1.888

1.882

10' longitude.

Inches.

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 

3.905 

3.892 

3.879 

3.867 

3.854

3.841 

3.828 

3.815 

3.803 

3.790 

3.777

3.764

15' longitude.

Inches.

6.421 

6.403 

6.386 

6.368 

6.351 

6.333

6.316 

6.298 

6.280 

6.262 

6.244, 

6.227

6.209 

6.191 

6.172 

6.154 

6.136 

6.118

6.100 

6.081 

6.063 

6.044 

6.026 

6.008

6.989 

5.970 

5.951 

5.933 

5.914 

5.895

5.876 

5.857 

5.838 

5.819 

5.800 

5.781

6.762

6.743

5.723 

5.704 

5.684 

6.665

5.646

20' longitude.

Inches.

8.561 

8.538 

8.514 

8.491 

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 

7.810 

7.784 

7.759 

7.733 

7.708

7.682 

7.657 

7.631 

7.605 

7.679 

7.553

7.627

25' longitude.

Inches.

10. 701 

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 

9.762 

9.730 

9.699 

9.667 

9.635

9.603 

9.571 

9.539 

9.507 

9.474 

9.442

9.409

30' longitude.

Inches.

12.842 

12. 807 

12. 772 

12. 737 

12. 701 

12.667

12.631 

12. 596 

12.660 

12.624 

12.489 

12.463

12.417 

12. 381 

12. 345 

12.308 

12. 272 

12.236

12.199 

12. 103 

12. 125 

12. 089 

12. 052 

12. 015

11. 978 

11. 941 

11. 903 

11.866 

11.828 

11. 791

11. 752 

11. 714 

11. 677 

11.638 

11.600 

11.662

11.623 

11.485 

11.446 

11.408 

11.369 

11.330

11.291

Ordinates of developed parallel.

Longitude interval.

/ 

5 

10 

15 

20 

25 

30

r 

5

10 

15 

20 

25 

30

0 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

43°

Inches. 

0.001 

.004 

.010 

.017 

.027 

.038

46°

Inches. 

0.001 

.004 

.010 

.017 

.027 

.038

47°

Inches. 

0.001 

.004 

.010 

.017 

.027 

.038

49°

Inches. 

0.001 

.004 

.010 

.017 

.02G 

.038

44°

Inches. 

0.001 

.004 

.010 

.017 

.027 

.038

46°

Inches. 

0.001 

.004 

.010 

.017 

.027 

.038

48°

Inches. 

0.001 

.004 

.010 

.017 

.026 

.038

50°

Inches. 

0.001 

.004 

.009

.017

.026 

.088

(348)
WOODWARD.] MAP CO-ORDINATES. 43

TABLE VIII. Co-ordinates for projection of maps. Scale ^ 

[Derivation of tablo explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

<? / 

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

-!«IS l-i ' s g-o-a

-E a a "a

<» C3 QJ 5

' 3

Inches.

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 

45. 899

57. 374

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

Abscissas of developed parallel.

5' longitude.

Inches. 

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

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

lO' longitude.

Inches. 

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

10.171 

10. 155 

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

8.891

15' longitude.

Inchef. 

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

15.256 

15. 232 

15. 208 

15.185 

15.161

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

20' longitude.

Inches. 

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

20.628 

20.497 

20.466 

20. 436 

20.404

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

25' longitude.

Inches. 

26. 137

26. 101 

26.065 

26. 029 

25. 993 

25. 958

25. 922

25. 884 

25. 847 

26.810 

25.772

25.735

25. 698

25. 659 

25. 621 

25.582 

25.544 

25.505

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

SO7 longitude.

Inches. 

31. 365

31.322 

31. 279 

31. 235 

31. 192 

31. 149

31. 106

31.061 

31. 017 

30. 972 

30. 927 

on ooo

OU. 006

30. 838

30. 791 

30. 745 

30. 699 

30. 653 

30.607

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

Ordinates of developed parallel.

Longitude interval.

/ 

6 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

25°

Indies. 

0. 002 o.doe

0. 014 

0.026 

0.040 

0.058

27°

0.002 

0.007 

0.015 0.027- 

0. 042 

0.061

26°

Indies. 

0.002 

0.007 

0.015 

0.026 

0.041 

0. 059

28°

0.002 

0.007 

0.01G 

0.028 

0.043 

0.003

Longitude interval.

5 

10 

15 

20 

25 

30

5 

10 

15 20'

25

30

28°

Inches. 

0.002 

0.007 

0.016 

0.028 

0.043 

0.0.63

30°

0.002 

0.007 

0.016 

0.029 

0.045

O.OG5

29°

Inches. 

0.002 

0.007 

0.016 

0.028 

0.044 

0.064

31°.

0.002 

0.007 

0.017 

0. 030 

0.046

0.067

(349)
44 FORMULAS AND TABLES. [BULL. 50.

TABLE VIII. Co-ordinqtes for projection of maps. Scale -$-5^.

O

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o / 

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

10 

20 

30 

40 

50

36 00 

10

20 

30 

40 

50

37 00

Meridional distances fromdegreeven parallels.

Inches. 

G8.880

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

11.489 

22. 978 

34.468 

. 45. 957 

57.446

68.935

11.491

22.983

34.474 

45. 965 

57.457

63.948

Abscissas of developed parallel.

5' longitude.

Inches. 

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

4.717 

4.708 

4.698 

4.688 

4.679

4.669

4.659 

4.649 

4.639 

4.629 

4.619

4.609

1CK longitude.

Inches. 

9.891

9.873 

9.856 

9.838 

9.821 

9.804

9.786

9.768 

9.750 

9.732 

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

9.435 

9.415 

9.396 

9.377 

9.357

9.338

9.318 

9.298 

9.278 

9.258 

9.238

9.219

15' longitude.

Inches. 

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

14. 152 

14. 123 

14.094 

14.065 

14. 036

14.007

13. 977 

13.947 

13. 917 

13. 887 

13. 858

18.828

20' longitude.

Inches. 

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

18.870 

18. 831 

18. 792 

18.758 

18.714

18. 676

18.636 

18.596 

18. 556 

18. 517 

18.477

18. 437

25' longitude.

Inches. 

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. 196

24. 150 

24.104 

24.058 

24.012 

23. 966

23.920

23. 872 

23.825 

23. 778 

23. 730 

23. 683

23.636

23.587 

23.539 

23.490 

23. 442 

23. 393

23.345

23.295 

OQ OIK 60. tfiv

23.195 

23. 146

28. 096

23. 046

30' longitude.

Inches. 

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

28.305 

28.246 

28. 188 

28. 130 

28.072

28. 014

27.954 

27.894 

27. 835 

27. 775 

27. 715

27.656

Ordinates of developed parallel.

Longitude interval.

i 

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

31°

Inches. 

0.002 

0.007 

0.017 

0.030 

0.046 

0.067

33°

0.002 

0.008 

0.017 

0.031 

0.048 

0.069

V 

32°

Inches. 

0.002 

0.007 

0.017 

0.030 

0.047 

0.068

34°

0.002 

0.008 

0.017 

0.031 

0.049 

0.070

Longitude interval.

r 

5 

10 

15 

20 

25 

30

5 

10 

15

20 

25 

30

34°

Inches. 

0.002 

0.008 

0.017 

0.031 

0.049 

0.070

36°

0.002 

0.008 

0.018 

0.032 

0.050 

0.072

35°

Incites. 

0.002 

0.008 

0.018 

0.031 

0.049 

0.071

37°

0.002 

0.008 

0.018 

0.032 

0.050 

0.073

(350)
WOODWARD.] MAP CO-ORDINATES. 45

TABLE VIII. Co-ordinates for projection of maps. Scale-gy^.

[Derivation ol table explained in section (5); use of table explained on page 22.]

©

Latitude of

parallel.

o /

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

10

20 

30 

40

50

-!«

g.82o § SIP'S S -S"0 ^

 §!§!' 

sis*

 o

Inches. 

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

11. 503 

23.006 

34. 510 

46.013

57.516

Abscissas of developed parallel.

5' longitude.

Inches. 

4.609

4.599 

4.589 

4.579 

4.568 

4.558

4.548

4.538 

4.527 

4.517 

4.606 

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

4.279 

4.268 

4.256 

4.245

4. 234

10' longitude.

Inches. 

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

8.558 

8.535 

8.513 

8.490

8.467

15' longitude.

Inches. 

13.828

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

12. 837 

12.803 

12. 769 

12. 735

12. 701

207 longitude.

Inches. 

18.437

18. 396 

18. 356 

18. 315 

18. 274 

18. 234

18. 193

18. 151 

18.109 

18,068 

18.1)26 

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

17. 116 

17.071 

17.025 

16.980

16. 935

25' longitude.

Inches. 

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 

21. 673 

21.618 

21.562 

21. 507

21. 451

21.395 

21. 338 

21. 282 

21. 225

21.169

30' longitude.

Inches. 

27.656

27. 594 

27. 533 

27.472 

27. 411 

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

25. 674 

25. GOG 

25.538 

25.470

25.402

Ordinates of developed parallel.

o .

?1 

'Sbfe

P

/ 

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

 §-'

P « f >

'5> &

§ = i-T

/ 

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

37°

Indies. 

0.002 

0.008 

0.018 

0.032 

0. 050 

0.073

39°

0.002 

(1. 008 

0. 01.8 

0. 03;-! 

0. 051 

0. 074

4.0°

Inches. 

0.002 

0.008 

0.019 

0.033 

0.052 

0.074

42°

0.002 

0.008 

0. 019 

0.033 

0.052 

0. 075

38°

Inches. 

0.002 

0.008 

0.018 

0.033 

0. 051 

0.073

40°

0.002 

0.008 

O.OW) 

0.033 

0.052 

0. 074

41°

Inches. 

0.002 

0.008 

0.019 

0.033 

O.C52 

0.075

43°

0.002 

0.008 

0.019 

0.033 

0.052 

0.075

(351)
46 FORMULAS AND TABLES. [BULL. 60.

TABLE VUL Co-ordinates far projection of maps. Scale -^^go- 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

.

o / 

43 00

10 

20 

30 

40 

50

44 00

10 

20 

30 

40 

60

45 00

10 

20 

30 

40 

60

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

Meridional from distances degree even parallels.

Inches. 

69. 019

11. 505 

23. 010 

34. 515 

46.020 

57.525

09.030

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 

57.567

69.068

11.513

23.027 

34.540 

46.053 

57.567

69.080

11.516 

23.031 

34.646 

46.062 

67.577

69.093

11.617 

23.035 

34.652 

46.070 

57.687

69. 105

Abscissas of developed parallel.

5' 'longitude.

Inches. 

4.222

4.211 

4.199 

4.188 

4.176 

4.166

4.153

4.142 

4.130 

4.118 

4.106 

4.095

4.083

4.071 

4.059 

4.047 

4.035 

4.023

4.011

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

8.789

3.776 

3.764 

3.751 

3.738 

3.725

3.713

10' longitude.

Inches. 

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

7.653 

7.527 

7.502 

7.476 

7.451

7.425

15' longitude.

Inches. 

12. 667

12.633 

12. 598 

12.664 

12. 529 

12.494

12.460

12.425 

12. 390 

12. 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

11.329 

11.291 

11.253 

11.214 

11. 176

11.138

20' longitude.

Inches. 

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 

15.656 

15.607

15.457

15.407 

15.357 

15.307 

16. 257 

15.206

15.156

15. 105 

15.054 

16.003 

14.952

14.901

14. 850

25' longitude.

Inches. 

21. 112

21.054 

20. 997 

20. 939 

20. 882 

20.824

20. 767

20. 708 

20. 649 

20. 691 

20.532 

20. 473

20.415

20.355 

20. 295 

20. 236 

20. 176 

20. 116

20.056

19.996 

19. 936 

19. 974 

19. 813 

19. 763

19. 692

19. 630 

19. 569 

19. 607 

19.445 

19.383

 19.322

19.259 

19.196 

19.134 

19.071 

19.008

18.945

18.882 

18. 818 

18. 754 

18. 690 

18.627

18.663

30' longitude.

Inches. 

25.334

25. 265 

25. 196 

25. 127 

25.058

24. 9S9

24. 920

24.840, 

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

22.658 

22.681 

22.505 

22.429 

22.352

22. 276

Ordinates of developed parallel.

« .

11 '3>o>

HV" §3

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

43°

Inches. 

0.002 

0.008 

0.019 

0.033 

0.052 

0.075

45°

0.002 

0.008 

0.019 

0.034 

0.053 

0.076

44°

Inches. 

0.002 

0.008 

0.019 

0.034 

0.052 

0.075

46°

0.002 

0.008 

0.019 

0.034 

0.053 

0.076

« .

t3 1 <

3 S *3 f* 

w>3 a 'S

0 O 

HV

5 

10 

15 

20 

25 

30

5 

10 

15 

20 

25 

30

46°

Incites. 

0.002 

0.008 

0.019 

0.034 

0.053 

0.076

48°

0.002 

0.008 

0.019 

0.033 

0.052 

0.075

47°

Inches. 

0.002 

0.008 

0.019 

0.034 

0.052 

0.076

49°

0.002 

0.008 

0.019 

0.033

0.052 

0.075

5 

10 '15 

20 

25 

30

49°

0.002 

0.008 

0.019 

0.033 

0.052 

0.076

50°

0.002 

0.008 

0.019 

0.033 

0.052 

0.076

(352)
WOODWARD.] MAP CO-ORDINATES. 47

TABLE IX. Co-ordinates for projection of maps. Scale ^nhnr.

[Derivation of table explained in section (5); use_of table explained on page 22.]

Latitude of

parallel.

O '

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 

65

28 00 

05 

10 

15 

20 

26 

1 30 

36 

40 

45 

60 

55

29 00

Meridional distances fromdegreeven 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

6.817 

11. 634 

17.451 

23.268 

29. 085' 

34. 903

 - 

Abscissas of developed parallel.

2J' 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 

2.697 

2.595 

2.593 

2.591 

2.590 

2.588 

2.586 

2.584

2.582 

2.580 

2.678 

2.576 

2.574 

2.572 

2.570 

2.668 

2.566 

2.664 

2.662 

2.560

2.668

5' longitude.

Inches.

5.299 

6.296 

5. 292 

5.288 

5.285 

6.281 

6.277 

5.274 

5.270 

5.266 

5.263 

5.259

5.256 

5.252 

5.248

5.244 

5.241 

6.237 

.6.233 

, 5. 229 

5.225 

5.222 

5.218 

5. 214

5.210 

5.207 

6.203 

6.199 

5.195 

6.191 

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 

5.127 

5.123 

5.119

5.115

iy longitude.

Inches.

7.949 

7.944 

7.938 

7. 933 

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 

7.761

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. 611 

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

12J' 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. 783

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 

15. 721 

15. 710 

15. 699 

15. 688 

15. 676 

15. 665 

16. 654 

16. 642

15.631 

15. 620 

15. 608 

15. 506 

15. 584 

15. 572 

15.561 

15.649 

15.537 

15. 525 

16.514 

15. 502

15.490 

15. 478 

15.466 

15.454 

15.442 

15.430 

15. 418 

16.405 

15. 393 

15. 381 

16.369 

15.357

15. 345

Ordinates of developed parallel.

 §- 

I? 

||3 

/

2*

5 7-i 

10 

124 

15

25°

Inches. 

0.000 

.002 

.004 

.007 

.010 

.015

20°

Indies. 

0. 000 

.002 

.004 

.007 

.010 

.015

2* 

6 

7* 

10 

12* 

15

27°

Inches. 

0.000 

.002 

.004 

.007 

.011 

.015

/

2-i 

5 

7* 

10 

12* 

15

27°

Inches. 0. 000' 

.002 

.004 

.007 

.011 

.015

28°

Inches. 

0.000 

.002 

.004 

.007 

.011 

.016

2* 

6

n

10 

12* 

15

29°

Inches. 

0.000 

.002 

.004 

.007 

.011 

.016

(353)
48 FORMULAS AND TABLES. [BULL. 60.

TABLE IX. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

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 

50 

55

32 00 

05 

10 

15 

20

25 

 30 

35 

40 

45 

50 

55

33 00

Meridional distances fromdegree even parallels.

Inches.

5.818 

11. 636 

17. 454 

23. 272 

29. 090 

34. 908

5. 819 

11.638 

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£' 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. 528 

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 

2.469 

2.467 

. 2.464 

2.462 

2.460 

2.458 

2.455

2.453

5' longitude.

Inches.

5.115 

5. Ill 

5.107 

5.103 

5.098 

5.094 

5.090 

5.086 

5.0S2 

5.078 

5.073 

5.069

5.065 

5.061 

5.057 

5. 052 

5.048 

5.044 

5.039 

5. 035 

5.031 

5.026 

5. 022 

5. 018

5.014 

5.00S 

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

7£' longitude.

Inciws.

7.673 

7.666 

7.660 

7.654 

7.648 

7.641 

7.635 

7.629 

7.623 

7. 61.6 

7.610 

7.604

7.598 

7.591 

7.585 

7.578 

7.572 

7. 3565 

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. 096 

10.087 

10. 079 

10. 070 

' 10.061 

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

12i' 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. 270

12. 265

15' longitude.

Indies.

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 devel-, 

oped parallel.

il. s t

to®

I'2

/

2j 

5 

7fc 

10 

12i 

15

2* 

5 

U 

10

12* 

15

29°

Inches. 

0.000 

.002 

.004 

.007 

.011 

.016

31°

0.000 

.002 

.004 

.008 

.012 

.017

00°

Indies. 

0.000 

.002 

.004 

.007 

.012 

.017

o T3 '

£>

'So (5 

§3 i-l-

/

2* 

5 

U 

10 

121

15

n

5 

7* 

10 

121 

15

ol°

Incite*. 

0.000 

.002 

.004 

.008 

.012 

.017

33°

0.000 

.002 

.004 

.008 

.012 

.017

32°

Inches. 

0.000 

.002 

.004 

.008 

.012 

.017

(354)
 WOODWARD.] MAP CO-ORDINATES. 49

TABLE IX. Co-ordinates for projection of maps. Scale -syfats.

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude'of 

parallel

o / 

33 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

60 

65.

34 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

,65

35 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

60 

65

36 00 

06 

10 

15 

' 20 

25 

30 

35 

40 

45 

60 

55

37 00

Meridional distancesfrom degreeven parallels.

Inches.

5.822 

11. 643 

17.465 

23. 287 

29. 109 

34. 930

6.823 

11.645 

17. 4G8 

23. 291 

29. 113 

34.936

6.824 

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.

24' 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 

2.386 

2.384 

2.381 

2.379 

2. :i76 

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

& longitude.

Inches.

4.906 

4.901 

4.897 

4.892 

4.887 

4.882 

4.878 

4.873 

4.868 

4.864 

4.859 

4.864

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

74' 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 

7.26T 

7.260 

7.253 

7.246 

7.239 

7. 231 

7.224 

7.217 

7.210 

7.203 

7.196

7.188 

7.181 

7.174 

7.166 

7.159 

7.161 

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 

9.766 

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 

9.694

9.584 

9.574 

9.665 

9.555 

9.545 

9.535 

9.525 

9.616 

9. 506 

9.496 

9.486 

9.476

9.466 

9.456 

9.446 

9.436 

9.426 

9.416 

9.406 

9.396 

9.386 

9.376 

9.366 

9.356

9.345

124' 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 

12.040 

1^.028 

12. 016 

12.004 

11.992

11.980 

11.968 

11. 956 

11.944 

11. 931 

11. 919 

11. 907 

11. 8951 

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

16 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.:U8 

.14.303 

14. 288 

H.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.

«> .

 § 3

 Sfc 

$2 °3 A

/

24 

5 

74 

10 

124 

15

24 

5

7*

10 

124 

16

33°

Inches. 

0.000 

.002 

.004 

.008 

.012 

.017

35°

0.000 

.002 

.004 

.008 

.012 

.018

34°

Inches. 

0.000 

.002 

.004 

.008 

.012 

.018

«> . 

^l

as

p/

24 ' 574

10124

16

24 

5 

74 

10 

124 

15

35°

Inches. 

0.000 

.002 

.004 

.008 

.012 

.018

37°

0.001 

.002 .005J 

.008 

.013 

.018

36°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.018

(365)

Bull. 50 4
50 FORMULAS AND TABLES. [BULL. 50.

TABLE IX. Co-ordinates for projection of maps. Scale ^Tre- 

[Derivation of table explained in section (5); use of table explained on page 22.]

of Latitude 

parallel.

0 /

37 00 

05 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55

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 

50 

55

41 00

Meridional distances from degreeven 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.

24' longitude.

Incites.

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 

2.282 

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 

4.647 

4.642 

4.637 

4.631 

4.626 

4.621 

4.616

4.011 

4. C06 

4.600 

4. 595 

4.590 

4.584 

4.579 

4.674 

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

T4' longitude.

Incites.

7.009 

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 

6.900 

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' longi-' 

tude.

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

124' 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 

il.lll 

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.

o .

If 'Ebi

P

2i 

5 

74 

10 

12* 

15

/

24 

5 

74 

1.0 

121 

15

37°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.018

39°

Inches.. 

0.001 

.002 

.005 

.008 

.013 

.019

38°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

o 

11 

|B3-s

/

24 

5 

74 

10 

124 

15

/

24 

5 

74 

10 

124 

15

39°

Inches. 

0.001 

.002 

. .005 

.008 

.013 

.019

41°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

40°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

(356)
WOODWARD.] MAP CO-ORDINATES. 51

TABLE IX. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

of Latitude 

parallel.

o / 

41 00 

05 

10 

15 

20 

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 degree even parallels.

Inches.

6.830 

11. 659 

17.489 

23. 319 

29. 149 

34. 978

5.831 

11. 661 

17.492 

23. 323 

29.154 

34. 984

eCsssT

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.

2J' 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 

4.286

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 

6.666 

6.558 

6.649 

6.641 

6.633

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 

S.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 

8.650 

8.638 

8.526 

8.514 

8.503 

8.491 

8.479 

8.468 

8.456 

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

12-i' 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. 699 

10.585 

10.670 

10.555 

10.541

10.626 

10.611 

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. 660 

12.642 

12. 524 

12.606 

12.489 

12.471 

12.453 

12.436

12.417

Ordinates of developed parallel.

<o .

13 « 

fig

%s j-s

/

2J 

5 

74 

10 

124 

15

24 

5 

74 

10 

124 

15

41o

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

43°

0.001 

.002 

.005 

.008 

.013 

.019

42°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

o .

 § 3

 Sfc Soo

Hi"" SB

/

24 

5 

74 

10 

124

15

24 

6 

H 10 

124 

15

43°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

45°

Inches. 

0.001 

.002 

.005 

.009 

.013 

.019

440

Inches. 

0.001 

.002 

.005 

.009 

.013 

.019

(357)
FORMULAS AND TABLES. [BULL. 50.

TABLE IX. Co-ordinates for projection of maps. Scale

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

0 /

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 from distances degree even 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 

35.016

 ~ -

sTayf

11.674

17.511

23.348 

29. 185 

35. 021

 -

5.838 

11. 676 

17. 514 

23.352 

29.190 

35.027

Abscissas of developed parallel.

2*.' 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

7y longitude.

Inches.

6.209 

6.200 

6.191 

6.181 

6.172 

6.163 

6.154 

6.145 

6.136 

6.127 

6.118 

6.109

6.100 

6.091 

6.081 

6.072 

6.063 

6.054 

6.044 

6. 035 

6.026 

6.017 

6.008 

5.998

5.989 

5.980 

5.970 

5.961 

6.951 

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 

5.085 

6.655

5.646

10' longitude.

Inches.

8.278 

8.266 

. 8. 254 

'8.242 

8.230 

8.218 

8.206 

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 

7.769 

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 

7.640

7.528

^'longitude.

Inches.

10. 348 

10.333 

10. 318 

10. 302 

10. 287 

10. 272 

10. 267 

10. 242 

10. 227 

10. 212 

10. 197 

10. 182

10. 166 

10. -151 

10. 136 

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 

9.763 

9.746 

9.730 

9.714 

9.698 

9.683 

9.667 

9.651 

9.635 

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 

12. 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 

11. 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. 763 

11. 714 

11.6(J5 

11.676 

11. 657 

11. 11.619' 638 

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

Ord-inates of developed parallel..

o> .

11

!! rf"~

2* 

5 

7* 

10 

12i 

15

"2* 

5

7*

10

12* 

15

45°

Inches. 

0.001 

.002 

.005 

.009 

.OJ3 

.019

47°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

46°

Inches. 

0. 001 

.002 

.005 

.009 

.013 

.019

 §- 

3$

'SbS 

§a

H?

/

2* 

5

u

10 

12* 

15

2* 

5 

7* 

10 

12* 

15

2* 

5 

7* 

10 

12* 

15

47°

Indies. 

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

48°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

50°

Inches. 

0.001 

.002 

.005 

.008 

.013 

.019

(358)
WOODWARD.] MAP CO-ORDINATES. 53

TABLE X. Co-ordinates for projection of maps. Scale

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

2500

1

2

3

4

5

6

7

8

9

10 

11

12

13

14

15

16

17

18

19

20

21

22

23

'2524

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

62

63

64

65

66

67

58

59

60

Abscissas of developed parallel.

1' longitude

Inches.

2.091

.091

.091

.091

.090

.090

.090

.089

.089

.089

2.088 

.088

.088

.087

.087

.087

.086

.086

.086

.085

2.085

.085

.085

.084

.084

.084

.083

.083

.083 083

2.082

.082

.082

.081

.081

.081

.081

.080

.080

.080

2.079

.079

.079

.079

.078

.078

.078

.078

.077

.077

2.077

.076

.076

.076

.076

.075

.076

.076

.074

.074

2.074

2' longitude.

Inches.

4.182

.182

.181

.181

.180

.180

.179

.179

.178

.177

4.176 

.176

.175

.175

.174

.174

.173

.173

.172

.171

4.170

.170

.169

.169

.168

.168

.167

.167

.166

.166

4.165

.165

.164

.164

.163

.163

.162

. 162

M61

.160

4. 159

.159

.158

.157

.157

, .356

.156

.155

.154

.154

4.153

.153

.152

.152

.151

.151

.150

.150

.149

.149

4.148

3' longitude.

Indies.

6.1,r3

' .272

.271

.270

.269

.268

.267

.267

.266

.265

6.264 

.263

.263

.262

.261

.260

.259

.259

.258

.257

6.256

.255

.254

.253

.252

.251

.250

.249

.248

.248

6.247

.246

.245

.244

.243

.242

.242

.241

.240

.239

6.238

.237

.237

.236

.235

.234

.233

.232

.232

.231

6.230

.229

.228

.227

.226

.225

.225

.224

.223

.222

6.221

4' longitude.

Inches.

8.364

.363

.362

.361

.360

.358

.356

.355

.354

.353

8.352 

.351

.350

.349

.348

.347

.346

.344

.343

.342

8.341

.340

.339

.338

.337

.336

.335

.334

.332

.331

8.330

.329

.328

.326

.325

.324

.323

.322

.320

.319

8,318

.317

.316

.315

.313

.312

.311

.310

.308

.307

8.306

.305

.304

.303

.302

.301

.299

.298

..297

.296

8.295

5' longitude.

Inches.

10. 455

.454

.452

.451

.-449

.448

.446

.445

.444

.442

10.441 

.440

.438

.437

.435

.434

.432

.431

.430

.428

10. 426

.424

.423

.422

.420

.418

.417

.415

.414

.413

10.412

.410

.409

.407

.406

.404

.403

.401

.400

.399

10. 397

.395

.394

.392

QQA . OiJU

.389

.387

.386

.385

.384

10. 383

.382

.380

.379

.378

.377

.375

.373

.372

.370

10.369

6' longitude.

Inches.

12. 546

.544

.542

.541

.539

.637

.535

.534

.532

.530

12. 529

.527

.525

.523

.522

.520

.518

.516

.515

.513

12.511

.509

.507

.506

.504

.502

.501

.499

.497

.495

12.494

.492

.490

.489

.487

.485

.484

.482

.480

.479

12.477

.476

.474

.472

.471

.469

.467

.466

.464

.462

12. 460

.458

.457

.455

.453

.452

.450

.448

.447

.445

12.443

7' longitude.

Inches.

14. 637

.635

.633

.631

.629

.627

.625

.623

.621

.619

14. 617 

.615

.613

.611

.609

.607

.605

.603

.601

.598

14. 596

.594

.592

.590

.588

.587

.585

.583

.581

.579

14. 577

.575

.573

.571

.569

.566

.564

.562

.560

.558

14.556

.554

.552

.550

. 548

!546

.544

.542

.540

.538

14. 536

.534

.532

.530

.528

.527

.525

.523

.521

. .519

14. 517

8' longitude.

Inches.

16. 728

.726

.724

.721

.719

1717

.714

.712

.709

.707

16. 705 

.703

.701

.698

.696

.694

.691

.689

.687

.684

16. 682

.680

.678

.675

.673

.671

.668

.666

.664

.662

16. 659

.657

.655

.652

.650

.648

.645

.643

.641

.638

16. 636

.634

.032

.029

.627

.625

.622

.620

.618

.615

16. 613

.611

.609

.606

.604

.602

.599

.597

.595

.593

16.590

9' longitude.

Inches.

18. 819

 .817

.814

.812

.809

.807

.804

.802

.799

.796

18. 793 

.791

.788

.786

.783

.781

.778

.776

.773

.770

18.767

.765

.762

.759

.757

.755

.752

.749

.747

.745

18. 742

.739

.736

.734

.731

.728

.726

.723

.721

.718

18.715

.712

.710

.707

.704

.702

.699

.697

.694

.692

18. 689

.686

.684

.681

.679

.670

.674

.671

.669

.667

18.664

10' longitude.

Inches.

20. 910

.907

.904

.900

.897

.894

.890

.887

.885

.883

20. 881° 

.878

.875

.872

.869

.866'

.864

.861

.858

.855

20.852

.849

.'846

.843

.841

.838

.835

.832

.829

.827

20.824

.821

.818

.815

.812

.810

.807

.804

.801

.798

20. 795

.792

.789

.786 704. . t o*

.781

.778

.775

.772

.769

20. 766

.763

.760

.758

.755

.752

.749

.747

.744

.741

20. 738

]j Longitude 

interval.

/

1

2

3

4

5

6

7

8

9

10

Ordi ofnates developed parallel.

Inches.

0.000

.000

.001

.002

.003

.005

.006

.008

.010

.013

4> '

 C 73 Sr

a 3

3.2

/

l

2

3

4

5

6

7

8

9

10

A

1 «'

§8 =§§

C-S

a«

Inches.

2.294

4.589

6.883

9.178

11. 472

13. 766

16. 061

18. 356

20. 650

22.944

(359)
54 FORMULAS AND TABLES. [BULL. 50.

TABLE X. Co-ordinates for projection of maps. Scale yr JTO-

[Derivation of table explained in section (5); use of table explained on page 22.]

of Latitude 

parallel.

o /

26 00

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

65

56

57

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

2.074

.074

.074

.073

.073

.073

.073

.072

.072

.072

2.071

.071

s .071

.070'

.070

.070'

.069

.069

.069

.068

2.068

.068

.068

.067

.067

.067

.066

.066

.066

.065

2.065

.065

.065

.064

.064

.064

.063

.063

.063

.062

2.062

.062

.062

.061

.061

.061

.060

.060

.060

.059

2.059

.059

.059

.058

.058

.058

.057

.057

.057

.056

2.056

2' longitude.

Inches.

4.148

.148

.147

.147

.146

.146

.145

.145

.144

.143

4.142

.142

.141

.141

.140

.139

.139

.138

.138

.137

4.136

.136

.135

.135

.134

. 133

.132

.132

.131

.131

4.130

.130

.129

.128

.128

.127

.127

.126

.126

.125

. 4.124

.124

.123

.123

.122

.121

.120

.120

.119

.119

4.118

.118

.117

.117

.116

.115

.115

.114

.113

.113

4.112

3' longitude.

Inches.

6.221

.220

.219

.218

.217

.216

.215

.214

;213

.213

6.212

.211

.210

.209

.208

.207

.206

.205

.204

.203

6.203

.202

.201

.200

.199

.199

.198

.197

.196

.195

6.194

.193

. 192

.191

.190

.189

.188

.187

.187

.186

6.185

.184

.183

.182

.181

.180

.179

.178

.177

.177

6.176

.175

.174

.173

.173

.172

.171

.170

.170

.168

6.168

4' longitude.

Inches.

8.295

.294

.292

.291

.290

.289

.288

.286

.285

.284

8.283

.282

.280

.279

.278

.277

.275

.274

.273

.272

8.271

.270

.268

.267

. 2fi6

.205

5' longitude.

Inches.

10. 369

.368

.366

.365

.363

.362

.3*0

.359

.357

.355

10.354

.352

.35.1

.349

.348

.346

.345

.343

.342

.340

10.339

.337

.336

.335

..Vt!

!332

.264! .330

.263 .329

.262 .327

6' longitude.

Inches.

12.443

.441

.439

.438

.436

.434

.432

.430

.429

.427

 12.425

.423

.421

.420

.418

.416

.415

.413

.411

.409

12.407

.405

.403

.402

.400

 .398

7' longitude.

Inches.

14. 517

.515

.513

.511

.509

.50&

.504

.502

.500

.498

14. 496

.494

.492

.490

.487

.485

.483

.481

.479

.477

14. 475

.473

.471

.469

.466

.464

.397; .462

.396i .460

.393| .458

.260 .326 .391 .456

8.259

.258

. '''<!

.256

.254

.253

.252

.251

.250

.248

8.247

.246

.245

.544

.242

.241

.240

.239

.238

.236

8.235

.234

.233

.232

.231

.230

.229

.228

.227

.226

8.224

10.324 12.389

.323

.321

.320

.318

.317

.315

.314

.312

.311

10.309

.308

.306

.305

OrtO

!302

.300

.299

.297

.296

10. 294

.293

.291

.290

.288

.287

.285

.284

.282

.281

10. 280

.387

.385

.384

.382

.380

.379

.377

.375

.373

12. 371

.369

.367

.366

364

!362

.360

.358

.357

.355

12.353

.351

.349

.348

.346

.345

.343

.341

.339

.337

12. 335

14.454

.452

.450

.448

.446

.443

.441

.439

.437

.435

14.433

.431

.429

.427

.425

.423

.421

.418

.416

.414

14.412

.410

.408

.406

.404

.402

.399

.397

.395

.393

14. 391

8' longitude.

Inches.

16.590

.588

.685

.583

.581

.578

.576

.673

.571

.568

16.566

.563

.560

- .558

.555

 .553

.551

.549

.546

.544

16.642

.640

.537

.535

.532

.530

.527

.525

.522

9' longitude.

Inches.

18. 664

.661

.658

.656

.653

.650

.648

.645

.642

.640

18.637

.634

.631

.629

.626

.623

.621

.618

.615

.612

18. 610

.607

.604

.602

.699

.596

.593

.591

.588

. 520 1 . 585

16. 518

.516

.513

.511

.509

.506

.504

.501

.499

.496

16. 494

.492

.489

.487

.484

.481

.479

.477

.475

 .472

16.470

.468

.466

.463

.461

.459

.457

.454

.452

.449

16.447

18.683

.580

.577

.575

.572

.669

.567

.564

.561

.559

18. 556

.553

.550

.548

-.545

.542

.540

.537

.534

. .532

18.529

.526

.524

.521

.519

.516

.514

.511

.508

.506

18.503

10' longitude.

Inches.

20. 738

.735

.732

.729

.726

.723

.720

.717

.714

.711

20. 708

.705

.702

.699

.696

.693

.690

.687

.684

.681

20.678

.675

.672

.669

.666

.663

.660

.657

.654

.651

20.648

.645

.642

.639

.636

.633

.630

.627

.624

.621

20.618

.615

.612

.609'

.606

.608

.600

.597

.594

.591

20. 588

.585

.582

.579

.576

.573

!570

.567

.564

.561

20. 559

Longitude 

|jinterval. 

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.000

.001

.002

.003

.005

.006

.008

.011

.013

|1 0 &

4. a

'

i

2

3

4

6

6

7

8

9

10

"3 D

II

'Cto

y *3 "

Inches.

2.295

4.590

6.884

9.179

11. 474

13. 769

16. 064

18.358

20. 653

22. 948

(360)
WOODWARD.] MAP CO-ORDINATES. 55

TABLE X. Co-ordinates for projection of maps. Scale Triw-

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

2700

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

Abscissas of developt-d parallel. v

V longitude.

Inches.

2.056

.056

.056

.055

.055

.055

.054

.054

.054

.053

2.053

.053

.053

.052

.052

.052

.051

.051

.051

.050

2.050

.050

.050

.049

.049

,049

.048

.048

.048

.047

2.047

.047

.046

.046

.046

.045

.045

.044

.044

.044

2.043

.043

.043

.042

r\An > \rx£i

.042

.041

.041

.041

.040

2.040

.040

.040

.039

.039

.039

.038

.038

.038

.037

2.037

2' longitude.

Indies.

4.112

.112

.111

.111

.110

.109

.109

.108

.107

.107

4.106

.iOG

.105

.104:

.104

.103

.102

.101

.101

.100

4.099

.099

.098

.098

.097

.096

.096

.095

.094

.094

4.093

.093

.092

.091

.091

.090

.089

.089

.088

.088

4.087

.087

.086

.085

.085 

.084

.084

.083

.082

.082

4.081

.081

.080

.079

.079

.078

.077

.077

.070

.075

4.075

3' longitude.

Inches.

6.168

.167

.166

.165

.164

.103

.162

.161

.100

.159

6.158

.157

.156

.155

.154

.153

.152

.151

.150

.150

6.149

.148

.147

.146

.145

.144

.143

.142

.141

.141

6.140

.139

.138

.137

.136

.135

.134

.133

.132

.131

6.130

.129

.128

.127

126 

!l25

.124

.123

.122

.122

6.121

.120

.119

.118

.117

.116

.115

.114

.113

.113

6.112

4' longitude.

Inches.

8.224

.223

.222

.220

.219

.218

.216

.215

.214

.213

8.211

.210

.209

.207

.206

.205

.204

.202

.201

.200

8.199

.198

.196

.195

.194

.192

.191

.189

.188

.187

8.186

.185

.184

.182

.181

.180

.178

,.177

.176

.175

8.174

.173

.172

.170

1G9 

!l68

.166

.165

.164

.103

8.162

.161

.160

.158

.167

.156

.154

.153

.162

.151*

8.150

5' longitude.

Inches.

10. 280

.278

.277

.275

.274

.272

.271

.269

.267

.265

10. 264

.262

.261

.259

.258

.256

.255

.254

.252

.250

10.248

.247

.245

.244

.242

.241

.239

 .238

.236

.235

10. 233

.232

.230

.229

.228

.226

.225

.224

.222

.220

10. 217

.216

.214

.213

911 t ALL

.210

.208

.207

.205

.204

10. 202

.201

.199

.198

.196

.195

.193

-.192

.190

.189

10. 187

6' longitude.

Inches.

12. 335

.333

.331

.330

.328

.326

.325

.323

.321

.319

12.317

.315

.314

.312

.311

.309

.307

.305

.303

.300

12.298

.296

.295

.293

.291

.289

.288

.286

.284

. . 282

12.280

.278

.276

.274

.272

.271

.269

.267

.265

. 263

12. 261

 .259

.257

.256

QHJ. 

. <i>J*

.252

. .250

.248

.246

.244

12. 242

.240

.238

.237

.235

.233

.231

.230

.228

.226

12. 224

7' longitude.

Inches.

14.391

.389

.387

.385

.383

.381

.379

.377

.375

.373

14.370

.368

.366

.364

.302

.359

.357

.355

.353

.351

14. 348

.346

.344

.341

.339

.337

.335

.332

.330

.328

14. 326

.324

.322

.319

.317

.315

.313

.310

.308

.306

14.304

.302

.300

.298

onn

. L\J\J

.294

.292

.290

.287

.285

14. 283

.281

.279

.277

.275

.272

.270

.268

.266

.264

14.262

8' longitude.

Incites,

16.447

.445

.442

.440

.437

.435

.432

.430'

.427

.425

16.422

.420

.417

.415

.412

.410

.407

.405

.403

.400

10. 398

.395

.393

.390

.388

.385

.383

.380

.378

.375

16.373

.370

.368

.365

.363

.360

.358

.355

.353

.350

16.348

.345

.343

.340

OOO

. oOo

.335

.333

.330

.328

.325

16. 323

.320

.318

.315

.313

.311

.308

.306

.303

.301

16.299

9' longitude.

Inches.

18. 503

.500

.497

.495

.492

.489

.487

.484

.481

.478

18.475

.472

.469

.467

.464

.461

.458

.456

.453

.450

18.447

.444

.442

.439

.436

.433

.430

.428

.425

.422

18.419

.416

.413

.411

.408

.405

.402

.400

.307

.394

18. 391

.388

.386

.383

'JQA

. OoU

.378

.375

.372

.369

.367

18.364

.361

.359

.356

.354

.351

.348

.345

.342

.340

18. 337

KX longitude.

Inches.

