DEPARTMENT OF THE INTERIOR

Ray Lyman Wilbur, Secretary

U. S. GEOLOGICAL SURVEY 

George Otis Smith, Director f^ .

Bulletin 809

FOEMULAS AND TABLES

FOR THE

CONSTRUCTION OF POLYCONIC PROJECTIONS

COMPILED BY 

C. H. BIRDSEYE

UNITED STATES

GOVERNMENT PRINTING OFFICE 

WASHINGTON : 1929
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CONTENTS

_ 

"V? , ' .

'" f /

Page

Preface ___-_______-____--__________--_--------_-_________- - - li.;. _ _ v

General considerations-._____________-_..-__----___-_____..___-_--_-- 1

Choice of a projection._____!__.___________._-_________________ . 1

Advantages and disadvantages of the polyconic projection __________ 1

Characteristics of the polyconic projection..__.____________________ 2

Theory of the American polyconic projection_________________________ 3

Clarke's spheroid..____________________________________________ 3

Constants of the generatingellipse________-_________________-___ 4

Radii of curvature. ____________________-!______________________ 4

Meridional arcs.________--_____--__--------______--___-------- 9

Arcs of the parallel.___________-____-___----______-____-_---_-_ 14

Rectangular coordinates._______-___----_--________-__-___----_ 15

Analysis of formulas._____.____-__-_-____--_-____.____---_---_- 19

Conversion data_______________________----__-_______-____-_---__. . 20

Construction of projections.________--------_-.---____-_--____------- 21

Different methods of construction_______________________________ 21

Geological Survey method__________ -_____.._-__--__________--__ 21

Interpolation for other scales. ___--__---_-i-_-____-______-_-_-_. 25

Modified polyconic projection of map of the world on the millionth scale. _ 25

General specifications.__________-_-_---__--________-__---_--___ 25

Joining of sheets____-__-________-__-__-_--_-_-_________-_---_. 27

Drawing of parallels.__________________________________________ 29

Description of tables____-_____----_-------_-____-_____- ----. 29

Method of construction of projection. __ .___._______'_____________ 31

Theory of the modified polyconic projection_ ____________________ 35

Nomenclature ____________________________________________ 35

Dimensions of the spheroid.________________________________ 36

Radii of curvature________________________________________ 37

Order of computations.____________________________________ 37

Lengths of the meridians.__________________________________ 38

Rectangular coordinates.____----------_______________---_- 41

Table 1. Coordinates for the projection of maps, scale 1 :96,000..-.__-- 43

2. Coordinates for the projection of maps, scale 1 :48,000._______ 51

3. Coordinates for the projection of maps, scale 1 :31,680-_______ 68

4. Coordinates for the projection of maps, scale 1 :24,000.-__.___ 94

5. Coordinates for modified polyconic projection of map of the

world, natural scale, in meters.._________________________ 120

6. Coordinates for modified polyconic projection of map of the

world, scale 1 :1,000,000, in inches.-..-___.________ 123

Index.....__.._._____.__._.---------.-..._._..________-_.__ 125

in
ILLUSTRATIONS

FIGURE 1. Elements of generating ellipse-___________________________

2. Elements of ellipsoid and tangent cone_____________________

3. Sector of tangent cone.___t._________________--_---_____--

4. Developed cone_-_-_-___--___-____-_______---_--________

5. Polyconic projection of 15-minute quadrangle....___________

6. Junction of sheets of map of the world_______-___-_-.__--_

7. Special scale used by the United States Geological Survey ___

8. Construction of modified polyconic projection._____________

9. Computation of modified polyconic projection tables. _______

	IV
PREFACE

The primary purpose of this publication is to provide tables for 

the construction of poly conic projections of topographic maps of 

standard quadrangles without any interpolation. Bulletin 650, 

"Geographic tables and formulas," gives many of the data needed, 

but the projection tables in that bulletin are incomplete, and many 

of them require difficult interpolation. The tables given herewith 

have been prepared with arguments for each meridian and parallel 

represented on maps of standard quadrangles, and the data are 

given in inches for each of the standard field scales employed by the 

Geological Survey. Tables in the same form have also been prepared 

for the two scales on which most of the quadrangle maps of the 

Geological Survey are published in final form 1:62,500,1:125,000 

and also for the scales 1:63,360, 1:20,000, 1:12,000, and 1:10,000. 

On account of lack of funds for printing, these tables have not been 

included in this publication, but it is hoped that they can be published 

at a later date.

A secondary purpose is to present in one publication all of the 

theory of the poly conic projection, with the formulas developed in 

detail and their use so explained that the engineer or cartographer 

with only an average knowledge of mathematics can understand and 

use them. Complete instructions are given for making polyconic 

projections of standard quadrangles by means of these tables.

The theory of the modified polyconic projection of the international map of the world is also explained, and tables for its construction are given with the data in meters on the natural scale as well as 

in inches on the scale of 1 :1,000,000. For the first time these data 

have been computed for each degree of latitude.

The tables have been computed by members of the computing section of the United States Geological Survey, under the supervision 

of George T. Hawkins. The author is indebted to David H. Baldwin 

and Edward W. Tibbott, of the Geological Survey, and to Oscar 

Adams, of the United States Coast and Geodetic Survey, for valuable advice and critical review. Notices of .errors and suggestions 

for improvement of the material are invited.

C. H. BIRDSEYE, 

Chief Topographic Engineer.

FORMULAS AND TABLES FOR THE CONSTRUCTION 

OF POLYCONIC PROJECTIONS

Compiled by C. H. BIRDSEYE

GENERAL CONSIDERATIONS

Choice of a projection. In mapping large areas the engineer is

confronted with the problem of representing accurately on the plane 

surface of a map the details that exist on the earth's spherical surface. 

As it is impossible to do this exactly, he must resort to the use of some 

convention that will represent the earth's surface with the least distortion. The systematic drawing on a plane surface of lines that 

represent reference lines on the spherical surface of the earth is 

called a map projection. There are many systems of projection, 

each of which fulfills certain desirable conditions but none of which 

is ideal. The choice of the proper projection to use for a certain 

map is not always easy but depends largely on the extent of the area 

to be represented and on the use to which the map will be put. The 

best treatise on map projection published in English is United States 

Coast and Geodetic Survey Special Publication 68, "Elements of 

map projection."

Advantages and disadvantages of the polyconic projection. The 

topographic engineer needs a projection which is simple in construction, which can be used to represent small areas on any part of the 

globe, and which, for each small area to which it is applied, preserves 

shapes, areas, distances, and azimuths in their true relation to the 

surface of the earth. For areas of smah1 extent the polyconic projection meets all these needs, and it was adopted for the standard 

topographic map of the United States, in which the 1° quadrangle 

is the largest unit and the 15' quadrangle is the average unit. Misuse 

of this projection in attempts to spread it over large areas that is, 

to construct a single map of a large area has developed serious errors 

and gross exaggeration of details. For example, the polyconic projection is not at all suitable for a single-sheet map of the United States 

or of a large State, although it has been so employed. Its greatest 

advantage lies jn the facts that it has been computed for all latitudes 

of the entire spheroid and that it represents a small area on any part 

of the earth's surface just as well as one on any other part.
2 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

Characteristics of the polyconic projection. The polyconic projection takes its name from the fact that it is based on the development 

of a large number of cones each conceived to be tangent to the spheroid at a parallel of latitude to be represented on the map. It has 

been computed for every minute of latitude from 0° to 90°, and existing tables make its construction very easy. It was devised by 

Ferdinand Hassler, the first superintendent of the United States 

Coast and Geodetic Survey, and has been computed by that bureau. 

The theory of the projection and tables for its construction are given 

in Coast and Geodetic Survey Special Publications 57 and 5.

In this projection a central meridian is drawn as a straight line, 

and the intersections of the parallels are spaced true to scale along 

this central meridian. Each parallel is then laid down separately 

by means of a cone whose base is tangent to the earth's surface at 

that parallel, with the vertex of the developed cone on the extension 

of the central meridian. The arcs of the parallels thus drawn are 

subdivided to true scale, and the meridians are drawn through 

these subdivisions. As a result the central meridian is shown as a 

straight line, and theoretically all other meridians are shown as 

curves. As the meridians and parallels nowhere intersect at right 

angles, except along the central meridian, and as all the other meridians are drawn as curves concave toward the central meridian, 

it is theoretically impossible to fit together in a row, east and west, 

two maps each of which is developed on its own central meridian, 

as their joining edges are curved in opposite directions. However, 

in practice and within certain limits this theoretical condition does 

not exist. It is impossible for a draftsman or an engraver to draw 

the limiting meridians of a 1° or smaller quadrangle within the 

latitudinal limits of the United States other than as straight lines. 

Moreover, as the projection is extended from the central meridian 

the length of the meridians is theoretically increased, but even in 

latitude 60° the difference in length between the line representing the 

limiting meridian of a 1 ° quadrangle and the line representing the central meridian is too small to be plotted, and the lengths of all the 

meridians on a projection of 1° or smaller may be assumed to be 

the same. Therefore, a row of maps east and west will join perfectly, 

although as the north edge of each map is shorter than the south 

edge the row will form a curve. A tier of maps north and south will 

also join with sufficient accuracy. Theoretically, there will be small 

gores between the edges of each east-west row of maps and the next 

row to the north or south, but in actual practice the distortion of map 

paper due to changes in atmospheric conditions is greater than the 

error of joining, so that by slightly stretching the outer tiers a moderate number of maps say five or six each way can be joined with 

approximately perfect accuracy. Seldom, if ever, will a map user
THEORY OP THE AMERICAN POLYCONIC PROJECTION 3

wish to join more than five or six quadrangle maps in any direction. 

The limits in the size of tables or wall space make further extension 

impracticable, and therefore the theoretical weaknesses of this 

projection can be*ignored so far as maps of small quadrangles are 

concerned.

THEORY OF THE AMERICAN POLYCONIC PROJECTION

Clarice's spheroid. The data in the following tables for the polyconic 

projection of maps are based on the dimensions of the spheroid 

determined by Col. A. R. Clarke, R. E., in 1866, as expressed by 

Clarke in meters but not as expressed by him in feet. Although the 

International Geophysical Union has adopted the Hayford spheroid 

as the most exactly determined representation of the size and shape

of the earth, and the dimensions of the Hayford spheroid are now used 

in geophysical research, still the Clarke spheroid represents very 

closely the true size and shape of the earth, and most of the existing 

tables for the projection of maps are based on it. In the following 

tables the data are merely converted from measurements on the 

spheroid in meters, given in United States Coast and Geodetic Survey 

Special Publication 5, to inches on the several map scales employed 

by the United Sitates Geological Survey. Some interpolation has 

been required in order to provide data for arguments for use in the 

construction of standard projections of 7^' and 15' quadrangles, 

such as latitude and longitude intervals of \%r , 2^', 3 %', and 7^'. 

Interpolation has also been employed in the conversion of the data, 

which may have resulted in errors of 0.001 inch in the tables, but 

one one-thousandth of an inch can not be plotted. .

Tables are given for all the standard field scales employed by-the 

Geological Survey for latitudes 0° to 51° or more. As the computation of special projections may be required, the fundamental formulas 

and demonstrations of their development are given with instructions 

for their use. The nomenclature employed in the formulas given in 

different publications on this subject differs, and in some demonstrations of the development of the formulas there may be some doubt 

as to the meaning of the symbols employed and some confusion in the 

use of mathematical expressions, such as an arc expressed in terms 

of the radius. An attempt has therefore been made to explain fully 

the meaning of each symbol or expression and to make the demonstrations and the instructions as to the use of the formulas so clear that a 

cartographer with only average knowledge of mathematics can follow 

them. In these demonstrations the following publications have been 

consulted freely and to some extent are quoted verbatim: United 

States Coast and Geodetic Survey Special Publications 5 and 57, 

Smithsonian Geographic Tables, and United States Geological Survey Bulletins 50 and 650.
4 FORMULAS TOR CONSTRUCTION OF POLYCONIC PROJECTIONS

Clarke expressed the dimensions of the spheroid in meters and also 

in English feet. According to him 1 meter = 39. 370432 inches = 

3.28086933 feet. The Smithsonian Geographic Tables and United 

States Geological Survey Bulletin 50, both prepared by R. S. Woodward, depend on the Clarke spheroid as expressed by him* in feet. 

Some of the tables given in United States Geological Survey Bulletin 

650 are extracts from the Smithsonian Geographic Tables and some 

are extracts from the United States Coast and Geodetic Survey 

tables. The polyconic projection tables computed by the United 

States Coast and Geodetic Survey depend on the dimensions of the 

spheroid as expressed by Clarke in meters, and the tables given herein 

depend on these dimensions and on the legal value in the United 

States of 1 moter = 39.37 inches = 3. 28083333 feet. This figure does 

not express the absolutely correct relation between the international 

meter and the inch, but it is close enough for all practical purposes of 

map projection. Therefore, in order to reduce the dimensions of the 

spheroid as given by Clarke and Woodward in feet, and any tables of 

length based thereon, to corresponding values given in the United 

States Coast and Geodetic Survey Tables and those in this publica39 37 tion, it is necessary to multiply by the fraction on Q7n4^2 = 0.99998903

Gog. 9.99999523-10).

Constants of the generating ellipse. The constants of the generating 

ellipse of a spheroid for which values are required in the computation 

of projection tables are defined as follows:

a = seinimajor axis. 

b = semiminor axis. 

e= eccentricity.

n = ~a+b

The values of these constants with their logarithms for the Clarke 

spheroid of 1866 expressed in meters as. used in computing the tables 

in this publication are :

a =6,378,206.4 meters. log a =6.8046985690.

b =6,356,583.8 meters. log b =6.8032237768.

e2 =0.0067686580. log e2 =7.8305025710-10.

n =0.0016979157. log n =7.2299161198-10.

Radii of curvature. The principal radii of curvature of an ellipsoid 

(see fig. 1 ) are

pm = the radius of curvature of a meridional section.

p n = the radius of curvature of a section normal to the meridian.

Both are constant for a given latitude, but for precise computations 

infinitely small sections of the circumference of the meridional ellipse 

must be considered, because meridional arcs cover a range of latitude,
and therefore pm must be evaluated for infinitely small changes in 

latitude.

In Figure 1, let APP'D represent a quadrant of the generating 

ellipse; AQQ'B, a quadrant of the circumscribed circle; EFF'D, a 

quadrant of the inscribed circle; P and P', two contiguous points on 

the ellipse at the ends of the infinitely small arc ds; PK and P'K 

( Pm), the normals at P and P', or the radius of curvature of the 

infinitely small meridional arc ds; PK' ( = pn)> the radius of curvature 

of a section normal to the meridian; OA ( = a), the semimajor axis; 

OD (= b), the semiminor axis; the angle XRP = <j>, the latitude of the 

point P; and the angle XOQ = ^, the geocentric latitude of the point P.

FIGURE 1. Elements of generating ellipse

Expressing the coordinates of the point P in parametric form, we 

have

x = a cos ^

y = b sin \f/

As the point moves from P to P' the small changes in x and y are 

PF (= dx) and FP' ( = ^y), respectively. If the two equations are 

differentiated, $ being regarded as a variable angle and x and y as 

functions of ^, then

dx = a sin ^ d\f/

dy= b cos \f/ d\J/

The triangles RPE and PP'F are similar and the angle PP'F = angle 

= </>, therefore

, ^ -dx tan <£= 5 

dy
6 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

Substituting the values of d\ and dy, we have

, a sin \j/ a tan ft=r r~T: tan w b cos b

or

tan ^ = tan

The eccentricity of the ellipse, represented by e, is defined by the 

equation

a2 -_tf =1 _b!