20. 559

.556

.553

.550

.547

.544

.541

.538

.535

.532

20. 528

.525

.522

.519

.516

.513

.510

.507

.504

.501

20.497

.494

.491

.488

.485

.482

.479

.476

.473

.469

20.466

.463

.460

.457

.454

.451

.448

.445

.442

.438

20. 435

.432

.429

.426

4.9 q . t£f>

.420

.417

.414

.411

.407

20.404

.401

.398

.395

.392

.389

.386

.383

.380

.377

20. 374

Longitude 

||interval. . 

/

1

2

3

4

5

6

7

8

9

10

of Ordinates developed parallel.

Inches.

0.000

.000

.001

.002

.003

.005

.007

.009

.011

.013

®«

T3^3

a > -" fci 3*3 .s

'

1

2

3

4

5

6

7

8

9

10

1-i M Q)

;£ 'd a2

 g-g

a*

Inches.

2.295

4.590

6.885

9.180

11.475

13. 771

16.066

18.361

20. 656

22. 951

(361)
FORMULAS AND TABLES. [BULL. 50.

TABLE X. Co-ordinates for projection of maps. Scale - 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude ofparallel. |

o /

2800

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

Abscissas of developed parallel.

1' longitude.

Indies.

2.037

.037

.037

.036

.036

.036

.035

.035

.035

.034

2.034

.034

.034

.033

.033

.033

.032

.032

.032

.031

2.031

.031

.031

.030

.030

.030

.029

.029

.029

.028

2.028

.028

.028

.027

.027

.027

.026

.026

.026

.025

2.025

.025

.025

.024

.024

.024

.023

.023

.022

.022

2.021

.021

.021

.020

.020

.020

.019

.019

.019

.018

2.018

2' longitude.

Inches.

4.075

.074

.073

.073

.072

.071

.070

.070

.069

.068

4.068

.067

.067

.066

.065

.065

.064

.064

.063

.063

4. 002

.062

.061

.061

.060

.060

.059

.058

.058

.057

4.056

.056

.055

.054

.054

.053

.053

.052

.051

.050

4.049

.049

.048

.048

.047

!046

.046

.045

.044

.044

4.043

.043

.042

.042

.041

.040

.040

.039

.038

.038

4.037

3' longitude.

Inches.

6.112

.111

.110

.109

.108

.108

.107

.106

.105

.104

6.103

.102

.101

.100

.099

.098

.097

.096

.095

.094

6.093

.092

.091

.090

.089

.088

.087

.086

.085

.084

6.083

.082

.081

.080

.079

.079

.078

.077

.076

.075

6.074

.073

.072

.071

.070

.069

.068

.067

.066

.065

6.064

.063

.062

.061

.060

.059

.058

 .058

.057

.056

6.055

4' longitude.

Indies.

8. 150

.149

.148

.146

 .145

.144

.142

.141

.139

.138

8.137

.136

.134

.133

.132

.130

.129

.128

.127

.125

8.124

.123

.122

.120

.118

.117

.116

.115

.113

.112

8.111

.110

.108

.107

.106

.104

.103

.102

.100

.099

8.098

.097

.095

.094

nnq

. uyo 

.092

.090

.089

.088

.087

8.086

.084

.083

.082

.080

.079

.078

.076

.075

.074

8.073

5' longitude.

Inches.

10. 187

.185

.184

.183

.181

.180

.178

.177

.175

.173

10. 171

.170

.168

.167

.165

.164

.162

.161

.159

.157

.10.155

.154

.152

.151

.149

.148

.146

.145

.143

.141

10. 139

.138

.136

.135

.133

.132

.130

.128

.127

.125

10. 123

.121

.120

.118

.117

.116

.114

' .113

.111

.109

10. 107

.106

.104

.103

.101

.100

.098

.097

.095

.093

10. 091

6' longitude.

Incites.

12. 224

..222

.220

.218

.216

.214

.212

.210

.208

.206

12. 205

.203

.201

.199

.197

.195

.193

.191

.189

.187

12.186

.184

.182

.180

.178

.176

.174

.172

.170

.168

12. 167

.165

.163

.161

.159

.157

.155

.153

.151

.149

12. 147

.145

.143

.141

lOQ

,. . J.OJ7

'..137

.}35

.133

.131

.129

12. 128

.126

.125

.123

.121

.119

.117

.115

.113

.111

12. 110

7' longitude.

Inches.

14. 262

.259

.257

.255

.252

.250

.247

.245

.243

.241

14.239

.237

.234

.232

.230

.228

. .225

.223

.221

.219

14. 217

.215

.212

.210

.208

.206

.203

.201

 .199

.197

14. 195

.193

.190

.188

.186

o .183

.181

.179

.176

.174

14. 172

.170

.168

.166

. 

ifid JLUT:

.162

.159

.157

.155

.153

14. 150

.148

.146

.143

.141

.139

.137

.134

.132

.130

14. 128

8' longitude.

Inches.

16. 299

.297

.294

.292

.289

..287

.284

.282

.279

.277

16.274

.272

.269

.267

.264

,.262

.259

.257

.254

.251

16.248

.246

.243

.241

.239

.236

.233

.230

.228

.225

16. 222

.220

.217

.215

.212

.210

.207

.205

.202

.199

16. 197

.194

.192

.189 107 JLOl

.184

.182

.179

.176

.174

16.171

.169

.166

.164

.161

.159

.156

.154

.151

.149

16. 146

9' longitude.

Indies.

18. 337

.334

.331

.328

.325

.322

.319

.316

.313

.310

18.308

.305

.302

.299

.296

.293

.290

-.287

.284

.281

18. 279

.276

.273

.270

.267

.264

.261

.258

.255

.252

18. 250

.247

.244

.241

.238

.235

.232

.229

.226

.223

18. 221

.218

.215

.212

. OOQ 6\Jo

.206

.203

'.200

.197

.195

18. 193

.190

.187

.185

.182

.179

.176

.173

.170

.167

18. 165

107 longitude.

Indies.

20. 374

.371

.368

.366

.363

.360

.356

.352

.349

.346

20.342

.339

.336

.332

.329

.326

.322

.319

.316

.313

20.310

.307

.304

.300

.297

.294

.291

.287

.284

.281

20. 278

.275

.272

.269

.265

.262

.259

.256

.253

.249

20.246

.243

.240

.236

.233

; .230

.626

.223

.220

.217

20. 214

.211

.208

.205

.202

.199

.196

.193

.190

.187

20. 183

1 Longitude 

interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.000

.001

.002

.003

.005

.007

.009

.011

.014

© .

 a "3 

P F P t 43 o

ts-g rf.S

/

1

2

3

4

5

6

7

8

9

10

1 B

C 0> 

O O

sic »

gi

Inches.

2.295

4.591

6.886

9.182

11.477

13. 772

16. 068

18.363

20. 659

22. 954.

,(362)
WOODWAUD.] MAP CO-ORDINATES. 57

TABLE X. Co-ordinates for projection of maps. Scale

[Derivation of table explained in section (5); use of table explained on page 22.]

|| Latitude of

parallel.

o /

2900

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

>IO 

TtO

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Abscissas of developed parallel.

c V longitude.

Indies.

2.018

.018

.018

.017

.017

.017

.016

.016

.016

.015

2.015

.015

.015

.014

.014

.014

.013

.013

.013

.012

2.012

.012

.Oil

.011

.011

.010

.010

.010

.009

.009

2.00S

.008

.008

.007

.007

.007

.006

.006

.006

.005

2.005

.005

.005 

fifid. . Ulrt

.004

.004

.003

.003

.003

.002

2.002

.002

.002

.001

.001

.001

.000

.000

.000

1.909

1.999

2' longitude.

Inches.

4.037

.037

.036

.036

.035

.035

.034

.033

.032

.031

4.030

.030

.029

.028

.028

.027

.026

.026

.025

.024

4.023

.023

' .022

.022

.021

.020

.019

.019

.018

.018

4.017

.017

.016

.016

.015

.014

.014

.013

.012

.011

4.010

.010

.009 

.009

.008

.008

.007

.006

.005

.005

4.004

.004

.003

.002

.002

.001

.001

.000

3. 999

3.99R

3.997

3' longitude.

Inches.

6. 055

.054

.053

.052

.051

.050

.049

.048

.047

. 046

6.045

.044

.043

.042

.041

.040

.039

.038

.037

' .036

6.035

.034

.033

.032

.031

.030

.029

.028

.027

.026

6.025

.024

.023

.022

.021

.020

.019

.018

.017

.016

6.015

.014

.013 

012 ion

.010

.009

.008

.007

.006

6.005

-.004

.003

.002

.001

.000

5.999

.998

.997

.996

5.9.95

4' longitude.

Inches.

8.073

.072

.071

.069

.068

.066

.065

.064

.062

.061

8.060

.058

.057

.056

.054

.053

.052

.050

.049

.048

8. 017

.045

% .044

.043

.041

.040

.039

.037

.036

.035

8.034

.032

.031

.030

.028

.027

.026

.024

.023

.021

8.020

.019

.017 

.016

.015

.013

.012

.Oil

.010

.009

8.007

.006

.005

.003

.002

.001

7.999

.998

.997

.995

7. 994

5' longitude.

Inches.

10. 091

.090

.088

.087

.085

.084

.082

.081

.079

.077

10. 075

.074

,072

.071

.069

.067

.066

.064

.062

.060

10. 058

.057

.055

.054

.052

:050

.049

.047

..045

.044

10. 042

.041

.039

.037

.036

.034

.033

.031

.029

.027

10.025

.023

.022 

.020

.019

.018

.016

.OH

.012

.011

10. 009

.007

.006

.004

.003

.001

9.999

.998

.996

.994

9.992

6' longitude.

Inches.

12.110

.108

.106

.104

.102

.100

.098

.096

.094

.092

12. 090

.088

.086

.084

.082

.080

.078

.076

.074

.072

12. 070

.068

.066

.064

.062

.060

.058

.056

.054

.052

12.050

.048

.046

.044

.042

.040

.038

.036

.035

.033

12. 031

.029

.027

AOC

. \J&\J

.023

.021

.019

.017

.015

.013

12.011

.009

.007

.005

.003

.001

11. 999

.997

.995

.993

11.991

7'Jongitude.

Inches.

14. 128

.126

.123

.121

.118

.115

.113

.110

.108

.106

14. 105

.103

.100

.098

.095

.092

.000

.087

.085

.084

14. 082

.079

.077

.074

.072

.069

.067

.065

.063

.060

14. 058

.056

.053

.051

.049

.047

.044

.042

.040

.038

14.036

.033

.031 

.029

.027

.024

.022

.020

.017

.015

14. 013

.010

.008

.006

.003

.001

13. 999

.996

.993

.991

13. 989

8' longitude.

Inches.

16. 146

.144

.141

.139

.136

,.134

.131

.129

.126

.123

16. 120

.118

.115

.113

.110

.108

.105

.102

.100

.097

16. 094

.092

.089

.086

.084

.081

.079

.076

.073

.070

16. 067

.065

.062

.000

.058

.055

.053

.050

.047

.044

16.041

.039

.036 

033

'.031

.028

.026

.023

.020

.017

16.014

.012

.009

.007

.(J04

.002

15. 999

.997

.994

.991

15. 988

9' longitude.

Inches.

18. 165

.162

.159

.156

.153

.150

.147

.144

.141

.138

18. 135

.132

.129

.126

.123

.120

.117

.114

.111

.108

18.105

.102

.099

.096

.093

.090

.087

.084

.081

.078

18. 076

.073

.070

.067

.064

.061

.058

.055

.052

.049

18. 046

.043

.040

(\1*7

. \JO t

.034

.031

.028

.025

.022

.019

18. 016

.013

.010

.007

.004

.'001

17. 998

.995

.992

.989

17. 980

10' longitude.

Inches.

20. 183

.180

.177

.173

.170

.167

.164

.161

.157

.154

20. 150

.147

.144

.140

.137

.134

.130

.127

.124

.120

20. 117

.114

.110

.107

.104

.100

.097

.094

.090

.087

20.084

.081

.077

.074

.071

.067

, .064

.061

.058

.054

20.051

.048

.044 

.041

.038

.034

.031

.028

.024

- .021

20. 018

.014

.010

.007

.004

.001

19. 997

..994

.991!

.988

19. 985

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.002

.004

.005

.007

.009

.011

.014

I!

M ^f«£-

/

1

2

3

4

5

6

7

8

9

10

I*1'

O O

sjs»a*

Inches.

2. 296

4.592

6.887

9.183

11.479

13. 775

16. 071

18. 366

20. 662

22. 958

(363)
58 FORMULAS AND TABLES. [BULL. 50.

TABLE X. Co-ordinates for projection of maps. Scale Triiro'

[Derivation of table explained in section (5); use of table explained on page 22.]

of Latitude 

parallel.

o /

3000

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

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.999

.999

.998

.998

.997

.997

.996

.996

.996

.995

1.995 

.995

.994

.994

.994

.994

.993

.993

.993

.992

1.992

.992

.991

.991

.990

.990

.990

.989

.989

.989

1.988

.988

.988

.987

.987

.987

.987

.986

.986

.986

1.985

.985

.985

!984

.984

.983

.983

.983

.982

1.982

.982

.981

.981

.981

.980

.980

.380

.979

.979

1.978

2' longitude.

Inches.

3.997

.090

.995

.995

.994

.993

.992

.992

.991

.991

3.990 

.989

.989

.988

.987

.986

.986

.985

.984

.984

3.983

.982

.982

.981

.981

.980

.979

.979

.978

.978

3.977

.976

.976

.975

.974

.974

.973

.972

.972

.971

3.970

.970

.969 

.968

.968

.967

.966

.966

.965

.964

3.963

.963

.962

.961

.961

.960

.959

.959

.958

.957

3.956

3' longitude.

Inches.

5.995

.994

.993

.992

.991

.990

.989

.988

.987

.986

5.985 

.984

.983

' .982

.981

.980

.979

.978

.977

.976

5.975

.974

.973

.972

.971

.970

.969

.968

.967

.966

5.965

.964

.963

.962

.961

.960

.959

.958

J957

.956

5.955

.954

.953

!951

.950

.949

.948

.947

.946

. 5. 945

.944

.943

.942

.941

.940

.939

.938

.937

.936

5.935

4' longitude.

Inches.

7;994

.993

.991

.990

.988

.987

.985

.984

.983

.981

7 QOA ». you 

.978

.977

.976

 .974

.973

.971

.970

.969

.968

7..907

.965

.964

.962

.961

.959

.958

.957

.955

.954

7.953

.951

.950

.948

.947

.945

.944

.943

.942

.941

7.940

.938

.937

.935 

.934

.933

.932

.930

.929

.928

7.926

.925

.924

.922

.921

.920

.918

.917

.916

.914

7.913

5' longitude.

Inches.

9.992

.990

.989

.987

.985

.984

.982

.981

.979

.977

9

Q7C 

. y 10

.974

.972

.970

.969

.967

.965

.964

.962

.960

9.958

.957

.955

.953

.952

.950

.948

.947

.945

.943

9.941

.940

.938

.936

.935

.933

.931

.930

.928

.926

9. 924

.923

.921

.919 

.'918

.916

.915

.913

.911

.909

9.907

.906

.904

.902

.901

.899

.897

.895

.894

.892

9.891

6' longitude.

Indies.

11. 991

.989

.987

.985

.983

.981

.979

.977

.975

.973

11.971 

.969

.967

.965

.963

.961

.959

.957

.955

.953

11. 950

.948

.946

.944

.942

.940

.938

. 936

.934

.932

11. 930

.928

.926

.924

.922

.920

.918

.916

.614

.912

11. 909

.907

.905

. QfN ouo 

.901

.899

.897

.895

.893

.891

11. 889

.887

.885

.883

.881

.879

.877

.875

.873

.871

11.869

7' longitude.

Incites.

13. 989

.987

. .985

.982

.980

.978

.975

.973

.970

.968

13. 966 

.963

1.961

!958

.956

.953

.951

.948

.940

.944

13. 942

.939

.937

.934

.932

.929

.927

.924

'.922

.920

13. 918

.915

.913

.910

.908

.905

.903

.900

.898

.896

13. 894

.891

.889

pop

. Sou

.884

.881

.879

.876

.874

.872

13. 870

.867

.865

.862

.860

.857

.855

.853

.851

.849

13. 847

8' longitude.

Inches.

15. 988

.985

.982

.980

.977

.974

.972

.969

.966

.964

15.961 

.959

.956

.954

. 951

.949

.946

.9*3

.940

.937

15. 934

.932

.329

.926

.923

.920

.9151

.915

.912

.909

15. 900

.904

.901

.898

.895

.893

.890

.888

.885

.882

15. 879

.877

.874

071 .oil 

.869

.867

.804

.861

.858

.855

15. 852

.850

.847

.844

.842

.839

.837

.834

.831

.829

15. 826

9' longitude.

Inches.

17. 986

.983

.980

.977

.974

.971

.968

.965

.962

.959

17. 956 

.953

.950

.947

.944

. .941

.938

.935

.932

.928

17. 925

.922

.919

.916

.913

.910

.907

.904:

.901

/.898

17. 895

.892

.889

.886

.883

.880

.877

.874

.871

.867

17. 804

.861

.858

.855 

.852

.849

.846

.843

.840

.836

17. 833

.830

.827

.824

.821

.818

.815

.812

.809

.807

17. 804

10' longitude.

Inches.

19. 985

.982

.978

.975

.971

.968

.965

.961

.958

.954

19. 951 

.948

.944

.941

.938

.934

.931

.927

.924

.921

19. 917

.914

.910

.907

.904

.901

.898

.894

.891

.887

19. 883

.880

.876

.873

.809

.806

.862

.859

.856

.852

19. 849

.845

.842

 .838 

.835

.831

.828

.824

.821

.818

19. 815

.812

.808

.805

.802

.798

.795

.792

.'788

.785

19. 782

j Longitude 1interval. 

f

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.002

.004

.005

.007

.009

.012

.014

o '

 a cs

is <3

a p

"

'

1

2

3

4

5

6

7

8

9

1.0

!§§i <3 .£3 grg

Inches.

2.296

4.592

6.888

9.184

11. 480

13. 777

16. 073

18.369

20. 665

22. 961

(364)
WOODWARD.] MAP CO-ORDINATES. 59

TABLE X. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

of Latitude parallel.

o /

3100

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

Abscissas of developed parallel.

1' Ion-" 

gitude.

Inches.

1.978

..978

.978

.977

.977

.977

 y

.976

.976

.976

.975

1.975 

.975

.974

.974

.974

.973

.973

.972

.972

.972

1.971

.971

.971

.970

.970

.970

.969

.969

.969

.968

1.968

.968

.968

.967

.967

.967

.966

.966

.965

.965

1.964

.964

.964

ooq * uoo 

.963

.963

.962

.962

.962

.961

1.961

.961

.960

.960

.960

.959

.959

.958

.958

.958

1.957

2' longitude.

Indies.

3.956

.955

.954

.954

.953

.953

.952

.951

.950

.950

.948

.948

.947

.946

.946

.945

.945

.944

.943

3.942

.942

.941

.941

.940

.940

.939

.938

.937

.936

3.935

.935

.934

. 933

.933

.932

.932

.931

.930

.929

3.928

.928

.927

926 

.*926

.925

.924

.923

.922

.922

3.921

.921

.920

.920

.919

.919

.918

.917

.916

.916

3. 915

3' longitude.

Inches.

5.935

.934

.933

.932

.931

.930

.928

.927

.926

.925

5.924 

.923

.922

.921

.920

.919

.918

.917

.916

.915

5.914

.913

.912

.911

.910

.909

.908

.906

.905

.904

5.903

.902

.901

.900

.899

.898

.897

.896

.895

.894

5.893

.892

.891

.890 

.889

.888

.887

.886

.884

.883

5.882

.881

.880

.879

.878

.877

.876

.875

.874

.873

5.872

4' longitude.

Inches.

7. 913

.912

.910

.909

.908

.906

.905

.903

.902

.900

7.899 

.897

.896

.894

.893

.891

.890

.889

,.887

.886

7.885

.883

.882

.880

.879

.877

.876

.875

.874

.872

7.871

.870

.869

.867

.866

.864

.863

.861

.860

.858

7.857

.855

.854

!851

.849

.847

.846

.845

.844

7.843

.841

.840

.839

 , .837

.836

.835

.833

.831

.830

7. 829

5' longitude.

Incites.

9.891

.889

.887

.886

.884

.882

.880

.879

.877

.875

9.873 

.871

.869

.868

.866

.864

.862

.861

. 859

.858

9.856

.854

.853-

.851

.849

.848

.846

.844

.842

.840

9.838

.836

.835

. .833

.831

.830

.828

.826

.825

.823

9.821

.819

.818

.816 

.814

.813

.811

.809

.807

.805

9.803

.801

.800

.798

.796

.794

.793

.791

.789

.787

9.786

6' longitude.

Inches.

11. 869

.867

.865

.863

' .861

.859

.857

.855

.853

.851

11. 848 

.846

.844

.842

.840

.838

.836

.834

.832

.830

11.827

.825

.823

.821

.819

.817

'.815

.813

.811

.808

11.806

.804

.802

.800

.798

.796

.794

.792

.790

.788

11. 785

.783

.781

. 779

!777

.775

.773

.771

.769

.766

11. 764

.762

.760

.758

.756

.754

.752

.750

.748

.746

11.744

7' longitude.

Inches.

13. 847

.845

.842

' .840

.837

.835

.832

.830

.827

.825

13. 823 

.820

.818

.816

.813

.811

.809

.806

.803

.801

13. 798

.796

.793

.791

.788

.785

. .783

.781

.778

.776

13.774

.771

.769

.766

.764

.761

.759

.756

-.754

.751

13. 749

.746

.744

.741 

.739

.736

.734

.731

.729

.727

13. 725

.722

.720

.717

.714

.712

.710

.707

.705

.703

13. 70L

8' longitude.

Inches.

15. 826

.823

.820

.818

.815

.812

.810

.807

.804

.801

15. 798 

.795

.793

.791

.788

.785

.782

.779

.776

.773

15.770

.768

.765

.762

.759

.756

.754

.751

.748

.745

15. 742

.739

.736

.734

.731

.728

.725

.723

.720

.717

15. 714

.711

.709

. 706 

.703

.701

.698

.695

.692

.689

15. 686

.684

.681

.679

.676

.673

.670

.667

.664

.661

15. 658

9' longitude.

Inches.

17.804

.801

.798

 .795

.791

.788

.785

.782

.778

.775

17. 772 

.769

.765

.762

.759

.756

.753

.750

.747

.744

17. 741

.738

.735

.732

.728

.726

.722

.718

.715

.712

17. 709

.706

.703

.700

.696

.693

.690

.687

.684

.681

17. 678

.675

.672

.669 

.665

.662

.659

.650

.053

.650

17. 646

.643

.640

.637

.634

.631

.628

.625

.622

.619

17. 616

10' longitude.

Inches.

19. 782

.779

.775

.772

.768

.765

.761

.758

.754

.751

10 74.7 iy. c±i

.743

.740

.736

.733

.729

.726

.723

.719

.716

19.712

.709

.705

.702

.698

.695

.691

.688

.685

.681

19. 677

.673

.670

.666

.663

.659

.656

.652

.649

.645

19. 642

.638

.635

.631 

.628

.624

.621

.617

.614

.610

19. 607

.603

.600

.596

.59?

.589

.586

.582

..579

.576

19. 573

II Longitude 

interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinate ofdeveloped parallel.

Inches.

0.000

.001

.001

.002

.004

. 005

.007

.009

.012

.015

i? ||

H .

'

1

2

3

4

5

6

7

8

9

10

Is0 0

;= a

? £

3.2 3"^

Inches.

2.296

4.593

6.889

9. 186

11.4S2

13. 779

16. 075

18.372

20. 668

22. 965

(305)
60 FORMULAS AND TABLES. [BTJLL. 50.

TABLE X. Co-ordinates for projection of maps. Scale 3 \ & 8 0 . 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

O 1

3200

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

2G

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

Abscissas of developed parallel.

1' longitude.

Inches.

1.957

.957

.957

.956

.956

.956

.955

.955

.955

.954

1.954

.954

.953

.953

.953

.952

.952

.952

.951

.951

1..950

.950

.949

.949

.949

.948

.948

.947

.947

.947

1.946

.946

.946

.945

.945

.945

.944

.944

.944

.943

1.943

.943

.942

.942

.942 

.941

.941

.940

.940

.940

1. 939

.939

.939

.938

.938

.938

.937

.937

.937

.936

1.936

2' longitude.

Incites.

3.915

.914

.913

. .912

.912

.911

.910

.909

.908

.908

3.907

.906

.905

.905

.904

.904

.903

.902

.901

.901

3.900

.899

.898

.898

.897

.896

.895

.895

.894

.893

3.893

.892

.891

.891

.890

.889

.888

.888

.887

 .886

3.886

.885

.884

o.884

 SS3 

. ooo

.882

.882

.881

.880

.879

3.879

.878

.877

.877

..876

.875'

.875

.874

.873

.872

3.871

3' longitude.

Inches.

5.872

.871

.870

.869

.868

.867

.866

.865

.864

.863

5.861

.860

.859

.858

.857

.856

.855

.854

.853

.852

5.850

.849

.848

.847

 . 846

.845

.844

.843

.842

.840

5.839

.838

.837

.836

.835

.834

.833

.832

.831

. 8:-!0

5.829

.828

.827

.826

.825 

.824

.823

.822

.821

.820

5.818

.817

.816

.815

.8U

.813

.812

.811

.810

.808

5.807

4' longitude.

Inches.

7.829

.828

.826

.825

.823

.822

' .820

.819

.817

.816

7.815

.813

.812

.810

.808

.807

.805

.804

.802

.801

7.800

.798

.797

.795

.794

.793

.792

.790

.788

.787

7.786

.784

.783

.781

.780

.778

.777

.775

-.774

.V73

7.772

.770

.769

.767

. 766 

.765

.763

.762

.760

.759

1 7.757

.756

.754

. 753

.751

.750

.748

.747

. .745

.744

7.743

5' longitude.

Indies.

9.786

.784

.782.

.781

.779

.777

.776

.774

.772

.770

9.768

.767

.765

.763

.762

.760

.758

.756

.754

.752

9.750

.748

.747

.745

.743

.742

.740

.738

.736

.734

9.732

.731

. 730

.728

.726

.725

.723

.721

.719

.717

9.714

.712

.711

.709

.707 

.705

.703

.702

.700

.698

9.696

.694

.693

.691

.689

.687

.685

.683

.681

.680

9.678

6' longitude.

Indies.

11. 744

.742

.740

.737

.735

. 733

.731

.728

.726

.724

11. 722

.720

.718

.716

.714

.712

.710

.708

.706

.704

11. 7U1

.699

.697

.694

.692

.690

.688

.686

.683

.681

11. 679

.677

.675

.673

.670

.668

.666

.664

. 662

.660

11.657

.655

.653

. 651

.649 

.647

.645

.643

.641

.638

11. 636

.633

.631

.629

.627

.625

.623

.621

.618

.616

11.614

7' lon1 gitude.

Inches.

13. 701

.698

.696

.693

.691

.688

.686

.683

.681

.679

13. 676

.674

.671

.669

.666

.664

.661

.659

.656

.654

13. 651

.649

.646

.644

.641

.639

.636

.634

.631

. 028

13. 625

.623

.620

.618

.615

.613

.610

.608

.6U5

.603

13. 600

.598

.595

.593

KQO 

. Ov£

.590

.587

.585

.682

.578

13. 575

.573

.570

.568

.565

.563

' .560

.558

.555

.553

13.550

8' longitude.

Inches.

15. 658

.655

.652

.650

.647

.644

.641

.639

.636

.633

15. 630

.627

.624

.621

.618

.615

.612

.609

.606

.604

15. 601

.598

.595

.592

.589

.586

.583

.580

.577

.575

15. 572

.569

 .566

.563

.560

.557

.554

.551

.548

.646

15.543

.540

.537

.534

.531 

.528

.525

.522

.519

.517

15. 514

.511

.508

.505

.503

.500

.497

.494

.491

.4R8

15. 486

9' longitude.

Inches.

17. 616

.613

.610

.606

.603

.600

.597

.593

.590

.587

17. 583

.580

.577

.574

.570

.567

.564

.561

.558

.554

17. 551

.548

.544

.541

.538

. .535

.531

.528

.525

.521

17. 518

.515

.511

.508

.505

.502

.498

.495

.492

.489

17. 486

.483

.479

.476

472 

!468

.465

.462

. 459

 .457

17. 454

.451

.448

.444

.441

.438

.434

.431

.428

.424

17. 421

10' longitude.

Inches.

19. 573

.570

.566

.563

.559

.556

.552

.549

.545

.541

19. 537

.534

.530

.527

.524

.520

.516

.513

.509

.505

19. 501

.498

.494

.491

.487

.483

.480

.476

.473

.469

19.465

.462

.458

.455

.451

.447

.444

.440

.436

.433

19. 429

.426

.422

.419

.415 

.411

..408

'. 404

-.401

.397

19. 393

.390

.386

.383

.379

.376

.372

.369

.365

.361

19. 357

Longitudeinterval.

>

/

1

2

3

4

5

6

J

8

9

10

Ordinates ofdeveloped parallel.

Indies.

0.000

.001

.001

.002

.004

.005

.007

.010

.012

.015

_c

 SI

1°&t

3

/

1

2

3

4

5

6

7

8

9

10

"a ai

g g

.2 a

SJ

0.2

g-O

Indies.

2.297

4.594

6.891

9.188

11.484

13. 781

16.078

18. 375

20. 672

22. 969

(366)
WOODWAKD-1 MAP CO-ORDINATES. 61

TABLE X. Co-ordinates for projection of maps. Scale -jr^-sir. 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

3300

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

30

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 Abscissas of developed parallel.

1' longitude.

Inches.

1.936

.936

.936

.935

.935

.934

.934

.933

.933

.932

.932

.931

.931

.930

.930

.930

.929

.929

.929

1.928

.928

.928

.927

.927

.927

.926

.926

. 926

.926

1.926

.925

.925

.924

.924

.923

.923

.'.122

!922

.922

1. 921

.921

.920

 .920 

.920

.919

.919

.918

.918

.918

1.917

.917

.917

.916

.916

.916

.915

.915

.915

.914

1.914

2' longitude.

Inches.

3.871

.870

.869

.869

.868

.867

.867

.866

.865

.865

3 864

.863

.862

.862

.861

.860

.860

.859

.858

.858

3.857

.856

.855

.854

.853

.853

.852

.851

.8&0

.849

3.849

.848

.847

.847

.846

.846

.845

.844

.843

.843

3.842

.841

.840

!839

.838

.837

.836

.836

.835

3.834

.834

.833

.832

.832

.831

.830

.829

.828

.828

3.827

3' longitude.

Inches.

5.807

.806

.805

.804

.803

.801

.800

.799

.798

.797

5.796 

.795

.794

.793

.792

.790

.789

.788

.787

.786

5.785

.784

.783

.782

.780

.779

.778

.777

.776

.775

5.774

.773

.772

.771

.769

.768.

.767

.766

.765

.764

6. 763

.702

.761

.760 

.758

.757

.756

.755

.754

.753

6.752

.751

.750

.749

.748

.747

.746

.744

.743

.742

5.741

4' longitude.

Inches.

7.743

.741

.740

.738

.737

.735

.734

.732

.731

.729

.726

.725

.723

.722

.720

.719

.717

.716

.714

7.713

.711

.710

.708

.707

.705

.703

.702

.700

.699

7.698

.696

6' longitude.

Inches.

9.678

.676

.674

.673

.671

.669

.667

.665

.664

.662

9.660 

.658

.657

.655

.653

.651

.649

.647

.645

.643

9.641

.640

.638

.636

.634

.632

.631

.629

.627

.625

9.623

.621

.6951 .619

. 693 | . 617

. 692 . 615

. 690 ' . 013

. 689 ' . Oil

.687 . 609

.686

.685

7.684

.682

.681

!678

.670

' .075

.673

.672

.670

7.669

.667

.666

.664

.663

.661

.660

.658

.657

.655

7.654

.607

.605

9.604

.602

.600

. 59!i 

.597

.595

.593

.591

.589

.588

9.586

.584

.583

.581

.579

.577

.575

.573

.571

.570

9.568

6' longitude.

Inches.

11. 614

.612

.610

.607

.605

.603

.601

.598

.596

.594

11. 592 

.590

.587

.585

.583

.581

.579

.577

.575

.572

11.670

.568

.566

.664

.561

.559

.557

.555

.653

.551

11. 548

.546

.544

.542

.540

.637

.535

.532

.530

.528

11.525

.5211

.521

ni o

..O lo

.510

.514

.512

.510

.508

.505

11.503

.501

.499

.497

.494

.492

.490

.488

.486

.484

11.482

V longitude.

Inches.

13.550

.547

.545

.542

.640

.537

.534

.532

.529

.627

13.524 

.522

.519

.517

.514

.512

.509

.506

.504

.500

13.498

.495

.493

.490

.487

.485

.482

.480

.477

.475

13.472

.470

.467

.465

.462

.460

.457

.455

.452

.449

13.a46

.444

.441

439

!434

.431

.429

.426

.423

13.420

.418

.415

.413

.410

.408

.405

.403

.400

.397

13.395

8' longitude.

IncJies.

15.486

.483

.480

.477

.474

.471

.468

.465

.462

.459

15. 456 

.453

.450

.447

.444

.441

.438

.435

.432

.429

15.426

.423

.420

.417

.414

.411

.408

.405

.402

.400

15.397

.394

.391

.388

.385

.382

.379

.376

.373

.370

15. 367

. L364

.361

oro

. OUO

.355

.352

.349

.346

.343

.340

15.338

.335

.332

.330

.327

.324

.321

.318

.315

.312

15.309

9' longitude.

Inches.

17.421

.418

.415

.411

.408

.405

.401

.398

.395

.392

17.388 

.385

.382

.378

.375

.372

.369

.366

.362

.359

17. 355

.352

.349

.345

.342

.339

.335

.332

.328

.325

17. 321

.318

.315

.312

.308

.305

.301

.298

.295

.291

17. 288

.285

.281

!274

.271

.267

.263

.260

.257

17. 255

.252

' .248

.245

.242

.238

.235

.231

.228

.225

17.222

IV longitude.

Inches.

19.357

.353

.349

.346

.343

.339

.335

.332

.328

.324

19.320 

.316

.312

.309

.305

.302

.298

.294

.291

.287

19.283

.280

.276

.272

.269

.265

.261

.258

.254

.250

19. 246

.243

.239

.236

.232

.228

.224

.221

.217

.213

19. 209

.205

.202

198 

!l94

.191

.187

.184

.180

.176

19. 172

.169

.165

.161

.168

.154

.150

.146

.142

.139

19. 136

1 Longitude 

interval.

/

1

2

3

4

5

6

7

8

9

10

Ordiuates ofdeveloped parallel.

Inches.

0.000

.001

.001

.002

.004

.005

.007

.010

.012

.015

s

or; 73 Co

a > -*S *- 

+3 42

$.

1

"21

3

4

5

6

7

8

9

10

C3 8

o S

33-jS

o.S g-a

Inches.

2.297

4.594

6.892

9.189

11. 486

13. 783

16.080

18. 378

20. 675

22. 972

(367)
62 FORMULAS AND TABLES. [BULL. 60.

TABLE X. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

3400

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

Abscissas of developed parallel.

1' longitude.

Inches.

1.914

.914

.913

.913

.913

.912

.912

.911

.911

.911 

1.910

.910

.909

.909

.909

.908

.908

.907

.907

.907

1.906

.906

.905

.905

.905

.904

.904

.903

.903

.903

1.902

.902

.901

.901

.901

.900

.900

.899

.899

.899

1.898

.898

.898

.897

QQT Ot7l

.897

.896

.896

.896

.895

1.895

.895

.894

.894

.893

.893

.893

.892

.892

.891

1.891

2' longitude.

Inches.

3.827

.827

.826

.825

.824

.824

.823

.822

.821

COT . oZl

3.820

.819

.819

.818

.817

.816

.815

.814

.813

.813

3.812

.811

.810

.809

 .808

.807

.806

.805

.805

.804

3.804

.803

.802

.802

.801

.800

.799

.799

.798

.797

3.797

.796

.795

.794

.794 

!793

.792

.792

.791

.790

3.789

.788

.787

.786

.786

.785

.784

.783

.783

.782

3..7S2

3' longitude.

Inches.

5.741

.740

.739

.737

.736

.735

.734

.733

.731

.730 

5! 729

.728

.726

.725

.724

.723

.722

.721

 .720

.719

5.718

.717

.715

.714

.713

.712

.711

.710

.709

.708

5.707

.706

.704

.703

.702

.701

.700

.699

.698

.696

5.695

.694

.693

.692

RQ1 * os J. 

.690

.689

.688

.687

.686

5.684

.683

.682

.681

.680

.678

.677

.676

.675

.674

5.673

4' longitude.

Inches.

7.654

.652

.651

.649

.648

.646

.645

.643

.642

.640 

7! 639

.637

.636

.635

.633

.632

.630

.629

.627

/ .626

7.624

.623

.621

.620

.618

.617

' .615

.614

.612

.610

7.609

.607

.606

.604

.603

.601

.600

.598

.597

.595

7.594

.592

.591

.589

EQQ

* UOO

.586

.585

.583

.582

.580

7.578

.577

.575

.574

.572

.571

.570

.568

.567'

.565

7.564

5' longitude.

Inches.

.9.568

.566

.564

.562

.560

.558

.556

.554

.552

.550 

9.549

.547

.545

.543

.541

.539

.537

.535

.533

.531

9.530

.528

.526

.524

.522

.520

.518

.516

.514

.512

9.511

.509

.507

.505

.503

.501

.499

.497

.495

.493

9.492

.490

.488

.486

.484 

.482

.480

.478

.476

.474

9.473

.471

.469

.467

.465

.463

.461

.459

.457

.455

9.454

6' longitude.

Inches.^

11.482

.480

' .478

.475

.473

.471

.468

.466

.463

.461 

11. 459

.457

.454

.452

.449

.447

.445

.442

.440

.438

li:436

.433

.431

.428

.426

.423

.421

.419

.417

.415

11. 413

.410

.408.

.406

.404

.401

.399

.397

.395

.392

11.390

.388

.386

.383

QQ1

 OoJ.

.378

.376

.374

.372

.370

11.368

.365

.363

.361

.359

.357

.354

.352

.350

.347

11.345

7' longitude.

Inches.

13.395

.392

.390

.387

.385

.382

.380

.377

.375

13! 369

.367

.364

.362

.359

.357

.354

.351

.348

.345

13.342

.339

.337

.334

.332

.329

.326

.324

.321

.318

13.315

.313

.310

.308

.305

.302

.300

.297

.294

.292

13.289

.286

.284

.281

!276

.273

.271

.268

.265

13.262

.260

.257

.255

.252

.250

.247

.244

.242

.239

13.236

8' longitude.

Inches.

15.309

.306

.303

.300

.297

.294

.291

.288

.285

15! 278

.275

.272

.269

.266

.263

.260

.257

.254

.251

15.248

.245

. .242

.239

.236

.233

.230

.227

.224

.221

15. 218

.215

.212

.209

.206

.203

.290

.197

.194

.191

15.187

.184

.181

.178

.175 

.172

.169

.166

.163

.160

15.157

.154

.151

.148

.145

.142

.139

.136

.133

.130

15. 127

9' longitude.

Inches.

17. 222

.219

.215

.212

.208

.205

.201

.198

.194

191 

1?! 188

.184

.181

.177

.174

.170

.167

.164

.160

.157

17. 154

.150

.147

.143

.140

.136

.133

.129

.126

.123

17. 120

.116

.113

.110

.106

.103

.099

.096

.092

.089

17.086

.082

.079

.075

.072 

.068

.065

.061

.058

.054

17.051

.048

.044

.041

.037

.034

. .030

.027

.024

.021

17. 018

10' longitude.

Inches.

19. 136

.132

.128

.125

.121

.117

.113

.109

.106

1O9 * \\J&

19.098

.094

.090

.087

.083

.079

.075

.072

.068

.064

19. 060

.056

.052

.048

.045

.041

.037

.033

.029

.026

19.022

.018

1 .014

.011

.007

.003

.000

18. 996

.992

.988

18.984

.980

.976

.973

'.965

.961

.958

.954

.950

18.946

.942

.939

.935

.931

.927

.923

.920

.916

.912

18. 909

Longitude interval.

1

2"** 

4

5

6

7

8

9

10

of Ordinates developed parallel.

Inches.

0.000

.001

.001

.002

.004

.006

.008

.010

.012

.015

B S

53 <3 J'S

f

1

2

3

4

5

6

7

8

9

10

'||

sl S*8

Inches.

2.298

4.595

6.893

9.190

11.488

13. 786

16.083

18.381

20. 678

22. 976

(368)
WOODWARD.] MAP CO-ORDINATES. 63

TABLE X. Co-ordinates for projection of maps. Scale -

[Derivation of table explained in section (5); use of table explained on page 22.]

of Latitude parallel.

o /

3500

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

51

62

63

64

65

56

67

58

69

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.891

.891

.890

.890

.890

.889

.889

.888

.888

.888

1.887 

 .887

.886

.886

.886

.885

.885

.884

.884

.884

1.883

.883

.882

.882

.882

.881

.881

.880

.880

.880

1.879

.879

.878

.878

.878

.877

.877

.876

.876

.876

1.876

.875

.874

Q*TA

 Ol'x

.874

.873

.873

.873

.872

.872

1.871

.871

.871

.870

.870

.870

.869

.869

.869

.868

1.868

2' longitude.