2 * «2

2

t* *J ^ M

 ____________ I ___ ___.

9 -9

a 

or

and

Substituting this value, we have

tan \f/ = Vl ~~ e2 tan ft 

but ___

. . , . , tan ^ tan \f/ ~Jl e2 tan ft sin \f/ = tan ^ cos ^ = - n 

+ tan2 </> - e2 tan2

/-, 2 sn e sn ___ 

___ cos <j> _ ______ cos </> ______ _ Vl e2 sin </>

V sin2 (/> _ 2 sin2 <ft Vcos2 0 + sin2 0 - e2 sin2 0 V 1 - e2 sin2 <£

1 ~r 5 T 6 5 ~ I

CDS'5 0 COS2 </> COS $

and

sin 1 1

cos \/ =

'/ VI + tan2 ft e2 tan2 ft 

1 1 cos

2 sin2 <^> Vcos2 </> + sin2 ^ e2 siii2 o 

COS"1 ft COS ft

Using the fundamental differential formula d tan x = sec2 x dx, we 

have

Substituting the value of tan \f/ and differentiating, we have 

sec2 ^ d\f/ = Vl ~~ e2 sec2 ft <Zft
THEORY OF THE AMERICAN POLYCONIC PROJECTION

v

or

sec2 0 d<f> /- $ , cos2 = V v 1 ~ e sec2 v0 a# cos2 = 

sec e sm

1

O o , 

 e sin'' <£

4

Let ds denote the infinitely small meridional arc PP' of the generating 

ellipse; pm = PK, the radius of curvature of the small arc; and d<t> 

the angle PKP', expressed in circular measure, through which the 

end of the radius moves in generating the small arc. . Then considering 

the infinitely small arc of the ellipse as an arc of a circle and using

> the relation arc = radius times generating angle, we get

Pm d<j> = ds.

But

ds = -\dx2 + Sy2 = Va2 sin2 ^ + b2 cos2

a2 sin2 \l/ + a2 (l e2 )cos2 \f/d\l/ = a, Vsin2 \(/ + cos2 \f/ e2 cos2

a -^L i 

also

 e2 cos2 

sin2

\ l e2 sm2 4) 

, )=-*/ ; TT 

)/ \ l-e2 s

V l-e2 sin2 0 ~ Vl- e2 sin2 ^ 

and

therefore

and

but

r

therefore

a(l-e2 ) 

Pm ~(l-e2 sin2 <*>)*---"--"---" --"--I^

If we pass a plane through any point P on the ellipsoid, parallel 

to the equatorial plane of the ellipsoid, this plane intersects the 

ellipsoid in a circle which represents the parallel at the point P, and 

the normals to the surface of the ellipsoid at every point on this
8 FORMULAS FOR CONSTRUCTION OF EOLYCONIC PROJECTIONS

parallel circle intersect in a point K' on the minor axis of the ellipsoid. 

If we pass a plane through the normals of any two contiguous points 

on the parallel circle and then let these normals approach each other 

until they coincide, we obtain a plane tangent to the given parallel 

and perpendicular to the meridian at the point of tangency. The 

radius of curvature in this plane corresponding to a small arc of the 

parallel is represented by PK', because the normals of each point on 

the arc intersect at K'. If we denote this radius by p n we have in 

the triangle PK'E',

, ' x 

cos <t>= 

Pn

Hence

a cos 0

_ a cos ty ^ V 1 e2sin2 <ft ^ ,,.,., 

' ^

___ ___ 

cos <£ cos 0 (1 e2 sin2 </>)»"

It is evident that p n is always greater than pm except when <f>= ± 90° ; 

in that event p a = pm.

Logarithms of pm and p n in English feet are given in the Smithsonian Geographic Tables for each minute from 0° to 90° and in Geological Survey Bulletin 50 for each minute from 21° to 51°; to reduce 

these logarithms to logarithms of the radii expressed in American 

feet to correspond to the relation with the legal value of the meter 

in the United States, 47.7 in the last (7th) place must be subtracted. 

To reduce logarithms of American feet to logarithms of meters (United 

States legal value) the logarithm 9.48401583-10 should be added. 

Consequently the logarithms given in the Smithsonian Geographic 

Tables or in Geological Survey Bulletin 50 may be used for computations of formulas and tables given in the present publication by 

adding the logarithm 9.48401106-10.

However, in connection with geodetic computations the Coast and 

Geodetic Survey has adopted several factors based on the Clarke 

spheroid as expressed in meters (United States legal value), and it is 

more convenient to use two of these factors, log A and log B, than to 

use the values of pm and p n given in the Smithsonian Geographic 

Tables. The logarithms of these factors have been computed to the 

seventh place for each minute from 0° to 72° and are given in Geological Survey Bulletin 650 and in Coast and Geodetic Survey Special 

Publication 8. These factors are

tii a arc 1

(l-e2 sin2 0) 

a(l-e2 ) arcl
THEORY OF THE AMERICAN POLYCONIC PROJECTION 9

V Introducing these factors into the formulas for pm and p n given above, 

we have

'

Pn A arc

In these factors arc I" is expressed in radians 1 and is 0.0000048481368 

log arc 1" = 4.6855748668-10, which is the same as log sin 1" to the 

tenth decimal place.

Meridional arcs. The length of an arc of a circle equals the length 

of its radius times the length of the arc expressed in radians. If a 

very short section of a meridional ellipse is considered as an arc of a 

circle, the length of this short section can be found by the use of 

simple formulas with sufficient exactness for use in ordinary largescale map projections. But if it is desired to find the length of a 

long arc or to determine exactly the length of a short arc, it is necessary to take the summation of the lengths of the infinitely small arcs 

making up the arc whose length is desired, by the process of integrating between the limiting parallels the variable lengths of the 

small arcs corresponding to infinitely small uniform subdivisions of 

the difference of latitude.

The length of a short meridional arc lying between two given parallels of latitude can be computed by the simple formulas given below, 

in which

0i and 02 are the latitudes, expressed in degrees, minutes, and 

seconds, of the ends of the arc.

0=7> (0i + 02 ) and is the mean latitude of the arc.

A0 = 02 0i and is here taken as the length of the arc expressed in 

radians.

A0'~ 02 0 and is here taken as the length of the arc expressed in 

minutes.

Arc 1' = 0.0002908882 radian, or the length of an arc of I' for a 

unit radius.

AM is the required length of the arc, or the meridional distance 

expressed in meters. Then, as the length of the arc equals the length 

of the radius times the arc expressed in radians, 

AM = pmA0 = pm arc I' A0' 

But

1 

pm ~B arc 1"

1 -A radian is an arc of a circle equal to its radius and is a unit arc in circular measure. Its value in degrees 

is §29, which equals 57°.29577951 or 3437'.746771 or 206264".80625.
10 FORMULAS FOR CONSTRUCf ION 6tf POLYCONIC PROJECTIONS

therefore

A arcl'A4>' = 60A4/ AiVi arcl"B B -- --- M

Log 60 = 1.7781513. Log B for the mean latitude <£ is given for each 

minute of latitude in Table 28, Geological Survey Bulletin 650, and 

in Coast and Geodetic Survey Special Publication 8. The approximate formula for AM should not be used for arcs of the meridian 

longer than 1°. The error will depend on the latitude but for 1° will 

be approximately 4- 0.8 meter, for 30' about + 0.4 meter, for 15' about 

+ 0.2 meter, and for 7^' about +0.1 meter. The latitude, the scale, 

and the size of the projection will control largely the selection of 

formulas.

For the computation of the length of a long meridional arc or the 

precise computation of a short arc, a formula must be used which will 

give the sum of the varying lengths corresponding to infinitely small 

subdivisions of the difference of latitude. In other words, the approximate formula AM = pmA<£ must be integrated between the limits of 

the latitudes of the ends of the arc. The expression will be integrated 

first in general form between latitude 0° and any latitude 4>.

<Z0 = an infinitely small difference in latitude, or the differential of 

the latitude.

M = the length of the arc in met'ers, from the Equator to latitude 0. 

Using the value of pm given in [I], we have

M _ r*a(l-e»)dfr 

JoU-e2 sin 2 0)*

Expanding the binomial reciprocal of the denominator, we have

Q IK QC

(1-e2 sin2 <£)-*=l+§e2 sin2 4> + ^e4 sin4 <£ + ?^e6 sin6 0

A o 10

i «5ltJ a o . i + 128 sm 0+ ' 

But,

sin2 0=H(1 cos 2<£)=7T H cos 2<£

31 1 sin4 $=-5 7: cos 2</>+^ cos 40

O 4 O

5 15 3 1 

sm6 0=y^ O-H cos 2</> + jg cos 40 oTo cos 60

o r <j <j 1 1

sin8 <t> = ~ cos 2(^ + cos 4(^~ COS 6<^ + COS 8<^

Substituting these values and arranging the terms as constants and as 

coefficients of cos 2<t>, cos 4$, etc., we have
THEORY OF THE AMERICAN FOLYCONIC PROJECTION 11

/-, 2 a^-- (l-e2 sm2 0) *= ' 3 2 45 4 175 6 11025 8

B

'3 2 15 4 525 6 , 2205 . , \

C

15 4 105 2205 ^ , \ _

64 e 256 e 

D

315 6 ,

512 e + 

E

4096" ' ;-

315 fi , \

2048 /

315 8 , \

16384 e ' /

cos 40

cos 60

cos 80

Then 

M J

4> 

a(l-e2 )[A-Bcos20 + Ccos40-Dcos604-Ecos80- 

o

 ]<Z0

But

m fmdx =4 mx 4- k and J*m cos nx dx= sin nx 4- k

fundamental form u 1 a s in

which 

m is a definite

coefficient 

x is a variable

quantity 

n is a coefficient

of the variable 

k is a constant.

Therefore

y a (1 e2 ) A d!0 = a (1 e2 ) A0 + k 

/a(l-e2 ) B cos. 20d0 = a(l-e2 ) B ^ sin 204-k

y a (1 e2 ) C cos 40 d<t> = a (1 e2 ) C j sii 

y a (1 e2 ) D cos 60 d<f> = a (1 e2 ) D TT si]

6243° 29 2
The value of M between the limits 0° and <t>° is the difference between 

the integrals when 4> = 0° and when 0 = 0°. If 4> = 0°, then sin 2<£, 

sin 4<£, etc., = 0, and the integral of e!ach of the five terms given above 

is equal to k. In the subtraction of integrals all the k's cancel. 

Therefore,

1 1 +^E sin 80- ....

° . ' . J 

Substituting the values of A, B, C, D, and E, we get

, 3 , , 45 4 , 175 6 , 11025 8 , 6 ^6 +256 e + I6384 e +

1/3 2 , 15 4 , 525 6 , 2205 8 , ~2V4 e + 16 e + 6l2 e +2048 6 + 

, 1/15 4 , 105 6 2205 

+ 4(64 e+256 e

--

1/35 6 , 315 

Let . j 

,3 2 45 4 ,175 6 , 11025 . 8 , \ f

4- o'-I- o* -+- o° +- o°-I- . . 1

^4 e ^64 e ^256 e 16384 6 + / 

= 6,367,399.6891 meters.

^15 4, 525 6j^ 

+e +e +

16 512 2048 

= 32,433.8882 meters.

, 105 2205 .

= 34.4187 meters. ] 

i

0.0454 meters.

.. 0.00006 meters. 

Then

£ [VI]

This expression, in which <f> is expressed in radians, 'gives the length 

of the arc of the meridian (in meters, if a is taken in meters) from the
'THEORY OF THE AMERICAN POLYCONIC PROJECTION 13

Equator to the parallel at latitude 0. The length of the arc of the

meridian represented by the difference between two values of 0 is

found by taking the difference in the values o'f M for the two latitudes.

Let M2 = length of the arc of the meridian from the Equator to

latitude 02 . 

MI = length of the arc of the meridian from the Equator to

latitude 0i. 

A M = M2 MI = length of the arc between latitudes fa and 02 .

0 = 77 (02 + 00 = mean latitude of the arc. Z

A0 = (/>2 0i 

Then

AM = AO (02 - 00 - « ^2 (sin 202 - sin 20J -\-~ A4 (sin 402 - sin 40t

But

-TjAe (sin 602 sin 600 + AS (sin 802 sin 800 

sin a sin j8 = 2 cos (a + /3) sin--(a j8)

Substituting

2 02, 4 02 , etc., for a and 2 01? 4 0i, etc., for /3, we have

-Ao (02 -00- 1 A2 f2 cos^ (202 + 200 sini (202-200 1 

+^A4 2 cos^(403 + 400 sin g (408-400

AM

008^(602

+ ^ A8 [2 cos I (802 + 800 sin | (802 - 800J 

But

i (20a + 200 = 20, i (402 + 400 =40, etc. 

and

i(202-200 = A0, i (402 -400 =2 A0, etc.

therefore

AM = AoA0 A2 cos 20 sin A0 + A4 cos 40 sin 2A0

 A6 cos 60 sin 3 A0 + A8 cos 80 sin 4 A0 .... -..[VII]

In the first term of the formula given above, A0 is expressed in radians, 

and the value of A0 is 6,367,399.6891 meters. If it is desired to use
14 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

the formula with A<£ -expressed in degrees, minutes, or seconds, values 

of AQ must be taken as follows :

= 111, 132.0894 meters log = 5.0458394793

oOU

meters log = 3.267688231 6

A"o = i ofjnnn AO = 30.8700 meters log =1.4895366

In computing lengths of arcs of the meridian for the projection tables 

given in this publication, in which the arcs are taken in terms of 

minutes, the following formula should be used, the last term containing A8 being dropped :

AM = 1,852.2015A4>'- 32,433.8882 cos 2</> sin A<£ + 34.4187 cos 4<£sin2A0 

-0.0454 cos 6<£ sin 3 A<£ + ..... ______________ ___ -[VIII]

log 1,852.2015 = 3.2676882316 

32,433.8882 = 4.5109990154 

34.4187 = 1.5367944629 

0.0454 = 8.6570559-10

Arcs of the parallel. For computations of the length of the arc of 

the parallel lying between two given meridians of longitude the formulas given below may be used, in which 

4> is the latitude of the parallel, expressed in degrees, minutes, 

and seconds.

r is the length of the radius of the parallel, expressed in meters.

p n is the length of the radius of curvature of the section normal to' 

the meridian, expressed in meters.

Xx and X2 are the longitudes of the ends of the arc, expressed in 

degrees, minutes, and seconds. \

AX = X2 Xi and is the arc of the parallel expressed in degrees or 

minutes or seconds, the unit depending on the formula used. If 

fractional parts of degrees or minutes or seconds are required they 

must be expressed decimally.

AP is the required length of the arc expressed in meters.

The radius of any parallel is equal to the product of the radius of 

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

of that latitude, as is seen in Figure 2 in the triangle PK'M, in which

r 

cos <f> = Therefore Pn '

r = p n cos (f> 

and the entire length of the parallel is

COS <£
THEORY OF THE AMERICAN POLYCONIC PROJECTION 15

Any arc of the parallel is equal to the entire length of the parallel 

divided by the number of units in the circumference and multiplied 

by the number of the same units in the arc. Therefore

-r, 2irp a COS 0 . . , .

= 360 ^ m degrees) 

But

1

pn A arc 1" 

therefore

2ir \/COS<A,._ .

(AX arc 

207T

But

10 T 207T 207T arcl =

180 

therefore

AP (meters) = 3600^^ AX (degrees)

= 60 AX (minutes) -[1X1

COS </>.,/ , N = r AX (seconds)

Rectangular coordinates.- In the poly conic system of map projection 

each parallel of latitude represented on the map appears as the developed circumference of the base of a right cone tangent to the spheroid 

along that parallel. Thus the parallel PN .(fig- 2) and the arc PiP2 

(fig. 3) will appear in projection as the arc of a circle PPiP2N (fig. 4) 

whose radius GPi = Hs equal to the slant height of the tangent cone 

PGN (fig. 2).

In constructing a map projection on this system the meridians and 

parallels are usually delineated by plotting and joining their points 

of intersection. The coordinates of these points may be expressed 

in the following manner (see figs. 3 and 4): For any parallel, as 

PPiP2N, take the origin Px at the intersection with the central meridian and let the rectangular axes of Y^G) and of X(PiQ) be respectively coincident with and perpendicular to this meridian.

Let AX represent the difference of longitude between the central 

meridian and the next adjacent one; AP7=PiP2 the arc of the parallel 

between the central meridian a.nd, the next adjacent one; 0 the angle
16 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

at the apex of the developed tangent cone between the central meridian 

and the next adjacent one;. </> the latitude of the parallel, which is 

also the angle at the apex of the tangent cone between a meridional 

element of the surface of the cone and its axis; Z the slant height of 

the tangent cone and the radius of the developed parallel; r the radius 

of the parallel in the plane of the parallel; and p a the radius of curvature at P! of the cross section of the ellipsoid through the point P! 

normal to the central meridian. 

Then from Figure 4, in the triangle GP2S, it is apparent that

x = I sin 0

and in the triangle PtP2S that

y = x tan

-f

*

FIGURE 2. Elements of ellipsoid and tangent FIGURE 3. Sector of tangent 

cone

Substituting the value of x and remembering that sin 0 = 2 sin ^ cos ^

£ 2i

we have

y = 2Zsin2 |

From Figure 3, in the triangle GPiK', it is apparent that

= n COt

The length of the are AP (fig. 3) is measured by the length of the 

radius r of the parallel times the central angle AX (in radians), and 

the same arc is also measured by the length Z of the radius of the 

developed cone times the angle 6 (in radians) ; therefore
THEORY OF THE AMERICAN POLYCONIC PROJECTION 17

But from Figure 3, in the triangle PiK'M, it is apparent that 

r=^pn cos <£; therefore

p n AX cos <t> d =~. I 

Substituting in this the value of I given above, we have

6 = AX sin <j>

Then, substituting in the expressions for x and y the values of I and 

8, we have'

... /A , ^ cot </> sin (AX sin <£) rvi 

x = Pn cot 4>sm (AX sin </>)= / .._._..[X]

2 cot 4> sin2 -~ (AX sin 0) 

y = 2pn cot 0 sin2 ^ (AX sin 0) = A _ , - - [XI]

arc

FIGURE 4. Developed cone

In the two formulas given above the expression AX sin 4> is approximately the convergence of the meridian, and it will give an angle 

in the same units as are used for AX. For example, if AX is taken 

in radians, degrees, or minutes the angle (AX sin </>) will be in radians, 

degrees, or minutes, respectively. The expression sin $ is really a 

coefficient of AX just as if it were a quantity like 2 or 4.

Log A is given for each minute of latitude from 0° to 72° in 

Table 28, Geological Survey Bulletin 650, and in Coast and Geodetic 

Survey Special Publication 8.

Log arc 1" = 4.6855749-10.

The formulas for x and y given above are exact expressions of the 

coordinates of the point P. But when AX is srnall substitution for

the quantities sin (AX sin 0) -and sin2 -^ (AX sin )<£) of the first two
18 FOKMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

terms of their expansions will yield formulas more convenient to 

use and at the same time give satisfactory results. These expressions are

sin (AX sin <£) = AX sin (j> z (AX sin $)3 + 

sin2 (AX sin 0) = (AX sin *) 2 - (AX sin 0)4 + 

Substituting these values in the formulas for x and y, we have 

x = p n cot <£ AX sin <£ p n cot <j> (AX sin 0)3 +» ««

But cot 0 sin <£ = cos <£; therefore

pnAX cos <f> -X p nAX cos <f> (AX sin

or

X = pnAX COS

But

1 ^ (AX sin <£) 2 +

1

x AXcos0 r _ 1 gin 2+ ^ ^ ."]_________[XII]

A arc 1 [_ b J

^ A arc I' 

therefore

also

y=2pn 

1

But

i i r i "i = 2PnAX2 isin 0 cos 0 1 r^ (AX sin 0)2 + ....

therefore

sin 0 cos 0=77 sin 2<£ and pn ="i ri i fj A. arc i

AX2 sm 2<^> F. 1

 rs sm 4Aarcl" | 12

H

 __ _ _ 

J

In these two formulas for x and y AX is expressed in radians. AX 

may be taken in seconds, minutes, or degrees by using the following 

relations:

AXr = AX" arc 1"

AX^AX' arc 1' = 60 AX'arc 1" 

AX* = AX° arc 1° = 36QO AX° arc 1"
THEORY OF THE AMERICAN POLYCONIC PROJECTION 19

and the formulas may be written as follows by substituting in the 

coefficient the proper value of AX expressed in terms of arc 1", so as to 

cancel the term arc 1" in the denominator, and by substituting in 

the series the proper value of AX expressed in terms of arc 1", arc 

1', or arc0 , as the case may require:

= -T- AX" cos vi t'-i . j. ,.,.,, .,,/ -\ 1 c(AX" arc 1" sin

(AX")2 arcl"sin24>r. 1

sin

AX in 

seconds [XIV]

60AX' cos

15(AV)2 arcl / sin20ri 1 , AX , ,, . , 2 , "I V- =_^ ^__ A v.^i - (AA; arc r sin 4>)2 + J

3600AX0 cos 

A

rV 1 /A . 0 10 . , N2 , "I 1-g (AX°arc 1° sin 0) 2 + ....

900(AX°)2 arcl°sin20r 1,.. 0 10 . ' ' 1 Y75(AX°arc 1 sin LZ ]

AX in 

minutes

AX in 

degrees

[XV]

The constants in these formulas with their logarithms are as follows:

arc 1" = 0.0000048481 radian 

arc 1' =0.0002908882 radian 

arc 1° =0.0174532925 radian

log=4.6855749-10 

log=6.4637262-10 

log=8.2418774-10

This group of formulas seems more complex than the formulas for 

x and y given in X and XI, but the terms are so arranged that their 

use will be found more convenient in making a large number of 

computations, especially if the terms within the brackets can be 

dropped.

Analysis of formulas. Analysis of the last group of formulas for 

x will show that for values of AX of 1° or less and for latitudes of 60° 

or less the terms within the brackets can be disregarded with a resulting maximum error of + 2.2 meters in the abscissa of the developed 

parallel. The ordinate of the developed parallel of 45° has the greatest value for the same value of AX, and for values of AX of 1° or less 

the terms within the brackets in the formulas for y can be disregarded with a resulting maximum error of +0.007 meter. The 

following table gives an idea of the errors in the values of x and y 

resulting from the use of the first term only of these formulas:

Value of AX

Errors in x, in meters.. 

Errors in y, in metersLatitude 25°

60'

+0. 915 

+.0017

SO7

+0.114 

+.0001

15'

+0. 014 

+.0000

w

+0.002 

+.0000

Latitude 50°

60'

+2. 121 

+.0071

3<X

+0. 267 

+.0004

15'

+0.033 

+.0000

7*

+0.004 

+.0000
20 TOEMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

Even the maximum error of 2.2 meters on the spheroid can not be 

plotted on any ordinary map projection; consequently where AX does 

not exceed 60 minutes it is sufficient to use only the first term in the 

bracket in any one of the last group of formulas for x and y.

Analysis of the formula for AP and of the rigid formula for x shows 

that for short arcs of the parallel of 30' or less and for latitudes of 50° 

or less there is very little difference between the actual lengths of 

the arcs of the parallels and the abscissas of their development, and 

that either formula may be used for the other. The following table 

gives an idea of these differences:

30'

50, 475. 93

50, 475. 82

Latitude 25°

15' .

25, 237. 96

25, 237. 95

7K'

12, 618. 98

12, 618. 98

]

30'

35, 849. 06

35, 848. 79

Latitude 50°

15'

17, 924. 53

17, 924. 50

 M

8, 962. 26

8, 962. 26

CONVERSION DATA

Values in meters on the spheroid can be transformed easily into 

measurements in inches on any map scale by reducing meters to 

inches and dividing the result by the scale relation. In the following 

table the two operations have been combined into one factor, and the 

table will be found convenient for use in conversion by logarithms or 

for use by direct multiplication in a computing machine. The tables 

are based on the United States legal value of 1 meter = 39.37 inches, 

log= 1.5951654

Scale

1:5,000 

1 : 10, 000 

1 : 12, 000 

1:20,000

1:24,000 

1 : 31, 250 

1:31,680 

1:48,000

1 : 62, 500 

1 : 63, 360 

1:96,000 

1 : 125, 000

1 : 192, 000 

1 : 250, 000 

1 : 500, 000 

1 : 750, 000

1 : 1, 000, 000

Log to be 

added

7. 8966954-10 

7. 5951654-10 

7. 5159842-10 

7. 2941354-10

7. 2149542-10 

7. 1003154-10 

7. 0943802-10 

.6.9139242-10

6. 7992854-10 

6. 7933502-10 

6. 6128942-10 

6. 4982554-10

6. 3118642-10 

6. 1972254-10 

5. 8961954-10 

5. 7201041-10

5. 5951654-10

Multiplication 

factor

0. 0078740000 

. 0039370000 

. 0032808333 

. 0019685000

. 0016404167 

. 0012598400 

. 0012427399 

.0008202083

. 0006299200 

. 0006213699 

. 0004101042 

. 0003149600

. 0002050521 

. 0001574800 

. 0000787400 

. 0000524933

. 0000393700

Other interesting data concerning scale relations will be found in 

Tables 40 and 44, Geological Survey Bulletin 650.
FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 21 

CONSTRUCTION OF PROJECTIONS

Different methods of construction. Poly conic projections may be 

constructed by hand,.by using the instructions and tables published 

in Coast and Geodetic Survey Special Publication 5, which gives the 

required values in meters on the surface of the spheroid, or by using 

the instructions and tables given in this publication with measurements in inches on the map scale desired; or they may be constructed 

mechanically by means of a Bumstead projection plate. The practice of the Geological Survey indicates preference in the reverse order 

from that given above. Directions for constructing projections by 

hand can be given best by means of practical examples, but in general 

a central meridian is assumed upon which the intersections of the 

parallels are plotted to scale. Each parallel is then developed 

separately as an arc of a circle with its center lying in the extension 

of the central meridian. The arcs of the developed parallels are 

subdivided to scale, and the meridians are drawn, through the corresponding subdivisions. However, in actual practice on projections 

of small quadrangles the parallels are not drawn as arcs of circles, 

but their intersections with the meridians are plotted from the 

computed x and y values, and the sections of the parallels between 

adjacent meridians are drawn as straight lines. On poly conic 

projections of quadrangles of 1° or smaller all meridians may be drawn 

as straight lines, and in large-scale projections of small quadrangles 

in low latitudes both meridians and parallels may be drawn as straight 

lines. For example, the curvature of the parallels of a projection of 

a 15' quadrangle in latitudes from 0° to 25° on a scale of 1 :48,000 or 

for a 7 }/6' quadrangle in any latitude on a scale of 1 : 31,680 or larger 

is so small that it can not be plotted.

The meridional distances given in the tables apply to the central 

meridian of the projection, but for any standard quadrangle the 

difference in the curvature of the several parallels is so slight that the 

distances given for the central meridian can be taken for all other 

meridians.

Geological Survey method. For making a polyconic projection by 

the Geological Survey method it is necessary to have a metal straightedge graduated in inches, with one inch at one end subdivided into 

hundredths of an inch, the scale being standardized and the straightedge being as long as the longest dimension of the projection; a good 

rigid-beam compass with micrometer movement; a hard chisel-point 

pencil; a plotting needle; and the tables in this publication.

To illustrate this method the construction of a polyconic projection 

on a scale of 1:48,000 of the 15-minute quadrangle lying between 

north latitudes 40° 15' and 40° 30' and between west longitudes 88° 00' 

and 88° 15' is described. (See fig. 5.) The projection will show 

each 5-minute meridian and parallel. The central meridian of the
22 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

projection will represent the meridian of longitude 88° 07^' and will 

be used for construction only. Likewise the perpendicular crossing 

the central meridian at latitude 40° 22}^' will be used for construction 

only. The geometry of the construction given below is slightly 

different from previously established practice, owing principally to an 

effort to eliminate the plotting of the small ordinates of curvature, 

which is very difficult in a projection of a small quadrangle.

In Table 2 the group of ordinates and meridional distances computed for latitude 40° may safely be used for all latitudes between 39° 

30' and 40° 30' without interpolation between the values given and 

those computed for latitudes 39° and 41°. The meridional distance

--

£06

1 

BE

1 

\J

1

-.7 =______ _y^ _

^ " /° 

15' 10

B. ^- ~ T 8.631"- - - - - i 

N \S 2.89J" \0 S.794-" >

/! \

/ ! i 1 1

"col I

KJ»'

j |2.900" ._

] < )' /

N°0/" »J\ """'

Si I ^1 1

1 I 2.904 "

IS

is! i

IK' '

' ^'' __, 

\|/- ?.90^

/

s. so/"

-8.70B" -~ ^

5SO/S"

a7^'____-.^

' ** i* ' 68»

FIGURE 5. Polyconic projection of 15-minute quadrangle

for iy<i of latitude is found to be 3.796 inches; for 5', 7.588 inches; 

for 7^' 11.383 inches; for 10', 15.179 inches; and for 15', 22.766 

inches. In the part of the table headed "Abscissas of developed 

parallel" the x values for 2^' and 7^' of longitude in latitude 40° 

15' are found to be 2.908 inches and 8.723 inches, respectively. The 

x values for latitude 40° 20', 40° 22J#, 40° 25', and 40° 30' are 

shown in Figure 5. It should be noted that the measurements given 

here and on Figure 5 were taken from an old table, and some of 

them contain small errors in the third decimal place, which have 

been corrected in Table 2. In the group of ordinates of developed 

parallel the y value for 7^' of longitude is found to be 0.006 inch, 

and for 2J^' of longitude 0.001 inch. These are all the measurements
CONSTRUCTION OF PROJECTIONS 23

needed to proceed with the constuction of tne projection. It is 

impossible to plot the y value for 2^' of longitude and difficult to 

make an individual plotting of the y value for 7}/% of longitude; 

but 0.006 can be added to or subtracted from any tabulated length 

of meridional arcs and the resultant distance measured on the metal 

scale, and this is done in the following description.

Draw the central construction meridian AB in vertical position 

near the center of the map; select the mid-point C as the center of the 

projection, and lay off from C the meridional distances for 2J^' and 

iy<L of latitude CE (3.796 inches) and CB' (11.383 inches) above 

and CD (3.796 inches) and CA'(11.383 inches) below. The over-all 

distance A'B' (22.766 inches) for 15' of latitude should be used to 

check the plotting. At the mid-point C erect the perpendicular FG, 

using the points A7 and B' as centers for long arcs and the points D 

and E as centers for short arcs. Lay off on the construction line FG 

the abscissas of the developed parallel for l^/i and 7*/£' of longitude 

for latitude 40° 221# CH and CI (2.902 inches) and CF' and CG' 

(8.706 inches).

With the points F' and G' as centers and a radius equal to the meridional distance for 7J^' of latitude plus the ordinate for 7^$' of longitude (11.383 + 0.006 = 11.389 inches), strike arcs at J and K. Then 

with the same points as centers and a radius of 11.377 (11.383 0.006) 

strike arcs at L and M. In striking these arcs use the metal point of 

the beam compass rather than the pencil point, and either scratch 

the paper lightly or place under the metal point a small piece of carbon 

paper made by rubbing a piece of thin tracing paper with a hard pencil. 

This obviates the inaccuracy of using the pencil point of the beam 

compass to take an exact measurement from the scale.