Inches.

3.782

.781

.780

.780

.779

.778

.777

.776

.775

.775

3.774

, .773

.772

.772

.771

.770

.769

.768

.767

.767

3.766

.765

.764

.763

.763

.762

.761

.760

.759

.759

3.768

.757

.757

.756

.755

.754

.754

.753

.752

.752

3.751

.750

.750

.749 

!?48

'.747

.746

.746

.745

.744

3.743

.742

.741

.741

.740

.739

.738

.737

.736

.735

3.735

3' longitude.

Inches.

5.673

.672

.670

.669

.668

.667

.666

.665

.663

.662

5.661 

. .660

.658

.657

.656

.655

.654

.652

.651

.650

6.649

.648

.647

.646

.645

.644

.643

.642

.641

.640

5.638

.637

.636

.634

.633

.632

.631

.630

.628

.627

5.626

.625

.623

ftOO

 \juu

.621

.620

.619

.618

.616

.615

5.614

.613

.611

.610

.609

.608

.607

.606

.605

.604

5.603

4' longitude.

Inches.

7.564

.562

.561

.559

.558

.556

.555

.553

.552

.550

7.548 

.547

.545

.544

.543

.541

.539

.638

.636

.634

7.632

.531

.529

.628

.626

.525

.523

.522

.520

.519

7.517

.516

.514

.513

.511

.510

.508

.507

.605

.603

7.601

.600

.498

.497 

!495

.493

.492"

.490

.489

.487

7.486

.484

.483

.481

.480

.478

.477

.475

.474

.472

7.470

5' longitude.

Inches.

9.454

.452

.450

.448

.446

.444

.442

.440

.438

.436

9.435 

.433

.431

.429

.427

.425

.423

.421

.419

.417

9.415

.413

.411

.409

.407

.405

.403

.401

.399

.397

9.396

.394

.392

.390

.388

.386

.384

.382

.380

.378

9.376

.374

.372

q*7rt tOi\J

 .368

.366

.364

.362

.360

.358

9.357

.355

.353

.351

.349

.347

.345

.343

.341

.339

9.338

6' longitude.

Inches.

11.345

.343

.341

.338

.336

.334

.331

.329

.327

.326

11.322 

.320

.318

.315

.313

.311

.308

.306

.304

.301

11. 299

.297

..294

.292

.289

.287

.284

.282

.279

.277

11.275

.272

.270

.267

.265

.263

.260

.258

.256

.254

11. 252

.250

.247

.245 

.*242

.240

.237

.235

.232

.230

11. 228

.226

.224

.221

.219

.217

.215

.213

.211

.208

11. 206

7' longitudeInches.

13. 236

.234

.231

.228

.225

.223

.220

.217

.214

.212

13.209 

.206

.203

.201

.198

.195

.193

.190

.187

.185

13. 182

.179

.176

.174

.171

.168

.165

.162

.160

.157

13.154

.152

.149

.147

. .144

.141

.139

.136

.133

.130

13. 127

.124

.122 "I1Q

 ny 

.116

.113

.111

.108

.105

.102

13.100

.097

.094

. .092

.089

.086

.084

.081

.078

.075

13. 073

8' longitude.

Inches.

15. 127

.124

.121

.118

.115

.112

.109

.106

.103

.100

15. 096 

.093

.090

.087

.084

.081

.078

.075

.072

.069

15.065

.062

.059

.056

.053

.050

.047

.044

.041

.038

15.034

.031

.028

.025

.022

.019

.016

.013

.010

.006

15. 002

14. 999

.996

QQO

 yyo 

.990

.987

.984

.981

.978

.974

14. 971

.968

.965

.962

.959

.956

.953

.950

.947

.944

14. 941

9' longitude.

Inches.

17. 018

.016

.011

.008

.004

.001

16. 997

.994

.990

.987

16. 983 

.980

.976

.973

.969

.966

.962

.958

.955

.951

16.948

.944

.941

.937

.934

.930

.927

.923

.920

.916

16. 913

 .909

.906

.902

.899

.895

.892

.888

.885

.881

16. 878

.874

.871

.867 

.864

.860

.857

.853

.850

.846

16.843

.839

.836

.832

.829

.825

.822

.818

.815

.811

16. 808

10' longitude.

Inches.

18. 909

.905

.901

.897

.893

.890

.886

.882

.878

.874

18. 870 

.866

.862

.858

.854

.861

.847

.843

.839

.835

18.831

.827

.823

.819

.815

.811

.808

.804

.800

.796

18. 792

.788

.784

.780

.777

.773

.769

.765

.761

.757

18. 753

.749

.745

.741 

.737

.733

.730

.726

.722

.718

18. 714

.710

.707

.703

.699

.695

.691

.687

.683

.679

18. 676

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.002

.004

.006

.008

.010

.013

.016

03 . 

 O^a

 Bfc ' § 3

GO TI 

I-5.S

/

1

2

3

4

5

6

7

8

9

10

a 

.2 a 

SS

QJ IT* £T

Indies.

2.298

4.596

6.894

9.192

11.490

13. 788

16.086

18.384

20. 682

22. 980

(369)
64 FORMULAS AND TABLES. [BULL. 60.

TABLE X. Co-ordinates for projection of maps. Scale Frivu- 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

O '

3600

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

Abscissas of developed parallel.

/ 1' longitude.

Inches.

1.868

.868

.867

.867

.867

.866

.866

.865

.865

.865

1.864

.864

.863

.863

.863

.862

.862

.861

.861

.861

1.860

.860

.859

.859

.859

.858

.858

.857

.857

.857

1.856

.856

.855

.855

.855

.854

.854

.853

.8"53

.853

1.852

.852

.851

.851

.851

.850

.850

.849

.849

.849

1.848

.848

.847

.847

.847

.846

.846

.845

.845

.845

1.844

2' longitude.

Inches.

3.735

.734

.733

.733

.732

.731

.730

..729

.729

.728

3.727

.726

.725

.725

.724

.723

.722

.721

.721

.720

3.719

.718

.717

.717

.716

.715

.714

.713

.713

.712

3.711

.710

.709

.708

.708

' .707

.706

.705

.705

.704

3.703

.702

.701

.701

.700 !e99

.698

.697

.697

.696

3.695

.694

.693

.693

.692

.691

.690

.689

.689

.688

3.687

3' longitude.

Indies.

5.603

.602

.601

.599

.598

.597

.596

.595

.594

.592

5.591

.590

.589

.587

.586

.585

.584

.583

.581

.580

5.579

.578

.577

.575

.574

.573

.572

.570

.569

.568

5.567

.566

.564

.563

.562

.561

.560

.558

.557

.556

5.555

.554

.553

.551

.550

.549

.548

.547

.546

.544

5.543

.542

.541

.540

.538

.537

.536

.535

.534

.532

5.531

4' longitude.

Inches.

7.470

.468

.467

.465

.464

.462

.461

.459

.458

.456

7.454

.453

.451

.450

.448

.447

.445

.444

.442

.440

7.438

.437

.435

.434

.432

.431

.429

.428

.426

.424

7.422

.421

.419

.418

.416

.415

.413

.412

.410

.408

7.406

.405

.403

.402

.400

!399

.397

.396

.394

.392

7.390

.389

.387

.386

.384

.383

.381

.380

.378

.377

7.375

5' Ion. 

gitude.

Inches.

9.338

.336,

.334

.332

.330

.328.

.326

.324

.322

.320

9.318

.316

.314

.312

.310

.308

.306

.304

.302

.300

9.298

.296

.294

.292

.290

.288

.286

.284

.282

.280

9.278

.276

.274

.272

.270

.268

.266

.264

.262

.260

9.258

.256

.254

.252

OKA ,6O\J

.248

.246

.244

.242

.240

9.238

.236

.234

.232

.230

.228

.226

.224

.222

.220

9.218

6' longitude.

Incites.

11.206

.204

.201

.199

.196

.194

.191

.189

.187

.184

11.182

.180

.177

.175

.172

.170

.167

.165

.163

.160

11.158

.156

, .154

.151

.149

.147

.144

.142

.139

.137

11.134

.132

.129

.127

.124

.122

.119

.117

.114

.112

11.110

.107

.105

.102

.100

!097

.095

.093

.090

.088

11.086

.083

.081

.079

.076

.074

.071

.069

.067

.065

11.062

7' longitude.

Inches.

13.073

.070

.067

.065

.062

.059

.057

.054

.051

.048

13.045

.042

.039

.037

.034

.031

.028

.026

.023

.020

13.017

.014

.011

.009

.006

.003

.000

12.998

.995

.992

12.989

.986

.983

.981

.978

.975

.972

.970

.967

.964

12.961

.958

.955

. .953

.950

!947

.944

.942

.939

.936

12.933

.930

.928

.925

.922

.920

.917

.915

.912

.909

12.906

8' longitude.

Inches.

14.941

.938

.935

.931

.928

.925

.922

.918

.915

.912

14.909

.906

.903

.899

.896

.893

.890

.886

.883

.880

14.877

.874

.871

.567

.804

.861

.858

.854

.851

.848

14.845

.842

.838

.835

.832

.829

.820

.822

.819

.816

14.813

.810

.807

.803

.800

.796

.793

.790

.787

.784

14.781

.778

.775

.772

.769

.765

.762

.759

.756

.753

14.750

9' longitude.

Inches.

16.808

.804

.801

.798

.794

.790

.787

.784

.780

.776

16.772

.769

'.765

.762

.758

.755

.751

.748

.744

.740

16.736

.733

.729

.726

.722

.719

.715

.712

.708

.704

16:700

.697

.694

.690

.686

.683

 .679

.670

.672

.668

16.664

.661

.657

.654

.650

.647

.643

.640

.636

.632

16.628

.625

.621

.618

.614

.611

.607

.604

.600

.597

16.593

10' lon- 

;itude.

Inches.

18.676

.672

.668

.664

.660

.656

.652

.648

.644

.640

18.636

.632

.628

.624

.620

.616

.612

.608

.604

.600

18.596

.592

.588

.584

.580

.576

.572

.568

.564

.560

18.566

.552

.548

.544

.540

.536

.532

.528

.524

.520

18.516

.512

.508

.504

CArt .OUU

.496

.492

.488

.484

.480

18.476

.472

.468

.464

.460

.456

.452

.448

 .444

.440

18.437

I Longitude | interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.003

.004

.006

.008

.010

.013

.016

* J

H*n o

oi "^ 3.s

/

. i

2

3

4

5

6

7

8

9

10

o5 

§S 

S§C-S

Hi

Inches.

2.298

4.597

6.895

9.194

11.492

13.790

16.089

18.387

20.686

22.984

(370)
WOODWARD. | MAP CO-ORDINATES. 65

TABLE X. Co-ordinates for projection of maps. Scale ST^T?- 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

3700

1

2

3

4

6

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

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.844

.844

.843

.843

.843

.842

.842

.841

.841

.840

1.840 

.840

.839

.839

.838

.838

.838

.837

.837

.836

1.836

.835

.835

.834

.834

.833

.833

.832

.832

.831

1.831

.831

.830

.830

.829

.829

.828

.828

.828

.827

1.827

.826

.826

ooc O&9

.825

.825

.824

.824

.824

.823

1.823

.823

.822

.822

.822

.821

.821

.820

.820

.819

1.819

2' longitude.

Inches.

3.687

.686

.685

.684

.683

.683

.682

.681

.680

.680

3.679 

'.679

.678

.677

.676

.675

.674

.673

.673

'.672

3.071

.670

.669

.669

.668

.667

.666

.665

.664

.664

3.663

.662

.661

.661

.660

.660

.659

.658

.657

.656

3.655

.654

.653 

.653i

.652

.651

.650

.650

.649

.648

3.647

.646

.645

.645

.644

.643

.642

.641

.641

.640

3.639

3' longitude.

Inches.

5.531

.530

.529

.528

.526

.525

.524

.523

.521

.620

6.519 

.518

.517

.516

.514

.513

.512

.611

..510

.508

6.507

.505

.604

.603

.502

.600

.499

.498

.497

.495

5.494

.492

.491

.490

.489

.488

.486

.485

.484

.483

5.482

.480

.479

.478 

.476

.475

.474

.473

.472

.471

5.470

.468

.467

.466

.465

.464

.463

.461

.460

.459

5.458

4' longitude.

Inches.

7.375

.373

.371

.370

.368

.306

.365

.363

.362

.360

7.358 

.357

.355

.354

.362

.350

.349

.347

.345

.344

7.342

.341

.339

.337

.336

.334

.332

.331

.329

.327

7.326

.324

.323

.321

.320

.318

.317

.315

.314

.312

7.310

.309

.307

OAK .OV/O

 .304

.302

 .300

.299

.297

.295

7.293

.292

.290

.289

.287

.285

' .284

.282

.281

.279

7.277

5' longitude.

Inches.

9.218

.216

.214

.212

.210

.208

.206

.204

.202

.200

9.198 

.196

.194

.192

.190

.188

.186

.184

.182

.180

9.177

.175

.173

.171

.169

.167

.165

.163

.161

.159

9.167

.155

.163

.151

.149

.147

.145

.143

.141

.139

9.137

.135

.133 "IQ1

 1.O-L

.129

.127

.125

.123

.121

.119

9.116

.114

.112

.110

.108

.106

.104

.102

.100

.098

9.096

6' longitude.

Inches.

11.062

.060

.057

.055

.052

.050

.047

.045

.043

.040

11.038 

.035

.033

.030

.028

.025

.022

.020

.018

.016

11.013

.011

.008

.006

.003

.001

10.998

.996

.993

.991

10.988

.986

.983

.981

.978

.976

.973

.971

.968

.966

10.964

.962

.959

new

 otH

.954

.962

.950

.947

.945

.942

10.940

.938

.935

.933

.930

.928

.925

.923

.920

.918

10.916

7' longitude.

Inches.

12.906

.903

.900

.897

.894

.891

.888

.885

.882

.880

12.877 

.874

.871

.868

.865

.862

.860

.857

.854

.851

12.848

.845

.842

.840

.837

.834

.831

.829

.826

.823

12.820

 .817

.814

.811

.808

.806

.803

.800

.797

.795

12.792

.789

.786

!?80

.777

.774

.771

.768

.765

12.763

.760

.757

.755

.752

.749

.746

.743

.741

.738

12.735

8' longitude

Inches.

14.750

.747

.744

.740

737

.734

.731

.728

.724

.721

14.717 

.714

.710

.707

.704

.701

.697

.694

.691

.688

14.684

.681

.677

.674

.671

.667

.664

.661

.658

.654

14.651

.647

.644

.641

.638

. .635

.632

.629

.625

.622

14.619

.616

.612

.609 ieoe

.603

.600

.596

.593

.590

14.686

.583

.580

.576

.573

.570

.566

.563

.560

.557

14.554

9' longitude.

Inches.

10.503

.589

.585

.582

.578

.574

.571

.567

.563

.560

16.556 

.552

.548

.646

.541

.637

.534

.530

.627

.523

16.519

.616

.512

.509

.505

.602

.498

.494

.491

.487

16.483

.480

.476

.472

.469

.465

.462

.458

.455

.451

16.447

.444

.440 

.437

.'429

.426

.422

.418

.414

16.410

.407

.403

.399

.395

.392

.388

.384

.381

.377

16.374

1(X longitude.

Inches.

18.437

.433

.429

.425

.421

.417

.413

.409

.405

.401

18.396 

.392

.388

.384

.380

.376

.372

.368

.364

.360

18.355

.351

.347

.343

.339

.335

.331

.327

.323

.319

18.314

.310

.306

.302

.298

.294

.290

.286

.282

.278

18.274

.270

.266

262 

.358

.254

.250

.246

.242

.238

18.233

.229

.225

.221

.217

.213

.209

.205

.201

.197

18.193

1 Longitude 

interval.

/

1

 2

3

4

6

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.003

.004

.006

.008

.010

.013

.016

° -i

1-2

""

'

1

2

3

4

5

6

7

8

9

10

^

a S

II3.3 a -a

Inches.

2.299

4.598

6.896

9.195

11.494

13.793

16.092

18.390

20.689

22.988

Bull. 50 5

(371)
66 FORMULAS AND TABLES. [BULL. 50.

TABLE X. Co-ordinates for projection of maps. Scale -j-f^tnr-

[Derivation of table explained in section (5); use of table explained on page 22.]

of Latitude 

parallel.

o /

3800

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

Abscissas of developed parallel.

1' longitude.

Inches.

1.819

.819

.818

.818

.817

.817

.817

.810

.816

.815

1.815

.815

.814

.814

.813

.813

.813

.812

.812

.811

1.811

.811

.810

.810

.809

.809

.809

.808

.808

.807

1.807

.807

.806

.806

.805

.805

.804

.804

.803

.803

1.802

.802

.801

!soo

.800

.800

.799

.799

.798

1.798

.798

.797

.797

.796

.796

.796

.795

.795

.794

1.794

2' longitude.

Inches.

3.639

.638

.63?

.636

.635

.634

.633

.632

.631

.631

3.630

.629

.628

.627

.626

.625

.624

.624

.623

.622

3.622

.621

.620

.619

.618

.617

.616

.615

.614

.614

3.613

.612

.611

.610

.609

.609

.608

.608

.607

.606

3.605

.604

.603 

.602

.601

.601

.600

.599

.598

.597

3.596

.596

.595

.594

.593

.593

.592

.591

.590

.590

3.589

3' longitude.

Inches.

5.458

.457

.456

.454

.453

.452

.451

.450

.448

.447

5.445

' .444

.443

.441

.440

.439

.438

.436

.435

.434

5.433

.432

.430

.429

.428

.427

.425

.424

.423

.421

5.420

.419

.417

.416

.415

.413

.412

.411

.410

.408

5.407

.406

.405

!402

.401

.400

.399

.398

.396

5.395

.394

.392

.391

.390

 .389

.388

.386

.385

.384

5.383

4' longitude.

Inches.

7.277

.275

.273

.272

.271

.269

.267

.266

.264

.262

7.260

.258

.257

.255

.254

.252

.251

.249

.247

.246

7.244

.242

.241

.239

.237

.236

.234

.232

.231

.229

7.227

.225

.224

.222

.220

.219

.217

.215

.214

.212

7.210

.208

.207

!203

.202

.200

.198

.196

.195

7.193

.191

.190

.188

.187

.185

.184

.182

.181

.179

7.177

5' longitude.

Inches.

' 9.096

.094

.092

.090

.088

.086

.084

.082

.080

.078

9.075

.073

.071

.069

.067

.065

.063

.061

.059

.057

9.054

.052

.050

.048

.046

.044

.042

.040

.038

.036

9.033

.031

.029

.027

.025

.023

.021

.019

.017

.015

9.012

.010

.008 

.006

.004

.002

.000

8.998

.996

.994

8.991

.989

.987

.985

.983

.981

.979

.977

.975

.973

8.971

6' longitude.

Inches.

10.916

.914

.911

.909

.906

.904

.901

.899

.896

.894

10.891

.889

.886

.884

.881

.878

.876

.873

.871

.868

10.865

.863

.860

.858

.855

.853

.850

.847

.845

.843

10.840

.838

.835

.833

.830

.828

.825

.823

.820

.818

10.815

.813

.810

QflQ .oUo 

.805

.803

.800

.798

.795

.792

10.789

.787

.784

.782

.779

.777

.775

.772

.770

.768

10.766

7' longitude.

Inches.

,12.735

.732

.729

.726

.723

.720

.717

.714

.711

.708

12.706

.703

.700

.697

.694

.691

.688

.685

.682

.679

12.676

.673

.670

.667

.664

.661

.658

.655

.652

.650

12.647

.644

.641

.638

.635

.632

.629

.626

.623

.020

12.017

.614

.611

CAQ

 UUo

.605

.602

.599

.596

.593

.590

12.587

.584

.581

.579

.576

.573

.571

.568

.565

.563

12.560

8' longitude.

Inches.

14.554

.551

.548

.544

.541

.538

.534

' .531

.528

.524

14.521

.517

.514

.510

.507

.504

.500

.497

.493

.490

14.487

.484

.480

.477

.474

.470

.467

.463

.460

.457

14.454

.450

.447

.443

.440

.436

.433

.430

.426

.423

14.420

.417

.413 

.410

.400

. .403

.400

.396

.393

.389

14.386

.383

.380

.376

.373

.370

.367

.364

.360

.357

14.354

9' longitude.

Inches.

16.374

.370

.366

.362

.359

.355

.351

.347-

.344

.340

16.336

.332

.328

.324

.321

.317

.313

.309

.305

.302

16.298

.294

.290

.287

.284

.280

.276

.272

.268

..264

16.260

.257

.253

.249

.245

.241

.237

.234

.230

.226

16.222

.218

.214

.210

!203

.199

.195

.192

.188

16.184

.180

.176

.173

.169

.166

.163

.159

.156

.152

16.149

10' longitude.

Inches.

18.193

.189

.185

.180

.176

.172

.168

.164

.159

.155

18.151

.147

.143

.138

.134

.130

.126

.122

.118

.113

18.109

.105

.101

.097

.092

.088

.084

.080

.076

.071

18.007

.063

.059

.054

.050

.046

.042

.038

.033

.029

18.025

.021

.017 

.012

.008

.004

.000

17.995

.991

.987

17.983

.979

.975

.971

.967

.963

.959

.955

.951

.947

17.943

Longitude ||interval. 

'

1

2

3

4

5

6

7

8

9

10

of Ordinates developed parallel.

Indies.

0.000

.001

.001

.003

.004

.006

.008

.010

.013

.016

41 '

2 > w n

ll

'

1

2

3

4

5

6

7

8

9

10

li

S a

<3.2

F3 "°

Inches.

2.299

4.598

6.898

9.197

11.496

13.795

16.094

18.394

20.693

22.992

(372)
WOODWARD.] MAP CO-ORDINATES. 67

TABLE X. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude ofHparallel. 

O 1

3900

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

P

44

46

46

47

48

49

50

51

52

53

54

55

56

> 57

68

59

60

Abscissas of developed parallel.

1' longitude.

Indies.

1.794

.794

.794

.793

.793

.792

.792

.792

.791

.791

1.790

.790

.789

.789

.789

.788

.788

.787

.787

.787

1.786

.786

.785

.785

.784

.784

.783

.783

.782

.782

1.781

.781

.780

.780

.780

.779

.779

.778

.778

.778

1.777

.777

.776

.776 

.776

.775

.775

.774

.774

.774

1.773

.773

.772

.772

.772

.771

.771

.770

.770

.770

1.769

2' longitude.

Inches.

3.589

.588

.587

.586

.685

.584

.583

.582

.581

.581

3.580

.579

.578

.577

.577

.576

.575

.574

.573

.573

3.572

.571

.570

.569

.568

.567

.566

.565

.564

.564

3.563

.562

.561

.560

.559

.558

.558

.557

.556

.555

3.555

.554

.553

.552 

.551

.650

.549

.548

.547

.546

3.646

.545

.544

.543

.542

.541

.541

.540

.539

.538

3.638

3' longitude.

Inches.

5.383

.382

.381

.379

.378

.377

.376

.375

.374

.372

5.370

.369

.368

.366

.365

.364

.362

.361

.360

.358

5.357

.356

.354

.353

.352

.350

.349

.348

-.347

.345

5.344

.343

.341

.340

.339

.338

.337

.335

.334

.333

5.332

.330

.329

.328 

.327

.325'

.324

.323

.322

.320

. 5.319

.318

.317

.315

.314

.313

.311

.310

.309

.307

5.306

4' longitudu.

Indies.

7.177

.175

.173

.172

.170

.168

.166

.165

.163

.162

7.160

.159

.157

.156

.154

.153

.151

.149

.147

.145

7.143

.142

.140

.139

.137

.135

.133

.131

.129

.128

 7.126

.124

.123

.121

.119

.117

\ .116

.114

.113

.111

7.109

.107

.106

.104

!l02

.101

.099

.097

.096

.094

7.092

.090

.089

.087

.086

.084

.082

.081

.079

.077

7.075

5' longitude.

Inches.

8.971

.969

.967

.965

.963

.961

.959

.957

.955

.953

8.950

.948

.946

.944

.942

.940

.938

.936

.934

.931

8.929

.927

.925

.922

.920

, .918

.916

.914

.912

.909

8.907

.905

.903

.901

.899

.897

.895

.893

.891

.888

8.886

.884

.882

.ooU OQA

.878

.876

.874

.872

.870

.868

8.865

.863

.861

.859

.857

.855

.853

.851

.849

.846

8.844

6' longitude.

'Inches.

10.766

.764

.761

.759

.756

.754

.751

.749

.746

.743

10.740

.738

.735

.732

.730

.728

.725

.723

.720

.718

10.715

.713

.710

.708

.705

.702

.700

.697

.695

.692

10.689

.687

.684

.682

.679

.677

.674

.672

.669

.667

10.664

.662

.659

.656 

.654

.651

.649

.646

.644

.641

10.638

.636

.633

.631

.628

.626

.623 621

.618

.616

10.613

7' longitude.

Inches.

12.560

.557

.554

.551

.548

.545

.542

.539

.536

.533

12.530

.527

.524

.521

.518

.515

.513

.510

.507

.004

12.501

.498

.495

.491

.488

.485

.482

.479

.476

.473

12.470

.467

.464

.462

.459

.456

.453

.450

.447

.444

12.441

.438

.435

.'429

.426

.423

.420

.417

.414

12.411

.408

.405

.402

.399

.396

.393

.390

.388

.385

12.382

8' longitude.

Indies.

14.354

.351

.347

.344

.340

.337

.333

.330

.327

.323

14.320

.317

.313

.310

.306

.303

.300

.296

.293

.290

14.286

.283

.279

.270

.272

.269

.265

.262

.258

.255

14.252

.248

.245

.241

.238

.235

.231

.228

.224

.221

14.218

.215

.211

.'204

.201

.197

.194

.190

.187

14.184

.180

.177

.174

.170

.167

.164

.160

.157

.153

14.160

9' longitude.

Inches.

16.149

.145

.141

.137

.133

.130

.126

.122

.118

.114

16.110

.106

.102

.099

.095

.091

.087

.083

.080

.070

16.072

.068

.064

.060

.050

.052

.048

.044

.040

.037

16.033

.029

.026

.022

.018

.015

.011

.007

.004

.000

15.996

.992

.988

.984 

!980

.976

.972

.968

.964

.960

15.957

.953

. 950

.946

.942

.938

.934

.930

.927

.923

15.919

10' longitude.

Inches.

17.943

.939

.935

.930

.926

.922

.917

.913

.909

.904

17.900

.896

.892

;887.

.883

.879

.875

.870

.800

.862

17.858

.854

. .850

.845

.841

.837

.833

.828

.824

.820

17.815

.811

.807

.802

.798

.794

.790

.786

.781

.777

17.773

.769

.765

.756

.752

.748

.743

.739

.735

17.730

.726

.722

.718

.714

.709

.705

.701

.697

.692

17.688

1 

Longitude interval.

i

1

2

3

4

5.

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000 :ooi

.001

.003

.004

.006

.008

.010

.013

.016

is'

il3.9

1

1

2

3

4

5

6

7

8

9

10

Cflj 

fl O

jgj

<S .2

j^T3

Inches.

2.300

4.599

6.899

9.198

11.498

13. 798

16. 097

18. 397

20. 696

22. 996

(373)
68 FORMULAS AND TABLES. [BULL. 50.

TABLE X. Co-ordinates for projection of maps. Scale -jre's^- 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

4000

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

67

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.769

.769

t .768

.768

.767

.767

.766

.766

.765

.765

1.764 

.764

.763

.763

.762

.762

.762

.761

.761

.761

1.760

.760

.759

.759

.759

.758

.758

.758

.757

.757

1.756

.756

.755

.755

.754

.754

.753

.763

.752

.752

1.751

.751

.750

.750 

.750

.749

.749

.748

.748

.748

1.747

.747

.746

.746

.746

.745

.745

.744

.744

.744

1.743

2' longitude.

Inches.

3.638

.537

.536

.535

.534

.533

.532

.531

.530

.530

3.529 

.528

.527

.526

.525

.524

.523

.522

.521

.521

3.520

.519

.518

.517

.516

.515

.515

.514

.513

.512

3.512

.511

.510

.509

.508

.507

.506

.505

.504

.504

3.503

.502

.501

.500 

.499

.498

.497

.496

.495

.494

3.494

.493

.492

.491

.490

.489

.488

.487

.486

.486

3.485

3' longitude.

Incites.

5.306

.305

.304

.302

.301

.300

.298

.297

.296

.295

5.293 

.292

.291

.289

.288

.287

.285

.284

.283

.282

5.280

.279

.278

.276

.275

.274

.272

'.271

.270

.269

5.267

.266

.265

.264

.262

.261

.260

.258

.257

.256

5.254

.253

.252

!249

.248

.246

.245

.244

.242

5.241

.240

' .238

.237

.235

.234

.233

.231

.230

.229

5.228

4/ longitude.

Inches.

7.075

.073

.071

.070

.068

.066

.065

.063

.061

.060

7.058 

.056

.054

.053

.051

.049

.047

.045

.044

.042

7.040

.038

.037

.035

.033

.032

.030

.028

.026

.025

7.023

.021

.020

.018

.016

.015

.013

.012

.010

.008

7.006

.004

.002 

flfli .vvl

6.999

.997

.998

.994

.992

.990

6.988

.986

.985

.983

.981

.980

.978

.976

.975

.973

6.971

5' longitude.

Inches.

8.844

.842

.840

.838

.835

.833

.831

.829

.827

.824

.820

.818

.816

.814

.811

.809

.807

.805

.803

8.800

.798

.796

.794

.792

.790

.787

.785

.783

.781

8.779

.777

.775

.773

.771

.769

.767

.765

.763

.760

8.757

.755

.753

.750 

.748

.746

.744

.742

.739

.737

8.735

.733

.731

.729

.727

.725

.722

.720

.718

.716

8.713

6' longitude.

Indies.

10.613

.610

.608

.605

.603

.600

.598

 .595

.692

.590

10.587 

.585

.682

.580

.577

.574

.572

.569

.567

.564

10.661

.559

.556

.554

.551

.549

.646

.643

.541

.538

10.535

.532

.529

.527

.524

.522

.519

.517

.514

.511

10.508

.506

.503 

501

!498

.496

.493

.491

.488

.486

1 10.483

.480

.477

.475

.472

.469

.467

.464

.461

.459

10.456

7' longitude.

Inches.

12.382

.379

.376

.373

.370

.367

.364

.361

,.358

.354

19 ^IPil JL4.GUJ-

.348

.345

.342

.339

.336

.333

.330

.327

.324

12.321

.318

.315

.312

.309

.306

.303

.300

.297

.294

12.291

.288

.285

.282

.279

.275

.272

.269

.266

.263

12.260

.257

.254

.251 

.248

.245

.242

.239

.236

.233

12.230

.227

.224

.221

.218

.215

.212

.208

.205

.202

12.199

8' longitude.

Inches.

14.150

.147

.143

.140

.137

.133

.130

.126

.123

.120

14.116 

.113 109

.106

.102

.099

.095

.092

.088

.085

14.081

.078

.074

.071

.067

.064

.060

.057

.053

.050

14,046

.043

.039

.036

.032

.029

.025

.022

.018

.015

14.011

.008

.005

.001 

13.998

.994

.991

.987

.984

.980

13.977

.973

.970

.966

.963

.959

.956

.952

.949

.946

13.942

9' longitude.

Indies.

15.919

.915

.911

.907

.903

.900

.896

.892

.888

.884

-\K QQA 

J-O.OOVJ

.876

.872

.868

.865

.861

.857

.853

.849

.845

15.841

.837

.833

.829

.826

.822

.818

.814

.810

.806

15.802

.798

.794

.790

.786

.782

.779

.775

.771

.767

15.763

.759

.755

!747

.744

.740

.736

.732

.728

15.724

.720

.716

.712

.708

.704

.700

.696

.692

.688

15.684

10' longitude.

Inches.

17.688

.684

.680

.675

.671

.667

.662

.658

.654

.650

17.645 

.641

.636

.632

.627

.623

.618 614

.610

.605

17.601

.597

.593

.588

.584

.580

.575

.571

.566

.562

17.558

.554

.549

.545

.540

.536

.631

.527

.622

.518

17.514

.510

.506

501

'.497

.493

.488

.484

.480

.476

17.471

.467

.463

.458

.454

.449

.445

.440

.436

.431

17.427

II Longitude 

interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.003

.004

.006

.008

.010

.013

.016

 §""' s *

' 3-2

3.3

/

l

2

3

4

5

6

7

8

9

10

!§'-

IssiS3 .a S"8

Inches.

2.300

4.600

6.900

9.200

11.500

13.800

16.100

18.400

20.700

23.000

(374)
WOODWARD.] MAP CO-ORDINATES. 69

TABLE X. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

4100

1

2

3

4

6

6

7

89'

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

44

45

46

47

48

49

60

61

62

63

64

65

66

67

68

69

60

Abscissas of developed parallel.

1' Iongitude.

Inches.

1.743

.743

.742

.742

.741

.741

.740

.740

:739

.739

1.738

.738

.738

.737

.737

.736

.736

.736

.735

.735

1.734

.734

.733

.733

.732

.732

.731

.731

.730

.730

1.729

.729

.729

'.728

.728

.727

.727

.727

.726

.726

1.725

.725

.724

.724 

.724

.723

.723

.722

.722

.722

1.721

.721

.720

.720

.719

.719

.718

.718

.717

.717

1.716

2' longitude.

Inches.

3.485

.484

.483

.482

.482

.481

.480

.479

.478

.478

3.477

.476

.475

.474

.473

.472

.471

.470

.469

.469

3.468

-.467

.466

.465

.464

.463

.462

.461

.460

.460

3.459

.458

.457

.456

.455

.454

.453

.452

.451

.451

3.450

.449

.448

.447 

.'446

.445

.444

.443

.442

.442

3.441

.440

.439

.438

.437

.430

.435

.434

.433

.433

3.432

3' longitude.

Inches.

6.228

.227

.226

.224

.223

.222

.220

.219

.218

.216

5.215

.214

.213

.211

.210

.209

.208

.206

.205

.204

6.202

.201

.200

.198

.197

.195

.194

.192

.191

.189

5.188

.187

.186

.184

.183

.182

.180

.179

.178

.176

' 5.175

.174

.173

.170

.169

.167

.166

.165

.163

5.162

.160

.159

.158

.156

.155

.153

.152

.150

.149

5.148

4/ longitude.

Inches.

6.971

.969

.967

.965

.964

.962

. .960

.959

.957

.955

6.953

.951

.950

 .948

.946

.945

.943

.942

.940

.938

6.936

.934

.932

.931

.929

.927

.925

.923

.922

.920

6.918

.916

.914

.912

.911

.909

.907

.905

.903

.902

6.900

.898

.896

!893

.891

.889

. .887

.886

.884

6.882

.880

.878

.877

.875

.873

.871

.869

.868

.866

6.864

5' longitude.

Inches.

8.713

.711

.709

.707

.704

.702

.700

.698

.695

.693

8.691

.689

.687

.685

.682

.680

.678

.676

.673

.671

8.669

.667

.665

.663

.660

.658

.656

.654

.652

.649

8.647

.645

.643

.640

.638

.636

.634

.632

.630

.628

8.625

.623

.621

.618 

.616

.614

.612

.610

.607

.605

8.603

.601

.598

.596

.594

.692

.589

.587

.685

.582

8.580

6' longitude.

Inches.

10.456

.453

.451

.448

.446

.443

.440

.438

.435

.433

10.430

.427

.424

.422

.419

.416

.413

.411

.408

.405

10.403

.400

.398

.395

.392

.390

.387

.384

.382

.379

10.377

.374

.372

.369

.367

.364

.361

.359

.356

.354

10.351

.348

.346

.'340

.338

.335

.332

.330

.327

10.324

.321

.319

.316

.313

.311

.308

.305

.303

.300

10.297

7' longitude.

Inches.

12.199

.196

.193

.190

.187

.184

.181

.178

.175

.172

12.168

.165

.162

.159

.156

.153

.150

.147

.144

.140

12.137

.134

.131

.1.8

.125

.122

.119

.116

.112

.109

12.106

.103

.100

.097

.094

.091

.088

.085

.082

.079

12.076

.073

.070

\ .066 

.063

.060

.057

.053

.050

.047

12.044

.041

.038

.035

.032

.028

.025

.022

.019

.016

12.013

8' longitude.

Inches.

13.942

.938

.935

.931

.928

.924

.921

.917

.913

.910

13.906

.903

.899

.896

.892

.889

.885

.882

.878

' .875

13.871

.868

.864

.860

.857

.853

.850

.840

.843

.839

13.836

.832

.829

.825

.822

.818

.815

.811

.808

.804

13.801

.797

.794 

.790

!787

.783

.779

.776

.772

.769

13.765

.762

.758

.765

.761

.748

.744

.740

.737

.733

13.729

9' longitude.

Inches.

16.684

.680

.676

.672

.668

.664

, .660

.656

.652

.648

15.645

.641

.637

.633

.629

.625

.621

.617

.613

.609

15.605

.601

.597

.693

.589

.685

.581

.677

.573

.569

15.565

.561

.657

.563

.549

.545

.541

.537

.533

.630

16.626

.522

.518

'.510

.606

.602

.498

.494

.490

16.485

.481

.477

.473

.469

.465

.461

.457

.453

.449

15.445

10' longitude.

Inches.

17,427

.423

.418

.414

.409

.405

.400

.396

.392

.387

17.383

.379

.374

.370

.365

.361

.356

.352

.348

.343

17.339

.335

.330

.326

.321

.317

.312

.308

.304

.299

17.295

.290

.286

.281

.277

.273

.268

.264

.259

.255

17.251

.246

.242

007

t£iij I

.233

.228

.224

.219

.215

.210

17.206

.201

.197

.192

.188

.183

.179

.174

.170

.165

17.161

Longitude 1interval. 

/

1

2

3

4

5

6

7

8

9

10

Ordinates of|| developed IIparallel. 

Inches.

O.'OOO

.001

.001

- .003

.004

.006

.008

.011

.013

.017

o .

£ o

s ta

h3«

J

'

1

 2

3

4

5

6

7

8

9

10

c $

IIS.2 a*

Inches.

2.309

4.601

6.901

9.202

11.502

13.802

16.103

18.403

20.704

23.004

(375)
70 FORMULAS AND TABLES. [BULL. 50.

TABLE X. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

of Latitude 

parallel.

o /

4200

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

4.3 :rO

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.716

.716

.716

.715

.715

.714

.714

.714

.713

.713

1 719 1. (LA

.712

.711

.711

.710

.710

.709

.709

.708

.708

1.707

.707

.706

.706

.706

.705

.705

.704

.704

.704

1.703

.703

.702

.702

.701

.701

.700

.700

.699

.699

1.698

.698

.697 

697

.697

.696

.696

.695

.695

.695

1.694

.694

.693

.693

.692

.692

.691

.691

.690

.690

1.689

2' longitude.

Inches.

3.432

.431

.430

.429

.428

.427

.426

.425

.424

.424

3.423 

.422

.421

.420

.419

.418

.417

.416

.415

.415

3,414

.413

.412

.411

.410

.409

.408

.407

.406

.405

3.405

.404

.403

.402

.401

.400

.399

.398

.397

.397

3.396

.395

.394

.0.70 3(W

.392

.391

.390

.389

.388

.387

3.387

.386

.385

.384

.383

.382

.381

.380

.379

.379

3.378

3' longitude.

Inches.

5.148

.147

.146

.144

.143

.142

.140

.139

.138

.136

5.135 

.133

.132

.130

.129

.128

.126

.125

.123

.122

5.121

.120

.118

.117

.116

.114

.113

.112

.110

.109

5.108

.107

.105

.104

.102

.101

.099

.098

.096

.095

5.094

.093

.091

.090 

.088

.087

.085

.084

.083

.082

5.081

.079

.078

.076

.075

.073

.072

.071

.069

.068

5.067

4' longitude.

Inches.

6.864

.862

.860

.859

.857

.855

.853

.851

.850

.848

6.846 

.844

.842

.840

.839

.837

.835

.833

.831

.830

6.828

.826

.824

.822

.821

.819

.817

.815

.814

.812

6.810

.808

.806

.804

.802

.801

.799

.797

.795

.794

6.792

.790

.788

7Qfi

 4oU

.785

.783

.781

.779

.777

.776

6.774

.772

.770

.768

.767

.765

.763

.701

.759

.758

' 6.756

5' longitude.

Inches.

8.580

.578

.576

.574

.571

.569

.567

.565

.562

.560

8.558 

.556

.553

.551

.549

.547

.544

.542

.540

.537

8.535

.533

.531

.529

.527

.524

.522

.520

.518

.516

8.513

.511

.508

.506

.504

.502

.499

.497

.495

.492

8.490

.488

.486

.483 

.481

.479

.477

.475

.473

.470

8.468

.466

.464

.461

.459

.457

.454

.452

.450

.447

8.445

6' longitude.

Inches.

10.297

.294

.291

.289

.280

.283

.281

.278

.275

.272

10.270 

.267

.264

.262

.259

.256

.253

.251

.248

.245

10.243

.240

.237

.235

.232

.229

.227

.224

.221

.219

10.216

.213

.210

.208

.205

.203

.200

.197

.194

.192

10.189

.186

.183

1Q1 .lol

.178

.175

.172

.170

.167

.165

10.162

.159

.150

.153

.151

.148

.145

.142

.139

.137

10.134

7' longitude.