With the points H and I as centers and a radius equal to the 

meridional distance for 7^£' of latitude (11.383 inches), strike arcs 

at N and O above and P and Q below. The true meridional distance 

as here used is generally taken in constructing the inner meridional 

distance of 7J/£' of latitude on a scale of 1:48,000 or larger, as it 

is impracticable to use the small ordinate for 2}/£' of longitude. 

However, should the more rigid construction be required, it may be 

done in the following manner: With points H and I as centers and a 

radius equal to the meridional distance for 7^' of latitude plus the 

ordinate for 2^' of longitude (11.383 + 0.001 = 11.384 inches), strike 

arcs at N and O. Then with thasame points as centers and a radius 

equal to the meridional distance minus the 2]/£' ordinate (11.383 

0.001 = 11.382 inches), strike arcs at P and Q.

With the points B' and A' as centers and radii equal to the proper 

abscissas, strike arcs at J, K, L, and M, and also at N, O, P, and Q. 

Check the length of the diagonals JM and KL, which should be 

exactly the same. Draw the straight lines JL and KM through the
24 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

intersections of the arcs at J, L, K, and M, and the straight lines NP 

and OQ through the intersections of the arcs at N, P, O, and Q. 

These lines represent the four meridians on the projection, and although theoretically they are curves concave to the central meridian, 

yet in practice they can be drawn only as straight lines. The four 

intersections at the top and the four at the bottom of the projection 

are the exact intersections of the four meridians with the limiting 

parallels.

With the beam compass set at the length of the meridional distance 

for 5' of latitude, plot along all four meridians down from J, N, O, 

and K and up from L, P, Q, and M, and check the middle 5' sections 

of the meridians, thus locating the intersections of the four meridians 

with the parallels 40° 20' and 40° 25',

All the necessary intersections for the projection of this 15' quadrangle have now been plotted without trying to make an individual 

plotting of 0.006 inch from the points F' and G', which only the most 

skilled draftsmen can accomplish, and the same setting, of the beam 

compass has been used for all equal measurements, thereby strengthening the construction.

Check the construction by measuring over-all distances and by 

testing corresponding diagonals of all combinations of projection 

blocks.

Although it is customary to show only the 5' intervals on a projection for a 15' quadrangle, it may be desired to develop the central 

parallel, which, in the projection under construction, would fall on 

latitude 40° 22^". If so, proceed in the following manner: With 

the beam compass set at the meridional distance for 7%' and plotting 

along the meridians down from J and K and checking by plotting up 

from L and M, locate the points F" and G", which are the intersections 

of the limiting meridians with the central parallel at latitude 40° 22 }/£'. 

The points H and I'already determined are the intersections of this 

parallel with the inner meridians, as no ordinates can be plotted at 

these intersections. Draw the parallels by drawing straight lines 

between the plotted intersections, as the curvature of the parallels 

of any standard quadrangle within the limits of the United States 

is too small to be drawn as a curve. Letter the latitude and longitude 

as shown in Figure 5, add the scale, the name of the quadrangle, and 

the initials or name of the person making the construction, and the 

projection is completed. It should, however, be checked carefully 

by another person.

In any projection where the ordinate of a developed parallel at the 

limiting meridians is less than 0.005 inch it is impracticable to plot 

the curvature, and the parallels should be represented as straight 

lines perpendicular to the central meridian. This will be true of 

projections of maps of standard 15' quadrangles between latitudes 0°
MODIFIED POLYCONIC PROJECTION 25

and 25° on the scale of 1: 48,000 and of standard ?}/£' quadrangles 

in any latitude on scales of 1:31,680 and larger.

Interpolation for other scales. This bulletin gives tables for all the 

standard field scales employed by the Geological Survey, but use of 

other projections may be required, and any table may, with certain 

limitations, be used for scales half as large or twice as large. The 

abscissas of developed parallels and the meridional distances are both 

in direct proportion to the scales and practically in proportion to the 

latitude and longitude intervals, so that the abscissa for 2' of longitude at latitude 40° on the scale of 1:24,000 is the same for 1' 

of longitude at latitude 40° on the scale of 1:12,000. Likewise the 

meridional distance given for a latitude interval of 2' on the scale of 

1:24,000 is the same for 1' on the scale of 1:12,000.

The ordinates of developed parallels are also directly proportional

to the scales, but the ordinates are also proportional to the squares 

of the distances from the central meridian, which may lead to confusion in interpolation for a different scale. For example: For a longitude interval of 5' in latitude 40° on a scale of 1:24,000 the ordinate 

of developed parallel is 0.0054 inch. The ordinate is not the same 

for a longitude interval of 2%' on a scale of 1:12,000 but is 0.027, 

or one-half as much.

The following rules may develop discrepancies in the third decimal 

place, but these will be too small to plot: To halve the scale (for example, to make a projection on a scale of 1:48,000 from tables for 

the scale of 1:24,000), use correct arguments for the scale desired 

and divide all values given in the table by 2. To double the scale 

(for example, to make a projection on a scale of 1:12,000 from tables 

for the scale of 1:24,000), use correct arguments for the scale desired 

and multiply all values given in the table by 2.

Polyconic projections on scales for which no convenient tables are 

given with data in inches are best constructed directly from the data 

given in Coast and Geodetic Survey Special Publication 5, the dimensions in meters on the spheroid being reduced to meters on the map 

scale and plotted by means of a metric scale. Instructions for making 

projections by this method are given in Special Publication 5 and 

also in Geological Survey Bulletin 788-E.

MODIFIED POLYCONIC PROJECTION OF MAP OF THE 

WORLD ON THE MILLIONTH SCALE

GENERAL SPECIFICATIONS

On November 22, 1909, the International Map Committee adopted 

uniform specifications for the sheets of the map of the world on a scate 

of 1:1,000,000. Each sheet of this series of maps covers an area of 

4° of latitude by 6° of longitude and is designated by a letter and a 

number preceded by the word "North" for the northern hemisphere
26 FOEMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

and by the word "South" for the southern hemisphere. Reckoning 

from the Equator to the north or to the south, each 4° belt of latitude 

is designated by a letter A for the belt from 0° to 4°, B for the belt 

from 4° to 8°, etc. Reckoning from the international date line at 

180° longitude (east or west of Greenwich) each zone of 6° of longitude 

is designated by a number 1 for the zone from 180° to 174° west 

longitude, 2 for the zone 174° to 168°, etc., up to 60 for the zone 174° 

to 180° east longitude. Thus the Boston sheet, covering the area 

between north latitudes 40° and 44° and between west longitudes 

66° and 72°, is designated "North.K-19."

The projection adopted for the sheets of this series of maps is a 

modified poly conic projection so designed as to represent all the 

meridians as straight lines on the map and to make the average scale 

error as nearly zero as possible by bringing the top and bottom parallels of the ordinary American polyconic development closer together 

without alteration, so that the scale will be true along these two 

parallels and along the meridians 2° east and west of the central 

meridian. The result is that the scales along the other interior 

meridians are reduced and the scale along the limiting meridians is 

enlarged. This arrangement gives four instead of three lines of 

strength in which the scale is true, and the maximum error in any 

other line is much less than in the American polyconic projection.

The top and bottom parallels of each sheet are drawn in the usual 

way, as circles with centers lying in the prolongation of the central 

meridian, but are actually plotted from the rectangular coordinates 

of the intersections of the two parallels with the several meridians. 

These two parallels are therefore subdivided true to scale. Straight 

lines representing the meridians are then drawn connecting corresponding intersections on the top and bottom parallels.

In the resolutions of the International Map Committee it is not 

stated how the 4° lengths of the meridians are to be subdivided. 

United States Coast and Geodetic Survey Special Publication 68 

states that "no doubt, an equal division of the central meridian was 

intended." Arthur R. Hinks, in his admirable treatise "Map projections," states, "it may be supposed that they are divided equally." 

Antoni Lomnicki, in a rjaper entitled "Projekcja Miedzynarodowej 

Mapy Swiata," published at Lwow in 1927, comments as follows: 

"It has been ascertained that these differences are so insignificant as 

to be a negligible quantity on a map drawn to a scale of 1/M, a fact 

which nevertheless should not be omitted in the instructions."

It has been the practice of the United States Geological Survey to 

compile the sheets in four quarters on the scale of 1:500,000 and to 

subdivide each meridian in proportion to the correct length of each 1° 

interval of latitude. Therefore, these new tables have been constructed on that basis.
MODIFIED POLYCONIC PROJECTION 27

JOINING OP SHEETS

Any 1° by 6° sheet will join exactly with the four sheets on its 

margins, but the corner sheets to complete a block of nine will not fit 

along their two adjacent edges simultaneously; they will fit on one 

edge, but there will be in theory on the other a small wedge-shaped 

gap, as is shown in Figure 6. In practice these gaps will be found 

to be very small) usually less tlian the average expansion or shrinkage 

of map paper. The map user will seldom desire to join together 

exactly more than nine sheets at once. Many objections have been 

made to the use of this projection because of this difficulty in joining 

corner sheets and because of distortions in scale, azimuth, and shapes 

near the east and west limits of the sheets, but there does not seem 

to be any other projection of sufficiently greater merit to offset the 

principal advantages of the modified poly conic projection, which are 

its ease of construction from simple tables and its adaptability to

FIGURE 6. Junction of sheets of map of the world

small groups of sheets representing areas in any part of the world. 

Any errors in a single sheet are negligible in view of the limitations 

of drafting, engraving, and quality of map paper. For example, the 

maximum error in scale occurs along the east and west meridians of 

a sheet representing an area between latitudes 0° and 4° and is about 

1/1300, or +0.076 per cent; on the scale of 1 :1,000,000 this amounts 

to about one-third of a millimeter in the total height of the sheet. 

The substitution of the Lambert conformal projection or the Albers 

conical equal-area projection has been suggested. The writer has 

investigated the effect of the use of the Lambert conformal projection 

for the millionth-scale sheets of the area of the United States and 

finds that, in the area between latitudes 24° and 52°, the Lambert 

conformal projection would probably be based on two standard 

parallels at latitudes 29° and 47°. Such a projection would introduce scale errors averaging about +1 per cent in sheets representing 

areas adjacent to the limiting parallels (24° and 52°) and averaging 

6243° 29 3
28 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

 1 per cent in sheets representing areas between latitudes 36° a.nd 

40°, although the scale would be correct in sheets for areas along the 

two standard parallels. Sheets on the modified polyconic projection 

representing areas between latitudes 24° and 28° introduce maximum 

scale errors of only 0.06 per cent, and between latitudes 48° and 52° 

of only 0.03 per cent, which are less than the usual distortion of map 

paper. Therefore for all practical purposes maps on the modified 

polyconic projection covering any area in the United States are as 

true to scale as maps on the Lambert conformal projection for areas 

along the standard parallels. Surely the necessity of correcting all 

distance measurements on a sheet by an amount as large as 1 per 

cent would be a distinct disadvantage. Of course it would be possible to select zones of lesser extent in latitude, even to the extreme 

case of considering each row of 4° by 6° areas a separate zone, with 

two standard parallels for each zone, but any of these selections 

would involve difficulty in joining sheets in adjacent zones, and much 

confusion would be caused if each country used one or more different 

pairs of standard parallels.

The resolutions of the International Map Committee state that 

"north of latitude 60° N. and south of latitude 60° S. it shall be permissible to join two or more adjoining sheets of the same zone, so that 

the combined sheet covers 12°, 18°, etc., of longitude." United 

States Coast and Geodetic Survey Special Publication 68 comments 

on this statement as follows:" The provisions also fail to state whether, 

in the sheets covering 12° of longitude instead of 6°, the meridians of 

true length shall be 4° instead of 2° on each side of the central meridian; but such was no doubt the intention." A. R. Hinks makes a 

similar statement in his book on map projections. The writer doubts 

the correctness of this interpretation but thinks that the committee 

had in mind simply the assemblage of two or more independently 

constructed sheets in a single map so as to avoid a series of maps of 

very small width. In other words, he thinks that the committee had 

in mind a printing and distribution problem rather than a cartographic 

problem. A row of 4° by 12° sheets would fail to join a row of 4° 

by 6° sheets immediately to the south by wedges similar to those 

illustrated in Figure 6, whether the sheets were constructed with 4° 

or 8° between the standard meridians, but if the interval were 8° 

the maximum scale error in the northern row would be increased four 

times. The Geological Survey has not yet compiled any sheets of the 

millionth-scale series for areas north of latitude 60°, and it hopes that 

before it is required to do so the International Map Committee will 

decide the matter definitely.
MODIFIED POLYCONIC PROJECTION 29 

DRAWING OF PARALLELS

There has been considerable discussion of the difficulty of drawing 

the arcs of circles representing the limiting parallels and the curves 

representing the three interior parallels, which Lomnicki calls shortened epicycloids. The maximum deviation of the curve representing a 1 ° arc of a parallel from the chord joining the ends of such a curve 

is in latitude approximately 45°, and on a scale of 1:1,000,000 the maximum ordinate from the mid-point of such a chord to the curve is 0.1 

millimeter. It is practically impossible for a draftsman to draw such 

a curve, as the deviation from a straight line is only about the width 

of a finely inked line. It is equally impracticable to construct and 

use a compass bar long enough to draw the arcs of the parallels, 

requiring for the scale of 1:1,000,000 a radius of about 4 meters for 

the circle representing the parallel of 60°, one of about 8 meters for the

parallel of 40°, and one of over 90 meters for the parallel of 4°. 

Therefore the United States Geological Survey constructs these parallels by drawing straight lines joining adjacent intersections of the 

parallels with meridians 1° apart. For arcs of parallels below 50° 

the deviation from true circles can not be detected even on an 

engraved copper plate, although theoretically such methods of construction introduce angles at the crossings of the meridians. Such 

errors on a printed map are less than the usual distortion of map paper. 

For short arcs of the parallels above 60° it may be practicable to use 

mechanically constructed curves. As a matter of fact, the Geological Survey compiles the millionth-scale sheets on a scale of 1:500,000 

by plotting the intersection of each half degree meridian and parallel, 

but in publication the engraver constructs a new projection on the 

copper plate instead of copying photographically the results of the 

cartographer's compilation.

DESCRIPTION OF TABLES

Table 5 gives the length of each developed meridian and the x and 

y coordinates of the intersection of each meridian with each of the 

developed parallels, in meters on the natural scale. To convert these 

data into map distances on the scale of 1:1,000,000, move the 

decimal point three places to the left and plot in millimeters. For 

the scale of 1:500,000 follow the same rule and then double all the 

measurements. Table 6 gives the data in inches on the scale of 

1:1,000,000. Each 1° length of the standard meridians (2° from the 

central meridian) and the x and y coordinates of the intersections of 

all three meridians east and west of the center meridian with the 

upper and lower developed parallels of each sheet (0°, 4°, 8°, 12°, 

etc.) were computed by the rigid formulas given hereafter in this 

paper. In making these computations the dimensions of the spheroid
30 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

given in the proceedings of the International Map Committee at the 

meeting in London in November, 1909, were used, as follows:

Semimajor axis a = 6,378,240 meters 

Semiminor axis b = 6,356,560 meters

These dimensions differ slightly from those developed by Col. A. R. 

Clarke in 1880, which were 

a = 6,378,249 meters 

b = 6,356,515 meters

After the x and y coordinates of the intersections of each of the 

meridians with the upper and lower parallels were computed, each 

4° length of the central meridian and of the meridians 1° and 3° 

from the central meridian were computed by simple formulas, as 

described hereafter in this paper. The length of the shortened 

central meridian could have been computed directly by the formulas 

given by M. Ch. Lallemand 1 and the lengths of the other developed 

meridians could then be computed by applying the simple formulas 

for the magnification 'of meridians of the polyconic projection. 

Each 4° length of these three meridians was then divided into 1° 

lengths in direct proportion to the true 1° lengths of the meridian as 

represented by the 1° lengths of the standard meridians 2° from the 

center. These 4° meridional lengths could be divided into four equal 

parts, and the errors introduced would be small for example, in the 

1° meridional length between latitudes 43° and 44° the maximum 

error would be about 30 meters, or 0.03 millimeter on a scale of 

1:1,000,000. This difference can not be plotted, but for the purpose

of analysis and for large-scale compilations it seemed desirable to

calculate the meridional lengths in their true relation. The x and y 

coordinates for the intersections of the meridians with the three 

inner parallels were then calculated by subdividing the 4° differences 

in the values of x and y into 1° units in the same proportion as the 

4° lengths of the meridians were subdivided. It would have been 

sufficient for all practical purposes to divide by 4 the 4° differences in 

the values of x and y and then add one-fourth, one-half, and threefourths of these quantities to the x and y values for the proper limiting 

parallel. Moreover, the simple approximate formulas for x and y 

(with slight modifications) given by Lallemand could have been 

used without seriously affecting the accuracy of the results.

Lomnicki has suggested that tables for the modified polyconic 

projection should be computed on the basis of the Hayford spheroid, 

which probably represents the actual shape of the earth better than

»Paris Acad. Sci. Compt. Rend., vol. 153, p. 561,1911.
MODIFIED POLYCONIC PROJECTION 31

any other spheroid yet developed. The dimensions of this spheroid 

were published by Hayford as follows:

<a = 6,378,388 meters 

b = 6,356,909 meters

The writer has computed the lengths of each 1° meridional arc for 

the standard meridian 2° from the central meridian between latitudes 

40° and 44°, based on the Hayford spheroid, and the table given 

below permits a comparison of these values with those based on the 

Clarke spheroid.

Lengths of meridian 2° from central meridian, in meters, natural scale

Latitude

40°-41° 

4l°-42° 

42°-43° 

43°-44°

40°-44°

Clarko 

spheroid,

1880

111,042.2 

111,061.8 

111,081.5 

111,101.3

444, 280. 8

Hayford 

spheroid

111,047.4 

111,066.8 

111,086.3 

111, 105. 9

444, 306. 4

The difference in the 4° length of the meridian is less than 20 

meters on the spheroid, or 0.02 millimeter on a scale of 1 :1,000,000. 

It is apparent that these small differences can not be plotted, but if 

for any reason the commission should desire to have these tables 

computed on the basis of the Hayford spheroid, the Geological 

Survey will be glad to do the work. However, before taking any 

such action it seems desirable to have comments and criticism on 

the tables presented herewith, particularly as to their general form. 

Moreover, it seems desirable to have the commission settle definitely 

the size of sheets and the arrangement of standard meridians to be 

used in latitudes above 60°.

METHOD OF CONSTRUCTION OF PROJECTION

If a map of a millionth-scale unit area is to be compiled in a single 

sheet on a scale of 1 :1,000,000, it will not be necessary to plot the x and 

y coordinates of the interior intersections but only to plot the intersections of each meridian with the upper and lower parallels and 

then draw the meridians as straight lines and subdivide each one 

of them either into four equal parts or in proportion to their actual 

1° lengths. If the map is to be compiled on a scale much larger 

than that of publication, it is advisable to plot the x and y coordinates 

of the intersection of each 1° meridian and parallel, and it may be 

desirable for the cartographer to construct the intersection of each 

half degree meridian and parallel.
u £ 

cjo

CO

CO

<u O

o 

o.

CO

00

CO

(0

in

(O

CO 

(O

(O

. o O) SI oc

CD 

CO

CO 

CO

CO

<M
MODIFIED POLYCONIC PROJECTION 33

It is often difficult to plot the small ordinates of the intersections, 

but it is practicable to add these values to or subtract them from 

the lengths of the meridional arcs and to construct the projection 

without making a single individual plotting of a small ordinate. 

This method involves the initial construction of the abscissa of the 

central parallel and permits the construction of each intersection, by 

coordinates, or only the intersections of the meridians with the 

limiting parallels, as may be desired. The difficulty of constructing 

abscissas at right angles to the central meridian near the upper 

and lower edges of the compilation sheet, together with the difficulty 

of making individual plottings of the small ordinates, seems to warrant the presentation of this method in this paper. In so doing the 

writer has taken the example of the construction of sheet K-18, 

embracing the area between latitudes 40° and 44° north and longitudes 72° and 78° west.

The following materials are required: A standard metal scale 1 

meter long subdivided throughout in centimeters and with 1 centimeter length at one end subdivided into tenths of millimeters (scales 

used by the United States Geological Survey accomplish the graduation of millimeters into tenths by means of diagonal scales; see fig. 7); 

a good rigid-beam compass with micrometer movement; a hard chiselpoint pencil; a plotting needle; and a copy of United States Geological 

Survey Modified Polyconic Projection Tables.

Make a working diagram of the projection and enter on it from the 

tables all the dimensions that are needed. (See fig. 8.)

Draw the central meridian AB, representing the meridian of 75° 

west, near the center of the map sheet; select the middle point C as 

the center of the projection, and lay off from C the meridional distances for 2° of latitude on the central meridian above and below the 

central parallel of 42° north; CB' = 222.11 millimeters and CA' = 

222.03 millimeters. Subdivide these into 1° lengths, as B'E = 111.07 

millimeters, CE = 111.04 millimeters; check the over-all distance 

A'B' = 444.14 millimeters. If there is any material difference between 

the computed lengths of CA' and CB' (more than 0.1 millimeter) lay 

off for purposes of construction the points A and B about 1 centimeter 

below and above A' and B', respectively, and exactly equidistant 

from C. At the point C erect the perpendicular FG, using the points 

A' and B' (or A and B) as centers of long arcs and the points D and E 

as centers of short arcs. This line FG is the X axis of the parallel 

representing latitude 42°. Lay off on the line FG the abscissas 

(x values) of the developed parallel for 1°, 2°, and 3° of longitude 

from the central meridian; CJ = CK = 82.80 millimeters, CH = CI = 

165.59 millimeters, and CF' = CG' = 248.36 millimeters.

With the points F' and G' as centers and a radius equal to the 

meridional distance between latitudes 42° and 44° along the meridian
34

3° from the central meridian plus the ordinate (y value) of the 

developed parallel for latitude 44° at the meridian 3° from the central 

meridian (222.28 + 4.36 = 226.64 millimeters), strike arcs at L and M. 

Then with the same points as centers and a radius equal to the meridional distance between latitudes 40° and 42° minus the ordinate for 

40° (222.20-4.31 = 217.89 millimeters), strike arcs at N and O. In 

drawing these arcs use the metal point of the beam compass rather 

than the pencil point, and either scratch the paper lightly or place 

under the metal point a small piece of carbon paper made by rubbing a 

piece of thin tracing paper with a hard pencil. This eliminates the

73° 72°

N

FIGURE 8. Construction of modified polyconic projection

inaccuracy of using the pencil point of the beam compass to take an 

exact measurement from the scale.

Then in a similar manner and with the points H and I and the 

points J and K as centers and with radii equal to the proper meridional 

distances plus or minus the corresponding ordinates, as the case may 

be, strike arcs at P, Q, R, and S and at T, U, V, and W. With the 

points B' and A' as centers and with radii equal to the proper abscissas 

strike arcs at L, M, N, and 0, at P, Q, R, and S, and at T, U, V, and W. 

(Note that theoretically these radii should be the chords joining the 

ends of the developed parallel, but in the maximum curvature of the 

developed 3° parallel of 60° latitude the difference between the chord
MODIFIED POLYCONIC PROJECTION 35

and the abscissa on the scale of 1 :1,000,000 is only + 0.04 millimeter, 

which can not be plotted.)

Before proceeding further check the over-all diagonals of the 

projection LO = MN and if not exactly the same try the diagonals 

CL = CM and CN = CO so as to locate and correct any inaccuracy 

of the construction thus far. Draw the developed- meridians as 

straight lines joining L and N, P and R, etc., and draw the developed

? limiting parallels as straight lines (or smooth curves) joining B' and 

T, A' and V, etc. This gives all of the projection except the three 

interior parallels.

With the beam compass set at the length of the developed meridional arc between 42° and 44° for each meridian, plot downward 

along the meridians from L and M, from P and Q, etc., locating the 

intersections F", G", H', I', etc. Then with the beam compass set 

at the length of the developed meridional arc between 40° and 42° 

for each pair of meridians plot upward along the meridians from N 

and 0, from R and S, etc., thus checking the locations of the intersections along the central parallel. In a similar manner locate the 

intersections of the meridians with the parallels of 41° and 43° by

> plotting 1° lengths of developed meridian from the extreme parallels 

and checking from the central parallel. Construct the three central 

parallels by drawing straight lines between adjacent points of intersection with meridians or by drawing smooth curves through these 

points.

Add the latitude and longitude designations of each degree intersection along the limiting meridians and parallels. Add the name and

^ number of the sheet, the scale, the type of projection, and the name of 

the man making the projection and the date on which it was made. 

These may seem to be matters of minor detail, but the writer has 

noticed failure to include these data so many times that he ventures 

to call attention to their importance. 

The projection is now completed and has been constructed in an

± orderly manner, with a minimum number of settings of the beam 

compass and without making a single individual plotting of any of 

the small ordinates. The projection should be checked carefully by 

another cartographer.

THEORY OF THE MODIFIED POLYCONIC PROJECTION

Nomenclature. The practical cartographer is often confused by 

the nomenclature relating to map projections, largely because cartographers and mathematicians of different countries use different symbols for the same thing. Except for one or two terms, the writer has 

used the nomenclature employed by the United States Coast and 

. Geodetic Survey in its recent publications. The symbols used in
36 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

developing the theory of the polyconic projection, with their corresponding definitions, are as follows:

a = semimajor axis of the earth or spheroid.

b = seminiinor axis of the earth or spheroid.

e = eccentricity of generating ellipse = .»/- %

V &

f == flattening of generating ellipse = - 

n = constant=- =- 

a + b

pm radius of curvature of a meridional section. 

p n = radius of curvature of a section normal to the meridian. 

<j> = astronomic or geographic latitude of a point on the earth. 

^ == geocentric latitude of a point on the earth. 

A<£ = difference of latitude between two points on the same meridian. 

X =?= longitude of a point on the earth with reference to Greenwich. 

AX = difference of longitude between two points on the same parallel 

or the angle at the pole between the meridians passing through 

these points.

M = length of arc of a meridian from the Equator to latitude <£. 

AM = length of arc of a meridian between two parallels. 

L = length of an arc of a parallel from the meridian of Greenwich

to longitude X.

AL = length of an arc of a parallel between two meridians. 

6 = angle at the apex of the developed tangent cone between the

central meridian and another meridian. 

I = slant height of the tangent cone or the radius of the developed

parallel. 

x = abscissa of any point on a developed parallel with reference to

the central meridian, 

y = ordinate of any point on a developed parallel with reference to

the tangent to that parallel at the central meridian. 

Dimensions of the spheroid. In the modified polyconic projection 

dimensions of the spheroid differing only slightly from those developed 

by Clarke in 1880 have been used, as follows:

a = 6,378,240 meters log a = 6.8047008568 

b = 6,356,560 meters log b = 6.8032221507

- = 0.9966009432 log -=9.9985212938-10 

a & a

-2 =0.9932134400 log ^=9.9970425877-10 

a a

e2 = 0.0067865600 log e2 = 7.8316496930-10

f=294.\99 log f = 7.5313588078-10

n = 0.0017024217 log n = 7.2310671463-10
MODIFIED POLYCONIC PKOJECTION 37

Radii of curvature. It is not necessary to compute the radius of 

curvature of a meridional section, as the meridional arcs are too long 

to permit the computation of their length by the approximate formula 

AM = pmA<£. However, in case it is desired to find the values of 

pm the following formula may be used:

a(l-e2)

Values of the radius of curvature of a section normal to the meridian 

(pn) are needed in the computation of x and y and must be computed 

for each fourth degree of latitude, 0°, 4°, 8°, etc. Values of pn are 

used in computing the lengths of the arcs of the parallel, but as the 

lengths of these arcs are not needed in constructing or checking the

projection, it is not necessary to compute the values of AL. The 

following formula is used for values of pn :

pn (l-e2sin20)* .

Values of pn and their logarithms for each fourth degree of latitude 

from 0° to 60° are given in the following table:

Radii and logarithms of radii of curvature of section normal to meridian for each 

fourth degree of latitude from 0° to 60°

[Values of pn in meters, based on Clarke spheroid of 1880] 

Latitude

0

4

8

12

16

20

24

28

32

36

40

44

48

52

56

60

Pn

6, 378, 240. 000

6, 378, 345, 318

6, 378, 659. 251

6, 379, 175. 780

6, 379, 884. 995

6, 380, 773. 276

6, 381, 823. 547

6, 383, 015. 586

6, 384,, 326. 402

6, 385, 730. 701

6, 387, 201. 280

6, 388, 709. 631

6, 390, 226. 444

6, 391, 722. 180

6,393,167.653

6, 394, 534. 596

Log Pn

6. 804*008568

6. 8047080207

6. 8047294026

6. 8047645694

6. 8048128504

6. 8048733134

6. 8049447921

6. 8050259049

6. 8051150824

6. 8052105995

6. 8053106023

6. 8054131497

6. 8055162481

6.8056178898 .

6. 8057160934

6. 8058089413

Order of computations. The procedure followed in computing the 

lengths of the meridional arcs and the values of the x and y coordi-, 

nates is not as simple as for the American polyconic projection; 

because only the length of the standard meridians and the x and y 

values of intersections of the meridians with the upper and lower 

parallels can be computed by the formulas used for the American 

polyconic projection. Lomnicki, in the publication cited above, 

gives rigid formulas for computing the x and y coordinates of any 

point on the map, but these formulas are very intricate, and their
38 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

use is not advised. Lallemand, in the paper cited above, gives 

approximate formulas for the length of the central meridian and for 

the x and y coordinates of intersections of the meridians with the 

central parallel. These formulas in their general terms are intricate, 

and in simplifying them for application to the scale of 1:1,000,000 

Lallemand has apparently used the Hayford spheroid rather than the 

Clarke spheroid of 1880. The writer has attempted to modify these 

simplified approximate formulas to apply to the Clarke spheroid of 

1880 and has given them below, following the formulas used in computing these tables. Lallemand 's formula for length of the central 

meridian (as modified) can be used without introducing serious errors, 

and the length of the other meridians can be computed with reasonable accuracy by applying simple factors of magnification. The 

writer has, however, further modified this approximate formula by 

giving a separate one for each meridian. Lallemand 's formulas for 

x and y (as modified) can be used for the coordinates of the intersections of the meridians with any of the parallels without introducing 

serious errors on the scale of 1: 1,000,000. Besides modifying these 

to conform to the Clarke spheroid of 1880, the writer has given a 

separate formula for x for each of the five parallels.

However, it seemed desirable to compute the tables presented 

herewith as follows: Compute the 1° lengths of the standard meridians 2° from the central meridian on the assumption that these 

lengths are exactly true to scale; compute the x and y coordinates of 

each meridian with the two standard (upper and lower) parallels; 

calculate the 4° meridional lengths for the central meridian and for the

meridians 1° and 3° from the central meridian; subdivide these 4°

 

meridional lengths into 1° lengths in the same proportion as the

computed 1° lengths of the standard meridian bear to the 4° length 

of that meridian; and finally calculate the x and y coordinates of the 

points of intersections of the meridians with the three inner parallels. 

By orderly tabulation and use of computing machines the task was 

not difficult. The values were computed to tenths of a meter on the 

natural scale, which, while far beyond the needs of map projection 

on a scale of 1 : 1,000,000, may be useful in making computations on 

a larger scale.