Inches.

12.013

.010

.007

.003

.000

11.997

.994

.991

.988

.984

11.981 

.978

.975

.972

.969

.966

.963

.960

.956

.953

11.950

.947

.944

.940

.937

.934

.931

.928

.924

.921

11.918

.915

.912

.909

.906

;903

.900

.897

.894

.890

11.887

.884

.881

Q77 ,0( 1

.874

.871

.868

.865

.862

.859

11.855

.852

.849

.845

.842

.839

.836,

.833

.830

.826

11.823

8' longitude.

Inches.

13.729

.725

.722

.718

.715

.711

.708

.704

.700

.697

13.693 

.690

.686

.683

.679

.676

.672

.669

.665

.661

13.657

.654

.651

.647

.644

.640

.636

.633

.629

.625

13.621

.617

.614

.610

.607

.603

.600

'.596

.592

.589

13.585

.582

.578

.575 

.571

.567

.564

.560

.557

.553

13.549

.545

.541

.537

.534

.530

.526

.522

.619

.515

13.512

9' longitude.

Inches.

15.445

.441

.437

.433

.429

.425

.421

.417

.413

.409

15.404 

.400

.396

.392

.388

.384

.380

.376

.372

.368

15.364

.360

.356

.352

.348

.344

.340

.336

.332

.328

15.323

.319

.315

.311

.307

.303

.299

.295

.291

.287

15.283

.279

.275

971 Ail

.267

.263

.259

.255

.251

.247

15.242

.238

.234

.230

.226

.222

.218

.214

.210

.206

15.201

10' longitude.

Inches.

17.161

.157

.152

.148

.143

.139

.134

.130

.125

.121

17.116 

.112

.107

.103

.098

.094

.089

.085

.080

.076

17.071

.067

.062

.058

.053

.049

.044

.040

.035

.031

17.026

.022

.017

.013

.008

.004.

16.999

.995

.990

.986'

16.981

.977

.972

.968 

.963

.959

.954

.950

.945

.941

16.936

.932

.927

.923

.918

.914

.909

.905

.900

.895

16.890

1 Longitude 

intervaL

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.003

.004

.006

.008

.011

.013

.017

iiS k += *4 i-8

3.2

/

i

2

3

4

5

6

7

8

9

10

fl <1>

3 a

sf

s 13

Inches.

2.301

4.602

6.902

9.203

11.504

13.805

16.106

18.406

20.707

23.008

(376)
WOODWARD.] MAP CO-ORDINATES. 71

TABLE X. Co-ordinates for projection of maps. Scale TI^JTT-

[Derivation of table explained in section (5) ; use of table explained on page 22.]

Latitude of

parallel.

o /

4300

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

1 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

Abscissas of developed parallel.

1' longitude.

Inches.

1.089

.689

.688

.688

 .687

.687

.686

.686

.685

.685

1.684 

.684

.683

.683

.083

.082

.682

.681

.681

.681

1.680

' .680

.679

.679

.678

.678

.677

.677

.676

.676

1.675

.675

.674

.674

.674

.673

.673

.672

.672

.672

1.671

.671

.670

.670 

.669

.669

.668

.668

.607

.667

1.666

.666

.665

.665

.664

.664

.663

.663

.662

.662

1.661

2' longitude.

Inches.

3.378

.377

.376

.375

.374

.373

.372

.371

.370

.370

3.369 

.368

.367

.366

.365

.364

.363

.362

.361

.361

3.360

.359

.358

.357

.356

.355

.354

.353

.352

.351

3.350

.349

.348

.347

.340.

.345

.344

.343

.342

.342

3.341

.340

.339

.338

.337

336

.335

.334

.333

.332

3.332

.331

.330

.329

.328

.327

.326

.325

.324

.323

3.323

3' longitude.

Inches.

5.067

.066

.064

.063

.061

.060

.058

.057

.056

.054

5.053 

.051

.050

.048

.047

.045

.044

.042

.041

.040

5.039

.037

.036

.035

.033

.032

.031

'.029

.028

.027

5.026

.024

.023

.021

.020

.018

.017

.015

.014

.013

5.012 

.010

.009

.\J\Ji 007

.006

.004

.003

.002

.000

4.999

4.998

.996

.995

.993

.992

.991

.989

.988

.980

.985

4.984

4' longitude.

Inches.

6.756

.754

.752

.751

.749

.747

.745

.743

.742

.740

6.738 

.736

.734

.732

.730

.728

.726

.724

.722

.720

6.719

.717

.715

.714

.712

.710

.708

.706

.704

.703

6.701

.699

.697

.695

.693

.691

.689

.687

.685

.683

6.682

.680

.678

.677

.675

.673

.671

.669

.607

.666

6.664

.662

.660

.658

.656

.654

.652

.650

.048

.646

6.645

5' longitude.

Inches.

8.445

.443

.441

.438

.436

.434

.431

.429

.427

.425

8.422 

.420

.418

.415

.413

. .411

.408

.406

.404

.402

8.399

.397

.395

.392

.390

.388

.385

.383

.381

.378

8.376

.374

.372

.369

.367

.365

.363

.360

.358

.356

8.353

.351

.349

oAa .0*0

.344

.342

.339

.337

.335

.333

8.330

.328

.325

.323

.320

.318

.315

.313

.310

.308

8.306

C' longitude.

Inches.

10.134'

.131

.128

.120

.123

.120

.117

.114

.111

.109

10.100 

.103

.100

.098

.095

.092

.090

.087

.084

.082

10.079

.076

.073

.070

.068

.065

.063

.060

.057

.054

10.051

.048

.045

.043

.040

.037

.034

.032

.029

.026

10.024

.021

.018

015 !ois

.010

.008

.005

.002

9.999

9.996

.993

.990

.988

.985

.982

.979

.976

.974

.971

9.968

7' longitude.

Inches.

11.823

.820

.817

.813

.810

.807

.804

.801

.797

.794

11.791 

.788

.785

.782

.778

.775

.772

. .769

.765

.762

11.759

.756

.753

.749

.746

.743

.739

.736

.733

.729

11.726

.723

.720

.716

.713

.710

.707

.704

.700

.697

11.694

.691

.688

.684 

.681

.678

.675

.672

.668

.665

11.662

.659

.656

.652

.649

.646

.642

.639

.636

.632

11.629

8' longitude.

Inches.

13.512

.508

.504

.501

.497

.493

.490

.486

.482'

.479

13.475 

.471

.467

.464

.460

.456

.453

.449

.445

.442

13.438

.434

.430

.427

.423

.420

.416

.413

.409

.406

13.402

.398

.394

.391

.387

.383

.380

.376

.372

.369

13.365

.361

.357

.354 

.350

.347

.343

.340

.336

.332

13.328

.324

.320

.316

.313

.309

.305

.301

.297

.294

13.290

9' longitude.

Inches.

15.201

.197

.193

.189

.185

.181

.177

.173

.169

.165

15.160 

.156

.152

.147

.143

.139

.135

 .131

.126

.122

15.118

.114

.110

.106

.102

.098

.093

.089

.085

.081

15.077

.073

.069

.065

.061

.057

.053

.049

.045

.040

15.035

.031

.027

AOQ .\JLO

.019

.015

.011

.007

.003

14.998

14.994

.990

.986

.981

.977

.973

.969

.965

.960

.956

14.952

10' longitude.

Inches.

16.890

.885

.881

.876

.872

.867

.863

.858

.854

.849

16.844 

.840

.835

.831

.826

.822

.817

.813

.808

.803

16.798

.794

.789

.785

.780

.776

.771

.767

.762

.757

16.752

.748

.743

.739

.734

.730

.725

.721

.716

.711

16.706

.702

.697

fiQQ . oyo 

.688

.684

.679

.674

.670

.665

16.660

.655

.650

.646

.641

.636

.632

.627

.023

.618

16.613

1 Longitude 

interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.003

.004

.006

.008

.011

.013

.017

^

TJ"3 o> _:

3 t>

£8

,12

/

l

2

3

4

5

6

7

8

9

10

li

13#'-* <3 S

Incites.

2.301

4.602

6.904

9.205

11.506

13.807

16.108

18.410

20.711

23.012

(377)
72 FORMULAS AND TABLES. [BULL. 50.

TABLE X. Co-ordinates for projection of maps. Scale TiirsTr-

[Derivaliou of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

4400

1

2

3

4

6

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

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.661

.661

.660

.660

.660

.659

.659

.658

.658

.658

1.657

.657

.656

.656

.655

.655

.654

.654

.653

.653

1.652

.652

.651

.651

.650

.650

.649

.649

.648

.648

1.647

.647

.646

.646

.645

.645

.644

.644

.643

.643

1.642

.642

.641

.641 

.641

.640

.640

.639

.639

.639

1.638

.638

.637

.637

.636

.636

.635

.635

.634

.634

1.633

2' longitude.

Inches.

3.323

.322

.321

.320

.319

.318

.317

.316

.315

.314

3.313

.312

.311

.310

.309

.308

.307

.306

.305

.304

3.304

.303

.302

.301

.300

.299

.298

.297

.296

.295

3.294

.293

.292

.291

.290

.289

.288

.287

. .286

.285

3.285

.284

.283

'.281

.280

.279

.278

.277

.277

3.276

.275

. .274

.273

.272

.271

.270

.269

.268

.267

3.266

3' longitude.

Inches.

4.984

.983

.982

.980

.979

.978

.976

.975 973

.972

4.970

.969

.967

.966

.964

.963

.962

.960

.959

.957

4.956

.954

.953

.951

.950

.949

.947

.946

.944

.943

4.942

.940

.939

.937

.936

.934

QQO 

 aOO

.931

.930

.928

4.927

.925

.924

!921

.920

.918

.917

.915

.914

4.913

.912

.910

.909

.908

.906

.905

.904

.902

.901

4.900

4' longitude.

Inches.

6.645

.643

.641

.639

.637

.635

.633

.631

.629

.627

6.626

.624

.622

.621

.619

.617

.615

.613

.612

.610

6.608

.606

.604

.602

.600

> .598

.596

.595

.593

.591

6.589

.587

.585

.583

.581

.579

.577

.575

.573

.572

6.570

.568

.566

.564 

.562

.560

.558

,.556

.554

.552

6.551

.549

.547

.545

.544

.542

.540

.538

.536

.535

6.533'

5' longitude.

Inches.

8.306

.304

.302

.299

.297

.295

.292

.290

.287

.285

8.283

.281

.278

.276

.274

.271

.269

.267

.264

.262

8.259

.257

.255

.252

.250

.247

.245

.243

.240

.238

8.236

.234

.231

.229

.226

.224

.221

.219

.217

.214

8.212

.210

.208

!203

.201

.198

.196

.193

.191

8.189

.187

.185

.182

.180

.177

.175

.173

.170

.168

8.166

6' longitude.

Inches.

9.968

.965

.962

.960

.957

.954

.951

.949

.946

.943

9.940

.937

.934

.931

.928

.925

.922

.919

.916

.913

9.911

.908

.905

.903

.900

.897

.894

.891

.889

.886

9.883

.880

.877

.875

.872

.869

.866

.864

.861

.858

9.855

.852

.849

.846 

.844

.841

.838

.835

.833

.830

9.827

.824

.821

.819

.816

.813

.810

.807

.805

.802

9.799

7' longitude.

Indies.

11.629

.626

.623

.619

.616

.613

.609

.606

.603

.599

11.596

.593

.590

.586

.583

.580

.576

.573

.569

.566

11.563

.560

.557

.553

.550

.547

.543

.539

.536

.533

11.530

.527

.524

.520

.517

.514

.510

.507

.504

.500

11.497

.494

.491

!484

.481

.478

.475

.471

.468

11.465

.462

.459

.455

.452

.448

.445

.441

.438

.435

11.432

8' longitude.

Inches.

13.290

.286

.282

.279

.275

.271

.268

.264

.260

.257

13.253

.249

.245

.241

.238

.234

.230

.226

.222

.219

13.215

.211

.207

.203

.200

.196

.193

.189

.185

.181

13.178

.174

.170

.166

.163

.159

.155

.151

.148

.144

13.140

.136

.132

.124

.121

.117

.113

.109

.106

13.102

. .098

.094.

.090

.087

.083

.079

.075

.072

.069

13.066

9' longitude

Inches.

14.952

.948

.944

.939

.935

.931

.926

.922

.918

.913

14.909

.905

.901

.897

.892

.888

.884

.880

' .875

.871

14.867

.863

.859

.855

.850

.846

.842

.838

.833

.829

14.825

.821

.817

.812

.808

.804'

.799

.795

.791

.786

14.782

.778

.774

.770 

.765

.761

.757

.753

.748

.744

14.740

.736

.732

.728

.724

.720

N

.716

.712

.708

.704

14.699

10'lon 

gitude

Inches.

16.613

.608

.603

.599

.594

.589

.585

.580

.576

.571

16.566

.561

.557

.552

.547

.543

.538

.533

.529

.524

16.519

.514

.510

.505

.500

.496

.491

.486

.481

.477

16.472

.467

.463

.458

.453

.449

.444

.439

.434

.430

16.425

.420

.416

.411 

.406

C .402

.397

.392

.388

.383

16.378

.374

.369

.364

.360

.355

.351

.346

.342

.337

16.332

Longitude interval.

i

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.003

.004

.006

.008

.011

.013

/.017

a

= 1

li

rf o

'

1

2

3

4

5

6

7

8

9

10

"3 <ri

II& .s g'd

Inches.

2.302

4.603

6.905

9.206

11.508

13.810

16.111

18.413

20.714

23.016

(378) ,
WOODWABD.] MAP CO-ORDINATES. 73

TABLE X. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

|| Latitude of

IIparallel. 

o /

4500

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

S3

34

35

36

37

38

39

40

41

42 

43

44

45

46

47

48

49

50

61

52

63

64

65

66

67

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.633

.633

.632

.632

.631

.631

.630

.630

.629

.629

1 A9Q l.OiO

.628

.627

.627

.627

.626

.626

.625

.625

.625

1.624

.624

.623

.623

.622

.622

' .621

.621

.620

.620

1.619

.619

.618

.618

.617

.617

.616

.616

.615

.615

1.614

.614

.613

C1Q .Old

.612

.612

.611

.611

.610

.610

1.609

.609

.608

.608

.607

.607

.606

.606

.605

.605

1.604

2' longitude.

Inches.

3.266

.265

.264

.263

.262

.261

.260

.259

.258

.258

3.257 

.256

.255

!254

.253

.252

.251

.250

.249

.248

3.247

.246

. .245

.244

.243

.242

.241

.240

.239

.239

3.238

.237

.236

.235

.234

.233

.232

.231

.230

.229

3.228

.227

.226

J224

.223

.222

.221

.220

.219

3.218

.217

.216

.215

.214

.213

.212

.211

.210

.210

3.209

3' longitude.

Inches.

4.900

.899

.897

.896

.894

.893

"

.891

.890

.888

.887

4.885 

.884

flfiP .OOO

.881

.880

.878

.877

.876

.874

.872

4.871

.869

.868

.866

.865

.863

.862

.860

.859

.857

4.856

.854

.853

.851

.850

.848

.847

.846

.844

.843

4.842

.840

.839

007

.OUI

.836

.834

.833

.832

.830

.829

4.828

.826

.825

.823

.822

.820

.819

.817

.816

.814

4.813

4' longitude.

Inches.

6.533

.531

.529

.527

.525

.623

.521

.620

.518

.516

6.514 

.512

.510

.508

.506

.504

.502

.500

.498

.498

6.494

.492

.490

.488

.486

.484

.482

.480

.478

.476

6.475

.473

.471

.469

.468

.466

.464

.462

.460

.458

6.456

.454

.452

.450 

!448

.447

.445

.443

.441

.439

6.437

.435

.433

.431

.429

.427

.426

.424

.422

.420

6.418

5' longitude.

Inches.

8.166

.164

.162

.160

.157

.155

.153

.150

.148

.145

8.142 

.140

.137

.135

.132

.130

.128

.125

.123

.120

8.118

.115

.113

.110

.108

.106

.103

.101

.098

.096

8.094

.092

.089

.087

.084

.082

.080

.077

.075

.072

8.070

.068

.065

.063 

.060

.058

.056

.053

.051

.048

8.046

.044

.041

.039

.036

.034

.032

.029

.027

.024

8.022

6' longitude.

Incites.

9.799

.796

.793

.790

.787

.784

.781

.778

.776

.772

9.770

.767

.764

.761

.759

.756

.753

.750

.747

.744

9.742

.739

.736

.733

.730

.727

.724

.721

.718

.715

9.713

.710

.707

.704

.701

.698

.695

.692

.689

.686

9.684

.681

.678

.676 

.672

.669

.666

.663

.660

.657

9.655

.652

.649

.646

.643

.640

.637

.634

.631

.629

9.627

7' longitude.

Indies.

11.432

.429

.420

.422

.419

.416

.412

.409

.406

.403

11.399 

.396

.392

.389

.385

.382

.378

.375

.371

.368

11.365

.362

.359

.355

.352

.349

.340

.342

.339

.335

11.332

.329

.325

.322

.318

.315

.311

.308

.304

.301

11.298

.294

.291

OQ7

.&O t

.284

.281

.277

.274

.270

.267

11.264

.261

.257

.254

.251

.247

.244

.241

.237

.234

11.231

8' longitude.

Inches.

13.066

.062

.058

.054

.050

.046

.042

.038

.034

.030

13.027 

.023

.019

.016

.012

.008

.004

.000

12.997

.993

12.989

.985

.981

.977

.973

.970

.966

.962

.958

.954

12.950

.946

.942

.939

.936

.931

.927

.923

.920

.916

12.912

.908

.904

!897

.893

.889

.885

.881

.877

12.874

.870

.866

.863

.859

.855

.851

.847

.844

.840

12.836

9' longitude.

Inches.

14.699

.695

.691

.686

.682

.678

.673

.669

.665

.660

14.656 

.652

0 .648

.643

.639

.634

.630

.625

.621

.616

14.612

.608

.603

.599

.594

.590

.585

.581

.577

.573

14.569

.665

.561

.656

.552

.648

.543

.639

.534

.630

14.626

.522

.517

.613 

.608

.504

.500

.495

.491

.487

14.483

.479

.476

.470

' .466

.462

.457

.453

.448

.444

14.440

W Iongitude.

Inches.

16.332

.328

.323

.319

.314

.310

.305

.300

.295

.290

16.284 

.279

.274

.270

'.265

.260

.255

.250

.246

.241

16.236

.231

.226

.221

.217

.212

.207

:202

.198

.193

16.188

.183

.178

.173

.169

 .164

.159

.154

.150

.145

16.140

.135

.130

.126 

.121

.116

.111

.106

.102

.097

16.092

.087

.082

.078

.073

.068

.064

.059

.054

.050

16.045

Longitude interval.

/

1

2

3

4

6

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.003

.004

.006

.008

.011

.013

.017

 § 3

is «? cj'2

H 

/

1

2

3

4

5

6

7

8

9

10

P ©

.° ®

3JJ

tS.SS

3

Inches.

2.302

4.604

6.906

9.208

11.510

13.812

16.114

18.416

20.718

23.020

(379)
74 FORMULAS AND TABLES. [BULL. 50.

TABLE X. Co-ordinates for projection of maps. Scale Tr^UTr- 

[Derivation of table explained in section (5); use of table explained on page 22.]

I Latitude of

parallel.

o /

4600

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

Abscissas of developed parallel.

1' longitude.

Inches.

1.604

.604

.603

.603

.603

.602

.602

.602

.601

.601

1.600

.600

.599

.599

.598

.598

.597

.597

.596

.596

1.595

.595

.594

.594

.593

.593

.592

.592

.591

.591

1.590

.590

.589

.589

.588

.588

.587

.587

.086

.586

1.585

.585

.584 

.584

.583

.583

.582

.582

.581

.581

1.580

.580

.519

.579

.578

.578

.577

.577

.576

.576

1.575

2' longitude.

Inches.

3.209

.208

.207

.206

.205

.204

.203

.202

.201

.200

3.199

.198

.197

.196

.195

.194

.193

.192

.191

.191

3.190

.189

.188

.187

.186

.185

\

.184

'.183

.182

.181

3.180

.179

.178

.177

.176

.175

.174

.173

.172

- .171

, 3.170

.169

.168

TCT .Io7 

.166

.165

.164

.163

.162

.161

3.160

.159

.158

.157

.156

.155

.154

.153

.152

.152

3.151

3' longitude.

Inches.

4.813

.812

.811

.809

.808

.807

.805

.804

.802

.801

4.799'

.798

.796

.795

.793

.792

.790

.789

.787

.786

4.784

.783

.781

.780

.779

.777

.776

.774

.773

.771

4.770

.768

.767

.765

.764

.762

.761

.759

.758

.756

4.755

.753

.752

.750 

!749

.747

.746

.745

.743

.742

4.741

.739

.738

.736

.735

.733

' .732

.730

.729

.727

4.726

4' longitude.

Inches.

6.418

.416

.414

.412

.410

.408

.406

.404

.402

.400

6.398

.396

.394

.392

. .390

.388

.386

.384

.382

.380

6.379

.377

.375

.373

.371

.369

.367

.3,65

.363

.361

6.360

.358

.356

.354

.352

.350

.348

.346

.344

.342

6.340

.338

.336

!332

.330

.328

.326

.324

.322

6.321

.319

.317

.315

.313

.311

.309

.307

.305

.303

6.302

5' longitude.

Inches.

8.022

.020

.017

.015

.012

.010

.008

.005

.003

.000

7.998

.996

.994

.991

.989

.986

.984

.981

.979

.976

7.974

.972

.969

.967

.964

.962

.959

.957

.954

.952

7.950

.948

.945

.943

.940

.938

.935

.933

.930

.928

7.926

.923

.921

nio

. flO

.916

.913

.911

.908

.906

.903

7.901

.899

.896

.894

.891

 .889

.886

.884

.881

.879

7.877

6' longitude.

Inches.

9.627

.624

.621

.618

.615

.612

.609

.606

.603

.600

9.598

.595

.592

.589

.586

.583

.580

.577

.574

.571

9.569

.566

.563

.560

.557

.554

.551

.548

.545

.642

9.539

.536

.533

.531

.528

.525

.522

.519

.517

.514

9.511

.508

.505

!499

.496

.493

.490

.487

.484

9.481

.478

.475

.472

.470

.467

.464

.461

.458

.455

9.452

7' longitude.

Inches.

11.231

.227

.224

.220

.217

.214

.210

.207

.204

.200

11.197

.194

.191

.187

.184

.181

.177

.174

.171

.168

11.164

.161

.158

.154

' .151

.147

.144

.140

.137

.133

11.129

.126

.123

.120

.116

.113

.110

.106

.103

.100

11.096

.093

.089

.086 

.082

.079

.075

.072

.068

.065

11.061

.058

.054

.051

.048

.045

.041

.038

.035

.031

11.028

8' longitude.

Inches.

12.836

.832

.828

.824

.820

.816

.812

.808

.804

.800

12.797

.793

.789

.785

.781

.777

.773

.770

.766

.762

12.758

.754

.750

.746

.742

.739

.735

.731

.727

.723

12.719

.715

.711

.707

.704

.700

.696

.692

.689

.685

12.681

.677

.673

.609 

.665

.602

.658

.654

.650

.046

12.642

.638

.634

.630

.626

.022

.619

.615

.611

.607

12.603

9' longitude.

Inches.

14.440

.436

.431

.427

.422

.418 "

.414

.409

.405

.400

14.396

.392

.388

.383

.379

.375

.370

.366

.362

.357

14.353

.349

.344

.340

.335

.331

r .327

.322

.318

.313

14.309

.305

.301

.296

.292

.288

.283

.279

.275

.270

14.266

.262

.257

!248

.244

.240

.235

.231

.226

14.222

.218

.214

.209

.205

.201

.196

.192

.188

.183

14.179

10' longitude.

Inches.

16.045

.040

.035

.030

.025

.020

.015

.010

.005

.000

15.996

.991

.986

.981

.977

.972

.967

.962

.958

.953

15.948

.943

.938

.933

.928

.923

.918

.913

.908

.903

15.899

.894

.889

.885

.880

.875

.870

' .865

.861

.856

15.851

.846

.841

OQfi .OOD

.831

.826

.821

.816

.811

.806

15.802

.797

.792

.788

.783

.778

.773

.768

.764

.759

15.754

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches. ,&

0.000

.001

.001

.003

.004

.006

.008

.011

.013

.017

® 

2 £ 

P

5.S

'

1

2

3

4

5

6

7

8

9

10

^

§

"*

2 J

m =3 a*

Inches.

2.302

4.005

6.907

9.210

11.512

13.814

16.117

18.419

20.722

23.024

(380)
WOODWABD.] MAP CO-ORDINATES.

TABLE X. Co-ordinates for projection of maps. Scale v 

[Derivation of table explained in section (5); nee of table explained on page 22.]

<*-<

114 &

o /

4700

1

2

r.

^

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

63

54

55

58

67

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.575

.575

.574

.574

.573

.573

.572

.572

.571

.571

1.570 

.570

.569

.569

.568

.568

.567

.667

.566

.566

1.565

.565

.564

.664

.563

.663

.562

.562

.561

.561

1.560

.560

.559

.559

.659

.558

.558

.557

.557

.557

1.556

.556

.555

.555

.554

.554

..553

.553

.552

.552

1.551

.551

.550

.550

.549

.549

.548

.548

.547

.547

1.546

2' longitude.

Inches.

3.151

.150

.149

.148

.147

.146

.145

.144

.143

.142

3J 41 

.140

.139

.138

.137

.136

.135

.134

.133

.132

3.131

.130

.129

.128

.127

.126

.125

.124

.123

.122

3.121

 .120

.119

.118

.117

.116

.115

.114

.113

.112

3.111

.110

.109

.108

.107

.106

.105

.104

.103

.102

3.101

.100

.099

.098

.097

.096

.095

.094

.093

.092

3.091

3' longitude.

Inches.

4.726

.724

.723

.721

.720

.718

.717

.715

.714

.712

4.711 

.709

.708

.706

.705

.703

.702

.700

.699

.697

4.696

.694 693

.691

.690

* .688

.687

.685

.684

.682

4.681

.679

.678

.676

.675

.673

.672

.670

.669

.668

4.667

.665

.664

.662

.661

.659

.658

.656

.655

.653

4.652

.650

.649

.647

.646

.644

.643

.641

.640

.638

4.637

4' longitude.

Inches.

G.302

.300

.298

.296

.294

.292

.290

.288

.280

.284

6.282 

.280

.278

.276

.274

.272

.270

.268

.266

.264

6.262

.260

.258

.256

.254

.252

.250

.248

.246

.244

6.242

.240

.238

.236

.234

.232

.230

.228

.226

.224

6.222

.220

.218

.216

.214

.212

.210

.208

.206

.204

6.202

.200

.198

.196

.194

.192

.190

.188

.186

.184

6.183

5' longitude

Inches.

7.877

.874

.872

.869

.867

.864

.862

.859

.857

.854

7.852 

.849

.847

.844

.842

.839

.837

.834

.832

.829

7.827

.824

.822

.819

.817

.814

.812

.809

.807

.804

7.802

.799

.796

.794

.792

.789

.787

.784

.782

.780

7.778

.775

.773

.770

.708

.765

.763

.760

.758

.755

7.753

.750

.748

.745

.743

.740

.738

.735

.733

.730

7.728

6' longitude.

Inches.

9.452

.449

.446

.443

.440

.437

.434

.431

.428

.425

9.422 

.419

.416

.413

.410

.407

.404

.401

.398

.395

9.393

.390

.387

.384

.381

.378

.375

.372

.369

.366

9.363

.360

.357

.354

.351

.348

.345

.342

.339

.336

9.334

.331

.328

.325

322

!319

.316

.313

.310

.307

9.304

.301

.298

.295

.292

.289

.286

.283

.280

.277

9.274

7' longitude.

Inches.

11.028

.024

.021

.017

.014

.010

.007

.003

.000

10.996

10.993 

.989

.986

.982

.979

.975

.972

.968

.965

.961

10.958

.954

.951

.947

.944

.940

.937

.933

.930

.926

10.923

.919

.916

.912

.909

.905

.902

.899

.895

.892

10.889

.885

.882

.878

.875

.871

.868

.864

.861

.857

10.854

.850

.847

.844

.840

.837

.833

.830

.827

.823

10.820

8' longitude.

Inches.

12.603

.599

.595

.591

.587

.583

.579

.575

.571

.567

12.563 

.559

.555

.551

.547

.543

.539

.535

.531

.527

12.524

.620

.516

.512

.508

.504

.500

.496

.492

.488

12.484

.480

.476

.472

.468

.464

.460

.456

.452

.448

12.445

.441

.437

.433

42Q

'.425

.421

.417

.413

.409

12.405

.401

.397

.393

.389

.385

.381

.377

.373

.369

12.366

9' longitude.

Indies.

14.179

.175

.170

.166

.161

.157

.152

.148

.143

.139

14.134 

.130

.125

.121

.11C

.112

.107

.103

.098

.094

14.089

.085

.080

.076

.071

.067

.062

.058

.053

.049

14.044

.040

.035

.031

.026

.022

.017

.013

.009

.004

14.000

13.995

.991

.986

QQO

!977

.973

.968

.964

.959

13.955

.951

.946

.942

.938

.933

.929

.924

.920

.915

13.911

10' longitude.

Inches.

15.754

.749

.744

.739

.734

.729

.724

.719

.714

.709

15.704 

.699

.694

.G89

.684

.679

.674

.669

.664

.659

15.655

.650

.645

.640

.635

.630

.625

.620

.615

.610

15.605

.600

.595

.590

.585

.580

.575

.570

.505

.560

15.556

.551

.546

.541

.636

.631

.526

.521

.516

.511

15.606

.501

.496

.491

.486

.481

.476

.471

.466

.461

15.457

 a ' 

a a

r

3-

/

i

2

3

4

5

6

7

8

9

10

<M

1|1 I-SP,

Inches.

0.000

.001

.001

.003

.004

.006

.008

.011

.013

.017

'S *3

g £

3 .J2

P -S

'

1

2

3

4

5

6

7

8

9

10

 3 .

 5 §

M'O ^

Inches.

2.303

4.606

6.908

9.211

11.514

13.817

16.120

18.422

20.725

23.028

(381)
76 FORMULAS AND TABLES. ,. 50.

TABLE X. Co-ordinates for projection of maps. Scale

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

4800

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

62

53

64

65

66

67

68

69

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.646

.546

.545

.645

.544

.544

.543

.543

.542

.542

1.641 

.541

.640

.640

.539

.539

.538

.538

.537

.537

1.536

.536

.535

.535

.634

.534

.533

.533

.532

.532

1.531

.531

.530

.530

, .529

.529

.628

.528

.527

.527

1.526

.526

.525

.525 

.624

.524

.523

.523

.522

.522

1.521

.521

.620

.620

.519

.519

.518

.618

.617

.517

1.516

2' longitude.

Inches.

3.091

.090

.089

.088

.087

.086

.085

.084

.083

.082

3.081 

.080

.079

.078

.077

.076

.075

.074

.073

.072

3.071

.070

.069

.068

.067

.066

.065

.064

.063

.062

3.061

.060

.059

.058

.057

.056

.055

.054

.053

.052

3.051

.050

.049

f\A& V*O

.047

.046

.045

.044

.043

.042

3.041

.040

.039

.038

.037

.036

.035

.034

.033

.032

3.031

3' longitude.

Inches.

4.637

.636

.634

.633

.631

.630

.628

.627

.625

.624

4.622 

.621

.619

.618

.616

.615

.614

.612

.611

.609

4.607

.606

.604

.603

.601

.600

.698

.597

.595

.594

4.592

.591

.689

.588

.586

.685

.583

.582

.680

.579

4.577

.576

.574

.573 

.571

.570

.568

.667

.565

.564

4.562

.561

.559

.558

.556

.655

.553

.552

.650

.549

4.547

4' longitude.

Inches.

6.183

.181

.179

.177

.175

.173

.171

.169

.167

.165

6.163 

.161

.159

.157

.155

A53

.151

.149

.147

.145

6.143

.141

.139

.137

.135

.133

.131

.129

.127

.125

6.123

.121

.119

.117

.115

.113

.111

.109

.107

.105

i 6.103

.101

.099

097 

!095

.093

.091

.089

.087

.085

6.083 /

.081

.079

.077

.075

.073

.071

.069

.067

.065

6.062

5' longitude.

Inches.

7.728

.725

.723

.720

.718

.715

.713

.710

.708

.705

7.703 

.700

.698

.695

.693

.690

.688

.685

.683

.680

7.678

.675

, .673

.670

.668

.665

.663

.660

.658

.655

7.653

.650

.648

.645

.643

.640

.638

.635

.633

.630

7.628

.625

.623

.620 

.618

.615

.613

.610

.608

.605

7.603

.600

.598

.595

.593

.590

.588

.585

.583

.580

7.578

6' longitude.

Inches.

9.274

.271

.268

..265

.262

.259

.256

.253

.250

.247

9.244 

.241

.238

.235

.232

.229

. .226

.223

.220

.217

9.214

.211

.208

.205

.202

.199

.196

.193

.190

.187

9.184

.181

.178

.175

.172

.169

.166

.163

.160

.157

9.154

.151

.148

.145 

!l42

.139

.136

.133

.130

.127

9.124

.121

.118

.115

.112

.109

.106

.103

.100

.097

9.094

7' longitude.

Inches.

10.820

.817

.813

.810

.806

.803

.799

.796

.792

.789 in J.U. 7ft^ I OO

.782

.778

.775

.771

.768

.764

.761

.757

.754

10.750

.747

.743

.740

.736

.733

.729

.726

.722

.719

10.715

.712

.708

.705

.701

.698

.694

.691

.687

.683

10.680

.676

.673

.669 

.666

.662

.659

.655

.652

.648

10.645

.641

.638

.634

.631

.627

.623

.620

.616

.613

10.609

8' longitude.

Inches.

12.366

.362

.358

".354

.350

.346

.342

.338

.334

.330

19 QOft J.4.O4U

.322

.318

.314

.310

.306

.302

.298

.294

.290

12.286

.282

.278

.274

.270

.266

.262

.258

.254

.250

12.246

.242

.238

.234

.230

.226

.222

.218

.214

.210

12.206

.202

.198

.194 

!l90

.186

.182

.178

.174

.170

12.166

.162

.158

.154

.150

.146

.142

. .138

.134

.130

12.125

9' longitude.

Inches.

13.911

.907

.902

.898

.893

.889

.884

.880

.875

.871

13.866 

.862

.857

.853

.848

.844

.839

.835

.830

.826

13.821

.817

.812

.808

.803

.798

.794

.789

.785

.780

13.776

.771

.767

.762

.758

.753

.749

.744

.740

.735

13.731

.726

.722

.717 

.713

.708

.704

.699

.695

.690

13.686

.681

.677

.672

.668

.663

.658

.654

.649

.645

13.640

10' longitude.

Inches.

15.457

.452

.447

.442

.437

.432

.427

.422

.417

.412

15.407 

.402

.397

.392

.387

.382

.377

.372

.367

.362

15.357

.352

.347

.342

.337

.332

.327

.322

.317

.312

15.307

.302

.297

.292

.287

.282

.277

.272

.267

.262

15.257

.252

.247

OJO tL't.Li

.237

.232

.227

.222

.217

.212

15.207

.202

.197

.192

.187

.182

.177

.172

.167

.162

15.156

Longitude interval.

i

I

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel..

Inches.

0.000

.001

.001

.003

.004

.006

.008

.011

.013

.017

"2 "3

 H £ ' G ®

a!

/

i

2

3

4

5

6

- 7

8

9

10

ll11

lig-0

Inches.

2.303

4.606

6.910

9.213

11.516

13.819

16.122

18.426

20.729

23.032

(382)
WOODWABD.] MAP CO-ORDINATES. 77

TABLE X. Co-ordinates for projection of maps. Scale irrtSTO- 

[Derivation of table explained in section (5);-use of table explained on page 22.]

Latitude of

parallel.

o /

4900

1

2

3

4

6

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

4,1 *«> 

44

45

46

47

48

49

60

61

52

63

64

55

56

57

58

69

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.616

.516

.615

.515

.514

.614

.613

.513

.612

.512

1.511 

.511

.510

.510

.509

.608

.508

.607

.607

.506

1.605

.505

.604

.504

.603

.503

.502

.502

.501

.501

1.600

.500

.499

.499

.498

.498

'.497

.497

.496

.496

1.495

.495

.494

.494 

!493

.493

.492

.492

.491

.491

1.490

.490

.489

.489

.488

.488

.487

.487

.486

.486

1.485

2' longitude.

Inches.

3.031

.030

'.029

.028

.027

.026

.025

.024

.023

.022

3.021 

'.020

.019

.018

.017

.016

.015

.014

.013

.012

3.011

.010

.009

.008

.007

.006

.005

.004

.003

.002

3.001

.000

2.999

.998

.997

.996

.995

.994

.993

.992

2.990

.989

.988

QQ7 »yo» 

.986

.985

.984

.983

.982

.981

2.980

'.979

.978

.977

.976

.975

.974

.973

.972

.971

2.970

3' longitude.

Inches.

4.647

.545

.544

.642

.641

.539

.638

.636

.535

.533

4.532 

.530

.629

.527

.626

.524

.523

.521

.520

.518

4.516

.515

.513

.512

.510

.509

.507

.506

.604

.603

4.601

.500

.498

.497

.495

.494

.492

.491

.489

.488

4.486

.485

.483

AOn T&u

.480

.479

.477

.-176

.474

.472

4.470

.469

.467

.466

.464

.463

.461

.460

.458

.457

4.455

4' longitude.

Inches.

6.062

.060

.058

.056

.054

.052

.050

.048

.046

.044

6.042 

.040

.038

.036

.034

.032

.030

.028

.026

.024

6.022

.020

.018

.016

.014

.012

.010

.008

.005

.003

6.001

5.999

.997

.995

.993

.991

.989

.987

.985

.983

5.981

.979

.977

.975> 

.973

.970

.968

.966

.964

.962

5.960

.958

.956

.954

.952

.950

.948

.946

.944

.942

5.940

,5' longitude.

Inches.

7.578

.575

.573

.670

.568

.665

.563

.560

.558

.655

7.553

.550

.648

.545

.643

.640

.537

.634

.532

.629

7.527

.524

.521

.619

.616

.614

.611

.609

.606

.504

7.502

.499

.497

.494

.492

.489

.486

.484

.481

.479

7.476

.474

.471

.409 

.466

.464

.461

.459

.456

.453

7.450

.448

.445

.443

.440

.438

.435

.433

.430

.428

7.425

6' longitude.

Inches.

9.094

.091

.088

.085

.082

.079

.076

.073

.070

.066

9.063 

.060

.057

.054

.051

.047

.044

.041

.038

.035

9.032

.029

.026

.023

.020

.017

.014

.011

.008

.005

9.002

8.999

.996

.993

.990

.987

.984

.981

.978

.975

8.971

.968

.965

.962 

.959

.956

.953

.950

.947

.944

8.941

.938

.935

.932

.929

.926

.923

.920

.917

.914

8.911

7' longitude.

Inches.

10.609

.606

.602

.599

.695

.692

.588

.585

.581

.578

10.674 

.571

.567

.564

.560

.557

'.553

.549

.546

.542

10.538

.535

.631

.628

.524

.620

.617

.513

.509

.505

10.502

.499

.495

.491

.488

.484

.481

.477

.474

.470

10.406

.463

.459

.456 

.452

.449

.445

.442

.438

.435

10.431

.428

.424

.421

.417

.414

.410

.407

.403

.400

10.396

8' longitude.

Inches.

12.125

.121

.117

.113

.109

.105

.101

.097

.092

.088

12.084 

.080

.076

.072

.067

.063

.059

.055

.051

.047

12.043

.039

.035

.030

.026

.022

.018

.014

.010

.006

12.002

11.998

.994

.990

.986

.982

.978

.974

.970

.966

11.962

.958

.954

ncn .you 

.946

.942

.938

.934

.930

.926

11.921

.917

.913

.909

.905

.901

.897

.893

.889

.885

11.881

9' longitude.

Inches.

13.640

.635

.631

.626

.622

.617

.613

.608

.604

.699

13.695 

.590

.686

.581

.676

.572

.567

.563

.558

.554

13.549

.544

.540

.535

.531

.526

.622

.617

.613

.508

13.503

.499

.494

.490

.485

.480

.476

.471

.467

.462

13.457

.453

.448

.444 

!439

.434

.430

.425

.421

.416

13.411

.407

.402

.398

.393

.389

.384

.380

.375

.371

13.366

HX longitude.

Inches.

15.156

.161

.146

.141

.136

.130

.125

.120

.116

.110

15.105 

.100

.095

.090

.085

.079

.074

' .069

.064

.059

15.054

.049

.044

.039

.034

.028

.023

.018

.013

.008

15.003

14.998

.993

.988

.983

.978

.972

.967

.962

.957

14.952

.947

.942

937 

!932

.926

.921

.916

.911

.906

14.901

.896

.891

.886

.881

.876

.871

.866

.861

.856

14.851

Longitude interval.