Lengths oj the meridians. The length of the standard meridians 2° 

from the central meridian is true to scale, and each 1° length may be 

computed by the following formula for the American polyconic projection (see VII, p. 13), it being sufficient for all practical purposes to 

use the first three terms only :

AM2 = A0A0 A2 cos 20 sin A</> + A4 cos 4<j> sin

- Ae cos 60 sin 3A0+ . . . . [XVII]
MODIFIED POLYCONIC PROJECTION 39

in which

AM2 = length of arc of the standard meridian, expressed in meters.

</> = H(02 + 00 = mean latitude of meridional arc.

A0= (</>2~0i) = arc of standard meridian, expressed in degrees.

A0 = 111,132.1753 meters log = 5.0458398153

A2 = 32,519.9882 meters log = 4.5121503781

A4 = 34.6017 meters log = l.5390974

A6 = 0.0458 meters log = 8.66108 -10

. FIGURE 9. Computation of modified polyconic projection tables

The formula given above may of course be used to compute either 

the 1° or the 4° length of the standard meridian, by using A$ = 1° or 

4°, respectively.

After the x and y coordinates of the intersections of all the meridians 

with the upper and lower parallels are computed, the length of the 

central meridian and of the meridians 1° and 3° from the central 

meridian may be computed by formulas developed as follows (see 

fig. 9):

In the right triangle B P2 ° P2 ""

AY2 = V(AM2 ) 2 - (AX2 ) 2 =
40 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

Expanding the radical as a binomial series into terms which can be 

handled conveniently, we have

but

AM0 = AY2 -(y2 ""-y2 °); 

therefore

AM,= AM, [i -K^J-idl)1]-^""-^] .. [xvin;

Similarly,

or

2

This equation can be solved easily by using the relation

AY 

Similarly,

or

AMAM 3 - AYAY 3 L! fi + + g l (ffi) s ~ g (gfj * + + J - -[XX] nm

This equation can be solved easily by using the relation

AY3=AM0 +(y3 ""-y3 0 )

After the 4° lengths of each meridian are found they may be 

subdivided into 1° lengths as follows: Take the difference between 

the 4° length of the standard meridian and the 4° length of each of 

the other meridians, divide these differences by 4, and subtract the 

results from or add them to each 1° length of the standard meridian. 

If the 4° lengths of a meridian are divided into four equal parts, as 

is the practice of most cartographers, the errors introduced are small; 

for example, in the belt between latitudes 40° and 41° the maximum 

error is 30 meters on the spheroid, or 0.03 millimeter on the scale of 

1 : 1,000,000. This difference can not be plotted, but if the sheets are 

compiled on a larger scale it may be advisable to subdivide the 4° 

lengths in true proportion.

The 4° lengths of these meridians can be computed in terms of 

millimeters on the scale of 1:1,000,000 without introducing serious 

errors by the use of Lallemand's approximate formulas, modified 

slightly to conform to the Clarke spheroid of 1880 and to the nomenclature used in this paper, as follows:
MODIFIED POLYCONIC PROJECTION , 41

Length of central meridian,

AM0 =444.40 mm. -2.35 mm. cos 2 4>____________ [XXI]

Length of meridian 1° from center,

AMX = 444.45 mm. -2.30 mm. cos 2 0_ _________ [XXII]

Length of meridian 2° from center,

AM2 = 444.50 mm. -2.25 mm. cos 2 0__________ P£XIII]

Length of meridian 3° from center,

AM3 = 444.70 mm.-2.10 mm. cos 2 4>___________ [XXIV]

Rectangular coordinates. In the modified polyconic projection 

each of the parallels marking the boundaries of zones of 4° of latitude is represented as the base of a right cone tangent to the spheroid 

along that parallel. Each 4° developed parallel is a circle with center 

on the prolongation of the central meridian and with radius Z = p ncot<£, 

and the origin of the rectangular coordinates of each parallel is the

point at which the developed parallel intersects the central meridian. 

The rectangular coordinates of the intersections of the meridians 

with the upper and lower parallels are computed in the same way as 

for the American polyconic projection. The tables presented with 

this paper were computed by means of the following rigid formulas 

(see X and XI, p. 17) :

x = p n cot 0 sin (AX sin <£) _ ____________ [XXV]

y = 2Pn cot 0 sin2 J^(AX sin 0)_ _________ [XXVI]-

As each meridian on the modified polyconic projection is drawn as 

a straight line, whereas a true polyconic representation of each meridian except the central one would be a curve, owing to the constantly 

changing values of convergence, the usual formulas for the x and y 

coordinates can not be used for the intersections with the. interior 

parallels. For all practical purposes it is sufficient to calculate the 

values of x and y for the intermediate intersections by dividing by 4 

the differences of the x and y values of the intersections of each meridian with the upper and lower parallels, adding one-fourth, one-half, 

and three-fourths of the x difference to the x value for the upper 

parallel (or subtracting them from the x value for the lower parallel), 

and adding one-fourth, one-half, and three-fourths of the y difference to the y value for the lower parallel (or subtracting them from 

the y value for the upper parallel.) If more accuracy is desired the 

values of the 4° differences in x and y can be subdivided into 1° 

units in the same proportion as the 4° lengths of the meridians are 

subdivided. In this event it is sufficient to use the proportional 

parts of the standard meridian in subdividing the coordinates of all 

the meridians, and the following procedure may be used :

Divide each 1° length of the standard meridian by the 4° length of 

that meridian and multiply the differences of the x and y values of the
42 FORMULAS FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

ends of each of the other 4° meridians by the corresponding decimal 

fractions thus obtained. Subtract the resulting x increments for the 

lower 1° interval from the corresponding x values for the lower 

parallel; then subtract the x increments for the second 1° interval 

from the x values just obtained for the parallel 1° above the lower 

parallel, etc. Follow the same procedure with the y values, except 

that the increments should be added to the y values of the lower 

parallel. As the decimal fractions vary but slightly from 0.25, the 

calculations can be simplified by applying one-fourth of the 4° difference T the residual of the decimal fraction, as follows:

AM2 (40°-41°) 111042.242 n 94QQ«« fiJ._ v n nnnrwwn* 

 ^444286.870 =°'24993365 ~ A~ °-00006635

111101.271

= 0.25006652 = % + 0.00006652 AM2 (40°-44°) "444286.870

In a map unit lying between latitudes 40° and 44° the maximum 

difference between subdivision of a 4° meridian into four equal parts 

and subdivision in true proportion is 1.38 meters in the x value and 

0.01 meter in the y value of points along the meridian 3° from the 

central meridian. These differences can not be plotted on a scale of 

1:1,000,000 or even on a scale of 1:500,000. However, in the tables 

presented with this paper the x values have been computed in direct 

proportion to the correct subdivision of the standard meridian.

Lallemand's approximate formulas for the rectangular coordinates 

were developed by him for the x and y coordinates of the central 

parallel of the projection. The writer has modified these formulas 

somewhat, and as given below they may be used for the x and y 

coordinates of any of the parallels on a scale of 1:1,000,000 without 

introducing serious errors. In these modified formulas for x the 

five coefficients of cos $ apply to the five parallels of the projection, 

the upper coefficient applying to the upper parallel, etc. AX is 

taken in degrees from the central meridian. Coordinates for }/%° 

intersections may be computed by taking values of AX=J^°, 1°, 

l/^°> etc. All values of x and y will be in millimeters on a scale of 

1:1,000,000.

x(in millimeters) = AX

"(111.40 

111.37 

111.33 

111.37

LUll.40

cos </> 0.08 cos

y(in millimeters) = AX2 [0.49 sin 2</>]__________[XXVIII]
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 43

TABLE 1. Coordinates for the projection of maps, scale

Latitude 

of 

parallel

0 /

0 00

10

15 

20

30

40

45

50

1 00 

10

15

20 

inoU

40 

45 

50

2 00 

10

15

on a)

30

40

45 

50

3 00

10

15

20

30 

40

45

50

4 00 

10

15

20

30

40

45

50

5 00 

10 

15 

20

30

40

45

50

6 00 

10 

15

20

30

40

45

50

7 00

Abscissas of developed parallel

Longitude interval

5'

Inches

3.804

.804

.804 

.804

3.804

.804

.804

.804

3.804 

.804

.804

.803

1 o. SfMouo 

.803 

.803 

.802

3.802 

.802 

.802

QA1

. OU1

3.801

.800

.800 

.800

3.799

.799

.798

.798

3.797 

.797

.796

.796

3.795 

.794

.794

.794

3.793

.792

.791

. 

701 1 VI

3.790 

.789 

.789 

.788

3.787

. 786

.785

.785

3.784 

.783 

.782

.781

3.780

.779

.778

.778

3.776

Iff

Inches

7.609

.609

.609 

.609

7.609

.608

.608

.608

7.608 

.607

.607

. .607

7.606 

.606 

.605 

.605

7.604 

.603 

.603

fifW 

. uuo

7.602

.601

.600 

.600

7.598

.597

.597

.596

7.595 

.593

.593

.592

7.590 

.589

.588

.587

7.586

.584

.583

.582

7.580 

.578 

.577 

.576

7.574

572

!571

.570

7.567 

.565 

.564

. .563

7.560

.558

.556

. .555

7.552

15'

Inches

11.413

.413

.413 

.413

11.413

.413

.412

.412

11.412 

.411

.411

.410

11.409 

.408 

.408 

.407

11.407 

.405 

.405

404

11.403

.401

.400 

.399

11. 398

.396

.395

.394

11. 392 

.390

.389

.388

11. 386 

.383

.382

.382

11. 378

.376

.374

Q7Q i O/O

11. 370 

.367 

.366 

.364

11. 361

. 358

.356

.355

11.351 

.348 

.346

.344

11. 340

.337

.335

.333

11.329

20''

Inches

15. 218

.218

.218 

.217

15. 217

.217

.216

.216

15. 215 

.215

.214

.214

1 e 910 10. Aid

.211 

.211 

.210

15. 208 

.207 

.206

.205

15. 203

.201

.200 

.199

15. 197

.195

.193

.192

15. 190 

.187

.185

.184

15. 181 

.178

.176

.174

15. 171

.168

.166

. 164

15. 160 

.156 

.154 

.152

15. 148

.144

.142

.139

15. 135 

.130 

.128

.125

15. 121

.115

.113

M10

15. 105

30'

Inches

22. 827

.826

.826 

.826

22. 826

.825

.825

.824

22.823 

.822

.821

.820

99 81 Q Lit, Ola

.817 

.816 

.815

22. 813 

.810 

.809

fins . OUo

22. 805

.802

.800 

.799

22.795

.792

.790

.788

22.784 

.780

.778

.776

22. 771 

.767

.764

.762

22. 757

.751

.749

. 746

22. 740 

.734 

.731 

.728

22. 732

. 716

.712

.709

22. 702 

.695 

.692

.688

22.681

.673

.669

.665

22.658

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

For latitude 0°

5

10

15 

20

25

30

For latitude 1°

For latitude 2°

5

10

15 

20

25

30

5 

10 

15 

20 

25 

30

For latitude 3°

5

10

15 

20

25

30

For latitude 4°

For latitude 5°

5

10

15 

20

25

30

5

10

15 

20

25

30

For latitude 6°

5 

10 

15 

20 

25

30

For latitude 7°

5

10

15 

20 

25

30

Meridional 

distance

Inches

3.779

7.557

11. 330 

15. 115

18. 893

22. 672

3.779

7.557

11.336 

15. 115

18. 893

22. 672

3.779 

7.557 

11. 336 

15. 115 

18. 894 

22. 672

3.779

7.558

11.336 

15. 115

18.894

22. 673

3.779

7.558

11.337 

15.115

18. 894

22. 673

3.779

7.558

11. 337 

15. 116

18. 895

22. 674

3.779 

7.558 

11.337 

15. 116 

18. 896

22. 675

3.779

7. 559

11.338 

15.117 

18. 896

22. 676

Ordinate of developed 

parallel

Inch

0.000

.000

.000 

.000

.000

.000

0.000

.000

.000 

.001

.001

.002

0.000 

.000 

.001 

.002 

.002 

. .003

0.000

.001.

.001 

.002

.004

.005

0.000

.001

.002 

.003

.005

.007

0.000

.001

.002 

.004

.006

.009

0.000 

.001 

.003 

.005 

.007

.010

0.000

.001

.003 

.005 

.008

.012

6243° 2<
44 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 1. Coordinates for the projection of maps, scale T^TTC Continued

Latitude 

of 

parallel

° '

7 00

10

15 

20

30

40

45 

50

8 00 

10

15

20 

30

40 

45 

50

9 00 

10 

15

20

30

40

45 

50

10 00

10

15

20

30 

40

45

50

11 00 

10

15

20

30

40

45

enOU

12 00 

10 

15 

20

30

40

45

50

13 00 

10

15

20

30 

40

45

50

14 00

' Abscissas of developed parallel

Longitude interval

5'

Inches

3.776

.775

.774 

.774

3.772

.771

.770 

.769

3.768 

.766

.765

.765

3. 763 

.761 

.760 

.760

3.758 

.756 

.755

.754

3.753

.751

.750 

.749

3.747

.745

.744

.743

3.741 

.739

.738

.737

3.735 

.733

.732

.731

3.729

.726

.725

.724

3.722 

.720 

.718 

,717

3.715

.712

.711

.710

3.708 

.705

.704

.703

3.700 

.697

.696

.695

3.692

10'

Inches

7.552

.550

.548 

.547

7.544

.541

.540 

.538

7.535 

.532

.531

.529

7.526 

.522 

.521 

.519

7.516 

.512 

.511

 PtAQ * uuy

7.505

.502

.500 

.498

7.494

.490

.488

.486

7.482 

.478

.476

.474

7.470 

.466

.464

.461

7.457

.453

.450

.448

7.444 

.439 

.437 

.434

7.430

* t*L> d91

.422

.420

7.415 

.410

.408

.405

7.400 

.395

.392

.390

7.384

15'

Inches

11.329

.325

.323 

.321

11.316

.312

.310 

.307

11. 303 

.298

.296

.294

11.289 

.284 

.281 

.279

11. 274 

.268 

.266

.263

11. 258

.252

.249 

.247

11.241

.235

.232

.229

11.223 

.217

.214

.211

11.205 

.199

.195

.192

11. 186

.179

.176

.172

11. 165 

.159 

.155 

.152

11. 145

.137

.134

.130

11.123 

.115

.111

.108

11.100 

.092

.088

.084

11.077

20'

Inches

15. 105

.100

.097 

.094

15.088

.083

.080 

.077

15.071 

.064

.061

.058

15. 052 

.045 

.042 

.038

15.032 

.025 

.021

.018

15.010

.003

14. 999 

.996

14.988

.980

.976

.973

14. 965 

.956

.952

.948

14.940 

.931

.927

.923

14.914

.905

.901

.896

14.887 

.878 

.873 

.869

14. 859

.850

.845

.840

14.830 

.820

.815

.810

14. 800 

.790

.784

.779

14.769

* 30'

Inches

22. 658

.649

.645 

.641

22.633

.624

.619 

.615

22. 606 

.597

.592

.587

22. 577 

.568 

.563 

.558

22.547 

.537 

.532

co«

. U£O

22. 516

.505

.499 

.493

22. 482

.470

.465

.459

22.447 

.435

.429

.422

22.410 

.397

.391

.384

22. 371

.358

.351

OAK.

. O1U

22. 331 

.317 

.310 

.303

22. 289

.275

.267

.260

22.245 

.230

.223

.215

22.200 

.184

.177

.169

22. 153

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

For latitude 7°

5

10

15 

20

25

30

For latitude 8°

For latitude 9°

5

10

15 

20

25

30

5 

10 

15 

20 

25 

30

For latitude 10°

5

10

15 

20

25

30

For latitude 11°

For latitude 12°

5

10

15 

20

25

30

5

10

15 

20

25

30

For latitude 13°

5 

10 

15 

20 

25

30

For latitude 14°

5

10

15 

20

25

30

Meridional

distance

Inches

3.779

7.559

11. 338 

15. 117

18. 896

22. 676

3.779

7.559

11. 338 

15. 118

18. 897

22. 677

3.780 

7.559 

11. 339 

15. 119 

18. 898 

22. 678

3.780

7.560

11.340 

15. 119

18.899

22. 679

3.780

7.560

11. 340 

15.120

18. 901

22.681

3.780

7.561

11. 341 

15. 122

18. 902

22.682

3.781 

7.561 

11. 342 

15. 123 

18.903

22.684

3.781

7.562

11.343 

15. 124

18.905

22.686

Ordinate 

of developed 

parallel

Inch

0.000

.001

.003 

.005

.008

.012

0.000

.001

'.003 

.006 !oio

.014

0.000 

.002 

.004 

.007 

.011 

.015

0.000

.002

.004 

.008

.012

.017

0.001

.002

.005 

.008

.013

.019

0.001

.002

.005

. 

fiAQ wy 

.014

.020

0.001 

.002 

.005 

.010 

.015

.022

0.001

.003

.006 

.010

.016

.023
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 45 

TABLE 1. Coordinates for the projection of maps, scale -S^HTS Continued

Latitude 

ot 

parallel

0 /

14 00

10

15 

20

30

40

45

50

15 00 

10

15

20

Oft OU

40 

45 

50

16 00 

10 

15

20

30

40

45 

50

17 00

10

15

20

30 

40

45

60

18 00 

10

15

20

30

40

45

19 00 

10 

15 

20,

30

40

45

50

20 00 

10

20' 15

30 

40

45

50

21 00

Abscissas of developed parallel

Longitude interval

5'

Inches

3.692

.689

.688 

.687

3.684

.681

. .680

' .678

3.676 

.673

.671

.670

3.667 

.664 

.662 

.661

3.658 

.655 

.653

.652

3.649

.646

.644 

.642

3.639

.636

.634

.633

3.629 

.626

.624

.623

3.619 

.616

.614

.613

3.609

.606

.604

CAO

. OU*

3.598 

.595 

.593 

.591.

3.588

. 684

!582

.580

3.576 

.573

.571

.569

3.565 

.561

.559

.557

3.553

10'

Inches

7.384

.379

.376 

.374

7.368

.363

.360

.357

7.351 

.346

.343

.340

7.334 

.328 

.325 

.322

7.316 

.310 

.307

.304

7.297

.291

.288 

.285

7.278

.272

.269

.265

7.259 

.252

.249

.246

7.239 

.232

.228

.225

7.218

.211

.208

 &trt 9fU

7.197 

.190 

.186 

.182

7.175

.168

.164

.160

7.153 

.145

.141

.138

7.130 

.122

.118

.114

7.107

15'

Inches

11.077

.068

.064 

.060

11. 052

.044

.040

.035

11.027 

.018

.014

.010

11.001 

10.992 

.987 

.983

10. 974 

.965 

.960

.956

10.946

.937

.932 

.927

10. 918

.908

.903

.898

10.888 

.878

.873

.868

10.858 

.848

.843

.838

10.827

.817

.811

 

fifiA OUO

10. 795 

.785 

.779 

.774

10.763

7 co * t\j£i

.746

.741

10.729 

.718

.712

.706

10. 695 

.683

.678

.672

10. 660

20'

Inches

14. 769

.758

.752 

.747

14. 736

.725

.719

.714

14.702 

.691

.685

.679

14.668 

.656 

.650 

.644

14.632 

.620 

.614

.607

14. 595

.582

.576 

.570

14. 557

.544

.538

.531

14. 518 

.505

.498

.491

14.478 

.464

.457

.450

14. 436

.422

.415

.408

14.394 

.379 

.372 

.365

14.350

.335

.328

.321

14.306 

.290

.283

.275

14.260 

.244

.237

.229

14. 213

30'

Inches

22. 153

.137

.129 

.121

22.104

.088

.079

.071

22.054 

.037

.028

.019 

.599 nr\i) &&. \J\J£i

21. 984 

.975 

.966

21. 948 

.930 

.920

01 1 

 oil.

21. 893

.874

.864 

.855

21. 835

.816

.806

.796

21. 777 

.757

.747

.737

21.716 

.696

.686

.675

21.654

.633

.623

fii o

 UJ.4

21. 591 

.569 

.558 

.547

21. 525

rno 

 uUu

.492

.481

21.458 

.436

.424

.413

21. 390 

.367

.355

.343

21. 320

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

For latitude 14°

5

10

15 

20

25

30

For latitude 15°

For latitude 16°

5

10

15 

20

25

30

5 

10 

15 

20 

25 

30

For latitude 17° <

5

10

15 

20

25

30

For latitude 18°

For latitude 19°

' For latitude 20° 

5

10

15 

20

25

30

5

10

15 

20

25

30

5 

10 

15 

20 

25

30

For latitude 21°

5

10

15 

20

25

30

Meridional 

distance

Inches

3.781

7.562

11.343 

15.124

18.905

22.686

3.781

7.563

11.344 

15. 125

18. 907

22.688

3.782 

7.563 

11. 345 

15. 127 

18. 908 

22. 690

3.782

7.564

11. 346 

15.128

18. 910

22. 692

3.782

7.565

11. 347 

15. 130

18. 912

22. 694

3.783

7.566

11. 348 

15. 131

18. 914

22.697

3. .783 

7.566 

11.350 

15. 133 

18. 916

22.700

3.784

7.567

11. 351 

15. 135

18. 919

22. 702

Ordinate of developed 

parallel

Inch

0.001

.003

.006 

.010

.016

.023

0.001

003 loos

.011

.017

.025

0.001 

.003 

.007 

.012 

.018 

.026

0.001

.003

.007 

.012

.019

.028

0.001

.003

.007 

.013

' .020

.029

0.001

.003 !oos

.014

.021

.031

0.001 

.004 

.008 

.014 

.022

.032

. 0.001

.004

.008 

.015

.023

.033
46 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 

TABLE 1. Coordinates for the projection of maps, scale ^-^u Continued

Latitude 

of 

parallel

0 /

21 00

10

15 

20

30

40

45

60

22 00 

10

15

20

3(1 ou 

40 

45 

50

23 00 

10 

15

20

30

40

45 

50

24 00

10

15

20

30 

40

45

50

25 00 

10

15

20

30

40

45

50

26 00 

10 

15 

20

30

40

45

50

27 00 

10

15

20

30 

40

45

50

28 00

Abscissas of developed parallel

Longitude interval

5'

Inches

3.553

.549

.547 

.545

3.541

.537

.535

.533

3.529 

.525

.523

.521

3. 517 

.512 

.510 

.508

3.504 

.499 

.497

4Q c

. tad

3.491

.486

.484 

.483

3.477

.473

.471

.468

3. 464 

.459

.457

.455

3.450 

.445

.443

.441

3.436

.431

.429

Ann

. 4^0

3.422 

.417 

.414 

.412

3.407

.402

.400

.397

3.392 

.387

.385

.382

3.377 

.372

.369

.367

3.362

10'

Inches

7.107

.099

.095 

.091

7.083

.075

.070

.066

7.058 

.050

.046

.042

7 noQ /. Uoo

.025 

.020 

.016

7.008 

6.999 

.995

QQft

. tftfU

6.982

.973

.968 

.964

6.955

.946

.941

.937

6.928 

.919

.914

.909

6.900 

.891

.886

.881

6.872

.862

.858

.853

6.843 

.834 

.829 

.824

6.814

SfU 

. o\r±

.799

.794

6.784 

.774

.769

.764

6.754 

.744

.739

.734

6.723

15'

Inches

10. 660

.648

.642 

.636

10.624

.612

.606

.600

10.587 

.575

.569

.562

10. 550 

.537 

.531 

.524

10. 511 

.498 

.492

.485

10. 472

.459

.452 

.446

10.432

.419

.412

.405

10. 392 

.378

.371

.364

10. 350 

.336

.329

.322

10.308

.294

.286

. 970 fit y

10. 265 

.250 

.243 

.236

10. 221

oftft 

. &K>

.199

.191

10. 176 

.161

.154

.146

10. 131 

.116

.108

.100

10.085

207

Inches

14. 213

.197

.189 

.181

14. 165

.149

.141

.133

14. 116 

.100

.091

.083

14. 066 

.049 

.041 

.032

14. 015 

13. 998 

.989

.981

13.963

.945

.937 

.928

13. 910

.892

.883

.874

13. 856 

.837

.828

.819

13.800 

.782

.772

.763

13. 744

.725

.715

.706

13.686 

.667 

.657 

.648

13.628

.608

.598

.588

13. 569 

.548

.538

.528

13.508 

.488

.477

.467

13.446

30'

Inches

21.320

.296

.284 

.272

21.248

.224

.211

.199

21. 174 

.150

.137

.125

21.099 

.074 

.061 

.049

21. 023 

20.997 

.984

.971

20. 945

.918

.905 

.892

20.865

.838

.824

.811

20.783 

.756

.742

.728

20.700 

.672

.658

.644

20.616

.587

.573

.559

20.530 

.501 

.486 

.471

20.442

.412

.398

.383

20.353 

.323

.308

.292

20.262 

.231

.216

.201

. 20. 170

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

i

For latitude 21°

5

10

15 

20

25

30

For latitude 22°

For latitude 23°

5

10

15 

20

25

30

5 

10 

15 

20 

25 

30

For latitude 24°

5

10

15 

20

25

30

For latitude 25°

For latitude 26° <

5

10

15 

20

25

30

5

10

15 

20

25

30

For latitude 27°

5 

10 

15 

20 

25

30

For latitude 28°

5

10

15 

20

25

30

Meridional 

distance

Inches

3.784

7.567

11. 351 

15. 135

18. 919

22. 702

3.70^

7.568

11. 352 

15. 137

18. 921

22. 705

3.785 

7.569 

11.354 

15. 138 

18.923 

22.708

3.785

7.570

11.355 

15. 140

18. 926

22. 711

3.786

7.571

11. 337 

15. 142

18.928

22. 714

3.786

7.572

11. 358 

15. 144

18. 930

22. 716

3.787 

7.573 

11.360 

15. 147 

18. 934

22.720

3.787

7.574

11.362 

15. 149

18. 936

22. 724

Ordinate 

 of developed 

parallel

Inch

0.001

.004

.008 

.015

.023

.033

0.001

.004

.009 

.015

.024

.025

0.001 

.004 

.009 

.016 

.025 

.036

0.001

.004

.009 

.016

.026

.037

0.001

.004

.010 

.017

.026

.038

0.001

.004

.010 

.017

.027

.039

0.001 

.004 

.010 

.018 

.028

.040

0.001

.005

.010 

.018

.029

.041
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 47 

TABLE 1. Coordinates for the projection of maps, scale Trfr-ro Continued

Latitude 

of 

parallel

0 /

28 00

10

15 

20

30

40

45

50

29 00 

10

15

20

30 

40 

45 

60

30 00 

10 

15

20

30

40

45 

50

31 00

10

15

20

30 

40

45

50

32 00 

10

15

20

30

40

45

50

33 00 

10 

15 

20

30

40

45

50

34 00 

10

15

20

30 

40

45

50

35 00

Abscissas of developed parallel

Longitude interval

5'

Inches

3.362

.356

.354 

.351

3.346

.341

.338

.335

3.330 

.325

.322

.319

3.314 

.308 

.306 

.303

3.298 

.292 

.289

.286

3.281

.275

.272 

.270

3.264

.258

.255

.253

3.247 

.241

.238

.235

3.229 

.224

.221

.218

3. 212

.206

.203 

.200

3.194 

.188 

.185 

.182

3.176

.170

.167

.164

3. 157, 

.151

.148

.145

3.139 

.132

.129

.126

3.120

10'

Inches

6.723

.713

.708 

.702

6.692

.681

.676

.671

6.660 

.649

.644

.639

6.628 

.617 

.611 

.606

6.595 

.584 

.578

.573

6.562

.551

.545 

.539

6.528

.517

.511

.505

6.494 

.482

.476

.470

6.459 

.447

.441

.435

6.424

.412

.406

.400

6.388 

.376 

.370 

.364

6.351

Q'JO 

. OOU

.333

.327

6. 315 

.302

.296

.290

6.277 

.265

.259

.252

6.240

15'

Inches

10. 085

.069

.061 

.054

10. 038

.022

.014

10.006

9.990 

.974

.966

.958

9. 049 tri«

.925 

.917 

.909

9.893 

.876 

.868

. 850 OOW

9.843

.826

.817 

.809

9.792

.775

.766

.758

9.740 

.723

.714

.706

9.688 

.671

.662

. .653

9.635

.617

.608 

 Ann DV/U

9.582 

.564 

.554 

.545

9.527

CAQ * uuy 

.500

.491

9.472 

.453

.444

.435

9. 416 

.397

.388

.379

9.360

20'

Inches

13. 446

.426

.415 

.405

13. 384

.363

.352

.342

13.320 

.299

.288

.277

IQ ncfl lo. ZOO

.234 

.223 

.212

13.190 

.168 

.157

.146

13.123

.101

.090 

.078

13.056

.033

.022

13.010

12. 987 

.964

.953

.941

12. 918 

.894

.882

.871

12. 847

.823

.811

. 

7QQ ( W

12. 775 

.751 

.739 

.727

12. 703

* fi7Q Oi a

.666

.654

12.629 

.605

.592

.580

12. 555 

.530

.517

.505

12. 480

30'

Inches

20. 170

.139

.123 

.107

20.076

.044

.028

20.012

19.980 

.948

.932

.916 

1)7. 10 OO^ USA

.851 

.835 

.818

19. 785 

.752 

.735

. 710 / la

19. 685

.652

.635 

.618

19. 584

.550

.532

.515

19. 481 

.446

.429

.411

19. 376 

.341

.324

.307

19. 271

.235

.217

. 199

19. 163 

.127 

.109 

.091

19.054 10 Itf. ma Ulo

18. 999

.981

18. 944 

.907

.888

.870

18. 832 

.795

.776

.757

18. 719

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

For latitude 28°

5

10

15 

20

25

30

For latitude 29°

For latitude 30°

5

10

15 

20

25

30

5 

10 

15 

20 

25 

30

For latitude 31°

5

10

15 

20

25

30

For latitude 32°

For latitude 33°

For latitude 34°

5

10

15 

20

25

30

5

10

15 

20

25

30

5 

10 

15 

20 

25

30

For latitude 35°

5

10

15 

20

25

30

Meridional 

distance

Inches

3.787

7.574

11. 362 

15. 149

18. 936

22. 724

3.788

7.576

11.363 

15. 151

18. 939

22. 727

3.788 

7.577 

11. 365 

15.154 

18. 942 

22. 731

3.789

7.578

11. 367 

15. 156

18.945

22. 734

3. 789

7.579

11. 369 

15.158

18. 948

22.738

3.790

7.580

11.370 

15. 161

18. 951

22. 741

3.791 

7.582 

11.372 

15.163 

18.954

22. 745

3.791

7.583

11.374 

15. 166

18. 957

22. 749

Ordinate of developed 

parallel

Inch

0.001

.005

.010 

.018

.029

.041

0.001

.005

.011 

.019

.029

.042

0.001 

.005 

.011 

.019 

.030 

.043

0.001

.005

.011 

.020

.031

.044

0.001

.005

.011 

.020

.031

.045

0.001

.005

.011 

.020

.032

.046

0.001 

.005 

.012 

.021 

.032

.046

0.001

.005

.012 

.021

.033

.047
48 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 1. Coordinates for the projection of maps, scale -T^THS Continued

Latitude 

of 

parallel

0 /

35 00

10

15 

20

30

40

45 

50

36 00 

10

15

20 

30

40 

45 

50

37 00 

10 

15

20

30

40

45 

50

38 00

10

15

20

30 

40

45

50 

on firi do vv

10

15

20

30 

40 

45

50

40 00 

10 

15 

20

30

40

45

50

41 00 

10

15

20

30 

40

45

50

42 00

Abscissas of developed parallel

Longitude interval

5'

Inches

3.120

.114

.110 

.107

3.101

.094

.091 

.088

3. 081 

.075

.072

.068 

3.062

.055 

.052 

.049

3.042 

.035 

.032

.029

3.022

.015

.012 

.009

3.002

2.995

.992

.988

2.982 

.974

.971

.968 

9 A. Ofi1 WH 

.954 

.950

.947

2.940 

.933 

.929

.926

2.918 

.911 

.908 

.904

2.897

.890

.886

.883

2. 875 

.868

.864

.861

2.854 

.846

.843

.839

2.832

KK

Inches

6.240

.227

.221 

.214

6.202

.189

.182 

.176

6.163 

.150

.143

.137

6.124 

.111 

.104 

.097

6.084 

.071 

.064

.057

. 6.044

.031

.024 

.017

6.004

5.990

.983

.976

5.963 

.949

.942

..935

5.921 

.907 

.900

.893

5.879 

.865 

.858

QC1

 oOl

5.837 

.823 

.816 

.808

5.794

.780

.773

.765

5.751 

.736

.729

.722

5.707 

.692

.685

.678

5.663

15'

Inches

9.360

.341

.331 

.321

9.302

.283

.273 

.264

9.244 

.225

.215

.205

9

1 Qc

. loO

.166 

.156 

.146

9.126 

.106 

.096

.086

9.066

.046

.036 

.026

9.005'

8.985

.975

.964.