/

I

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.003

.004

.006

.008

.011

.013

.017

«

 S-3

a S

31

/

i

2

3

4

6

6

7

8

9

10

"3 rf

o o ' 33 'SI

%v

Inches.

2.304

4.607

6.911

9.214

11.518

13.822

16.125

18.429

20.732

23.036

(383)
78 FORMULAS AND TABLES. [nun. 50.

TABLE XI. Co-ordinates for projection of maps. Scale- 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

2500

01

02

03

04

05

06

07

08

4)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

Abscissas of developed parallel.

1' longitude.

Inches.

2.208

.208

.208

.207

.207

.207

.206

.206

.206

.205

2.205

.205

.204

.204

.204

.204

.203

.203

.203

.202

2.202

.202

.201

.201

.201

.200

.200

.200

.200

.199

2.199

.199

' .198

.198

.198

.197

.197

.197

.197

.196

2.196

.196

.195

.195

.194

.194

.194

.193

.193

2.193

.193

.192

.192

.192

.191

.191

.191

.190

.190

2.190

2' longitude.

Inches.

4.416

.416

.415

.414

.414

.413

.413

.412

.411

.411

4.410

.410

.409

.408

.408

.407

.406

.406

.405

.405

4.404

.403

.403

.402

.402

.401

.400

.400

.399

.399

4.398

.397

.397

 .396

.396

.395

.394

.394

.393

.393

4.392

.391

.391

390 

!390

.389

.388

.388

.387

.386

4.386

.385

.385

.384

.383

.383

.382

.382

.381

.380

4.380

3' longitude.

Inches.

6.624

.623

.623

.622

.621

.620

.619

.618

.617

.616

6.615

.614

.613

.613

.612

.611

.610

.609

.608

.607

6.606

.605

.604

.603

.602

.601

.601

.600

.599

.598

6.597

- .596

.595

.594

.593

.592

.592

.591

.590

.589

6.588

.587

.586

.585 

.584

.583

.582

.581

.580

.580

6.579

.578

.577

.576

.575

.574

.573

.572

.571

.571

6.570

4' longitude.

Incites.

8.832

.831

.830

.829

.828

.826

.825

.824

.823

.822

8.820

.819

.818

.817

.816

.814

.813

.812

.810

.809

8.808

.807

.800

.804

.803

.802

.801

.800

.798

.797

8.796

.795

.794

.792

.791

.790

.789

.788

.786

.785

8.784

.783

 .782

!?79

.778

.776

.775

.774

.773

8.772

.770

.769

.768

.767

.766

.764

.763

.762

.761

8.760

5' longitude.

Inches.

11.040

.039

.038

.036

.034

.033

.032

.030

.028

.027

11.025

.024

.022

.021

' .019

.018

.016

.014

.013

.011

11.010

.008

.007

.005

.004

.002

.001

10.999

.998

.996

10.995

.993

.992

.990

.989

.987

.986

.984

.983

. .981

10.980

.978

.977

.975 

.974

.972

.970

.969

.967

.966

10.964

.963

.961

.960

.959

.957

.955

.954

.952

.951

10.949

6' longitude.

Inches.

13.249

.247

.245

.243

.241

.240

.238

.236

.234

.232

13.231

.229

.227

.225

.223

.222

.219

.217

.216

.214

13.212

.210

.208

.207

.205

.203

.201

.199

.198

.196

13.194

.192

.190

.189

.187

.185

.183

.181

.180

.178

13.176

.174

.172

.171 

.169

.167

.165

.163

.161

.159

13.157

.156

.154

.152

.150

.148

.147

.145

.143

.141

13.139

7' longitude.

Inches.

15.457

.455

.453

.450

.448

.446

.444

.442

.440

.438

15.436

.434

.431

.429

.427

.425

.422

.420

.418

.416

15.414

.412

.410

.408

.406

.403

.401

.399

.397

.395

15.393

.391

.389

.387

.385

.382

.380

.378

.376

.374

15.372

.370

.368

.366 

.364

.361

.359

. '.357

.354

.352

15.350

.348

.346

.344

.342

.340

.338

.336

.333

.331

15.329

8' longitude.

Inches.

17.665

.662

.660

.658

.655

.653

.650

.648

.646

.643

17.641

.638

.636

.634

.631

.629

.626

.623

.621

.618

17.616

.614

.611

.609

.606

.604

.602

.599

.597

.594

17.592

.590

.587

.585

.582

.580

.578

.575

.573

.570

17.568

.566

.563

.661 

.558

.566

.553

.550

.548

.646

17.543

.541

.538

.536

.534

.531

.529

.526

.524

.522

17.519

9' longitude.

Indies.

19.873

.870

.868

.865

.862

.859

.857

.854

.851

.849

19.846

.843

.840

.838

.835

.832

.829

.826

.823

.821

19.818

.815

.813

.810

.807

.804

.802

.799

.796

.794

19.791

.788

.786

.783

.780

.777

.775

.772

.769

.767

19.764

.761

.759

TKG ,70D

.753

.750

.747

.744

.741

.739

19.736

.733

.731

.728

.725

.723

.720

.717

.714

.712

19.709

10' longitude.

Inches.

22.081

.078

.075

.072

.069

.066

.063

.060

.057

.054

22.051

.048

.045

.042

.039

.036

.032

.029

.026

.023

22.020

.017

.014

.011

.008

.005

.002

21.999

.996

.993

21.990

.987

.984

.981

.978

.975

.972

.969

.966

.968

21.960

.957

.954

.'948

.945

.941

.938

.935

.932

21.929

-.926

.923

.920

.917

.914

.911

.908

.905

.902

21.899

II Longitude 

interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0,000

.001

.OOJ

.002

.003

.005

.007

.009

.011

.014

 o'a

 J 1

>ls

'

1

2

3

4

5

6

7

8

9

10

||g^j

Inches.

2.423

4.846

7.268

9.691

32.114

14.537

16.960

19.382

21.805

24.228

(384)
WOODWARD.] MAP CO-ORDINATES. 79

TABLE XI. (Jo-ordinates for projection of maps. Scale jnrfanj- 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

2600

1

2

3

4

5

6

7

8

9

10 

11

K

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

62

63

64

65

66

67

68

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

2.190

.190

.189

.189

.189

.188

.188

.188

.187

.187

2.187 

.186

.186

.186

.185

' .185

.185

.184

.184

.184

2.184

.183

.183

.183

.182

.182

.182

.181

.181

.181

2.180

.180

.180

.179

.179

.179

.179

.178

.178

.178

2.177

.177

.177

.176

.176

.175

.175

.175

.175

2.174

.174

.173

.173

.173

.173

.172

.172

.172

.171

2.171

2' longitude.

Inches.

4.380

.379

.379

.378

.377

.377

.376

.375

.375

.374

4.373 

.373

.372

.372

.371

.370

.370

.369

.368

.368

4.367

.367

.366

.365

.365

.364

.363

.363

.362

.362

4.361

.360

.360

.359

.358

.358

.357

.357

.356

.355

4.355

.354

.353

!352

.351

.351

.350

.350

.349

4.348

.348

.347

.346

.346

.345

.345

.344

.343

.343

4.342

3' longitude.

Inches.

6.570

.569

.568

.567

.566

.665

.564

.563

.562

.661

6.560 

.559

.558

.557

.556

.656

.555

.553

.653

.652

6.651

.550

.549

.648

.547

.546

.545

.644

.543

.542

6.541

.540

.539

.538

.538

.537

.536

.535

.534

.533

6.532

.531

.630

.529

!527

.526

.525

.524

.523

6.523

.522

.520

.519

.519

.518

.517

.516

.515

.514

6.513

4' longitude.

Inches.

8.760

.758

.757

.756

.754

.753

.752

.751

.750

.748

8.747 

.746

.744

.743

.742

.741

.740

.738

.737

.736

8.734

.733

.732

.731

.729

.728

.727

.726

.724

.723

8.722

.720

.719

.718

.717

.716

.714

.713

.712

.710

8.709

.708

.707

.706 

.704

.703

.702

.700

.699

.698

8.697

.696

.694

.692

.692

.690

.689

.688

.687

.686

8.684

5' longitude.

Inches.

10.949

.948

.946

.944

.943

.941

.940

.938

.937

.935

10.933 

.932

.930

.929

.927

.926

.925

.922

.921

.919

10.918

.916

.915

.913

.912

.910

.908

.907

.905

.904

10.902

.900

.899

.897

.896

.894

.893

.891

.889

.888

10.886

.885

.883

 !880

.878

.877

.875

.874

.872

10.871

.869

.867

.865

.864

.863

.861

.860

.858

.857

10.855

6' longitude.

Inches.

13.139

.138

.136

.133

.132

.130

.128

.126

.124

.123

13.120 

.118

.117

.115

.113

.111

.109

.107

.105

.103

13.102

.100

.098

.096

.094

.092

.090

.088

.087

.085

13.083

.081

.079

.077

.075

.073

.072

.070

.067

.066

13.064

.062

.060

.058 

.057

.054

.052

.051

.049

.047

13.045

.043

.041

.039

.037

.036

.034

.032

.030

.028

13.026

7' longitude.

Inches.

15.329

.327

.325

.322

.320

.318

.316

.314

.312

.310

15.307 

.305

.303

.301

.298

.296

.294

.291

.289

.287

15.285

.283

.281

.279

.276

.274

.272

.270

.268

.266

16.263

.261

.259

.256

.254

.252

.250

.248

.245

.243

15.241

.239

.237

!233

.230

.228

.226

.224

.221

15.219

.217

.214

.212

.210

.208

.206

.204

.202

.200

15.197

8' longitude.

Inches.

17.519

.517

.614

.511

.509

.506

.504

.502

.499

.497

17.494 

.491

.489

.486

.484

.482

.479

.476

.474

.471

17.469

.466

.464

.462

.458

.456

.454

.451

.449

.446

17.444

.441

.438

.436

.434

.431

.429

.426

.423

.420

17.418

.416

.414

.411 

.409

.406

.403

.401

.398

.396

17.394

.391

.388

.385

.383

.381

.378

.376

.374

.371

9' longitude.

Inches.

19.709

.706

.704

.700

.697

.695

.692

.689

.687

.684

.19.680 

.678

.675

.672

.669

.667

.664

.660

.658

.655

19.652

.650

.647

.644

.641

.638

.636

.633

.630

.627

19.624

.621

.618

.615

.613

.610

.607

.605

.601

.598

19.590

.593

.590

.588

.585

.581

.579

.576

.673

.570

19.668

.565

.561

.558

.556

.553

.551

.648

.545

.543

17.368 -19.539

1(X longitude.

Inches.

21.899

.896

.893

.889

.886

.883

.880

.877

.874

.871

21.867 

.864

.861

.858

.855

.852

.849

.845

.842

.839

21.836

.833

.830

.827

.823

.820

.817

.814

.811

.808

21.805

.801

.798

.795

.792

.789

.786

.783

.779

.776

21.773

.770

.767

764 

'.761

,,757

.754

.761

.748

.745

21.742

.739

.735

.731

.729

.726

.723

.720

.717

.714

21.710

II Longitude 

interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.002

.003

.005

.007

.009

.011

.014

 § 3

||3 s

'

i

2

3

4

5

6

7

8

9

10

_

a i

|| siS

Inches.

2.423

4.846

7.269

9.692

12.116

14.539

16.962

19.385

21.808

24.231

(385)
80 FORMULAS AND TABLES. [BULL. 50.

TAB:LE XI. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

2700

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

16

17

18

]9

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

Abscissas of developed parallel.

1' Ion 

gitude

Inches.

2.171

.171

.170

.170

.170

.169

.169

.169

.168

.168

2.168

.167

.167

.167

.166

.166

.166

.165

.165

.165

2.164

.164

.164

.163

.163

.163

.162

.162

.162

.161

2.161

.161

.160

.160

.160

.160

.159

.159

.159

.158

2.158

.158

.157

.157 

.157

.156

.156

.156

.155

.155

2.155

.154

.154

.154

.153

.153

.153

.152

.152

.152

2.151

2' Ion 

gitude

Inches.

4.342

.341

.341

.340

.339

.339

.338

.338

.337

.336

4.336

.335

.334

.334

.333

.332

.332

.331

.330

.330

4.329

.328

.328

.327

.326

.326

.325

.324

.324

.323

4.322

.322

.321

.320

.320

.319

.318

.318

.317

.317

4.316

.315

.315

114. .OJL:z

.313

.313

.312

.311

.311

.310

4.309

.309

.308

.307

.307

.306

.305

.305

.304

.304

4.303

3' Ion 

gitude

Inches.

6.513

.512

.511

.510

.509

.508

 .507

.506

.505

.504

6.503

.502

.501

.500

.499

.499

.497

.496

.496

.495

6.493

.492

.491

.490

.489

.488

.487

.487

.485

.484

6.484

.483

.481

.481

.480

.479

.478

.477

.476

.475

6.474

.473

.472

.471 

.470

.469

.468

.467

.466

.465

6.464

.463

.462

.461

.460

.459

.458

.457

,.456

.455

6.454

4' Ion 

gitude

Inches.

8.684

.683

.682

.680

.679

.678

.676

.675

.674

.672

8.671

.670

.668

.667

.6(56

.665

.663

.662

.661

.660

8.658

.656

.655

.654

.652

.651

.650

.649

.647

.646

8.645

.644

.642

.641

.640

.638

.637

.636

.634

.633

8.632

.630

.629

ftOQ U4O

.626

.625

.624

.623

.621

.620

8.619

.618

.616

.615

.614

.612

.611

.610

.608

.607

8.606

5' Ion 

gitude

Inches.

10.855

.853

.852

.850

.848

.817

.845

.844

.842

.840

10.839

.837

.835

.834

.832

. .831

.829

.827

.826

.824

10.822

.820

.819

.817

.815

.814

.812

.811

.809

.807

10.806

.804

.802

.801

.799

.798

.796

.794

.793

.791

10.789

.788

.786

fTQE .lOO

.783

.781

.780

.778

.776

.775

10.774

.772

.770

.768

.767

.765

.763

.762

.760

.759

10.757

6' Ion 

gitude

Inches.

13.026

.024

.022

.021

.018

.016

.015

.013

.010

.009

13.007

.005

.003

.001

12.999

.997

.995

.993

.991

.989

12.987

.985

.983

.981

.979

.977

.975

.973

.971

.969

12.967

.965

.963

.961

.959

.958

.955

.953

.952

.950

12.947

.946

.944 

942

.'940

.938

.936

.934

.932

.930

12.928

.926

.924

.922

.920

.919

.916

.914

.913

.911

12.908

7' Ion 

gitude

Inches.

15.197

,.195

.193

.191

.188

.186

.184

.182

.179

.177

15.175

.172

.170

.168

.165

.163

.161

.158

.156

.154

15.151

.149

.147

.144

.142

.140

.137

.135

.133

.130

15.128

.126

.123

.121

.119

.117

.114

.112

.110

.108

15.105

.103

.101 

,\Jay nod

.096

.094

.092

.090

.087

.085

15.083

.081

.078

.076

.074

.072

.069

.067

.065

.063

15.060

8' Ion 

gitude

Inches.

17.368

.366

.363

. .361

.358

.355

.353

.350

.347

.345

17.342

.340

.337

.334

.332.

.330

.326

.324

.322

.319

17.316

.313

.310

.308

.305

.302

.300

.298

.294

.292

17.290

.287

.284

.282

.279

.277

.274

.271

.269

.266

17.263

.261

.258

OKO .£0t>

.253

.250

.248

.246

.242

.240

17.238

.235

.232

.230

.227

.225

.222

.219

.217

.214

17.211

9' Ion 

gitude

Inches.

19.539

.536

.534

.531

.527

.525

.522

.519

.516

.513

19.510

.507

.504

.501

.498

.496

. .492

.489

.487

.484

19.480

.477

.474

.471

.468

.465

.462

.460

.456

.453

19.451

.448

.444

.442

.439

.436

. .433

.430

.427

.425

19.421

.418

.416 

.413

.409

.407

.404

.401

.398

.395

19.392

.390

.386

.383

.381

.378

.374

. 372

.369

.366

19.363

10' Ion 

gitude

Inches.

21.710

.707

.704

. .701

.697

.694

.691

.688

.684

.681

21.678

.675

.671

.668

.665

.662

.658

.655

.652

.649

21.645

.641

.638

.635

.631

.628

.625

.622

.618

.615

21.612

.609

.605

.602

.599

.596

.592

.589

.586

.583

21.579

.576

.573

KtTA

.O l\J

.566

.563

.560

.557

.553

.550

21.547

.544

.540

.537

.534

.531

.527

.524

.521

.518

21.514

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped .parallel.

Inches.

0.000

.001

.001

.002

.004

.005

.007

1 .009

.012

.014

O *

^73

II

ilS

/

1

2

3

4

5

6

7

8

9

10

Q O

 2 a

3J3 (U CD O -* a^

Inches.

2.423

4.84.7

7.270

9.694

12.117

14.541

16.964

19.388

21.811

24.235

(386)
' WOODWARD.] MAP CO-ORDINATES. 81

TABLE XI. Co-ordinates for projection of maps. Scale

Derivation of table explained in section (5) ; use of table explained on page 22.]

Latitude ofparallel.

o /

2800

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

,JO*lt>

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Abscissas of developed parallel.

V longitude.

Inches.

2.151

.151

.151

.150

.150

.1.00

.149

.149

.149

.148

2.148 

.148

.147

.147

.147

.146

.146

.146

.145

.145

2.145

.144

.144

.144

.143

.143

.143

.142

.142

.142

2.141

.141

.141

.140

.140

.140

.139

.139

.139

.138

2.138

.138

.137

107 .J.OI

.137

.136

.136

.136

.135

.135

2.135

.134

.134

.134

.133

.133

.133

.132

.132

.132

2.131

2' longitude.

Inches.

4.303

.302

.302

.301

.300

.300

.299

.298

.298

.297

4.296 

.296

.295

.294

.294

.293

.292

.292

.291

.290

4.290

.289

.288

.288

.287

.286

.286

.285

.284

.284

4.283

.282

.281

.281

.280

.279

.279

.278

.277'

.277

4.276

.275

.275

.274 

.273

.273

.272

.271

.271

.270

4.269

.269

.268

.267

.267

.266

.265

.265

.264

.263

4.203

3' longitude.

Inches.

6.454

.453

.452

.451

.450

.449

.448

.447

.446

.445

6.444 

.443

.442

.441

.440

.439

.438

.437

.436

.435

0.434

.433

.432

.431

.430

.439

.428

.427

.426

.425

6.424

 .423

.422

.421

.420

.419

'.418

.417

.416

.415

6.414

.413

.412

.411 

.410

.409

.408

.407

.400

.405

6.404

.403

.402

.401

.400

.399

.398

.397

.396

.395

6.394

4' longitude.

Inches.

8.006

.604

.003

.602

.600

.599

.598

.596

.595

.594

8.592 

.591

.590

.588

.587

.586

.584

.583

.582

.580

8.579

.578

.576

.575

.574

,572

.571

.570

.508

.507

8.566

.564

.563

.561

.500

.559

.557

.556

.555

.553

8.552

.551

.549

.548 

'.547

.545

.544

.543

.541

.540

8.539

.537

.536

.535

.533

.532

.531

.529

..528

'.527

8.525

.0' longitude.

Inches.

10.757

.755

.754

.752

.750

.749

.747

.745

. .744

.742

10.740 

.739

.737

.735

.734

.732

.730

.729

.727

.725

10.724

.722

.720

.719

.717

.715

.714

.712

.710

.709

10.707

.705

.703

.701

.700

.098

.696

.695

.693

.691

10.690

.688

.686

.685 

.683

.681

.680

.678

.676

.675

10.673

.671

.670

.668

.606

.005

.663

.661

.660

.058

10.656

6' longitude.

Inches.

12.908

.907

.905

.902

.901

.899

.896

.895

.893

.890

12.889 

.887

.884

.883

.881

.878

.877

.875

.872

.871

12.869

.806

.805

.803

.800

.859

.857

.854

.853

.851

12.848

.846

.844

.842

.840

.838

.836

.834

.832

.830

12.828

.826

.824

QOO

 O44

.820

.818

.816

.814

.812

.810

12.808

.806

.804

.802

.800

.798

.796

.794

.792

.790

12.788

7' longitude.

Inches.

15.000

.058

.056

.053

.051

.049

.046

.044

.042

.039

15.037 

.035

.032

.030

.028

. .025

.023

.021

.018

.016

15.014

.011

.009

.007

.004

.002

.000

14.997

.995

.993

14.990

.987

.985

.982

.980

.978

.975

.973

.971

.968

14.966

.964

.961

.959 

!957

.954

.952

.950

.947

.945

14.943

.940

.938

.936

.933

.931

.929

.926

.924

.922

14.919

8' longitude.

Incites.

17.211

.209

.206

.203

0 .201

.198

.195

.193

.190

.187

17.185 

.182

.179

.177

.174

.171

'.109

.106

.163

.161

17.1.08

.155

.153

.150

.147

.145

.142

.139

.137

.134

17.131

.128

.126

.122

.120

.118

.114

.112

.110

.106

17.104

.102

.098

.096 

.094

.090

.088

.086

.082

.080

17.078

.074

.072

.070

.000

.004

.002

.058

.056

.054

17.050

9' longitude.

Inches.

19.363

.360

.357

.354

.351

.348

.345

.342

.339

.336

19.333 

.330

.327

.324

.321

.318

.315

.312

.309

.306

19.303

.300

 .297

.294

.291

.288

.285

.282

.279

.270

19.273

.209

.266

.263

.260

.257

.254

.251

.248

.245

19.242

.239

.236

OoO .£i>3

.230

.227

.224

.221

.218

.215

19.212

.209

.206

.203

.200

.197

.194

.191

.188

.185

19.182

10' longitude.

Inches.

21.514

,.511

.508

.504

.501

.498

.494

.491

.488

.484

21.481 

.478

.474

.471

.468

.464

.461

.458

.454

.451

21.448

.444

.441

.438

.434

.431

.428

.424

.421

.418

21.-M4

.410

.407

.403

.400

.397

.393

.390

.387

.383

21.380

.377

.373

.370 

.367

.363

.360

.357

.353

.350

21.347

.343

.340

.337

.333

.330

.327

.323

.320

.317

21.313

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

1 Ordinatos of! developed parallel. ,

Inches.

0.000

.001

.001

.002

.004

.005

.007

.009

.012

.015

o_-

 3 4

|i

Is

/

i

2

3

4

5

0

7

8

9

10

"3 M

§

1J

a 3

Inches.

2.424

4.848

7.271

9.095

12.119

14.543

16.967

39.390

21.814

24.238

Bull. 50 6

(387)
FORMULAS AND TABLES. [BULL. 50.

TABLE XI. Co-ordinates for projections of maps. Scale -3-t>$w

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

2900

01

02

03

04

05

06

07

08

09

10

11

12

13

14

Ib

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

Abscissas of developed parallel.

1' longitude.

Inches.

2.131

.131

.131

.130

.130

.130

.129

.129

.128

.128

2.128

.127

.127

.127

.126

.126

.126

.125

.125

.125

2.124

.124

.124

.123

.123

.123

.122

.122

.121

.121

2.121

.121

.120

.120

.119

.119

.119

.118

.118

.118

2.117

.117

.117 

.116

.116

.116

.115

.115

.115

.114

2.114

.114

.113

.113

.112

.112

.112

.111

.111

.111

2.110

2' longitude.

Inches.

4.263

.262

.261

.261

.260

.259

.258

.258

.257

.256

4.256

.255

.254

.254

.253

.252

.251

.251

.250

.249

4.249

.248

.247

.247

.246

.245

.244

.244

.243

.242

4.242

.241

.240

.240

.239

.238

.238

.237

.236

.236

4.235

.234

.233 

ooo Loo

.232

.231

.231

.230

.229

.229

4.228

.227

.226

.226

.225

.224

.224

.223

.222

.222

4.221

3' Jongitude.

Inches.

6.394

.393

.392

.391

.390

..389

.388

.387

.385

.385

6.383

.382

.381

.380

.379

.378

.377

.376

.375

.374

6.373

.372

.371

.370

.369

.368

.367

.366

.364

.364

6.363

.362

.361

.360

.358

.358

.356

.355

.354

.353

6.352

.351

.350 

.349

.348

.347

.346

.345

.344

.343

6.342

.341

.340

.339

.337

.337

.335

.334

.333

.332

6.331

4' longitude.

Inches.

8.525

.524

.522

.521

.520

.518

.517

.516

.514

.513

8.511

.510

.508

.507

.506

.504

.503

.502

.500

.499

8.497

.496

.494

.493

.492

.490

.489

.488

.486

.485

8.484

.482

.481

.480

.478

.477

.475

.474

.472

.471

8.470

.468

.467

!464

.463

.461

.460

.458

.457

8.456

.454

.453

.452

.450

.449

.447

.446

.444

.443

8.442

5' Ion- ; 6' longitude, gitude.

Inches. Inches.

10.656

.655

.653

.651

.649

.648

.646

.644

.642

.641

10'.639

.637

.635

.634

.632

.630

.628

.627

.625

.623

10.621

.620

.618

.616

.614

.613

.611

.609

.607

.606

10.604

.603

.601

.599

.597

.596

.594

.592

.590

.589

10.587

.585

.583

EDO .Do & 

.580

.678

.576

.575

.573

.571

10.569

.568

.566

.564

.562

.561

.559

.557

.555

.554

10.552

12.788

.786

.784

.782

.779

.778

.775

.773

.771

.769

12.767

.765

.763

.761

.758

.757

.754

.752

.750

.748

12.746

.744

.742

.740

.737

.736

.733

.731

.729

.727

12.725

.724

.721

.719

.717

.715

.713

.711

.700

.707

12.704

.703

.700

!696

.694

.692

.690

.688

.686

12.683

.682

.679

.677

.675

.673

.671

.669

.667

.665

12.662

7' longitude.

Inches.

14.919

.917

.914

.912

.909

.907

.904

.902

.899

.897

14.895

.892

.890

.888

.885

.883

.880

.878

.875

.873

14.870

.868

.865

.863

.860

.858

.855

.853

.850

.848

14.846

.844

.841

.839

.836

.834

.832

.829

.827

.825

14.822

.820

.817

.815 

.812

.810

.807

.805

.802

.800

14.797

.795

.792

.790

.787

.785

.783

.780

.778

.776

14.773

8' longitude.

Inches.

17.050

.048

'.045

.042

.039

.037

.034

.031

.028

.026

17.022

.020

.017

.014

.011

.009

.006

.003

.000

16.998

16.994

.992

.989

.986

.983

.981

.978

.975

.972

.970

16.967

.965

.962

.959

.956

.954

.950

.948

.945

.942

16.939

.937

.934

!928

.926

.922

.920

.917

.914

16.911

.909

.906

.903

.900

.898

.894

.892

.889

.886

16.883

9' longitu'de.

Inches.

19.182

.179

.175

.173

.169

. .166

.163

.160

 .156

.154

19.150

.147

.144

.141

.138

.135

.131

.129

.125

.122

19.119

.116

.112

.110

.106

.103

.100

.097

.093

.091

19.088

.085

.082

.079

.075

.073

.069

.066

.063

.060

19.057

.054

.050 

.048

!044

.041

.038

.035

.031

.029

19.025

.022

.019

.016

.012

.010

.006

.003

.000

18.997

18.994

10' longitude.

Inches.

21.313

.310

.306

.303

.299

.296

.292

.289

.285

.282

21.278

' .275

.271

.268

.264

.261

.257

.254

.250

.247

21.243

.240

.236

.233

.229

.226

.222

.219

.215

.212

21.209

.206

.202

.199

.195

.192

1QQ .loo

.185

.181

'.178

21.174

.171

.167 

.164

!l60

.157

.153

.150

.146

.143

21.139

.136

.132

.129

.125

.122

.118

.115

.111

.108

21.104

Longitude interval.

1

2

3

4

5

6

7

8

9

10

Ordinates of developed parallel.

Inches.

0.000

.001

.001

.002

.004

.005

.007

.010

.012

.015

 o'a BE ^3 c? 11

i

i

2

3

4

5

6

7

8

9

10

fl °°

O O

 S a

<».S a*

Inches.

2.424

4.848

7.273

9.697

12.121

14.545

16.969

19.394

21.818

24.242

(388)
WOODWABD.] MAP CO-ORDINATES. 83

TABLE XI. Co-ordinates for projection of maps. Scale -

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o t

3000

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

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

62

53

64

65

66

67

68

59

60

Abscissas of developed parallel.

1' longitudo.

Inches.

2.110

.110

.110

.109

.109

.109

.108

.108

.107

.107

2.107 

.106

.106

.106

.105

.105

.105

.104

.104

.104

2.103

.103

.103

.102

.102

.101

.101

.101

.100

.100

2.100

.099

.099

.099

.098

.098

.098

.097

.097

.097

2.096

.096

.095

.095

.095

.094

.094

.094

.093

.093

2.093

.092

.092

.092

.091

.091

.091

.090

.090

.089

2.089

2' longitude.

Inches.

4.221

.220

.219

.219

.218

.217

.217

.216

.215

.214

4.214 

.213

.212

.212

.211

.210

.209

.209

.208

.207

4.207

.206

.205

.204

.204

.203

.202

.202

.201

.200

4.200

.199

.198

.197

.197

.196

.195

.195

.194

.193

4.192

.192

.191

.190

.190

.189

.188

.188

.187

.186

4.185

.185

.184

.183

.183

.182

.181

.180

.180-

.179

4.178

3' longitude.

Inches.

6.331

.330

.329

.328

.327

.326

.326

.324

.322

.322

6.320 

.319

.318

.317

.316

.315

.314

.313

.312

.311

6.310

.309

.308

.307

.306

.304

.304

.302

.301

.300

6.299

.298

.297

.296

.295

.294

.293

.292

.291

.290

6.289

.288

.286

.286

.284

.283

.282

.281

.280

.279

6.278

.277

.276

.275

.274

.273

.272

.271

.269

.268

6.267

4' longitude.

Inches.

8.442

.440

.439

.437

.436

.434

.433

.432

.430

.429

8.427 

.426

.424

.423

.422

.420

.419

.418

.416

.415

8.413

.412

.410

.409

.408

.406

.405

.403

.402

.400

8.399

^398

.396

.395

.394

.392

.391

.389

.388

.386

8.385

.384

.382

.381

.379

.378

.376

.376

.374

.372

8.371

.370

.368

.366

.365

.364

.362

.361

.359

.358

8.356

5' longitude.

Inches.

10.552

.550

.648

.546

.646

.543

.541

.539

.537

.536

10.534 

.532

.530

.529

.627

.525

i

.523

.522

.520

.518

10.516

.515

.513

.511

.509

.507

.506

.504

.502

.600

10.499

.497

.495

.493

.492

.490

.488

.486

.484

.483

10.481

.479

.477

.476

.474

.472

.470

.469

.467

.465

10.463

.462

.460

.458

.456

.454

.453

.451

.449

.447

10.445

6' longitude.

Inches.

12.662

.660

.658

.656

.654

.652

.650

.647

.645

.643

12.641 

.639

.637

.635

.632

.631

.628

.626

.624

.622

12.620

.618

.616

.613

.611

.609

.607

.605

.603

.601

12.599

.596

.595

.592

.690

.688

.586

.684

.581

.580

12.577

.575

.573

.571

.569

.567

.565

.503

 .560

.559

12.556

.554

.652

.650

.548

.645

.544

.541

.539

.536

12.534

7' longitude.

Inches.

14.773

.770

.768

.765

.763

.760

.758

.755

.752

.750

14.748 

.745

.743

.741

.738

.736

.733

.731

.728

.726

14.723

.721

.718

.715

.713

.710

.708

.706

.703

.701

14.699

.696

.694

.691

.689

.686

.684

.681

.678

.676

14.673

.671

.668

.666

CRA 

 Otrfc

.661

.659

.657

.654

.652

14.649

.647

.644

.641

.639

.636

.634

.631

.629

.626

14.623

8' longitude.

Inches.

16.883

.880

.878

.874

.872

.869

.866

.863

.860

.858

16.854 

.852

.849

.846

.843

.841

.838

.835

.832

.830

16.826

.824

.821

.818

.815

.812

.810

.806

.804

.801

16.798

.795

.793

.790

.787

.784

.782

.778

.775

.773

16.770

.767

.764

.762

.758

.756

.753

.750

.747

.745

16.742

.739

.736

.733

.730

.727

.725

.722

.718

.715

16.712

9' longitude.

aiches.

18.994

.990

.987

.984

.981

.977

.976

.971

.967

.965

18.961 

' .958

.955

.952

.949

.946

.942

.940

.936

.933

18.930

.927

.923

.920

.917

.913

.911

.907

.904

. .901

18.898

.895

.892

.888;

.886

.882

.879

.876

.872

.869

' 18.866

.863

.859

.857

.853

.850

.847

.844

.841

.838

18.834

.832

.828

.824

.822

.818

.815

.812

.808

.805

18.801

10' longitude.

Inches.

21.104

.100

.097

.093

.090

.086

.083

.079

.075

.072

21.068 

.065

.061

.058

.054

.061

.047

.044

.040

.037

21.033

.030

.026

.022

.019

.015

.012

.008

.005

.001

20.998

.994

.991

.987

.984

.980

.977

.973

.969

.966

20.962

.959

.955

.952

.948

'.945

.941

.938

.934

.931

20.927

.924

.920

.916

.913

.909

.906

.902

.898

.894

20.890

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.002

.004

.006

.007

.010

.012

.016

*

O 11' C S

i5.2'

1

1

2

3

4

6

6

7

8

9

10

"3 ri

 ° a

 c §

3=0

Inches.

2.424

4.849

7.273

9.698

12.122

14.547

16.971

19.396

21.820

24.245

(389)
84 FORMULAS AND TABLES. [BULL. 50.

TABLE XI. Co-ordinates for projection of maps. Scale ^tru- 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

3100

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

26

27

28

29

30

31

32

33

34

35

* 36

37

38

39

40

41

42

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

2.089

.089

.088

.088

.087

.087

' .087

.086

.086

.086

2.085

.085

.085

.084

.084

.083

.083

.083

.082

.082

2.082

.081

.081

.081

.080

.080

.079

.079

.079

.078

2.078

.078

.077

.077

.076

.076

.076

.075

.075

.075

2.074

.074

.074

.073 

.073

.072

.072

.072

.071

.071

2.071

.070

.070

.069

.009

.069

.068

.068

.068

.067

2.067

2' longitude.

Inches.

4.178

.177

.177

.176

.175

.174

.174

.173

.172

.171

4.171

.170

.169

.168

.168

.167

.166

.106

.165

.164

4.163

.163

.162

.161

.160

.160

.159

.158

.157

.157

4.156

.155

.154

.154

.153

.152

.152

.151

.150

.149

4.149

.148

.147

.146 

.146

'.145

.144

.143

.143

.142

4.141

.141

.140

.139

.138

.138

.137

.136

.135

.135

4.134

3' longitude.

In9i.es.

0.267

.260

.265

.264

.202

.262

.260

.259

.258

.257

6.256

.255

.254

.253

.252

.250

.249

.248

.247

.246

6.245

.244

.243

.242

.241

.239

.238

.237

.236

.235

6.234

.233

.232

.231

.229

.228

.227

.226

.225

.224

6.223

.222

.221

.218

.217

.216

.215

.214

.213

6.212

.211

.210

-.208

.208

.206

.205

.204

.203

.202

6.201

4' longitude.

Inches.

8.350

.354

.353

.352

.350

.349

.347

.346

.344

.343

8.341

.340

.338

.337

.336

.334

.332

.331

.330

.328

8.327

.325

.324

.322

.321

.319

.318

.316

.315

.314

8.312

.310

.309

.308

.300

.304

.303

.302

.300

.299

8.298

.290

.294

.293

!290

.288

.287

.280

.284

8.282

.281

.280

.278

.277

.275

.274

. .272

.271

.209

8.208

5' longitude.

Indies.

10.445

.443

.441

.439

.437

.436

.434

.432

.430

' .428

10.420

.425

.423

.421

.419

.417

.415

.414

.412

.410

10.408

.406

.404

' .403

.401

.399

.397

'.395

.393

.392

10.390

.388

.386

.384

.382

.380

.379

.377

.375

.373

10.372

.369

.368

.366 

.364

.362

.360

.358

.357

.355

10.353

.351

.349

.347

.346

.344

.342

.340

.338

.336

10.334

6' longitude.

Inches.

12.534

.532

.530

.527

.525

.523

.521

.518

.517

.514

12.512

.510

.508

.505

.503

.501

.499

.497

.494

.492

12.490

.488

.485

.484

.481

.479

.477

.475

.472

.470

12.468

.466

.403

.401

.459

.457

.455

.452

.450

.448

12.446

.443-

.442

!437

.435

.433

.430

.428

.426

12.424

.422

.419

.417

.415

.413

.410

.409

.406

.404

12.401

7' longitude.

Inches.

14.623

.620

.618

.615

.612

.610

.608

.605

.603

.600

14.597

.595

.592

.589

.587

.584

.582

.580

.577

.574

14.572

.569

.566

.564

.561

.559

.556

.554

.551

.549

14.546

.543

.540

.538

.535

.533

.530

.528

.525

.523

14.521

.517

.515

!510

.507

.505

.502

.500

.497

14.494

.492

.489

.486

' .484

.482

.479

.477

.474

.471

14.468

8' longitude.

Inches.

16.712

.709

.706

.703

.700

.698

.694

.691

.689

.686

16.082

.680

.677

.674

.671

.668

.665

.662

.659

.656

16.654

.650

.647

.645

.642

.638

.636

.633

.630

.627

16.624

.621

.618

.615

.612

.609

.606

.603

.600

.598

16.595

.591

.589

!582

.580

.577

.574

.571

.568

16.565

.562

.559

.556

.554

.550

.547

.545

.542

.538

16.535

9' longitude.

Inches.

18.801

.797

.795

.791

.787

.785

.781

.778

.775

.771

18.768

.765

.761

.758

.755

.751

.748

.745

.742

.738

18.735

, .732

.728

.725

.722

.718

.715

.712

.708

.706

18.702

.698

.695

.692

.688

.685

.682

.679

.675

.672

18.670

.665

.662

!655

.652

.649

.645

.643

.639

18.635

.633

.629

.625

.623

.619

.616

.613

.609

.606

18.602

10' -longitude.

Inches.

20.890

.886

.883

.879

.875

.872

.868

.864

.861

.857

20.853

.850

.846

.842

.839

.835

.831

.828

.824

.820

20.817

.813

.809

.806

.802

.798

.795

.791

.787

.784

20.780

.776

.772

.769

.765

.761

.758

.754

.750

.747

20.744

.739

.736

!?28

.725

.721

.717

.714

.710

20.706

.703

.699

.695

.692

.688

v .684

.681

.677

.673

20.669

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.002

.004

.006

.008

.010

.013

.016

 §""'

31

'

i

2

3

4

5

6

78'

9

10'

a o

.2 a

IIo.S S 73

Inches.

2.425

4.850

7.275

9.700

12.124

14.549

16.974

19.399

21.824

24.249

(390)
WOOD WARD. J MAP CO-ORDINATES

TABLE XI. Co-ordinates for projection of maps. Scale yir^nnr-

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o t

3200

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

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

AQfrO

44

45

46

47

48

49

60

61

52

53

54

65

66

67

68

69

60

Abscissas of developed parallel.

1' longitude.

Inches.

2.067

.006

.066

.066

.065

.065

.065

.064

.064

.003

2.003 

.003

.062

.002

.001

.001

.061

.000

.000

.060

2.059

.059

.058

.058

.058

.057

.057

.057

.050

.056

2.055

.055

.055

.054

.054

.054

.053

,.053

.052

.052

2.052

.051

.051

.050 

.050

.050

.049

.049

.049

.048

2.048

.047

.047

.047

.040

.046

.046

.046

.045

.044

2.044

2' longitude.

Inches.

4.134

.133

.132

.131

.131

.130

.129

.128

.128

. .127

4.126 

.125

.125

.124

.123

.122

.122

.121

.120

.119

4.119

.118

.117

.116

.115

.115

.114

.113

.112

.112

4.111

.110

.109

.109

.108

.107

.106

.106

.105

.104

4.103

.103

.102

.101 

.100

.100

.099

.098

.097

.096

4.090

.095

.094

.093

.093

.092

.091

.090

.090

.089

4.088

3' longitude.

Inches.

6.201

.199

.198

.197

.196

.195

.194

.193

.191

.190

6.189 

.188

.187

.186

.184

.184

.182

.181

.180

.179

6.178

.177

.175

.174

.173

.172

.171

.170

.169

.167

6.160

.105

.104

.103

.102

.101

.160

.158

.157

.156

6.155

.154

.153

.151 

.150

.149

.148

.147

.146

.145

6.144

.142

.141

.140

.139

.138

.137

.136

.134

.133

6.132

4' longitude.

Inches.

8.268

.206

.204

.203

.261

.260

.258

.257

.255

.254

8.252 

.251

.249

.248

.240

.245

.243

.242

.240

.238

8.237

.236

.234

.232

.231

.230

.228

.226

.225

.2-23

8.222

.220

.219

.217

.210

.214

.213

.211

,210

.208

8.207

.205

.204

.202 

.200

.199

.198

.190

.194

.193

8.192

.190

.188

.187

. .185

.184

.182

.181

.179

.178

8.176

5' longitude.

Incites.

10.334

.332

.330

.328

.320

.325

.323

.321

.319

.317

10.315 

.313

.311

.309

.307

.300

.304

.302

.300

.298

10.290

.294

.292

.290

.288

.287

.285

.283

.281

.279

10.277

.275

.273

.271

.269

.268

.266

.204

.202

.200

10.258

.256

.254

.252 

.250

.249

.247

.245

.243

.241

10.239

.237

.235

.233

.231

.230

.228

.226

.2-24

.222

10.220

6' longitude.

Inches.

12.401

.399

.397

..394

.392

.390

.388

.385

.383

.380

12.379 

.376

.374

.371

.369

.367

.365

.362

.360

.358

12.366

.353

.351

.349

.346

.344

.342

.340

.337

.335

12.333

.331

.328

.326

.323

.322

.319

.317

.314

.312

12.310

.308

.305

Of 10 .OvO

.300

.299

.290

.294

.292

.289

12.287

 .285

.283

.280

.278

.276

.274

.271

.209

.200

12.265

7' longitude.

Inches.

14.468

.405

.463

.400

.457

.455

.452

.449

.447

.4-14

14.442 

.439

.436

.433

.430

.428

.426

.423

.420

.417

14.415

.412

.409

.407

.404

.402

.399

.390

.393

.391

14.388

.386

.383

.380

.377

.3J5

.372

.370

.307

.304

14.302

.359

.350

Or-^

,»X>tJ

.351

.349

.340

.313

.340

.337

14.335

.332

.330

.327

.324

.322

.319

.310

.314

.311

14.309

8' longitude.

Inches.

16.535

.532

.629

.526

.522

.520

.517

.514

.510

.507

16.505

.502

.498

.495

.492

.490

.486

.483

.480

.477

16.474

.471

.468

.405

.462

.459

.456

.453

.450

.446

16.444

.441

.438

.434

.431

.429

.426

.422

.419

.416

16.414

.41.0

.407

.404 

.401

.398

.395

.392

.389

.386

16.383

.380

.377

.374

.370

.368

.365

.302

.358

.355

10.353

9' longitude.

Inches.

18.602

.598

.595

.501

.588

.585

.581

.578

.574

.571

18.568 

.564

.561

.557

.553

.551

.647

J544

.540

.536

18.534

.530

.520

; .523

.519

.517

.513

.509

.506

.502

18.499

.496

.492

.489

.485

.482

.479

-.475

.472

.468

18.4.65

.462'

.458

.454 

.451

.448

.445

.441

.437

.434

18.431

.427

.424

.420

.417

.414

.410

.407

.403

.400

18.397

10' longitude.

Inches.

20.669

.665

.661

.657

.653

.650

.646

.642

.638

.634

20.631

.027

.623

.619

.615

.612

.608

.604

.600

.596

20.593

.589

.585

.581

.577

.574

.570

.566

.562

.558

20.555

.551

.547

.543

.539

.530

.532

.528

.524

.520

20.517

.513

.509

.505 

.501

.498

.494

.'190

.486

.482

20.479

.475

.471

467

.463

.400

.450

.452

.448

.444

20.441

Longitude interval.

/

1

2

3

4

5

6

7

8

. 9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.003

.004

.006

.008

.010

.013

.010

*

« "S *

s > -M U

-E o

J '"=

/

1

2

3

4

5

6

7

8

9

10

ll

2 3

5 _»

3 ^

Inches.

2.425

4.851

7.270

9.702

12.127

14.552

10.978

* 19.403

21.829

24.254

(391)
86 FORMULAS AND TABLES. [BULL. 50,

TABLE XI. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

3300

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

4A ?to

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

2.044

.044

.043

.043

.042

.042

.042

.041

.041

.040

2.040 

.040

.039

.039

.039

.038

.038

.037

.037

.037

2.036

.036

.035

.035

.035

.034

.034

.033

.033

.033

2.032

.032

.032

.031

.031

.030

.030

.030

.029

.029

2.028

.028

.028

(Y>7 .\)&{

.027

.026

.026

.026

.025

.025

2.025

.024

.024

.023

.023

.023

.022

.022

.021

.021

2.021

2' longitude.

Inches.

4.088

.087

.087

.086

.085

.084

.083

.083

.082

.081

4.080 

.080

.079

.078

.077

.076

.076

.075

.074

.073

4.073

.072

.071

.070

.069

.069

.068

.067

.066

.065

4.065

.064

.063

.062

.062

.061

.060

.059

.058

.058

4.057

.056

.055

.055 

.054

.053

.052

.051

.051

.050

4.049

.048

.048

0 .047

.046

.045

.044

.044

.043

.042

4.041

3' longitude.

Inches.

6.132

.131

.130

.129

.127

.126

.125

.124

.123

.121

6.121 

.119

.118

.117

.116

.115

.113

-.112

.111

.110

6.109

.108

.106

.105

.104

.103

.102

.100

.099

.098

6.097

.096

.095

.094

.092

.091

.090

.089

.088

.086

6.085

.084

.083

non ,\jo6

.081

.079

.078

.077

.076

.075

6.074

.073

.071

.070

.069

.068

.067

.065

.064

.063

6.062

4' longitude.

Inches.

8.176

.175

.173

.172

.170

.168

.167

.165

.164

.162

8.161 

.159

.158

.156

.154

.153

.151

.150

.148

.146

8.145

.144

.142

.140

.139

.137

.136

.134

.132

.131

8.130

.128

.126

.126

.123

.122

.120

.118

.117

.115

8.114

.112

.111

 ino JLuy 

.108

.106

.104

.103

.101

.100

8.098

.097

.095

.094

.092

.090

.089

.087

.086

.084

8.083

5' longitude.

Inches.

10.220

.218

.216

.214

.212

.210

 .208

.206

.204

.202

10.201 

.199

.197

.195

.193

.191

.189

.187

.185

.183

10.181

.179

.177

.175

.173

.171

.169

.167

.165

.163

10.162

.160

.158

.156

.154

 - 152

.150

.148

.146

.144

10.142

.140

.138

1Q(J .lob 

.134

.132

.130

.128

.126

.124

10.123

.121

.119

.117

.115

.113

.111

.109

.107

.105

10.103

6' longitude.

Inches.

12.265

.262

.260

' .257

1255

.253

.250

.248

.245

.243

12.241 

.239

1 .236

.234

.232

.229

.227

.224

.222

.220

12.218,

.215

.213

.211

.208

.206

.203

.201

.199

.196

12.194

.102

.190

.187

.185

.182

.180

.178

.175

.173

12.171

.169

.166

.164 

!l61

.159

.157

.154

.152

.149

12.148

.145

.143

.140

.138

.136

.133

.131

.128

.126

12.124

V longitude.

Inches.

14.309

.306

.303

.300

.297

.295

.292

.289

.286

.283

14.281 

.279

.276

.273

.270

.267

.265

.262

.259

.256

14.254

.251

.248

.246

.243

.240

.237

.234

.232

.229

14.227

.224

.221

.218

.216

.213

.210

.207

.204

.202

14.199

.197

.194

.191 

!l88

.185

.183

.180

.177

.174

14.172

.169

.167

.164

.161

.158

.155

.153

.150

.147

14.145

8' longitude.

Inches.

16.353

.350

.346

.343

.340

.337

.334

.330

.327

.324

16.322 

.318

.315

.312

.309

.306

.302

.299

.296

.293

16.290

.287

.284

.281

.278

.274

.271

.268

.265

.262

16.259

.256

.253

.250

.246

.243

.240

.237

.234

.230

16.228

.225

.222

.&LQ O1Q

.216

.212

.209

.206

.202

.199

16.197

.194

.190

.187

.184

.181

.178

.174

.171

.168

16.166

9' longitude.

Inches.

18.397

.393

.390

.386

.382'

.379

.375

.372

.368

.364

18.362 

.358

.355

.351

.347

.344

.340

.337

.333

.329

18.327

.323

.319

.316

.312

.309

.305

.301

.298

.294

18.292

.288

.284

.281

.277

.274

.270

.266

.263

.259

18.256

.253

.249 

94.fi .&VJ

.242

.238

.235

.231

.228

.224

18.221

.218

.214

.211

.207

.203

.200

.196

.193

.189

. 18.186

10' longitude.

Inches.

20.441

.437

.433

.429

.425

.421

.417

.413

.409

.405

20.402 

.398

.394

.390

.386

.382

.378

.374

.370

.366

20.363

.359

.355

.351

.347

.343

.339

.335

.331

.327

20.324

.320

.316

.312

.308

.304

.300

.296

.292

.288

20.285

.281

.277

070 .Aid

.269

.265

.261

.257

.253

.249

20.246

.242

.238

.234

.230

.226

.222

.218

.214

.210

20.207

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.003

.004

.006

.008

.010

.013

.016

*« "2 «

*» s >C '£ ®

73 +J

3.2

/

1

2

3

4

5

6

7

8

9

10

Is.2 °

S §

o.S a*

Inches.

2.426

4.852

7.277

9.703

12.129

14.555

16.981

19.406

21.832

24.258

(392)
WOODWARD.] MAP CO-ORDINATES. 87

TABLE XI. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of. parallel.

o /

3400

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

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

4^^to

44

45

46

47

48

49

50

51

52

53

54

55

56

67

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

2.021

.020

.020

.019

.019

.019

.018

.018

.017

.017

2.017 

.016

.016

.015

.015

.015

.014

.014

.013

.013

2.013

.012

.012

.011

.011

.011

.010

.010

.009

.009

2.009

.008

.008

.007

.007

.007

.006

.006

.005

.005

2.005

.004

.004

firyt ,UUO

.003

.003

.002

.002

.001

.001

2.001

.000

.000

1.999

.999

.999

.998

.998

.997

.997

1.997

2' longitude.

Inches.

4.041

.041

.040

.039

.038

.037

.037

.036

.035

.034

4.033 

.033

.032

.031

.030

.029

.029

.028

.027

.026

4.025

.025

.024

.023

.022

.021

.021

.020

.019

.018

4.017

.017

.016

.015

.014

.013

.013

.012

.011

.010

4.009

.009

.008

(MV7 .UUl

.006

.005

.005

.004

.003

.002

4.001

.001

.000

3.999

.998

.997

.997

.996

.995

.994

3.993

3' longitude.

Inches.

6.062

.061

.060

.058

.057

.056

.055

.054

.052

.051

6.050 

.049

.048

.046

.045

.044

.043

.042

.040

.039

6.038

.037

.036

.034

.033

.032

.031

.030

.028

.027

6.026

.025

.024

.022

.021

.020

.019

.018

.016

.015

6.014

.013

.012 

.010

.009

.008

.007

.006

.004

.003

6.002

.001

.000

5.998

.997

.996

.995

.994

.992

.991

5.990

4' longitude.

Inches.

8.083

.081

.080

.078

.076

.075

.073

.072

.070

.068

8.067 

.065

.064

.062

.OGO

.059

.057

.056

.054

.052

8.051

.049

.048

.046

.044

 .043

.041

.040

.038

.036

8.035

.033

.032

.030

.028

.027

.025

.024

.022

.020

8.019

.017

.016

.014 

.012

.011

.009

.008

.006

.004

8.003

.001

.000

7.998

.996

.'995

.993

.992

.990

.988

7.987

5' longitude.

Inches.

10.103

.101

.099

.097

.095

.093

.091

.089

.087

.085

10.083 

. .081

.079

.077

.075

.073

.071

.069

.067

.066

10.063

.061

.059

.057

.055

.053

.051

.049

.047

.045

10.043

.041

.039

.037

.035

.033

.031

.029

.027

.025

10.023

.021

.019

.017 

.015

.013

.011

.009

.007

.005

10.003 °

.001

9.999

.997

.995

.993

.991

.989

'.987

.985

9.983

6' longitude.

Inches.

12.124

.122

.119

.117

.115

.112

.110

.107

.105

.103

12.100 

.098

.095

.093

.091

.088

.086

.083

.081

.079

12.076

.074

.071

.009

.067

.064

.062

.059

.057

.055

12.052

.050

.047

.045

.043

.040

.038

.035

.033

.031

12.028

.026

.023

021 !oi9

.016

.014

.011

.009

.007

12.004

.002

11.999

.997

.995

.992

.990

.987

.985

.983

11.980

7' longitude.

Inches.

14.145

.142

.139

.136

.134

.131

.128

.125

.122

.120

14.117 

.114

.111

.108

.106

.103

.100

.097

.094

.092

14.089

.086

.083

.080

.078

.075

.072

.009

.066

.064

14.061

.058

.055

.052

.050

.047

.044

.041

.038

.036

14.033

.030

.027

024 

!022

.019

.016

.013

.010

.008

14.005

.002

13.999

.996

.994

.991

.988

.985

.982

.980

13.977

8' longitude.

Inches.

16.16C

.162

.159

.156

.153

.150

.146

.143

.140

.137

16.134 

.130

.127

.124

.121

.118

.114

.111

.108

.105

16.102

.098

.095

.092

.089

.086

.082

.079

.076

.073

16.070

.066

.063

.060

.057

.054

'050

.047

.044

.041

16.038

.034

.031

flOQ .UZo

.025

.022

.018

.015

.012

.009

16.006

.002

15.999

.996

.993

.990

.986'

.983

.980

.977

15.974

9' longitude.

Inches.

18.186

.183

.179

.175

.172

.168

 .165

.161

.157

.154

18.150 

.147

.143

.139

.136

.132

.129

.125

.121

.118

18.114

.111

.107

.103

.100

.096

.093.

.089

.085

.082

18.078

.075

.071

.067

.064

.060

.057

.053

.049

.046

18.042

.039

.035

031 

'.028

.024

.021

.017

.013

.010

18.006

.003

17.999

.995

.992

.988

.985

.981

.977

.974

17.970

10' longitude.

Inches.

20.207

.203

.199

.195

.191

.187

.183

.179

.175

.171

20.167 

.163

.159

.155

.151

.147

.143

.139

.135

.131

20.127

.123

.119

.115

.111

.107

.103

.099

.095

.091

20.087

.083

.079

.075

.071

.067

.063

.059

.055

.051

20.047

.043

.039

/\oc .UOO

.031

.027

.023

.019

.015

.011

20.007

.003

19.999

.995

.991

.987

.983

.979

.975

.971

19.967

II Longitude 

interval.

i

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.001

.003

.004

.006

.008

.010

.013

.016

If« c

II

i

1

2

3

4

5

6

7

8

9

10

73 .2

O to 

o 3

11

«a a*3

Inches.

2.426

4.852

7.279

9.705

12.131

14.557

16.983

19.410

21.836

24.262

(393)
FORMULAS AND TABLES. [BULL. 50.

TABLE XI. Co-ordinates for projection of maps. Scale -^^w. 

[Derivation of table explained ia section (5); use of table explained on page 22.]

Latitude of

parallel.

0 /

3500

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

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

44

45

46

47

 48

49

. 60

61

52

53

64

55

56

57

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.997

.996

.996

.995

.995

.995

.994

.994

.993

.993

1.993 

.992

.992

.991

.991

.991

.990

.990

.989

.989

1.988

.988

.988

.987

.987

.986

.986

.986

.985

.985

1.984

.984

.984

.983

.983

.982

.982

.982

.981

.981

1.980

.980

.980

- .y Q7Qi y 

.979

.978

.978

.977

.977

.977

1.976

.976

.975

.975

.975

.974

.974

.973

.973

.973

1.972

2' longitude.

Inches.

3.993

.993

.992

.991

.990

.989

.989

.988

.987

.986

3.985 

.984

.984

.983

.982

.981

.980

.980

.979

.978

3.977

.976

.975

.975

.974

.973

.972

.971

.971

. .970

3.969'

.968

.967

.966

.966

.965

.964

.963

.962

.962

3.961

.960

.959

QKQ .y jo 

.957

.957

.956

.955

.954

.953

3.953

.952

.951

.950

.949

.948

.948

.947

.946

.945

3.944

3' longitude.

Inches.

5.990

.989

.988

.986

.985

.984

.983

.981

.980

.979

5.978 

.977

.975

.974

.973

.972

.971

.969

.968

.967

5.965

.964

.963

.902

.961

.959

.958

.957

.956

.955

5.953

.952

.951

.950

.948

.947

.946

.945

.944

.942

5.941

.940

.939

007

. yo i 

.936

.935

.934

.932

.931

.930

5.929

.928

.926

.925

.924

.923

.92%-'

.920

.919

.918

5.917

4' longitude.

Inches.

7.987

.985

.984

.982

.980

.979

.977

.975

.974

.972

7.970 

,969

.967

.966

.964

.962

.961

.959

.958

.956

7.954

.952

.951

.949

.948

.946

.9-14

.943

.941

.940

7.938

.936

.934

.933

' .931

.930

.928

.926

.926

.923

7.922

.920

.918 

.916

.915

.913

' .912

.910

.908

.907

7.905

.904

.902

.900

.899

.897

.895

.894

.892

.890

7.889

5' longitude.

Inches.

9.983

.981

.979

.977

.975

.973

.971

.969

.967

.905

9.963 

.961

.959

.957

.955

.953

.951

.949

.947

.944

9.942

.940

.938

.936

.934

.932

.930

.928

.926

.924

9.922

.920

.918

.916

.914

.912

.910

.908

.906

.904

9.902

.900

.898 

.895

!893

.891

.889

.887

.885

.883

9.881

.879

.877

.875

.873

.871

.869

.867

.865

.863

9.861

6' longitude.

Inches.

11.980

.978

.975

.973

.971

.908

' .966

.963

.960

.958

11.956 

.953

.951

.948

.946

.944

.941

.939

.936

.933

11.931

.929

.926

.924

.921

.919

.917

.914

.912

.909

11.907

.904

.902

.899

.897

.894

.892

.890

.887

.885

11.882

.880

.878 

.875

.872

.870

' .867

.865

.863

.800

11.858

.855

.853

.851

.848

.845

.843

.840

.838

.836

11.833

7' longitude.

Inches.

13.977

.974-

.971

.908

.900

.903

.900

.957

.954

.951

13.948 

.945

.943

.940

.937

.934

.931

.929

.926

.922

13.919

.917

.914

.911

.908

.905

.903

.900

.897

.894

13.891

.888

.885

.882

.880

.877

.874

.871

.868

.860

13.863

.860

.857

.854 

!851

.848

.845

.842

.840

.837

13.834°

.831

.828

.826

.823

.819

.817

.814

.811

.808

13.805

8' longitude.

Inches.

15.974

.970

.907

.904

.961

.958

.954

.950

.947

.944

15.941 

.938

.934

.931

.928

.925

.922

.918

.915

.911

15.908

.905

.902

.898

.895

.892

.889

.886

.882

.879

15.876

.872

.869

.866

.862

.859

.856

.853

.850

.846

15.843

.840

.837

QQQ .OOO

.830

.826

.823

.820

.817

.814

15.810

.807

.804

.801

, .798

 .794

.790

.787

.784

.781

15.778

9' longitude.

Inches.

17.970

.907

.963

.959

.956

.952

.949

.944

.941

.937

.930

.926

.923

.919

.915

.912

.908

.905

.900

17.896

.893

.889

.886

.882

.878

.875

.871

.868

.864

17.860

.856

.852

.849

.845

.842

OPS .000

.834

.831

.827

17.824

.820

.816

.01.4 Q1O

.808

.805

.801

.797

. .794

.790

17.787

.783

.779

.776

.772

.768

.764

.761

.757

.753

17.750

10' longitude.

Inches.

19.967

.963

.959

.955

.951

.947

.943

.938

.934

.930

19.926 

.922

.918

.914

.910

 .906

.902

.898

.894

.889

19.885

.881

.877

.873

.869

.865

.861

.857

.853

.849

19.845

.840

.830

.832

.828

.824

.820

.816

.812

.808

19.804

.800

.796

.787

.783

.779

.775

.771

.767

19.763

.759

.755

.751

.747

.742

.738

.734

.730

.726

19.722

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Indies.

0.000

.001

.001

.003

.004

.006

.008

.011

.013

.017

 §"3

'-£ o

p-1 

'^rt

/

1

2

3

4

5

6

7

8

9

10

a =3

o o

II3.2 S"0

Inches.

t

2.427

4.853

7.280

9.706

12.133

14.560

16.986

19.413

21.839

24.266

(394)
WOODWABD.] MAP CO-ORDINATES. 89

TABLE XI. Co-ordinates for projection of maps. Scale

[Derivation of table explained iii section (5); use of table explained on page 22.]

of Latitude 

parallel.

o /

3600

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

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

66

57

68

59

60

Abscissas of developed parallel.

1' longitude.

Indies.

1.972

.972

.971

.971

.971

.970

.970

.969

.969

.968

1.968

.968

.967

.967

.960

.966

.065

.965

.905

.904

1.964

.963

.963

.903

.902

.962

.901.

.901

.000

.000

1.960

.959

.959

.958

.958

.957

.057

.057

.956

.956

1.955

.955

.955

.954

.954

.953

.953

.952

.952

.952

1.951

.951

.950

.950

.950

.949

.949

.948

.948

.947

1.947

2' longitude.

Inches.

3.944

.944

.943

.942

.941

.940

.939

.939

.938

.937

3.936

.935

.934

.934

.933

.932

.931

.930

.929

.929

3.928

.927

.926

.925

.924

.923

.923

.922

1 .921

.920

3.919

.918

.918

.917

.916

.915

.914

.913

.913

.912

3.911

.910

.909

.908

.908

.907

.906

.905

.904

.903

3.902

.902

.901

-.900

.899

.898

.897

.897

.896

.895

3.894

3' longitude.

Inches.

5.917

.915

.914

.013

.912

.910

.909

.908

.907

.905

5.904

.903

.902

.900

.899

.898

.896

.895

.894

.893

5.891

.890

.889

.888

'.887

.885

.884

.883

.881

.880

6.879.

.878

.876

.875

.874

.872

.871

.870

.869

.868

5.866

.865

.864

.863

.801

.800

.859

.857

.856

.855

5.854

.852

.851

.850

.849

.847

.846

.845

.844

.842

6.841

4' longitude.

Inches.

7.889

.887

.886

.884

 .882

.880

.879

.877

.876

.874

7.872

.870

.869

.867

.806

.864

.862

.860

.859

.857

7.855

.854

.852

.850

.849

.847

.845

.844

.842

.840

7.838

.837

.835

.834

.832

.830

.828

.827

.825

.824

7.822

.820

.81.8

.817

.815

.813

.812

.810

.808

.807

7.805

.803

.802

.800

.798

.796

.795

.793

.702

.790

7.788

5' longitude.

Inches.

9.861

.850

.857

.855

.853

.850

.848

.846

.844

.842

0.840

.838

.836

.834

.832

.820

.827

.825

.823

.821

9.819

.817

.815

.813

.811

.808

.806

.804

.802

.800

9.798

.796

.794

.792

.790

.787

.785

.783

.781

.779

9.777

.775

.773

.771

.709

.766

.764

.762

.760

.758

9.756

.754

.752

.750

.748

.745

.743

.741

.739

.737

9.735

6' longitude.

Inches.

11.833

.831

.828

' .826

.824

.821

.818

.816

.813

.811

11.808

.806

.803

.801

.798

.795

.79:i

.701

.788

.786

11.783

.780

.778

.776

.773

.770

.768

.765

.703

.761

11.758

.755

.753

.750

.748

.745

.743

.740

.738

.735

11.732

.730

.728

.725

.723

.720

.717

.715

.713

.710

11.707

.705

.702

.700

.608

.695

.692

.690

.687

.685

11.682

7' longitude.

Inches.

13.805

.803

.800

.797

.794

.791

.788

.785

.782

.779

13.770

.773

.770

.70S

.765

.701

.758

.756

.753

. .750

13.747

.744

.741

.738

.735

.732

.729

.720

.723

.721

13.7 L7

.71.4

.712

.709

.700

.702

.700

.697

.694

.691

13.688

.685

.682

.679

.677

.673

.670

.667

.665

.662

13.658

.656

.653

.650

.647

.644

.641

.638

.635

.632

13.629

8' longitude.

Indies.

15.778

.774

.771

.768

.765

.701

.758

.754

.751

.748

15.744

.741.

.7;is

.734

.731

.727

.724

.721

.718

.714

15.710

.707

.704

.701

.098

.094

.690

.687

.684

.681

15.677

.674

.670

.667

.664

.660

.657

.654

.650

.647

15.643

.640

.637

.634

.630

.626

.623

.620

.617

.614

15.610

.606

.603

.600

.597

.593

.590

.586

.583

.580

15.576

9' longitude.

Inches.

17.750

.746

.743

.739

.735

.731

.727

.724

.720

.710

17.712

.708

.705

.701

.098

.093

.689

.686

.682

.679

17.674

.671

.667

.663

.6CO

.655

.652

.648

.644

.641

17.636

.633

.629

.626

.622

.617

.614

.610

.607

.603

17.599

.595

.591

.588

.584

.580

.576

.572

.569

.565

17.561

.557

.554

.550

.546

.542

.538

.535

.531

.527

17.523

10' longitude.

Indies.

19.722

.718

.714

.710

.706

.701

.097

.693

.689

.685

19.080

.676

.672

.668

.604

.659

.655

.651

.047

.613

19.638

.634

.630

.626

.022

.617

.613

.609

.605

.601

19.596

.592

.588

.584

.580

.575

.571

.567

.563

.559

19.554

.550

.540

.542

.538

.533

.529

.525

.521

.517

19.512

.508

.504

.500

.496

.491

.487

.483

.479

.475

19.470

II Longitude 

interval.

i

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Indies.

0.000

.001

.002

.003

.004

.006

.008

.011

.014

.017

a >

** £

1-4.5

i

1

2

3

4

5

6

7

8

9

10

"3 oi

O ^

 r *3

Si'5 &

Inches.

2.427

4.854

7.281

9.708

12.134

14.561

16.988

19.415

21.842

 24.269

(395)
90 FORMULAS AND TABLES. [BULL. 50.

TABLE XI. Co-ordinates for projection of maps. Scale Tjrfar<r» 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

3700

01

02

03

04

05

06

07

08

09

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

53

54

55

56

57

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.947

.947

.946

.946

.945

.945

.944

.944

.943

.943

1.943

.942

.942

.941

.941

.940

.940

.940

.939

.939

1.938

.938

.937

.937

.937

.936

.936

.935

.935

.934

1.934

.934

.933

.933

.932

.932

.931

.931

.931

.930

1.930

.929

.929

QOQ .U4O

.928

.928

.927

.927

.926

.926

1.925

.925

.925

.924

.924

.923

.923

.922

.922

.921

1.921

2' longitude.

Inches.

3.894

.893

.892

.891

.891

.890

.889

.888

.887

.886

3.885 

.884

.884

.883

.882

.881

.880

.879

.878

.878

3.877

.876

.875

.874

.873

.872

.871'

.871

.870

.869

3.868

.867

.866

.866

.865

.864

.863

.862

.861

.860

3.860

.859

.858

.857 

.856

.855

.854

.853

.853

.852

3.851

.850

.849

.848

.847

.847

.846

.845

.844

.843

3.842

3' longitude.

Inches.

5.841

.840

.838

.837

.836

.834

.833

.832

.830

.829

5.828 

.827

.825

.824

.823

.821

.820

.819

.818

.816

5.815

.814

.812

.811

.810

.809

.807

.806

.805

.803

5.802

.801

.800

.708

.797

.796

.794

.793

.792

.791

5.789

.788

.787

!784

.783

.782

.780

.779

.778

5.776

.775

.774

.772

.771

.770

.768

.767

.766

.764

5.763

4' longitude.

Inches.

7.788

.786

.784

.783

.781

.779

.778

.776

.774

.772

7.771 

.769

.767

.766

.764

.762

.760

.768

.757

.755

7.753

.752

.750

.748

.746

.745

.743

.741

.740

.738

7.736

.735

.733

.731

.730

.728

.726

.724

.722

.721

7.719

.717

.716

.714

.712

.710

.709

.707

.705

.704

7.702

.700

.698

.696

.695

.693

.691

.690

.688

.686

7.684

5' longitude.

Inches.

9.735

.733

.730

.728

.726

.724

.722

.720

. .717

.715

9.713 

.711

. .709

.707

.704

.702

.700

.698

.696

.694

9.691

.689

.687

.685

.683

.681

.678

.676

.674

.672

9.670

.668

.666

.664

.662

.659

.657

.655

.653

.651

9.649

.646

.644

642

less

.636

.633

.631

.629

9.627

.625

.623

.620

.618

.616

.614

.612

.610

.607

9.605

6' longitude.

Inches.

11.682

.680

.677

.674

.672

.669

.666

.664

.661

.659

11.656 

.653

.051

.048

.645

.043

.641

.038

.635

.033

11.630

.627

.625

.622

.620

.617

.614

.612

.609

.606

11.604

' .602

.599

.597

.594

.591

.589

.587

.584

.581

11.579

.576

.573

.571 

.568

.566

.563

.560

.558

.555

11.552

.550

.548

.545

.542

.540

.537

.534

.532

.529

Il.o27

7' longitude.

Inches.

13.629

.626

.623

.620

.617

.614

.611

.608

.604

.602

13.599 

.595

.593

.590

.586

.583

.581

.577

.574

.572

13.668

.565

.562

.559

.556

.553

.550

.547

.544

.541

J3.538

.536

.532

.530

.527

.523

.520

.518

.514

.511

13.509

.505

.502

.499 

.496

.493

.490

.487

.484

.481

13.478

.475

.472

.469

.466

.463

.460

.457

.454

.450

13.448

8' longitude.

Inches.

15.576

.573

.569

.566

.562

.658

.555

.552

.548

. .545

15.542 

.538

.534

.531

.527

.524

.521

.517

.514

.510

15.506

.503

.500

.496

.493

.490

.486

.482

.479

.475

15.472

.470

.466

.462

.459

.455

.452

.449

.445

.442

15.438

.434

.431

.428 

.424

.421

.418

.414

.410

.407

15.403

.400

.397

.393

.390

.386

.382

.379

.376

.372

15.369

9' longitude.

Inches.

17.523

.519

.515

.511

.508

.603

.500

.496

.491

.488

17.484 

.450

.476

.473

.468

.464

.461

.456

. .453

.449

17.445

.441

.437

.433

.429

.426

.421

.418

.414

.410

17.406

.403

.399

.395

.392

.387

.383

.380

.375

.372

17.368

.364

.360

.356 

.352

.348

.345

.340

.337

.333

17.329

.325

.321

.317

.313

.310

.305

. .302

.298

.293

17.290

10' longitude.

Inches.

19.470

.466

.401

.457

.453

.448

.444

.440

.435

.431

19.427 

.422

.418

.414

.409

.405

.401

.396

.392

.388

19.383

.379

.375

.370

.366

.362

.357

.353

.349

.344

19.340

.337

.332

.328

.324

.319

.315

.311

.366

.302

19.298

.293

.2£9

Ot K

.41 U

.280

.270

.272

.267

.263

.259

19.254

.250

.246

.241

.237

.233

.228

.224

.220

.215

19.211

Longitude interval.

i

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.002

.003

.004

.006

.008

.011

.014

.017

« '

' S v

& 

'

1

2

3

4

6

6

7

8

9

10

Is

a!

S.9

3

Inches.

2.427

4.855

7.282

9.709

12.136

14.564

16.991

19.418

21.846

24.273

(396)
 WOODWAED.] MAP CO-ORDINATES. 91

TABLE XI. Co-ordinates for projection of maps. Scale -

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

3800

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

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

Abscissas of developed parallel.

1' longitude.

Inches.

1.921

.921

.920

.920

.919

.919

.918

.918

.918

.917

1.917 

.916

.916

.915

.915

.915

.914

.914

.913

.913

1.912

.912

.911

.911

.911

.910

.910

.909

.909

.908

1.908

.908

.907

.907

.906

.906

.905

.905

.904

.904

1.904

.903

.903

!902

.901

.901

.900

.900

.900

1.899

.899

.898

.898

.897

.897

.897

.896

.896

.895

1.895

2' longitude.

Inches.

3.842

.841

.840

.840

.839

.838

.837

.836

.835

.834

3.834 

.833

.832

.831

.830

.829

.828

.827

.827

.826

3.825

.824

.823

.822

.821

.820

.819

.819

.818

.817

3.816

.815

.814

.813

.813

.812

.811

.810

.809

.808

3.807

.806

.805

!804

.803

.802

.801

.800

.799

3.798

.798

.797

.796

.795

.794

.793

.792

.792

.791

3.790

3' longitude.

Inezes.

5.763

.762

.761

.759

.758

.757

.755

.754

.753

.752

5.750 

.749

.748

.746

.745

.744

.743

.741

.740

.739

5.737

.736

.734

.733

.732

.731

.729

.728

.727

.725

5.724

.723

.721

.720

.719

.717

.716

.715

.713

.712

5.711

.710

.708 

.707

.705

.704

.703

.701

.700

.699

5.698

.696

.695

.694

.692

.691

.690

.689,

.687

.686

5.684

4' longitude.

Inches.

7.684

.683

.681

.679

.678

.676

.674

.672

.670

.669

7.667 

.665

.664

.662

.660

.658

.657

.655

.653

.652

7.650

.648

.646

.644

.642

.641

.639

.637

.636

.634

7.632

.630

.628

.627

.625

.623

.622

.620

.618

.616

7.615

.613

.611

609 

'.607

.606

.604

.602

.600

.599

7.597

.595

.594

.592

.590

.588

.586

.585

.583

.581

7.579

5' longitude.

Inches.

9.605

.603

.601

.599

.597

.594

.692

.590

.588

.586

9.584 

.581

.579

.677

.575

.673

.571

.568

.566

.564

9.562

.559

.557

.555

.653

.651

.548

.646

.644

.542

9.640

.538

.535

.533

.531

.529

.527

.625

.522

.520

9.618

.516

.513

.511 

.609

.607

.605

1 .502

.500

.498

9.496

.494

.492

.489

.487

.485

.483

.481

.479

.476

9.474

6' longitude.

Inches.

11.527

.524

.521

.519

.516

.513

.511

.509

.506

.603

11.501 

.498

.495

.493

.490

.488

.485

.482

.480'

.477

11.474

.471

.469

.466

.464

.461

.458

.456

.453

.450

11.448

.440

.443

.440

.438

.435

.432

.430

.427

.425

11.422

.419

.416

.414 

.411

.408

.406

.403

.401

.398

11.395

.393

.390

.387

.385

.383

.380

.377

.375

.372

11.369

7' longitude

Inches.

13.448

.445

.441

.439

.436

.432

.429

.427

.423

.420

13.418 

.414

.411

.408

.405

.402

.399

.396

.393

.390

13.387

.383

.380

.377

.374

.371

. .368

.365

.362

.359

13.356

.353

.350

.347

.344

.341

.338

.335

.331

.329

13.326

.322

.319

.316 

.313

.310

.307

.303

.301

.298

13.294

.292

.289

.285

.282

.280

.276

.273

.271

.267

13.264

8' longitude.

Inches.

15.369

.366

.362

.358

.355

.351

.348

.345

.341

.338

16.334 

.330

.327

.324

.320

.317

.314

.310

.306

.303

15.299

.295

.292

.288

.285

.282

.278

.274

.271

.267

15.264

.261

.257

.254

.260

.246

.243

.240

.236

.233

16.230

.226

.222

!214

.211

.208

.204

.201

.198

15.194

.190

.187

.183

.180

.177

.173

.170

.166

.162

15.158

9' longitude.

Inches.

17.290

.286

.282

.278

.275

.270

.266

.263

.258

.255

17.251 

.247

.243

.239

.235

.231

.228

.223

.220

.216

17.212

.207

.203

.199

.195

.192

.187

.184

.180

.176

17.172

.168

.164

.160

.157

.152

.149

.146

.140

.137

17.133

.129

.124

!l!6

.113

.109

.104

.101

.097

17.093

.089

.086

.081

.077

.074

.069

.066

.062

.058

17.053

IV longitude.

Inches.

19.211

.207

.202

.198

.194

j.189

.185

.181

.176

.172

19.168 

.163

.159

.155

' .150

.146

.142

.137

.133

.129

19.124

.119

.115

.110

.106

.102

.097

.093

.089

.084

19.080

.076

.071

.067

.063

.058

.054

.050

.045

.041

19.037

.032

.027 /y>o .V4O

.018

.014

.010

.005

.001

18.997

18.992

.988

.984

.979

.975

.971

.966

.962

.958

.953

18.948

1 Longitude 

interval.

/

1

2

3

4

6

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches,

0.000

.001

.002

.003

.004

.006

.008

.011

. .014

.017

 §"3

3 <Q * *-»

3.9

/

1

2

3

4

5

6

1

8

9

10

a S

11sf g"d

Inches.

2.428

4.855

7.283

9.711

12.138

14.566

16.994

19.422

21.849

24.277

(397)
92 FofclULAS AND TABLES. [BULL. 50.

TABLE XI. Co-ordinates for projection of maps. Scale ao fl u0 . 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

3900

01

02

03

04

05

06

07

08

09

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

86

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

63

64

55

56

57

68

69

60

Abscissas of developed parallel.

1' longitude.

Indies.

1.895

.894

.894

.893

.893

.893

.892

.892

.891

.891

1 QQA l.oyu 

.890

.889

.889

.888

.888

.888

.887

.887

.886

1.886

.885

.885

.884

.884

.884

.883

.883

.882

.882

1.881

.881

.880

.880

.879

.879

.879

.878

.878

.877

1.877

 .876

.876

.875

Qf7K .0 IO

.875

.874

.874

.873

.873

1.872

.872

.871

.871

 .870

.870

.870

.869

.869

.868

1.868

2' longitude.

Inches.

3.790

.789

.788

.787

.786

; 785

>

.784

.783

.782

.782

3.781 

.780

.779

.778

.777

.776

.775

.774

.773

.773

3.772

.771

.770

.769

.768

.767

.766

.765

.764

.764

3.763

.762

.761

.760

.759

.758

'.757

' .756

.755

.755

3.754

.753

.752

.751

.750

.749

.748

.747

.746

.746

3.745

.744

.743

.742

.741

.740

.739

.738

.J38

.737

3.736

3' longitude.

Inches.

5.684

.683

.682

.680

.679

.678

.676

.675

.674

.672

5.671 

.670

.668

.667

.665

.664

.663

.662

.660

.659

5.657

.656

.655

.653

.652

.651

.649

.648

.647

.645

6.644

.643

.641

.640

.638

.637

.636

.635

.633

.632

6.630

.629

.628

.620

COK

tO£i)

.624

.622

.621

.620

.618

5.617

.616

.614

, .613

.611

.610

.609

.608

.608

.605

6.603

4' longitude.

Inches.

7.579

.578

.570

.574

.572

.570

.568

.567

.565

.563

7.561 

.560

.558

.556

.554

.552

.550

.549

.547

.545

7.543

.542

.540

.538

.536

.534

.532

.631

.529

.527

7.525

.524

.522

.620

.518

.516

. .514

 .513

.511

.500

7.507

.506

.504

.502

.500

.498

.496

.495

.493

.491

7.489

.488

.486

.484

.482

.480

. .478

.477

.475

.473

7.471

5' longitude.

Inches.

9.474

.472

.469

.467

.405

.463

.460

.458

.456

.454

9.451 

.449

.447

.445

.442

.440

.438

.436

.433

.431

9.429

.427

.424

.422

.420

.418

.415

.413

 .411

.409

9.406

.404

.402

.400

.397

.395

.393

.391

.388

.386

9.384

.382

.379

.377

375 .'373

.370

.368

.366

.364

9.361

.359

.357

.355

.352

.350

.348

.346

.344

.341

9.339

6' longitude.

Inches.

11.369

.366

.393

.361

.358

.356

.353

.350

.347

.345

11.342 

.339

.336

.334

.331

.329

.326

.323

.320

.318

11.315

.312

.309

.307

.304

.302

.299

.296

.293

.291

11.288

.285

.282

.280

.277

.275

.272

.269

.200

.264

11.201

.258

.255

.253

OCA ,£.O\J

.248

.245

.242

.239

.237

11.234

.231

.228

.226

.223

.221

.218

.215

.213

.210

11.207

7' longitude.

Inches.

13.264

.261

.257

.254

.251

.248

.245

.242

.238

.236

13.232 

.229

.226

.223

.219

.217

.213

.210

.207

.204

13.201

.198

.194

.191

.188

.185

.182

.179

.175

.173

13.109

.166

.163

.160

.156

.154

.150

.147

.144

.141

13.138

.135

.131

.128

.125

.122

.119

.116

.112

.110

13.106

.103

.100

.097

.093

.091

.087

.084

.082

.078

13.075

 8' longitude.

Inches.

15.158

.155

.151

.148

.144

.141

.137

.134

.130

.126

15.122 

.119

.115

.112

.108

.105

.101

.098

.094

.090

15.086

.083

.079

.076

.072

.069

.065

.062

.058

.054

15.050

.047

.043

.040

.036

.033

.029

.020

.022

.018

15.014

.011

.007

.004

.000

14.997

.993

.990

.986

.982

14.978

.975

.971

.968

.964

.961

.957

.954

.950

.946

14.942

9' longitude.

Inches.

17.053

.050

.045

.041

.037

.033

.029

.025

.021

.017

17.013 

.009

.005

.001

16.996

.993

.988

.985

' .980

.977

16.972

.969

.964

.960

.956

.952

.948

.944

.940

.936

16.932

.928

.924

.920

.915

.912

.907

.004

.899

.896

16.891

.888

.883

.879

.875

.871

.867

.863

.859

.855

16.851

.847

.843

.839

.834

.831

.826

.823

.819

.815

16.810

10' longitude.

Inches.

18.948

.944

.939

.935

.930

.926

.921

.917

.912

.908

18.903 

.899

.894

.890

.885

.881

.876

.872

.867

.863

18.858

.854

.849

.845

.840

.836

.831

.827

.822

.818

18.813

.809

.804

.800

.795

.791

.786

.782

.777

.773

18.768

.764

.759

.755

750

!?46

.741

.737

.732

.728

18.723

.719

.714

.710

.705

.701

.696

.692

.688

.683

18.678

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.002

.003

.004

.006

.008

.011

.014

.017

o '

 O cS 

3 >

 *J fcH

1s~S

3-2

/

1

2

3

4

5

6

7

8

9

10

"3 m

11 5 S

1-2

g 

Inches.

2.428

4.856

7.284

9.712

12.140

14.509

16.997

19.425

21.853

24.281

(398)
WOODWARD.] MAP CO-ORDINATES.

TABLE XI. Co-ordinates for projection of maps. Sea 'e ^innr-

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

4000

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

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

Abscissas of developed parallel.

1' longitude.

Incites.

1.868

.867

.867

.866

.866

.866

.865

.865

.864

.864

1.863

.863

.862

.862

.861

.861

.860

.860

.860

.859

1.859

.858

.858

.857

.857

.856

.856

.855

.855

.855

1.854

.854

.853

.853

.852

.852

.851

.851

.850

.850

1.849

.849

.849

QAQ

 O4O

.848

.847

.847

.846

.846

.845

1.845

.844

.844

.844

.843

.843

.842

.842

.841

.841

1.840

2' longitude.

Inches.

3.736

.735

.734

.733

.732

.731

.730

.729

.728

.728

3.727

.726

.725

.724

.723

.722

.721

.720

.719

.718

3.717

.717

.710

.715

.714

.713

.712

.711

.710

.709

3.708

.707

.706

.706

.705

.704

.703

.702

.701

.700

3.699

.698

.697

.696 

.695

.095

.694

.693

.692

.691

3.690

.689

.688

.687

.686

.685

.684

.684

.683

.682

3.681

3' longitude.

Inches.

5.603

.602

.601

 .599

.598

.597

.595

.594

.593

.591

5.690

.588

.587

.586

.584

.583

.581

.580

.579

.578

5.576

.575

.573

.572

.570

.569

.568

.506

.565

.564

6.562

.561

.560

.558

.557

.555

.554

.553

.551

.550

5.548-

.547

.546

545 

!543

.542

.540

.53!)

.537

.536

5.535

.533

.532

.531

.529

.528

.527

.525

.524

.522

5.521

4' longitude.

Inches.

7.471

.470

.468

.466

.464

.462

.460

.459

.457

.455

7.453

.451

.449

.448

.446

.444

.442

.440

.438

.437

7.435

.433

.431

.429

.427

.420

.424

.422

.420

.418

7.416

.415

.413

.411

.409

.407

.405

.404

.402

.400

7.398

.396

.394

.393 

.391

.389

.387

.385

.383

.382

7.380

.378

.376

.374

.372

.371

.369

.367

.365

.363

7.361

5' longitude.

Indies.

9.339

.337

.334

.332

.330

.328

.325

.323

.321

.319

9.316

.314

.311

.309

.307

.305

.302

.300

.298

.296

9.293

'.291

.289

.286

.284

.282

.279

.277

.275

.273

9.270

.268

.266

.264

.261

.259

.256

.254

.252

.250

9.247

.245

.243

.241 

.238

.236

.234

.231

.229

.227

9.224

.222

.220

.218

.215

.213

.211

.209

.206

.204

9.201

6' longitude.

Indies.

11.207

.204

.201

.199

.196

.194

.191

.188

.185

.183

11.180

.177

.174

.171

.168

.166

.163

.161

.158

.155

11.152

.150

.147

.144

.141

.138

.135

.133

.130

.128

11.125

.122

.119

.117

.114

.111

.108

.105

.102

.100

11.097

.095

.092

.089 

.086

.084

.081

.078

.075

.072

11.069

.067

.064

.062

.059

.056

.053

.051

.048

.045

11.042

7' longitude.

Inches.

13.075

.072

.068

.065

.062

.059

.056

.053

.049

.047

13.043

.040

.036

.033

.030

.027

.023

.021

.017

.014

13.011

.008

.005

.001

12.998

.995

.991

.988

.985

.982

12.979

.976

.972

.970

.966

.963

.959

.956

.953

.950

12.946

.944

.940

.'934

.931

.928

.924

.921

.918

12.914

.911

.908

.905

.902

.899

.895

.893

.889

.886

12.882

8' longitude.

Inches.

14.942

.939

.935

.932

.928

.925

.921

.918

.914

.910

14.906

.902

.898

.895

.891

.888

.884

.881

.877

.874

14.870

.806

.862

.858

.854

.851

.847

.844

MO

.837

14.833

.830

.826

.822

.818

.814

.810

.807

.803

.800

14.796

.793

.789

.786 

.782

.778

.774

.770

.766

. .763

14.759

.756

.752

.749

.745

.742

.738

.734

.730

.726

14.722

9' longitude.

Inches.

16.810

.807

.802

.798

.794

.790

.786

.7^2

.778

.774

16.770

 .765

.761

.757

.753

.749

.744

.741

.736

.733

16.728

.725

.720

.716

.711

.708

.703

.699

.695

.691

16.687

.683

.679

.675

.671

.666

.662

.658

.654

.650

16.645

.642

.637

G34:

!e26

.621

.6*7

.612

.609

16.604

.600

.596

.592

.588

.584

.580

.576

.572

.567

16.563

W longitude.

Inches.

18.678

.674

.669

.665

.660

.656

.651

 .647

.642

.638

18.633

.628

.023

.019

.614

.610

.005

.601

.596

.592

18.587

.583

.578

.573

.568

.564

.559

.555

.550

.546

18.541

.537

.532

.528

.523

.518

.513

.509

.504

.500

18.495

.491

.486

!477

.473

.468

.463

.458

.454

18.449

.445

.440

.436

.431

.427

.422

.418

.413

.408

18.403

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.002

.003

.004

.006

.009

.011

.014

.017

J|

3.1

'

i

2

3

4

5

6

7

8

9

10

a o

.0 0

"3

o.2 f^"13

Inches.

2.429

4.857

7.286

9.714

12.143

14.572

17.000

19.429

21.857

24,280

(399)
94 FORMULAS AND TABLES. [BULL. 50.

TABLE XL Co-ordinates for projection of maps. Scale

[Derivation of table explained in section (5) ; use of table explained on page 22.]

Latitude of

parallel.

o /

4100

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

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

44

45

46

47

48

49

50

61

52

63

64

65

66

57

68

69

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.840

.840

.839

.839

.838

.838

.837

.837

.837

.836

1.836 

.835

.835

.834

.834

.833

.833

.832

.832

.831

1.831

.830

.830

.830

.829

.829

.828

.828

.827

.827

1.826

.826

.825

.825

.824

.824

.823

.823

.822

.822

1.821

.821

.821

QQA

 0&0

.820

.819

.819

.818

.818

.817

1.817

.816

.816

.815

. .815

.814

.814

.814

.813

.813

1.812

2' longitude.

Inches.

3.681

.680

.679

.678

.677

.676

.675

.674

.673

.672

3.671 

.670

.669

.668

.668

.667

.666

.665

.664

.663

3.662

.661

.660

.659

.658

.657

.656

.655

.654

.654

3.653

.652

.651

.650

.649

.648

.647

.646

.645

.644

3.643

.642

.641

!639

.638

.637

.637

.636

.635

3.634

.633

.632

.631

.630

.629

.628

.627

.626

.625

3.624

3' longitude.

Inches.

5.521

.519

.518

.517

.515

.514

.512

.511

.510

.508

5.507 

.5^6

.504

. .503

.501

.500

.498

.497

.496

.494

6.493

.491

.490

.489

.487

.486

.485

.483

.482

.480

5.479

.477

.476

.474

.473

.472

.470

.469

.467

.466

5.464

.463

.462

!459

.458

.456

.455

.453

.452

5.451

.449

,448

.446

.445

.443

.442

.441

.439

.438

5.437

4' longitude.

Inches.

7.361

.359

.358

.356

.354

.352

.350

.348

.346

.344

7.342 

.341

;339

.337

.335

.333

.331

.330

.328

.326

7.324

.322

.320

.318

.316

.314

.313

.311

.309

0 .307

7.305

.303

.301

.299

.297

.296

.294-

.292

.290

.288

7.286

.284

.282

!279

.277

.275

.273

.271

.269

7.268

.266

.264

.262

.260

.258

.256

.254

.252

.251

7.249

5' longitude.

. Inches.

9.201

.199

.197

.194

.192

.190

.187

.185

.183

.180

Q y.j, 17Qjo 

.176

.173

.171

.169

.166

.164

.162

.159

.157

9.155

.152

.150

.148

.145

.143

.141

.138

.136

.134

9.131

.129

.126

.124

.121

.119

.117

.114

.112

.110

9.107

.105

.103

.100 

.098

..096

.093

.091

.089

.086

9.084

.082

.079

.077

.075

.072

.070

.068

.065

.063

9.061

6' longitude.

Inches.

11.042

.039

.036

.033

.030

.028

.025

.022

.020

.017

11.014 

.011

.008

.005

.003

.000

10.997

.994

.991

.988

10.986

.983

.980

.978

.976

.972

.969

.966

.963

.961

10.958

.955

.952

.949

.946

.943

.940

.937

.935

.932

10.929

.927

.924

!918

.915

.912

.910

.907

.904

10.901

.898

.895

.893

.890

.887

.885

.882

.879

.876

10.873

7' longitude.

Inches.

12.882

.879

.876

.872

.869

.866

.862

.859

.856

.853

.846

.843

.839

.837

.833

.830

.827

.823

.820

12.817

.813

.810

.807

.804

.800

.797

.794

.790

.788

12.784

.781

.777

.774

.770

.767

.764

.760

.757

.754

12.750

.748

.744 

.741

.738

.734

.731

.728

.725

.721

12.718

.715

.711

.708

.705

.701

.699

.695

.692

.689

12.685

8' longitude.

Incites.

14.722

.718

.715

.711

.707

.704

.700

.696

.693

.689

14.685 

.682

.678

.674

.670

.666

.662

.659

.655

.651

14.648

.644

.640

.637

.633

.629

. .626

.622

.618

.614

14.610

.606

.602

..598

.594

.591

.587

.583

.580

.576

14.W2

.669

.565

.561 

.558

.554

.550

' .546

.542

.638

14.635

.531

.627

.624

.520

.616

.613

.509

.505

.502

14.498

9' longitude.

Inches.

16.663

.558

.555

.650

.546

.642

.537

.533

.529

.625

16.520 

.517

.512

.508

'.504

.600

.495

.492

.487

.483

16.479

.474

.470

.466

.462

.457

.454

.449

.445

.441

16.437

.432

.428

.423

.419

.415

.411

.406

.402

.398

16.393

.390

.385

.381 

.377

.373

.368

.365

.360

.356

16.352

.348

.343

.339

.335

.330

.327

.322

.318

.314

16.310

10' longitude.

Inches.

18.403

.398

.394

.389

.384

.380

.375

.370

.366

.361

18.356 

.352

.347

.342

.338

.333

.328

.324

.319

.314

18.310

.305

.300

.296

.291

.286

.282

.277

.272

.268

18.263

.258

.253

.248

.243

.239

.234

.229

.225

.220

18.215

.211

.206

!l97

.192

.187

.183

.178

.173

18.169

.164

.159

.155

.150

.145

.141

.136

.131

.127

18.122

Longitude interval.

i

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Incites.

0.000

.001

.002

.003

.004

.006

.009

.011

.014

.018

 § 3

£ 1

j S""

i

1

2

3

4

5

6

7

8

9

10

li11S .3 k-J-O

Inches.

2.429

4.858

7.287

9.716

12.145

14.574

17.003

19.432

21.861

24.290

(400)
WOODWARD.] MAP CO-ORDINATES. 95

TABLE XI. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallelr

o /

4200

01

02

03

04

05

06

07

08

09

10

11

12

IE

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

66

57

68

69

60

Abscissas of developed parallel.

1' longitude

Inches.

1.812

.812

.811

.811

.810

.810

.809

.809

.808

.808

1.807

.807

.806

.806

.805

.805

.805

.804

.804

.803

1.803

.802

.802

.801

.801

.800

.800

.799

.799

.798

1.798

.797

.797

.796

.796

.796

.795

.795

.794

.794

1.793

.793

.792

.792 

.791

.791

.790

.790

.789

.789

1.788

.788

.787

.787

.786

.786

.786

.785

.785

.784

1.784

2' longitude.

Inches.

3.624

.623

.622

.622

.621

.620

.619

.618

.617

.616

3.615

.614

.613

.612

.611

.610

.609

.608

.607

.606

3.605

.604

.603

.603

.602

.601

.600

.599

.598

.597

3.596

.595

.594

.593

.592

.591

.590

.589

.588

.587

3.586

.685

.684

.684 

.683

.682

.581

.680

.579

.678

3.677

.576

.675

.574

.673

.572

.671

.670

.669

.568

3.567

3' longitude.

Inches.

6.437

.435

.434

.432

.431

.429

.428

.427

.425

.424

6.422

.421

.419

.418

.416

.415

.414

.412

.411

.410

5.408

.407

.405

.404

.402

.401

.399

.398

.397

.395

5.394

.392

.391

.389

.388

.387

" .385

.384

.382

.381

5.380

.378

.377

.375 

.374

.372

.371

.369

.368

.367

5.365

.364

.362

.361

.359

.358

.357

.355

.354

.353

5.351

4' longitude

Inches.

7.249

.247

.245

.243

.241

.239

.237

'.236

.234

.232

7.230

.228

.226

.224

.222

.220

.218

.216

.214

.213

7.211

.209

.207

.205

.203

.201

.199

.198

.196

.194

7.192

.190

.188

.186

.184

.182

.180

.178

.176

.175

7.173

.171

.169

.167 

.165

.163

.161

.159

.158

.156

7.154

.152

.150

.148

.146

.144

.142

.140

.138

.137

7.134

6' longitude

Inches

9.061

.058

.056

.054

.051

.049

.046

.044

.042

.039

9.037

.035

.032

.030

.0.17

.025

.023

.020

.018

.016

9.013

.011

.008

.006

.004

.001

8.999

.997

.994

.992

8.989

.987

.985

.982

.980

.978

.975

.973

.970

.968

8.966

.963

.961

!956

.954

.951

.949

.947

.944

8.942

.940

.937

.935

.93.2

.930

.928

.925

.923

.921

8.918

6' longitude

Inches.

10.873

.870

.867

.865

.862

.869

.856

.853

.850

.847

. 10.844

.842

.839

.836

.833

.831

.828

.825

.822

.819

10.816

.813

.810

.808

.805

.802

.799

.796

.793

.790

10.787

.785

.782

.779

.776

.774

.771

.768

.765

.762

10.759

.756

.753

.751 

.748

.745

.742

.739

.736

.733

10.730

.728

.725

.722

.719

.717

.714

.711

.708

.705

10.702

7' longitude

Inches

12.685

.682

.678

.676

.672

.669

.666

.662

.659

.655

12.652

.649

.645

.642

.638

.636

.632

.629

.625

.622

12.619

.615

.612

.609

.606

.602

.599

.696

.592

.589

12.685

.582

.679

.675

.572

.569

.566

.662

.659

.656

12.552

.649

.545

.643 

.639

.636

.532

.629

.526

.522

12.619

.616

.612

.509

.505

 .503

.499

.496

.492

.489

12.485

8' longitude

Inches.

14.498

.494

.490

.486

.482

.478

.474

.471

.467

.463

14.459

.456

.452

.448

.444

.441

.437

.433

.429

.426

14.422

.418

.414

.410

.406

.402

.398

.395

.391

.387

14.383

.380

.376

.372

.368

.365

.361

.357

.353

.350

14.346

.342

.338

!330

.326

.322

.318

.315

.311

14.307

.304

.300

.296

.292

.289

.285

.281

.277

.274

14.269

9' longitude

Inches.

16.310

.305

.301

.297

.293

.288

.284

.280

.276

.271

16.267

.263

.258

.254

.249

.246

.241

.237

.232

.229

16.224

'.220

.215

.212

.207

.203

.198

.195

.190

.186

16.181

.177

.173

.168

:164

.160

.156

.151

.147

.143

16.139

.134

.130

.126 

.122

.117

.113

.108

.105

.100

16.096

.092

.087

 .083

.078

.076

.070

.066

.061

.058

16.052

10* Ion 

gitude

Inches.

18.122

.117

.112

.108

.103

.098

.093

.089

.084

.079

18.074

.070

.065

.060

.055

.051

.046

.041

.036

.032

18,027

.022

.017

.013

.008

.003

17.998

.994

.989

.984

17.979

.975

.970

.965

.960

.956

.951

.946

.941

.937

17.932

.927

.922

Q1Q .yio 

.913

.908

.903

.898

.894

.889

17.884

.880

.875

.870

.865

.861

.856

.851

.846

.842

17.836

1 Longitude 1interval. 

/

1

2

3

4

6

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.002

.003

.004

.OOfi

.009

.011

.014

.018

1-3

3 o " 'a

I

1

2

3

4

5

6

7

8

9

10

"3 m

V

"C +3

3.2 S"°

Inches.

2.429

4.859

7.288

9.718

12.147

14.576

17.006

19.435

21.865

24.294

(401)
96 FORMULAS AND TABLES. [BULL. 50.

TABLE XI. Co-ordinates for projection of maps. Scale -$

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

4300

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

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.784

.783

.783

.782

.782

.781

.781

.780

.780

.779

1.779

.778

. .778

.777

.777

.776

.776

.775

.775

.774

 1.774

.773

.773

.772

.772

.771

.771

.770

.770

.769

1.769

.768

.768

.767

.767

.766

.766

.765

.765

.764

1.764

.764

.763

.763 

.762

.762

.761

.761

.760

.760

1.759

.759

.758

.758

.757

.757

.756

.756

.755

.755

1.754

2' longitude.

Inches.

3.567

.566

.565

.564

.563

.562

.561

.560

.559

.558

3.557

.556

.556

.555

.554

.553

.552

.551

.550

.549

3.548

.547

.546 545

.544

.543

.542

.641

.540

.639

3.538

.537

.536

.535

.534

.533

.532

.531

.530

.629

3.528

.527

.526

!524

.523

.522

.521

.520

.519

3.518

.517

.516

.515

.514

.513

.612

.511

.510

.510

3.509

3' longitude.

Indies.

5.351

.349

.348

.346

.345

.344

.342

.341

.339

.338

5.336

.335

.333

.332

.330

.329

.327

.326

.324

.323

5.321

.320

.318

.317

.316

.314

.313

.311

.310

.308

5.307

.305

.304

.302

.301

.299

.298

.296

.295

.293

5.292

.291

.289

!286

.285

.283

.282

.280

.279

5.278

.276

.275

.273

.272

.270

.269

.267

.266

.264

5.263

4' longitude.

Inches.

7.134

.132

.130

.128

.126

.125

.123

.121

.119

.117

7.115

.113'

.111

.109

.107

.105

.103

.101

.099

.097

7.095

.093

.091

.090

.088

.086

.084

.082

.080

.078

7.076

.074

.072

.070

.068

.066

.064

.062

.060

.058

. 7.056

.054

.052

.050 

.048

.046

.044

\042

.040

.038

7.037

.035

.033

.031

.029

.027

.025

.023

.021

.019-

7.017

5' longitude.

Inches.

8.918

.915

.913

.910

.908

.906

.903

.901

.898

.896

8.893

.891

.889

.886

.884

.881

.879

.876

.874

.871

8.869

.866

.864

.862

.859

.857

.854

.852

.849

.847

8.844

.842

.840

.837

.835

.832

.830

.827

.825

.822

8.820

.818

.815

DID

.O-LO

.810

.808

.805

.803

.800

.798

8.796

.793

.791

.788

.786

.783

.781

.778

.776

.774

8.771

6' longitude.

Inches.

10.702

.699

.696

.693

.690

.687

.684

,681

.678

.675

10.672

.669

.667

.664

.661

.658

.655

.652

.649

.646

10.643

.640

.637

.634

.631

.628

 .625

.622

.619

.616

10.613

.610

.608

.605

.602

.599

.596

.593

.590

.587

10.584

.582

.579

.576 

.573

.570

.567

.564

.561

.558

10.555

.552

.549

.546

.543

.540

.537

.534

.531

.529

10.526

7' longitude.

Inches.

12.485

.482

.478

.475

.471

.468

.465

.461

.458

.454

12.451

.447

.445

.441

.438

.434

.431

.427

.424

.420

12.417

.413

.410

.407

.403

.400

.396

.393

.389

.386

12.382

.379

.376

.372

.369

.365

.362

.358

.355

.351

12.348

.345

.342

QQQ 

.OOO

.335

.331

.328

.324

.321

.317

12.314

.311

.307

.304

.300

.297

.293

.290

.286

.284

12.280

8' longitude.

Inches.

14.269

.265

.261

.257

.253

.250

.246

.242

.238

.234

14.230

.226

.222

.218

.214

.210

.206

.202

.198

.194

14.190

.186

.182

.179

.175

.171

.167

.163

.159

.155

14.151

.147

.144

.140

.136

.132

.128

.124

.120

.116

14.112

.109

.105

.101 

.097

.093

.089

.085

J081

.077

14.074

.070

.066

.062

.058

.054

.050

.046

.042

.038

14.034

9' longitude.

Inches.

16.052

.048

.043

.039

.034

.031

.026

.022

.017

.013

16.008

.004

.000

15.996

.991

.987

.982

.978

.973

.969

15.964

' .960

.955

.952

.947

.943

.938

.934

.929

.925

15.920

.916

.912

.907

.903

.898

.894

.889

.885

.880

15.876

.872

.868

QCQ .obo 

.859

.854

.850

.845

.841

.836

15.833

.828

.824

.819

.815

.810

.806

.801

.797

.793

15.789

10' longitude.

Inches.

17.836

.831

.826

.821

.816

.812

.807

.802

.797

.792

17.787

.782

.778

.773

.768

.763

.758

.753

.748

.743

17.738

.733

.728

.724

.719

.714

.709

.704

.699

.694

17.689

.684

.680

.675

.670

.665

 .660

.655

.650

.645

17.640

.636

.631

.626 

.621

.616

.611

.606

.601

.596

17.592

.587

.582

.577

.572

.567

" .562

.557

.552

.548

17.543

[1 Lofrgitude 

interval.

i

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.002

.003

.004

.006

.009

.011

.014

.018

 § is

pj S*

£ J>

H^-2

'

1

2

3

4

5

6

7

8

9

10

"3 DO d o> ° a

§ *

10 .3 g-O

Inches.

2.430

4.860

7.289

9.719

12.149

14.579

17.009

19.438

21.868

24.298

(402)
 WOODWARD.] MAP CO-ORDINATES. 97

TABLE XI. Co-ordinates for projection of maps. Scale jtfihny-

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

4400

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

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

AQttO

44

45

46

47

48

49

50

51

62

53

54

55

56

67

68

69

60

Abscissas of developed parallel.

l''longitude.

Inches.

1.754

.754

.753

.753

.752

.752

.751

.751

.750

.750

1.749

.749

.748

.748

.747

.747

.746

.746

.745

.745

1.744

.744

.743

.743

.742

.742

.741

.741

.740

.740

1.739

.739

.738

.738

.737

.737

.736

.736

.735

.735

1.734

.734

.733 700 loij

.732

.732

.731

ft.731

.730

.730

1.729

.729

.729

.728

.728

.727

.727

.726

.726

.725

1.725

2' longitude.

Inches.

3.509

.508

.507

.506

.505

.604

.503

.502

.601

.600

3.499

.498

.497

.496

.495

.494

.493

.492

.491

.490

3.489

.488

.487

.486

.485

.484

.483

.482

.481

.480

3.479

.478

.477

.476

.475

.474

.473

.472

.471

.470

3.469

.468

.467 

.466

.465

.464

.463

.462

.461

.460

3.459

.4f>8

.457

.456

.455

.454

.453

.452

.451

.480

3.449

3' longitude.

Inches.

6.263

.261

.260

.258

.257

.255

.254

.252

.251

.249

5.248

.247

.245

.244

.242

.241

.239

.238

.236

.235

5.233

.232

.230

.229

.227

.226

.224

.223

.221

.220

6.218

.217

.215

.214

.212

.211

.209

.208

.206

.205

5.203

.202

.200

.J.«Jl7 10Q

.197

.196

.194

.193

.191

.190

5.188

.187

.186

.184

.183

.181

.180

.178

.177

.175

5.174

4' longitude.

Inches.

7.017

.015

.013

.011

.009

.007

.005

.003

.001

' 6.999

6.997

.996

.994

.992

.990

.988

.986

.984

.982

.980

6.978

.976

.974

.972

.970

.968

.966

.964

.962

.960

6.958

.956

.954

.952

.950

.948

.946

.944

.942

.940

6.938

.936

.934

nqn ,yd£

.930

.928

.926

.924

.922

.920

6.918

.916

.914

.912

.910

.908

.906

.904

.902

.900

6.898

5' longitude.

Inches.

8.771

.769

.766

.764

.761

.759

.756

.754

.751

.749

8.746

.744

.742

.739

.737

.734

.732

.729

.727

.724

8.722

.719 .r.i

.714

.712

.709

.707

.704

.702

.699

8.697

.695

.692

.690

x>.687

'.685

.682

.680

.677

.675

8.672

.670

.667

.665 

.662

.660

.G57

.655

.652

.650

8.647

.645

.643

.640

.638

.635

.633

.630

.628

.625

8.623

6' longitude.

Inches.

10.526

.623

.520

.517

.514

.511

.608

.605

.502

.499

10.496

.493

.490

.487

.484

.481

.478

.475

.472

.469

10.466

.463

.460

.457

.464

.451

.448

.445

.442

.439

10.436

.434

.431

.428

.425

.422

.419

.416

.413

.410

10.407

.404

.401

QQQ tOUO

.395

.392

.389

.386

.383

.380

10.377

.375

.372

.369

.366

.363

>

.360

.357

.354

.351

10.348

V longitude.

Inches.

12.280

.277

.273

.270

.266

.263

.259

.256

.252

.249

12.245

.242

.239

.235

.232

.228

.225

.221

.218

.214

12.211

.207

.204

.200

.197

.193

.190

.186

.183

.179

12.176

.173

.169

.166

.162

.159

.155

.152

.148

.145

12.141

.138

.134

.127

.124

.120

.117

.113

.110

12.106

.104

.100

.097

.093

.090

.086

.083

.079

.076

12.072

8' longitude.

Inches.

14.034

.030

.026

.022

.018

.014

.010

.006

.002

13.998

13.994

.991

.987

.983

.979

.975

.971

.967

.963

.959

13.955

.951

.947

.943

.939

.935

.931

.927

.923

.919

13.916

.912

.908

.904

.900

.896

.892

.888

.884

.880

13.876

.872

.868

OCA

 ,o\rf

.860

.856

.852

.848

.844

.840

13.836

.833

.829

.825

.821

.817

.813

.809

.805

.801

13.797

9' longitude.

Inches.

15.789

.784

.780

.775

.771

.766

.762

.757

.753

.748

15.744

.740

.736

.731

.727

.722

.718

.713

.709

.704

15.700

.695

.691

.686

.682

.677

.673

.668

.664

.659

15.655

.651

.646

.642

.637

.633

.628

.624

.619

.615

15.610

.606

.601

CQ7 .Qu i

.592

.688

.583

.579

.574

.670

15.665

.662

.557

.653

.548

.544

.539

.535

.630

.526

15.521

IV longitude.'

Inches.

17.643

.538

.633

.528

.523

.618

.513

.608

.503

.498

17.493

.489

.484

.479

.474

.469

.464

.459

.454

.449

17.444

.439

.434

.429

.424

.419

.414

.409

.404

.399

17.394

.390

.385

.380

.375

.370

.365

.360

.355

.350

17.345

.340

.335 

330

!325

.320

.315

.310

.305

.800

17.205

.291

.286

.281

.276

.271

.266

.261

.266

.251

17.246

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinatee ofdeveloped parallel.

Inches.

0.000

.001

.002

.003

.004

.006

.009

.011.

.014

.018

 3*3

B E 2 ffi 31

/

1

2

3

4

6

6

7

8

9

10

*3 oo

o o

IS«a a-s

Inches.

2.430

4.801

7.291

9.722

12.152

14.582

17.013

19.443

21.874

24.304

Bull. 50 7

(403)
98 FORMULAS AND TABLES. [BULL. 50.

TABLE XI. Co-ordinates for projection of maps. Scale ydnny- 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

O 1

4500

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

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Abscissas of developed parallel.

1' longitude.

Inches.

1.725

.724

.724

.723

.723

.722

.722

.721

.721

.720

1.720

.719

.719

.718

.718

.717

.717

.716

.716

.715

1.715

.714

.714

.713

.713

.712

.712

.711

.711

.710

1.710

.709

.708

.708

.707

.707

.706

.706

.705

.705

1.704

.704

.703

.703 

.702

.702

.701

.701

.700

.700

1.699

.699

.698

.698

.697

.697

.696

.696

.695

.695

1.694

2' longitude.

Inches.

3.449

.448

.447

.446

.445

.444

.443

.442

.441

.440

3.439

.438

.437

.436

.435

.434

.433

.432

.431

.430

3.429

.428

.427

.426

.425

.424

.423

.422

.421

.420

3.419

.418

.417

.416

.415

.414

.413

.412

.411

.410

3.409

.408

.407

.406 

.405

.404

.403

.402

.401

.400

3.399

.398

.397

.396

.395

.394

.393

.392

.391

.390

3.389

3' longitude.

Inches.

5.174

.172

.171

.169

.168

.166

.165

.163

.162

.160

5.159

.157

.156

.154

.153

.151,

.150

.148

.147

.145

5.144

.142

.141

.139

.138

.136

.135

.133

.132

.130

5.129

.127

.125

.124

.122

.121

.119

.118

.116

.115

5.113

.112

.110

.109 

!l07

.106

.104

.103

.101

.100

5.098

.097

.095

.094

.092

.091

.089

.088

.086

.085

5.083

4' longitude.

Inches.

6.898

.896

.894

.892

.890

.888

.886

.884

.882

.880

6.878

.876

.874

.872

.870

.868

.866

.864

.862

.860

y 6.858

.856

.854

.852

.850

.848

.846

.844

.842

.840

6.838

.836

.834

.832

.830

.828

.826

.824

.822

.820

6.818

.816

.814

!sio

.808

.806

.804

.802

.800

6.798

.796

.794

.792

.790

.788

.786

.784

.782

.780

6.778

6' longitude.

Inches.

8.623

.620

.618

.615

.613

.610

.608

.605

.603

.600

8.598

.595

.593

.590

.588

.585

.583

.580

.578

.575

8.573

.570

.568

.565

.563

.560

.558

.555

.553

.550

8.548

.545

.542

.540

.537

.535

.532

.530

. .627

.525

8.522

.520

.517

!512

.510

.507

.505

.502

.500

8.497

.495

' .492

.490

.487

.485

.482

.480

.477

.475

8.472

6' longitude.

Inches.

10.348

.345

.342

.339

.336

.333

.330

.327

.324

.321

10.318

.315

.312

.309

.306

.303

.300

.297

.294

.291

10.288

.285

.282

.279

.276

.273

.270

.267

.264

.261

10.258

.254

.251

.248

.245

' .242

.239

.236

.233

.230

10.227

.224

.221

Of Q

 ulO

.215

.212

.209

.206

.203

.200

10.197

.194

.191

.188

.185

.182

.179

.176

.173

.170

10.166

7' longitude.

Inches.

12.072

.069

.065

.062

.058

.055

.051

.048

.044

.041

12.037

.034

.030

.027

.023

.020

.016

.013

,.009

.006

12.002

11.999

.995

.992

.988

.985

.981

.978

.974

.971

11.967

.963

.959

.956

.952

.949

.fl45

.942

.938

.935

11.931

.928

.924

!917

.914

.910

.907

.903

.900

11.896

.893

.889

.886

.882

.879

.875

.872

.868

.865

11.861

8' longitude.

Inches.

13.797

.793

.789

.785

.781

.777

.773

.769

.765

.761

13.757

.753

.749

.745

.741

.737

.733

.729

.725

.721

13.717

.713

.709

.705

.701

.697

.693

.689

.685

.681

13.677

.672

.668

.664

.660

.656

.652

.648

.644

.640

13.636

.632

.628

.624 

.620

.616

.612

.608

.604

.600

13.596

.592

.588

.584

.680

.576

.572

.568

.564

.560

13.555

9' longitude.

Inches.

15.521

.517

.512

.508

.503

.499

.494

.490

.485

.481

15.476

.472

.467

.463

.458

.454

.449

.445

.440

.436

15.431

.427

.422

.418

.413

.409

.404

.400

.395

.391

15.386

.381

.376

.372

.367

.363

.358

.354

.349

.345

15.340

.336

.331

097

,Ou I

.322

.318

.313

.309

.304

.300

15.295

.291

.286

.282

.277

.273

.268

.264

.259

.255

15.250

10' longitude.

Inches.

17.246

.241

.236

.231

.226

.221

.216

.211

.206

.201

17.196

.191

.186

.181

.176

.171

.166

.161

.156

.151

17.146

.141

.136

.131

.126

.121

.116

.111

.106

.101

17.096

.090

.085

.080

.075

.070

.065

.060

.055

.050

17.045

.040

.035

.030 

.025

.020

.015

.010

.005

.000

16.995

.990

.985

.980

.975

.970

.965

.960

.955

.950

16.944

Longitude interval.

i

1

2

3

4

5

6

. 7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.002

.003

.004

.006

.009

.011

.014

.018

 §"'

£ S

^ 0

JiST*

'

1

2

3

4

5

6

7

8

9

10

"3 m

a o

 ^ £

SS.2 g*a

Inches.

2.431

4.862

7.292

9.723

12.154

14.585

17.016

19.446

21.877

24.308

(404)
WOODWARD.] MAP CO-ORDINATES. 99

TABLE XI. Co-ordinates for projection of maps. Scale sg & 00 . 

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

o /

4600

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

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

Abscissas of developed parallel.

1' longitude.

Inches.

1.694

.694

.693

.693

.692

.692

.691

.691

.690

.690

1.689

.689

.683

.688

.687

.687

.686

.086

.685

.685

1.684

.684

.683

.683

.B82

.682

.681

.680

.680

.679

1.679

.678

.678

.677

.677

.676

.676

.675

.675

.674

1.674

.673

.673

672 !o72

.671

.671

.670

.670

* .669

1.669

.668

.668

.067

.667

.666

.666

.665

.665

.664

1.664

2' longitude.

Inches.

3.389

.388

.387

.386

.385

.384

.383

.382

.381

.380

3.379

.378

.376

.375

.374

.373

.372

.371

.370

.369

3.368

.367

.366

.365

.304

.363

.362

.361

.360

.359

3.358

.357

.3oG

J .355

.354

.353

.352

.351

.350

.349

3.348

 .347

.346

.345 

.344

' .343

.342

.340

.339

.338

3.337

.336

.335

.334

.333'

.332

.331

.330

.329

.328

3.327

3' longitude.

Inches.

5.083

.082

.080

.079

.077

.075

.074

.072

.071

.069

5.068

.066

.065

.063

.062

.060

.059

.057

.056

.054

5.052

.051

.049

. .048

.046

.045

.043

.041

.040

.038

5.037

.035

.034

.032

.031

.029

.028

.020

.025

.023

5.021

.020

.018

.017 

.015

.014

.012

.011

.009

.008

5.006

.005

.003

.002

.000

4.998

.997

.9%

.994

.992

4.991

4' longitude.

Inches.

6.778

.776

.774

.772

.770

.767

.765

.763

.761

.759

6.757

.755

.753

.751

.749

.747

.745

.743

.741

.738

6.736

.734

.732

.730

.728

.726

.724

.722

.720

.718

6.716

.714

.712

.710

.708

.706

.704

.702

.700

.698

6.695

.693

.691

.689 

.687

.685

.683

.681

.679

.677

6.075

.673

.671

.669

.666

.664

.662

.660

.658

.656

6.654

5' longitude.

Inches.

8.472

.469

.467

.464

.462

.459

.456

.454

.451

.449

8.446

.444

.441

.438

.436

.433

.431

.428

.426

.423

8.420

.418

.415

.413

.410

.408

.405

.402

.400

.397

8.395

.392

.390

.387

.384

.382

.379

.377

.374

.372

8.369

.366

.304

01' I

.ODJ.

.359

.356

.354

.351

.348

.346

8.343

.341

.338

.336

.333

.330

.328

.325

. .323

.320

8.318

6' longitude.

Inches.

10.166

.163

.160

.157

.154

.151

.148

.145

.142

.139

10.136

.133

.129

.126

.123

.120

.117

.114

.111

.108

10.105

.102

.099

.096

.093

.090

.086

.083

.080

.077

10.074

.071

.068

.064

.061

.058

.055

.052

.049

.046

10.043

.040

.037

AGO vOO

.031

.028

.025

.021

.018

.015

10.012

.009

.006

.003

.000

9.997

.994

.991

.988

.985

9.982

7' longitude.

Inches.

11.861

.857

.8.H

.850

.847

.843

.839

.836

.832

.829

11.825

.822

.817

.814

.810

.807

.803

.800

.796

.792

11.789

.785

.782

.778

.775

.771

.767

.763

.760

.756

11.753

.749

.746

.742

.738

.735

.731

.728

.724

.721

11.717

.713

.710

.703

.699

.696

.691

.688

.684

11.681

.677

.674

.670

.666

.663

.659

.656

. .652

.649

11.645

8' longitude.

Inches.

13.555

.551

.647

.543

.539

.634

.530

.526

.522

.618

13.614

.510

.506

.502

.498

.494

.490

.486

.482

.477

13.473

.469

.465

.461

.457

.453

.448

.444

.440

.436

13.432

.428

.424

.419

.415

.411

.407

 .403

.399

.395

13.390

.386

.382

o*7Q .O'o

.374

.370

.366

.362

.358

.354.

13.350

.346

.342

.33S

.333

.329

.325

.321

.317

.313

13.309

' 9' longitude.

Inches.

' 15.250

.245

.241

.236

.232

.226

.221

.217

.213

.208

15.204

.199

.194

.189

.185

.180

.176

.171

.167

.161

15.157

.152

.148

.143

.139

.134

.129

.124

.120

.115

15.111

.106

.102

.097

.092

.088

.083

.079

.074

.070

15.064

.060

.055

.051 

.046

.042

.037

.032

.027

.023

15.018

.014

.009

.005

14.999

.995

.990

.986

.981

.977

14.972

107 longitude.

Inches.

16.944

.939

.934

.929

.924

.918

.913

.908

.903

.898

10.893

.888

.882

.877

.872

.867

.862

.857

.852

.840

16.841

.836

.831

.826

.821

.816

.810

.805

.800

.795

16.790

.785

.780

.774

.709

.7(34

.759

-.754

.749

.744

16.738

.733

.728

»TOO * I £t&

.718

.713

.708

.702

.697

.692

11.687

.682

.677

.672

.666

.661

.656

.651

.646

.641

16.636

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

of Ordi natesdeveloped parallel.

Inches.

0.000

.001

.002

.003

.004

.006

.009

.011

.014

.018

il

' £» <3?

^0 Hi .3

/

1

2

3

4

5

6

7

8

9

10

Us

II

£.2 a^

Inches.

2.431

4.863

7.294

9.725

12.156

14.588

17.019

19.450

21.882

24.3i3

(405)
100 FORMULAS AND TABLES. [BULL. 50.

TABLE XI. Co-ordinates for projection of maps. Scale Ttro^tr-

[Derivation of table explained in section (5); use of table explained on page 22.]

Latitude of

parallel.

O 1

4700

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

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

Abscissas of developed parallel.

1' longitude.

Inches.

1.664

.663

.663

.662

.661

.661

.660

.660

.659

.659

1.658 

.658

.657

.657

.656

.656

.655

.655

.654

.654

1.653

.653

.652

.652

.651

.650

.650

.649

.649

.648

1.648

- .647

.647

.646

.646

.645

.645

.644

.644

.643

1.643

.642

.642

.641 

!641

.640

.639

.639

.638

.638

1.637

.637

.636

.636

.635

.635

.634

.634

.633

.633

1.632

2' longitude.

Inches.

3.327

.326

.325

.324

.323

.322

.321

.320

.319

.318

3.317 

.316

.315

.314

.313

.312

.310

.309

.308.

.307

3.306

.305

.304

.303

.302

.301

.300

.299

.298

.297

3.296

.295

.294

.293

.292

.291

.290

'.289

.287

.286

3.285

.284

.283

OQQ .ZoZ

.281

. .280

.279

.278

.277

.276

3.275

.274

.273

.272

.271

.270

.269

.268

.266

.265

3.265

1 3' longitude.

Inches.

4.991

.989

.988

.986

.984

. .983

.981

.980

.978

.977

4.975 

.974

.972

.970

.969

.967

.966

.964

.963

.961

4.959

.958

.956

.955

.953

.951

.950

.948

.947

.945

"4.944

.942

.941

.939

.937

.936

.934

.933

.931

.930

4.928

.927

.925

QOQ ,u£d

.922

.920

.918

.917

.915

.914

4.912

.911

.909

.908

.906

.904

.903

.901

.900

.898

4.897

4' longitude.

Inches.

6.654

.652

.650

.648-

.646

.644

.642

.640

.638

.636

6.634 

.632

.629

.627

.625

.623

.621

.619

.617

.615

6.612

.610

.608

.606

.604

.602

.600

.598

.596

.594

6.592

.590

.588

.586

.583

.581

.579

.577

.575

.573

6.571

.569

.566

.564 

.562

.560

.558

.556

.554

.552

6.550

.548

.546

.544

.541

.539

.537

.535

. .533

.531

6.529

5' longitude.

Inches.

8.318

.315

.313

.310

.307

.305

.302

.300

.297

.294

Q OQO

O*At?A

.289

.286

.284

.281

.279

.276

.273

.271

.268

8.265

.263

.260

.258

.255

.252

.250

.247

.244

.242

8.239

.237

.234

.232

.229

.226

.224

.221

.218

.216

8.213

.211

.208 

.205

.203

.200

.197

.195

.192

.190

8.187

.184

.182

.179

.176

.174

.171

.169

.166

.163

8.161

6' longitude.

Inches.

9.982

.979

.976

' .973

.969

.966

' .963

.960

.956

.953

o y.you Qf\n 

.947

.944

.941

.938

,935

.931

.928

.925

.922

9.919

.916

.913

.910

.906

.903

.900

.897

.893

.890

9.887

.884

.881

.878

.875

.872

.869

.866

.862

.859

9.856

.853

.850

.847 

.844

.841

.837

.834

.831

.828

9.824

.821

.818

.815

.812

.809

.806

.803

.799

0 .796

9.794

7' longitude.

Inches.

11.645

.642

.638

.635

.630

.627

.623

.620

.616

.612

' 11.609 

.605

.601

.598

.594

.591

.586

.583

.579

.576

11.572

.568

.565

.561

.557

.553

.550

.546

.542

.539

11.535

.532

.528

.525

.521

.517

.514

.510

.506

.502

11.499

.495

.491

.488 

!484

.481

.476

.473.

.469

.466

11.462

.458

-.455

.451

.447

.444

' .440

.437

.432

.429

11.426

8' longitude.

Inches.

13.309

.305

.301

.297

.292

.288

.284

.280

.275

.271

1 Q OGT lo./b/ 

.263

.258

.254

.250

.246

.242

.238

.234

.230

13.225

.221

.217

.213

.208

.204

.200

.196

.191

.187

13.183

.179

.175

.171

.166

.162

.158

.154

. .150

.146

13.142

.138

.133

190 . L£o

.125

.121

.116

.112

.108

.104

13.099

.095

.091

.087

.082

.078

.074

.07.0

.066

.062

13.058

9' longitude.

Inches.

14.972

.908

.963

.959

.953

.949

.944

.940

.935

.930

14.926 

.921

.916

.911

.907

.902

.897

.892

 .888

.883

14.878

.873

.869

.864

.859

.854

.850

 .845

.840

.836

14.831

.827

.822

.818

.812

.808

.803

.799

.793

.789

14.784

.780

.774 

.770

.765

.761

. .755

.751

.746

.742

14.737

.732

.728

.723

.718

.713

.709

.704

.699

.694

14.691

10' longitude.

Inches.

16.636

.631

.626

.621

.615

.610

.605

.600

.594

.589

16.584 

.579

.573

.568

.563

.558

.552

.547

.542

.537

16.531

.526

.521

.516

.510

.505

.500

.495

.489

.484

16.479

.474

.469

.464

.458

.453

.448

.443

.437

.432

16.427

.422

.416 

.411

.406

.401

.395

.390

.385

.380

16.374

.369

.364

.359

.353

.348

.343

.338

.332

.327

16.323

Longitude interval.

/

1

2

3

4

5

6

7

8

9

10

Ordinates ofdeveloped parallel.

Inches.

0.000

.001

.002

.003

.004

.006

.009

.011

.014

.018

3-3

 Sfc " SS

^1

/

1

2

3

4

5

6

7

«

9

10

gj 

£ (5

O C3

sjs S.s a-d

Inches.

2.432

4.863

7.294

9.726

12.157

14.589

'17.020

19.452

21.88:1

24.315

(406)
WOODWARD.] MAP CO-ORDINATES. 101

TABLE XI. Co-ordinates for projection of maps. Scale z 

[Derivation of table explained in section (5); use of table explained on page 22.]

o .

o^

33 cfl 3*

O 1

4800

01

02

03

04

06

06

07

08

09

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

38

37

38

39

40

41

42

43

44

46

46

47

48

49

60

61

62

63

64

66

66

67

68

69

60

Abscissas of developed parallel.

1' longitude.

Indies.

1.632

.632

' .631

.631

.630

.630

.629

.629

.628

.6-28

1.627 

.627

.626

.625

.625

.624

.624

.623

.623

.022

1.622

.621

.621

.620

.620

.619

.619

.618

.617

.617

1.616

.616

.615

.615

.614

.614

.613

.613

.612

.612

1.611

.611

.610

.610

.609

.608

.608

.607

.607

.606

1.606

.605

.605

.604

.604

.603

.603

 .602

.602

.601

1.600

2' longitude.

Inches.

3.265

.264

.263

.262

.260

.259

.258

.257

.256

.255

3.254 

.253

.252

.251

.250

.249

.248

.247

.246

.245

3.243

.242

.241

.240

.239

.238

.237

.236 '235

.234

3.233

.232

.231

.230

.229

.228

.227

.226

.225

.223

3.222

.221

.220

.219

.218

.217

.216

.215

.214

.213

3.212

.211

.210

.209

.208

.207

.206

.205

.204

.202

3.201

3' longitude.

Indies.

4.897

.895

.894

.892

.891

.889

.888

.886

.884

.883

4.881

.880

.878

.876

.875

.873

.872

.870

.869

.867

4.865

.864

'.862

.861

.859

.857

.856

.854

.852

.851

4.849

.848

.846

.845

.843

.842

.840

.838

.837

.835

4.833

.832

.830

.829

.827

.825

.824

.822

.821

.819

4.818

.816

.814

.813

.811

.810

.808

.807

.805

.804

4.801

4' longitude.

Inches.

6.529

.527

.525

.623

.521

.619

.517

.515

.512

.510

6.508 

.506

.604

.602

.600

.498

.496

.494

.492

.489

6.487

.485

.483

.481

.478

.476

.474

.472

.470

.468

6.466

.464

.462

.460

.468

.466

.453

.461

.449

. .447

6.444

.442

.440

.438

.436

.434

.432

.430

.428

.426

6.424

.422

.419

.417

.415

.413

.411

.409

.407

.405

6.402

5' longitude.

Inches.

8.161

.159

.156

.154

.151

.148

.146

.143

.140

.138

8.135 

.133

.130

.127

.125

.122

.119

.117

.114

.111

8.108

.106

.103

.101

.098

.096

.093

.090

.087

.085

8.082

.080

.077

.074

.072

.069

.066

.064

.061

.058

8.055

.053

.050

.048

.045

!042

.040

.037

.034

.032

8.029

.027

.024

.021

.019

.016

.014

.011

.009

.006

8.002

6' longitude.

Inches.

9.794

.791

.788

.785

.781

.778

.775

.772

.769

.766

9.763 

.760

.756

.753

.750

.747

.743

.740

.737

.734

9.730

.727

.724

.721

.718

.716

.712

.709

.705

,.702

9.699

.696

.692

.689

.686

.683

.680

.677

.674

.670

9.667

.664

.661

.658

654 iesi

.648

.645

.641

.638

9.635

.632

.629

.626

.623

.620

.617

.614

.611

.607

9.603

7' longitude.

Inches.

11.426

.423

.419

.416

.411

.408

.404

.401

.397

.393

11.390 

.386

.382

.378

.375

.371

.367

.364

.360

.356

11.352

.348

.345

.341

.337

.334

.330

.327

.322

.319

11.315

.312

.308

.304

.301

.297

.293

.290

.286

.282

11.278

.274

.271

.267

O/*O

.'259

.256

.252

.248

.245

11.241

.238

.234

.230

.227

.223

.220

.216

.213

.208

11.203

8' longitude.

Inches.

13.058

.054

.050

.046

.042

.038

.034

.030

.025

.021

13.017 

.013

.008

.004

.000

12.996

.991

.987

.983

.978

12.974

.970

.966

.962

.957

.953

.949

.945

.940

.936

12.932

.928

.923

.919

.915

.911

.906

.902

.898

.894

12.889

.885

.881

.877

orro O* &

.868

.864

.860

.855

.851

12.847

.843

.838

.834

.830

.826

.822

.818

.814

.810

12.804

9' longitude.

Inches.

14.691

.686

.682

.677

.672

.667

.663

.658

.653

.648

14.644 

.639

.634

.029

.025

.620

.615

.611

.606

.601

14.695

.691

.686

.582

.676

.572

.567

.563

.557

.553

14.648

.644

.639

.634

.630

.625

.520

.515

.511

.505

14.600

.495

.491

.486

.481

.476

.472

.467

.462

.458

14.463

.449

.443

.439

.434

.430

.426

' .421

.416

.411

14.404

10' longitude.

Inches.

16.323

.318

.313

.308

.302

.297

.292

.287

.281

.276

16.271 

.266

.260

.256

.250

.245

.239

.234

.229

.223

16.217

.212

.207

.202

.196 :i9i

.186

.181

.175

.170

16.166

.160

.164

.149

.144

.139

.133

.128

.123

.117

16.111

.106

.101

.096

.090

!085

.080

.075

.069

.064

16.059

.054

.048

.043

.038

.033

.028

.023

.018

.012

16.005

o> .

§5

/

1

2

3

4

6

6

7

8

9

10

fib'

if e

l-s ft

Inches.

0.000

.001

.002

.003

.004

.036

.009

.Oil

.014

.018

0) _ 

It' S Q

H?-2

1

1

2

3

4

5

6

7

8

9

10

"3 oj d a)

0 0

« d

°C S

"S-3 "

Inches.

2.432

4.864

7.296

9.728

12.160

14.592

17.024

19.466

21.888

24.320

(401
.102 FORMULAS AND TABLES. [BULL. QO.

TABLE XI. Co-ordinates for projection of maps. Scale 

[Derivation of table explained in section (5); wse of table explained on page 22.]

Latitude of

parallel.

o /

4900

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

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

Abscissae of developed parallel.

1' longitude.

Inches.

1.600

.600

.599

.599

.598

.598

.597

.597

.596

.596

1.595 

.595

.594

.593

.593

.592

.592

.591

.591

.590

1.590

.589

.589

.588

.588

.587

.587

.586

.586

.585 

1.584

.584

.583

.583

.582

.582

.581

.581

.580

.580

1.579

.578

.578

.577 

.577

.576

.576

.575

.575

.574

1.574

.573

.573

.572

.571

.571

.570

.570

.569

.569

1.568

2' longitude.

Inches.

3.201

.200

.199

.198

.197

.196

.195

.194

.192

.191

3.190 

.189

.188

.187

.186

.185

.184

.183

.182

.181

3.179

.179

.178

.176

.175

.174

.173

.172

.171

.170 

3.169

.168

.167

.166

.165

.163

.162

.161

.160

.159

3.158

.157

.156

.155 

.154

.153

.152

.151

.150

.149

3.147

.146

.145

.144

.143

.142

.141

.140

.139

.138

3.136

3' longitude.

Inches.

4.801

.800

.798

.797

.795

.793

.792

.790

.789

.787

4.786 

.784

.782

.780

.779

.777

.776

.774

.772

.771

4.760

.768

.766

.765

.763

.762

.700

.758

.757

.755 

4.753

.752

.750

.748

.747

.745

.744

.742

.740

.739

4.737

.735

.734

.732 

.731

.729

.728

.726

.724

.723

4.721

.719

.718

.716

.714

.713

.711

.710

.708

.706

4.705

4' longitude.

Inches.

6.402

.400

.398

.396

.394

.391

.389

.387

.385

.383

6.381 

.378

.376

.374

.372

.370

.368

.365

.363

.361

6.359

.357

.305

.353

.351

.349

.346

.344

.342

.310 

0.338

.336

.333

.331

.329

.327

.325

.323

.320

.318

6.316

.314

.312

.310 

.308

.306

.304

.301

.299

.297

0.295

.292

.290

.288

.286

.284

.282

.280

.278

 .275

0.273

5' longitude.

Inches.

8.002

.000

7.997

.994

.992

.989

.986

.984

.981

.978

7.976 

.973

.970

.967

.964

.962

-.959

.956

.954

.951

7.948

.946

.944

.941

.938

.936

.933

.930

.928

.925 

7.922

.919

.916

.914

.911

.908

.906

.903

.900

.898

7.895

.892

.890

.887 

.884

.882

.879

.876

.874

.871

7.868

.865

.863

.860

.857

.855

.852

.849

.847

.844

7.841

6' longitude.

Inches.

9.603

.600

.596

.593

.590

.587

.584

.581

.577

.574

9.571 

.568

.564

.561

.557

.554

.551

.548'

.545

.542

9.538

.536

.533

.529

.526

.523

.520

.517

.514

.510 

9.507

.503

.500

.497

.494

.490

.487

.484

.481

.478

9.475

.471

.468

.465 

.461

.458

.455

.452

.449

.446

9.442

.439

.436

.432

.429

.426

.422

.419

.416

.413

9.409

7' longitude.

Inches.

11.203

.200

.196

.192

.189

.185

.181

.178

.173

.170

11.166 

.162

.158

.154

.150

.147

.143

.139

.136

.132

11.128

.125

.122

.117

.114

.110

.106

.103

.099

.095 

11.091

.087

.083

.080

.076

.072

.068

.065

.061

.057

11.054

.049

.046

.042 

.038

.035

.031

.027

.024

.020

11.016

.012

.008

.004

.000

10.997

.993

.989

.986

.982

10.977

8' longitude.

Inches.

12.804

.800

.795

.791

.787

.782

.778

.774

.770

.766

12.762

.757

.752

.748

.743

.739

.735

.730

.726

.722

12.718

.714

.710

.706

.702

.698

.693

.689

.685

.680 

12.676

.671

.666

.662

.658

.654

.650

.646

.641

.637

12.633

.628

.624

.020 

.615

.611

.607

.602

.598

.594

12.590

.585

.581

.576

.572

.568

.563

.559

.555

.550

12.546

9' longitude.

Inches.

14.404

.400

.395

.390

.386

.380

.376

.371

.366

.361

14.357 

.351

.346

.341

.336

.332

.327

.322

.317

.313

14.307.

.304

.299

.294

.289

.285

.279

.275

.270

.265 

14.260

.255

.250

' .245

.241

.235

.231

.226

.221

.216

14.212

.206

.202

.197 

.192

.188

.183

.178

.173

.169

14.163

.158

.153

.148

.143

.139

.134

.129

.125

.119

14.114

10' longitude.

Inches.

16.005

.000

15.994

.989

.984

.978

.973

.968

.962

.957

15.952 

.946

.940

.935

.929

.924

.919

.913

.908

.903

15.897

.893

.888

.882

.877

.872

.866

.801

.850

.850 

15.845

.839

.833

.828

.823

.817

.812

.807

.801

.700

15.791

.785

.780

.769

.764

.759

.753

.748

.743

15.737

.731

.726

.720

.715

.710

.704

.690

.694

.688

15.082

II Longitude 

interval.

/

1

2

3

4

5

6

7

8

9

10

Ordi ofnates developed parallel.

Inches.

0.000

.001

.d02

.003

.004

.006

.009

.011

.014

.018

\

||^"3

i

i

2

3

4

5

6

7

8

9

10

ll2 .5

0.2 313

Inches.

2.432

4.865

7.297

9.730

12.162

14.594

17.027

19.459

21.892

24.324

(408)
 WOODWARD.] AREAS OF QUADRILATERALS. 103

TABLE XII. Areas of quadrilaterals of Earth's surface of 1° extent in latitude and

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

O '

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

22 00

22 30

Area in 

square miles.

4752.33

52.16

51.63

50.75

49.52

47.93

46.00

43.71

41.07

38.08

34.74

31.04

27.00

22.61

17.86

12.76

07.32

01.52

4695.38

88.89

82.05

74.86

67.32

59.43

51.20

42.63

33.71

24.44

14.82

04.87

4594.67

83.92

72.94

61.61

49.94

37.93

25.59

12.90

4499.87

86.51

72.81

58.78

44.41

29.71

14.67

4399.30

Middle latitude of quadrilateral.

o / 

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

44 00

44 30

45 00

Area in 

square miles.

4399.30

83.60

67.57

51.21

34.52

17.61

00.17

4282.50

64.51

46.20

27.56'

08.61

4189.33

69.74

49.83

29.60

09.06

4088.21

67.05

45.67

23.79

01.69

3979.30

56.59

33.59

10.28

3886.67

62.76

38.56

14.06

3789.26

64.18

38.80

13.14

3687.18

60.95

34.42

07.62

3580.54

53.17

25.54

3497.62

69.44

40.98

12.26

3383.27

'(409)
104 FORMULAS AND TABLES. [BUIX. 50.

TABLE XII. Areas of quadrilaterals of Earth's surface of 1° extent in latitude and

longitude.

[Derivation of table explained in section (6) ; use of table explained on page 23.]

Middle latitude of quadrilateral.

o / 

45 00

45 30

46 00

46 30

47 00

47 30

48 00

48 30

49 00

49 30

50 00

60 30

61 00

61 30

62 00

62 30

63 00

63 30

64 00

64 30

66 00

65 30

66 00

66 30

57 00

67 30

68 00

68 30

69 00

69 30

60 00

60 30

61 00

61 30

62 00

62 30

63 00

63 30

64 00

' 64 30

66 00

66 30

66 00

66 SO

67 00

67 30

Area in 

square miles.

3383.27

64.01

24.49

3294.71

64.68

34.39

03.84

3173.04

41.99

10.69

3079.15

47.37

15.34

2983.08

60.58

17.85

2884.88

51.68

18.27

2784.62

60.76

16.67

2682.37

47.85

13.13

2578.19

43.05

07.70

2472.16

36.42

00.48

2364.34

28.02

2291.61

64.82

17.94

2180.89

43.66

06.26

2068.68

30.94

1993.04

64.97

16.75

1878.37

39.84

Middle latitude of quadrilateral.

o / 

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

76 00

76 30

77 00

77 60

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

86 00

86 30

87 00

87 30

88 00

88 30

89 00

89 30

90 00

Area in 

square miles.

1839.84

01.16

1762.33

23.36

1684.24

45.00

05.62

1566.10

26.46

1486.70

46.81

06.81

1366.69

26.46

1286.12

45.68

05.13

1164.49

23.75

1082.91

41.99

00.99

959.90

18.73

877.49

36.18

794.79

53.34

11.83

670.27

28.64

586.97

45.24

03.47

461.66

19.81

377.93

36.02

294.08

62.11

10.12

168.12

126.10

84.07

42.04

00.00

(410)
WOODWARD.] AREAS OF QUADRILATERALS. 105

TABLE XIII. Areas of quadrilaterals,of Earth's surface of 30' extent in latitude and

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

0 1

0 15

0 45

1 15

1 45

2 15

2 45

3 15

3 43

4 15

4 45

' 5 15

5 45

6 15

6 45

7 15

7 45

8 15

8 45

9 15

9 45

10 15

10 45

11 15

11 45

12 15

12 45

13 15

13 45

14 15

14 45

15 15

15 45

16 15

16 45

17 15

17 45

18 15

18 45

19 15

19 45

20 15

20 45

21 15

21 45

22 15

22 45

Area in 

square miles.

1188.08

1188.00

1187.82

1187.56

1187.20

1186.76

1186.24

1185.62

1184.92

1184.13

1183.24

1182.28

1181.22

1180.08

1178.85

1177.53

1176.13

1174.63

1173.06

1171.39

1169.63

1167.80

1165.86

1163.85

1161.75

1159.56

1157.29

1154.93

1152.48

1149.95

1147.33

1144.63

1141.84

1138.96

. 1136.00

1132.96

1129.83

1126.62

1123.32

1119.93

1116.47

1112.92

1109.28

1105.57

1101.77

1097.88

Middle latitude of quadrilateral.

o /

22 45

23 15

23 45

24 15

24 45

25 15

25 45

26 15

26 45

27 15

27 45

28 16

28 45

29 16

29 45

30 15

30 45

3t 15

31 45

32 15

32 45

33 15

33 45

34 15

34 45

35 15

. 35 45

36 15

36 45

37 15

37 45

38 15

88 45

39 15

39 45

40 15

40 45

41 15

41 45

42 15

42 45

43 15

43 45

44 15

44 46

45 15

Area in 

square miles.

1097.88

1093.92

1089.87

1085.74

1081.62

1077.23

1072.85

1068.40

1063.86

1059.24

1054.64

1049.76

1044.90

1039.97

1034.95

1029.85

1024.68

1019.43

1014.10

1008.69

1003.20

997.64

992.00

986.29

980.50

974.64

968.70

962.68

956.60

950.43

944.21

937.88

931.51

925.06

918.63

911.94

905.27

898.54

891.73

884.85

877.91

870.90

863.82

856.67

849.46

842.18

(411)
106 FORMULAS AND TABLES. [BULL. 50.

TABLE XIII. Areas of quadrilaterals of Earth's surface of 30' extent in latitude and

longitude. 

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

o / 

45 45

46 15

46 45

47 15

47 45

48 15

48 45

49 15

49 45

50 15

50 45

51 15

51 45

52 15

52 45

53 15

53 45

54 15

54 45

55 15

55 45

56 15

56 45

57 15

.57 45

58 15

58 45

59 15

59 45

60 15

60 45

61 15

61 45

62 15

62 45

63 15

63 45

64 15

64 45

65 15

65 45

66 15

66 45

G7 15

67 45

Area in 

square miles.

834.83

827.42

819.94

812.40

804.79

797.13

789. S9

7S1.60

778.74

765.83

757.85

749.82

741.72

733.57

725.36

717.08

708.76

700.38

C91.94

683.44

674.89

666.29

657.64

648.93

640.17

631.36

622.49

613.59

604.62

595.62

586.56

577.45

568.30

559.11

549.86

540.58

531.25

521.88

512.46

503.01

493.51

483.97

474.40

464.78

455.13

Middle latitude of quadrilateral.

0 /

67 45

68 15

68 45

69 15

69 45

70 15

70 45

71 15

71 45

72 15

72 45

73 15

73 45

74 15

74 45

75 15

75 45

76 15

76 45

77 15

77 45

78 15

78 45

79 15

79 45

80 15

80 45

81 15

81 45

82 15

82 45

83 15

83 45

84 15

84 45

85 15

85 45

86 15

86 45

87 15

87 45

88 15

88 45

89 15

89 45

Area in 

square miles.

455.13

445.45

435.72

425.96

416.16

406.34

396.47

386J58

376.05

366.70

356.71

346.69

336.65

326.58

316.48

306.36

296.21

286.04

275.84

265.62

255.38

245.12

234.83

224.53

214.21

203.88

193.62

183.15

172.77

162.37

151.95

141.63

131.09

120.64

110.18

99.72

89.25

78.76

68.27

57.78

47.28

36.78

26.27 

15.76

5.26

(412)
WOODWARD.] AREAS OF QUADRILATERALS. 107

TABLE XIII. Areas of quadrilaterals of Earth's surface of 30' extent in latitude and

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

o /

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 00

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

Area in 

square miles.

11H8.05

1187.92

1187.70

1187.39

1186.99

11SG.51

1185.95

1185.28

1184.53

1183.70

1182.77

1181.76

1180.66

1179.48

1178.20

1176.84

1175.39

1173.86

1172.23

1170.52

1168.73

1166.84

1164.86

1162.81

1160.67

1158.44

1156.12

1153.72

1151.23

1148.65

1145.99

1143.25

1140.41

1137.50

1134.49

1131.41

1128.24

1124.98

1121.64

1118.21

1114.71

1111.11

1107.44

1103.68

1099.84

Middle latitude of quadrilateral.

o /

23 00

a3 30

24 00

24 30

25 00

25 30

26 00

26 30

27 00

27 30

28 00

28 30

29 00

29 HO

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

Area in 

square miles.

1095.91

> 1091.90

1087.81

1083.64

1079.39

1075.05

1070.64

1066.14

1061.56

1056.90

1052J6

1047.34

1042.44

1037.47

1032.41

1027.27

1022.06

1016.77

1011.40

1005.96

1000.43

994.83

989.16

983.41

977.58

' 971.68

965.70

959.65

953.52

947.32

941.05

934.71

928.29

921.80

915.25

908.61

901.91

895.14

888.30

881.39

874.41

867.37

860.25

853.07

845.82

(413)
108 FORMULAS AND TABLES. [BULL. 50.

TABLE XIII. Areas of quadrilaterals of Earth's surface of 30' extent in latitude and

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quad- 

'rilateral.

o / 

45 30

46 00

46 30

47 00

47 30

48 00

48 30

49 00

49 30

50 00

60 30

51 00

61 30

52 00

62 30

63 00

63 30

54 00

54 30

66 00

65 30

56 00

66 30

67 00

67 30

58 00

58 30

69 00

69 30

60 00

60 30

61 00

61 30

62 00

62 30

63 00

63 30

64 00

64 30

65 00

66 30

66 00

. 66 30

67 00

67 30

Area in 

square miles.

838.51

831.13

823.68

. 816.18

808.60

800.97

793.27

785.50

777.68

769.79

761.85

753.84

745.78

737.65

729.47

721.23

712.93

704.57

696.16

687.70

679.17

670.60

861.97

653.29

644.55

635.77

626.93

618.05

609.11

600.13

591.09

582.01

672.88

563.71

654.49

546.23

635.92

626.57

517.17

507.74

498.26

488.75

479.19

469.60

459.96

Middle latitude of quadrilateral.

o '' / 

68 00

08 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

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

86 00

86 30

87 00

87 30

88 00

88 30

89 00

89 30

90 00

Area in 

square miles.

450.29

440.59

430.84

421.06

411.25

401.41

391.53

381.62

371.68

361.71

351.71

341.68

331.62

321.53

311.42

301.28

291.12

280.94

270.73

260.60

250.25

239.98

229.68

219.37

209.05

198.70

188.34

177.96

167.57

157.16

146.74

136.31

125.87

115.42

104.95

94.48

84.01

 73.62

63.03

62.53

42.03

31.53

21.02

10.51

00.00

(414)
WOODWAHD.] AREAS OF QUADRILATERALS. 109

TABLE XIV. Areas of qiiadrilaterals of Earth's surface of 15' extent in latitude 

, and longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

o / // 

0 07 30

0 10 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 80

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

5 37 30

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

290.93

296.91

296.89

296.87

29G.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

295.63

Middle latitude of quadrilateral.

O 1 II

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

11 07 30

11 15 00

Area in 

square miles.

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

293.60

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 '

291.59

291.47

(415)
110 FORMULAS AND TABLES. [BULL. 50.

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

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

o / //

11 22 30

11 30 00

11 37 30

11 45 00

11 52 30

12 00 00

12 70 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

16 37 30

Ifi 45 00

16 52 30

Area in 

square miles.

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

284.92

284.74

284.56

Middle latitude of quadrilateral.

O 1 II

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

IS 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

22 07 30

22 15 00

22 22 30

22 30 00

Area in 

square miles.

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. G8

278.46

278.23

278.00

277.78

277.55

277.32

277.09

276.86

276.63

276.39

276.16

275.92

275.68

275.44

275.20

274.96

(416)
WOOnWABD.J AREAS OF QUADRILATERALS. Ill

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

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

o / // 

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 62 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

27 37 30

27 45 00

27 52 30

28 00 00

28 07 30

Area in 

square miles.

274.72

274.47

274.22

273.98

273.73

273.48

273.23

272.98

272.72

27ii.47

272.21

271.95

271.69

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

263.93

263.64

263.34

263.04

262.74

Middle latitude of quadrilateral.

O 1 II

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 W 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

33 07 30

33 15 00

33 22 30

33 30 00

33 37 30

33 45 00

Area in 

square miles.

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

257.14

256.82

256.49

256.17

255.84

' 255.62

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

249.76

249.41

249.06

248.71

248.36

248.00

(417)
112 FORMULAS AND TABLES. [BULL. 50.

TABLE XIV. Areas of quadrilaterals of Earlltfs surface of 15' extent in latitude and

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

0 / //

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

38 37 30

38 45 00

38 52 30 

39 00 00 

39 07 30 

39 15 00 

39 22 30

Area in 

square miles.

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 

239.91 

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 

233.28 

232.88

232.48 

232.07 

231.67 

231.27 

230.86

Middle latitude of quadrilateral.

O I II

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 08 

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 £2 30 

43 30 00 

43 37 30 

43 45 00

43 52 30 

44 00 00 

44 07 30 

44 15 00 

44 22 30

44 30 00 

44 37 30 

44 45 00 

44 52 30 

45 00 00

Area in 

square miles.

230.45 

230.04 

229.63 

229.22 

228.81

22S.40 

22T.99 

227.57 

227.15 

226.73

226.32 

22.5.90 

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 

2,19.04 

5118.60 

218.16

217.73 

217.28 

216.84 

216.40 

215.96

215.51 

215.06 

214.61 

214.17 

213.72

213.27 

212.82 

212.37 

211.91 

211.46

(418)
 WOODWARD.] AREAS OF QUADRILATERALS. 113

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

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

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

1 46 30 00

40 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

49 37 30

49 45 00

49 52 30

50 00 00

50 07 30

50 15 00

50 22 30

50 30 00

60 37 30

Area in 

square miles.

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

20452

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

- 193i93

193.44

192.94

192.45

191.95

191.46

190.96

190.46

189.96

Middle latitude of quadrilateral.

O 1 II

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

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

Area1 in 

square miles.

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

171.39

170.86

170.33

169.79

169.26

168.72

168.1P

167.65

167.11

. 166.67

Bull. 50-. 8

(419)
114 FORMULAS AND TABLES. [BULL. 60.

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

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

o u 

56 22 30 

66 30 00 

56 37 30 

56 45 00 

56 52 30

67 00 00 

57 07 30 

67 15 00 

67 22 30 

67 '30 00

57 37 30 

57 45 00 

57 52 30 

58 00 00 

58 07 30

68 15 00 

58 22 30 

68 30 00 

68 37 30 

58 45 00

68 52 30 

69 00 00 

69 07 30 

69 15 00 

59 22 30

59 30 00 

59 37 30 

59 46 00 

59 62 30 

60 00 00

60 07 30 

60 15 00 

60 22 30 

60 30 00 

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 46 00 

6^ 52 30

Area in 

square miles.

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 

147.21

146.64 

146.07 

145.50 

144.93 

144.36

143.79 

143.22 

142.65 

142.08 

141.50

Middle latitude of quadrilateral.

Oil/

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 62 30 

65 00 00

65 07 30 

65 16 00 

65 22 30 

65 30 00 

65 37 30

65 45 00 

65 52 30 

66 00 00 

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

Area in 

square miles.

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 

131.00 

130.47 

129.88

129.29 

128.70 

128.12 

127.53 

126.94

126.34 

125.75 

126.16 

124.67 

123.97

123.38 

122.78 

122.19 

121.59 

120.99

120.40 

119.80 

119.20 

118.60 

118.00

117.40 

116.80 

116.20 

115.59 

114.99

(420)
 WOODWARD.] AREAS OF QUADRILATERALS. 115

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

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

o i // 

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

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 46 00

72 52 30

73 00 00

73 07 30

Area in 

square miles.

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

94.78

94.16

93.54

92.92

92.30

91.08

91.05

90.43

89.80

89.18

88.55

87.93

87.30

Middle latitude of quadrilateral.

0 / II

73 15 00

73 22 30

73 30 00

73 37 30

73 45 00

73 62 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

7fl 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

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

Area in 

square miles.

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

76.32

74.69

74.05

73.42

72.78

72.14

71.51

70.87

70.24

69.60

68.96

68.32

67.68

67.04

66.41

65.77

65.13

64.49

63.85

63.20

62.56

61.92

61.28

60.(i4

60.00

69.35

58.71

(421)
116 FORMULAS AND TABLES. [BULL. 50.

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

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

O 1 II

78 52 30

79 00 00

79 07 30

79 15 00

71) 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

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

Area in 

square miles.

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

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

Middle latitude of quadrilateral.

O 1 II

84 30 00

84 37 30

84 45 00

84 52 30

85 00 00

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

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.

28.86

28.20

27.54

26.89

26.24

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.] 0

14.44

13.79

13,13

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

(422)
WOODWARD.] AREAS OF QUADRILATERALS. 117

TABLE X.V. Areas of qiiadrilaterals of Earth's surface of 10' extent in latitude and

longitude,

[Derivation of table explained in section (G); use of table explained on page 23.]

Middle latitude of quadrilateral.

 o /

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 65

6 05

6 15

6 25

6 35

6 45

6 55

7 05

7 15

7 25

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

13L.25

131.21

131.16

131.12

131.07

131.03

130.98

130.93

Middle latitude of quadrilateral.

o /

7 35

7 45

7 65

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 65

12 05

12 15

12 25

12 35

12 45

12 55

13 05

13 15

13 25

13 35

13 45

13 65

14 05

14 15

14 25

14 35

14 45

14 55

Area in 

square miles.

130.88

130.84

130.79

130.73

130.68

130.63

130.57

130.61

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

129.64

129.47

129.39

129.32

129.24

129.16

129.08

129.00

128.92

128.84

128.76

128.67

128.59

128.60

128.41

128.33

128.24

128.14

128.05

127.96

127.87

127.77

' 127.67

(423)
118 FORMULAS AND TABLES. [BULL. 50.

TABLE XV. Areas of quadrilaterals of Earth's surface of 10' extent in latitude and

longitude.

[DeriTation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

o /

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

22 05

22 15

22 25

Area in 

square miles.

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

1.26.00

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

122.56

122.42

122.28

Middle latitude of quadrilateral.

o /

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

29 25

29 35

29 45

29 55

Area in 

square miles.

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

x 119.85

119.69

119.53

119.37

119.21

119.04

118.87

118.7 L

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

115.37

115.18

114.99

114.81

(424)
 WOODWARD.] AREAS OF QUADRILATERALS. 119

TABLE XV. Areas of quadrilaterals of Earth's surface o/KX extent in latitude and

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

o /

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 46

33 55

34 05

34 15

34 25

34 35

24 45

34 55

' 35 05

35 15

35 25

35 35

35 45

35 55

36 05

36 15

36 25

36 35

36 45

36 55

37 05

37 16

37 25

Area in 

square miles.

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

107.86

107.63

107.41

107.19

106.96

106.74

106.61

106.29

106.Q6

105.83

105.60

105.37

Middle latitude of quadrilateral.

O 1

37 35

37 45

37 55

38 05

38 16

38 25

38 35

38 45

38 55

39 05

39 15

39 25

39 35

39 45

39 65

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

44 05

44 15

44 25

44 35

44 45

44 55

Area ia 

square miles.

105.14

104.91

104.68

104.44

104.21

103.97

103.74

103.50

103.26

103.02

102.78

102.64

102.30

102.06

101.82

101.57

101.33

101.08

100.83

100.59

100.34

100.Q9

99.^84

99.59

99.33

99.08

98.83

98.57

98.32

98.06

97.80

97.65

97.29

97.03

96.77

96.60

96.24

96.98

95.71'

95. 4S

95.19

94.92

94.65

94.38

94.11

(425)
120 FORMULAS AND TABLES. [BULL. 50.

TABLE XV. Areas of quadrilaterals of Earth's surface of 1CK extent in latitude and

longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

0 /

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

60 25

50 35

50 45

50 55

61 05

61 15

51 25

51 35

51 45

51 55

52 05

52 15

52 25

Area in 

square miles.

93.84

93.58

93.30

93.03

92,76

92.48

92.21

91.94

91.66

91.38

91.10

90.82

90.56i

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

86.68

85.39

85.09

84.80

84.50

84.21

83.91

83.61

83.31

83.01'

82.71

82.41

82.11

81.81

81.51

81.20

' Middle latitude of quadrilateral.

o / 

52 35

52 45

52 65

63 05

63 15

53 25

63 35

53 45

53 55

54 05

54 15

54 25

54 35

54 45

54 55

55 05

65 15

55 25

65 35

65 45

55 55

56 05

66 15

56 25-

66 35

56 45

56 55

57 05

57 15

57 25

57 35

57 45

67 65

58 05

58 15

58 25

58 35

68 45

58 55

69 05

59 15

59 25

59 35

59 45

59 55

Area in 

square mile.s.

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

76.67

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

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

(426)
 WOODWARD.J AREAS OF QUADRILATERALS. 121

TABLE XV. Areas of quadrilaterals of Eartli's surface of 10' extent in latitude and

longitude,

[Derivation of table explained in section (6); use of table explained on page 23.]

Middlt latitude of quadrilateral.

o /

60 05

60 16

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

64 05

64 15

64 25

64 35

64 45

64 65

65 05

65 15

65 25

65 35

65 45

65 55

66 05

66 16

66 25

66 35

66 46

66 55

67 05

67 15

67 26

Area in 

square miles.

66.61

fi6.18

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

58.33

57.99

67.64

57.29

56.94

66.69

56.24

65.89

65.54

65.19

64.83

64.48

64.13

63.78

53.42

63.06

62.71

62.35

62.00

51.64

51.28

Middle latitude of quadrilateral.

O '

67 35

67 45

67 65

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

70 45

70 65

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

73 45

73 55

74 05

74 15

74 25

74 35

74 45

74 55

Area in 

square miles.

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

45.61

45.15

44.78

44.42

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

(427)
122 FORMULAS AND TABLES. [BULL. 60.

TABLE XV. Areas of quadrilaterals of EarWs surface of 10' extent in latitude

and longitude.

[Derivation of table explained in section (6); use of table explained on page 23.]

Middle latitude of quadrilateral.

o / 

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

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 65

81 05

81 15

81 25

81 35

81 45

81 55

82 05

82 15

82 25

Area in 

square miles.

34.42

34.04

33.66

33.29

32.91

32.63

32.16

31.78

31.40

31.03

30.65

30.27

29.89

29.51

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

21.60

21.12

20.73

20.35

19.97

19.58

19.20

18.81

18.43

18.04

17.65

Middle latitude of quadrilateral.

o /

82 35

82 45

82 55

83 05

83 16

83 25

83 35

83 45

83 55

84 05

84 15

84 25

84 35

84 45

84 55

85 05

85 15

85 25

85 35

. 85 45

85 65

86 05

86 15

86 25

86 35

86 46

86 55

87 05

87 15

87 25

87 35

87 45

87 55

88 05

88 15

88 25

88 36

, 88 45

/ 88 55

89 05

89 15

89 25

89 35

89 46

89 55

»

Area in 

square miles.

17.27

16.88

, 16.60

16.11

16.73

15.34

14.95

14.57

14.18

13.79

'13.40

13.02

12.63

12.24

11.86

11.47

11.08

10.69

10.30

9.92

9.53

9.14

8.75

 8.36

7.97

7.59

7.20

6.81

6.42

6.03

5.64

6.25

4.86

4.47

4.09

3.70

3.31

2.92

2.53

2.14

1.75

1.36

0.97

0.58

0.19

(428;
WOODWARD.] MAP SCALE RELATIONS. 123

TABLE XVI. A^ial intervals corresponding to 0.01 inch on maps of various scales. 

[Derivation of table explained in section (13).]

Scale.

77^ 1.014 inches to 1 mile .....

Intervals 

in feet.

208.333

105. 600

104. 167

52.800

52.083

26.400

25. 000

(429)
124

Miscellaneous Constants.

log. 

Base of Naperian logarithms...... .......... £ = 2.7182818 0.4342945

Log e = modulus of common logarithms._ jn = 0.4342945 9.6377843 10 

Radius in seconds of arc..................... 206264.8 5.3144251

Radius in minutes of arc.................... 3437.7468 3.5362739

Radius in degrees of arc ................... 57.29578 1.7581226

Ratio of circumference to diameter of circle, it = 3.14159265 0.4971499

Dimensions of the Earth as represented by Clarice's spheroid (of 1866J.

Semi axis major.........................feet a = 20926062 7.3206875

Semi axis minor.........................feet b = 20855121 7.3192127

(Eccentricity)2 ............................. e2 = 0.00676866 7.8305030 10

Perimeter of meridian ellipse .......... miles 24859.76

Circumference of equator.............. miles 24901.96

Area of earth's surface ......square miles 196940400

Relations between English and metric units of length. Clarice's values.

No. inches in 1 meter........................ 39.370432 1.5951702

No. feetin 1 meter.......................... 3.2808693 0.5159889

No. yards in 1 meter........................ 1.0936231 0.0388677

No. meters in 1 inch....................__ 0.0253998 8.4048298 10

No. meters in 1 foot ........................ 0.3047973 9.4840111 10

No. meters in 1 yard........................ 0.9143917 9.9611323-10

No. meters in 1 mile ........................ 1609.3296 4.2066450

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