8. 944 ' 

.923

.913

.903-

0 000, O. OO4 '

.861' 

.850

.840:

8.819 

.798 

.787

.777

8.755 

.734 

.723 

.713

8.691

.670

.659

.648

8.626 

.605

.594

.583

8.561 

.539

.528

.517.

8. 495

20'

Inches

12. 480

.454

.441 

.429

12. 403

. .377

. 365 

.352

12. 326 

.300

.287

.274 

12. 248

!221 

.208 

.195

12. 168 

.142 

.128

.115

. 12.088

.061

.048 

.034

12.007

11.980

.996

.953

11. 925

.898

.884

.870

11.842 

.814 

.800

.786

11. 758 

.730 

.716

7fl9 . (U*

11. 674 

.645 

.631 

.617

. 11.588

.559

.545

.531

11.502 

.473

.458

.444

11.414 

.385

.370

.356

11. 326

30'

Inches

18. 719

..681

.662 

.643

18. 605

.566

.547 

.528

18. 489 

.450

.430

.411

1 Q 071 lo. Oil

.332 

.312 

.292

18. 252 

.213 

' .193

.172

18. 132

.092

.072 

.051

18. Oil

17.970

.949

. .929

17.888 

.846

.826

 .805

17:763 

.722 

.701

.680

17.638 

.595 

.574

eco

. OOo

17. 511 

.468 

.447 

.425

17. 382

.339

.318

.296

17.253 

.209

.187

.165

17. 122 

.078

.056

.033

16. 989

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

For latitude 35°

5

10

15 

20

25

30

For latitude 36°

For latitude 37°

5

10

15 

20

25

30

5 

10 

IS, 

20 

25 

30

For latitude 38°

510-

15 

20

25

30 f

;

For latitude 39°

For latitude 40°

5

10

15 

2025'

30

5 

10

15 

20 

25 

30

For latitude 41°

5 

10 

15 

20 

25

30

For latitude 42°

5

10

15 

20

25

30

Meridional

distance

Inches

3.791

7.583

11.374 

15. 166

18. 957

22. 749

3.792

7.584

11. 376 

15.168

18. 961

22. 752

3.793 

7.585 

11. 378 

15. 171 

18. 964 

22. 757 ;

3.793

7.587)

11.380 

15. 173

18. 967 !

22.761

3.794'

7. 588 11.382' 

15. 176

18. 970

22.765.

3.795 

7. 589'

11.384 

15. 179 

18. 974 

22. 768

3.795 

7. 59L 

11.386 

15. 181' 

18. 977

22. 772

3.796

7.592

11.388 

15.184

18. 980

22.776

Ordinate 

of developed 

parallel

Inch

0.001

.005

.012 

.021

.033

.047

0.001

. nn^ \AJij

.012 

.021

. 

fMQ voo 

.047

0.001 

.005 

.012 

.021 

 .033 

.048

0.001

.005

.012 

.021

.034

.048

0.001

.005

.012 

.022

.034

.049

0.001

Oft*

. l/UO

.012 

.022 

.034 

.049

0.001 

.005 

.012 

.022 

.034

.049

0.001

.005

.012 

.022

.034

.050

' ' :
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 49

TABLE 1. Coordinates for the projection of maps, scale T^TTO Continued

Latitude 

of 

parallel

0 /

42 00

10

15 

20

30

40

45

50

43 00 

10

15

20

inOu

40 

45 

50

44 00 

10 

15

20

30 

40

45 

50

45 00

10

15

20

30 

40

45

60

46 00 

10

15

20

30

40

45

50

47 00 

10 

15 

20

30

40

45

50

48 00 

10

15

20

30

40

45

50

49 00

Abscissas of developed parallel

Longitude interval

5'

Inches

2.832

.824

.820 

.817

2.809

.802

.798

.794

2.787 

.779

.775

.772

2.764 

.756 

.753 

.749

2.741 

.733 

.730

. 726

2.718 

.710

.706 

.703

2.695

.087

.683

.679

2.671 

.663

.659

.655

2.647 

.639

.635

.631

2.623

.615

.611

.607

2.599 

.591 

.587 

.583

2.575

.567

.563

.559

2.550 

.542

.538

.534

2.526

.517

.513

.509

2.501

10'

Inches

5.663

.648

.641 

.633

5.619

.604

.596

.589

5.574 

.558

.551

.543

S

KOQ . 0/0

.613 

.505 

.498

5.482 

.467 

.459

.452

5.436 

.421

.413 

.405

5.389

.374

.366

.358

5.342 

.327

.319

.311

5.295 

.279

.271

.263

6.247

.231

.223

91 *\

 «lu

6.199 

.182 

.174 

.166

5.150

.134

.125

.117

5.101 

.084

.076

.068

5.051

.035

.026

.018

5.001

15'

Inches

8.495

.472

.461 

.450

8.428

.405

.394

.383

8.360 

.338

.326

.315

O. 8 909 fiuft

.269 

.258 

.246

8.223 

.200 

.189

.177

8.154 

.131

.119 

.108

8.084

.061

.049

.037

8.014 

7.090

.978

.966

7.942 

.918

.906

.894

7.870

.846

.834

QOO

. O4A

7.798 

.774 

.762 

.749

7.725

.700

.688

.676

7.651 

.627

.614

.602

7.577

.552

.540

.527

7.502

20'

Inches

11. 326

.297

.282 

.267

11.237

.207

.192

.177,

0

11. 147 

.117

.102

.087

11.056 

.026 

11.011 

10.995

10.965 

.934 

.918

QAO

. yuo

10. 872 

.841

.826 

.810

10. 779

.747

.732

.716

10. 685 

.653

.637

.621

10.590 

.558

.542

.526

10. 494

.462

.446

.430

10. 897 

.365 

.349 

.332

10.300

.267

.251

.235

10.202 

.169

.152

.136

10.103

.070

.053

..036

10.003

30'

Inches

16. 989

.945

.923 

.900

16.856

.811

.788

.766

16. 721 

.675

.653

.630 

ifl <;84 ID. u&i

.539 

.516 

.493

16,447 

-.401 

.378

.355

16. 308 

.262

.238 

.215

16. 168

.121

' .098

.074

16: 027 

15. 980

.956

.932

15.884 

.837

.813

.789

15. 741

.693

.669

.644

15.596 

.547 

.523 

.499

15. 450

.401

.376

.352

15.303 

.253

.228

.204

15.154

.104

.079

.055

15.005

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

For latitude 42°

5

10

15 

20

25

30

For latitude 43°

For latitude 44°

5

10

15 

20

25

30

5 

10 

15 

20 

25 

30

For latitude 45°

5 

10

15 

20

25

30

For latitude 46°

For latitude 47°

For latitude 48°

*

5

10

15 

20

25

30

5

10

15 

20

25

30

5 

10 

15 

20 

25

30

For latitude 49°

5

10

15 

20

25

30

Meridional

distance

Inches

3.796

7.592

11.388 

15. 184

18. 980

22. 776

3.797

7.593

11.390 

15. 187

18. 984

22. 781

3.797 

. 7. 595 

11.392 

' 15. 189 

18. 987 

22. 785

3.798 

7.596

11.394 

15. 192

18. 990

22. 789

3.799

7.597

11.396 

16. 195

18.994

22. 793

3.799

7.599

11.398 

15. 198

18. 997

22. 797

3.800 

7.600 

11.400 

15.200 

19.000

22.801

 3.801

7.601

11.402 

15.203

19. 004

22. 805

Ordinate 

of developed 

parallel

Inch

0.001

.005

.012 

.022

.034

.050

0.001

.006

.012 

.022

.035

.050

0.001 

.000 

.012 

.022 

.035 

.050

0.001 

.006

.012 

.022

.035

.050

0.001

.006

.012 

.022

.035

.050

0.001

.006

.012 

.022

.035

.050

0.001 

.005 

.012 

.022 

.034

.050

0.001

.005

.012 

.022

.034

.049
50 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 1.- Coordinates for the projection of maps, scale -^-g^-s Continued

Latitude 

of 

parallel

0 /

49 00

10

15 

20

30

40

45

50

50 00 

10

15

20

30 

40 

45 

50

51 00 

10

15

20

30

40

45 

50

52 00

10

15

20

30 

40

45

50

53 00 

10 

15

20

30 

40

45

50

54 00 

10 

15 

20

30

40

45

50

55 00 

10

15

20

30 

40

45

50

56 00

Abscissas of developed parallel

Longitude interval

5'

Inches

2.501

.492

.488 

.484

2.476

.467

.463

.459

2.450 

.442

.438

.433 

2.425

.416 

.412 

.408

2.399 

.391 

.386

.382

2.373

.365

.360 

.356

2.347

.338

.334

.330

2.321 

.312

.308

.303

2

OAe

. zyo 

.286 

.281

.277

2.268 

.259 

.255

OCA

. 4dU

2.241 

.232 

.228 

.223

2.214

.205

.201

.196

2.187 

.178

.173

.169

2.160 

.151

.146

.142

2.132

10'

Inches

5.001

4.985

.976 

.968

. 4.951

.934

.926

.918

4.901

.884

.875

.867 

4.850

.833 

.824 

.815

4.798 

.781 

 .772

.764

4.746

.729

.720 

.712

4.694

.677

.668

.659

4.642 

.624

.615

.607

4.589 

.571 

.562

.554

4.536 

.518 

.509

Wl

. utKI

4.482 

.464 

.455 

.446

4.428

.410

.401

.392

4.374 

.356

.347

.338

4.320 

.301

.292

.283

4.265

15'

Inches

7.502

.477

.465 

.452

7.427

.402

.389

.376

7.351 

.326

.313

.300

7

V7A

. £l\

.249 

.236 

.223

7.197 

.172 

.159

.146

7.120

.094

.081 

.068

7.042

.015

7.002

6.989

6.963 

.936

.923

.910

n OOA 0.884 

.857 

.844

.830

6.804

.777 

.764

71ft * JUU

6.723 

.697 

.683 

.670

6.643

.616

.602

.588

6.561 

.534

.520

.507

6.479 

.452

.438

.425

6.397

20'

Inches

10.003

9.970

.953 

.936

9.902

.869

.852

.835

9.801 

.767

.750

.733

9. 

fiQQ Otfif

.665 

.648 

..631

9.596 

..562 

..545

..528

9.493

.458

.441 

.424

9.389

.353

.336

.319

9.284 

.249

.231

.213

9.178 

.143 

.125

.107

9.072 

.036 

.018

Q filYl o. UUU

8.965 

.929 

.911 

..893

8.857

.821

.803

.785

8.748 

.712

.694

.676

8.639 

.603

.584

.566

. 8. 529

30'

Inches

15.005

14.954

.929 

.904

14.854

.803

.778

.753

14. 702 

.651

.625

.600

14. 549 

.498 

.472 

.446

.14.395 

.343 

.317

9Q1 

. zvl

14.239

.187

.161 

.135

14. 083

.031'

14.004

13. 978

13. 926 

.873

..846

.820

13.767 

.714 

.687

.661

13.607 

.554 

.527

.500

13.447 

.393 

.366 

.339

13.285

.231

.204

.177

13. 122 

.068

.041

13. 013

12. 959 

.904

.877

.849

12.794

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

For latitude 49°

5

10

15 

20

25

30

For latitude 50°

For latitude 51°

5

10

15 

20

9^4iJ

30

5 

10 

15 

20 

25 

30

For latitude 52°

5

10

15 

20

25

30

For latitude 53°

For latitude 54°

For latitude 55°

5

10-

15 

20

25

30

5 

10

15 

20 

25 

30

5 

10 

15 

20 

25

30

For latitude 56°

5

10

15 

20

25

30

Meridional 

distance

Inches

3.801

7.601

11.402 

15.203

19.004

22. 805

3.801

7.603

11.404 

15.206

1Q (Ifl7 iy. uv*

22.809

3.802 

7.604 

11. 406 

15.208 

19. Oil 

22. 813

i

3.803

7.605

11.408 

15. 211

19.014

22. 817

3.803

7.607

11.410 

15. 214

19. 017

22. 821

3.804

7

nf\o 

. bus

11.412 

15. 216 

19. 020 

22.824

3.805 

7.609 

11.414 

15. 219 

19.024

22.828

3.805

7.611

11.416 

15. 221

19. 027

22.832

Ordinate of developed 

parallel

Inch

0.001

.005

.012 

.022

.034

.049

0.001

.005

.012

fl99 

. U£A

.034

!049

0.001 

.005 

.012 

.022 

.034 

.049

0.001

.005

.012 

.022

.034

.048

0.001

.005

.012 

.021

.033

.048

0.001 

.005

.012 

.021 

.033 

.047

0.001 

.005 

.012 

.021 

.033

.047

0.001

.005

.012 

.021

.032

.046
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 51

TABLE 2. Coordinates for the projection of maps, scale

Latitude 

of 

parallel

0 /

0 00

05

07M 

10

15

20

WA

25

30 

35 

37H

40 

45

60 

52H 

55

1 00 

05 

07^

10

15

20"MA 

25

30

35

37^

40

45

50

52H

55

2 00

05

OVA

10

15

20

22^

25

30

35

37^

40

45

50

52H

55

. 3 00

Abscissas of developed parallel

Longitude interval

2^'

Inches

3.804

.804

.'804 

.804

3.804

.804

.804

.804

3.804 

.804 

.804

.804

3 O. SfU Olri

.804 

.804 

.804

3.804 

.804 

.804

.804

3.804

.803

.803 

.803

3.803

.803

.803

.803

3.803

.802

.802

.802

3.802

.802

.802

.802

3.802

.801

-.801

.801

3.801

.801

.800

.800

3.800

.800

.800

.799

3.799

6'

Inches

7.609

.609

.609 

.609

7.609

.609

.609

.609

. 7.609 

.608 

.608

.608 

7 flfia f « uuo 

.608 

.608 

.608

7.608 

.608 

.607

.607

7.607

.607

.607 

.607

7.606

.606

.606

.606

7.605

.605

.605

.605

7.604

.604

.604

.603

7.603

.603

.602

.602

7.602

.601

.601

.601

7.600

.600

.599

.590

7.598

7H'

Inches

11. 413

.413

.413 

.413

11.413

.413

.413

.413

11.413 

.413 

.413

.413 

11. 412

.412 

.412 

.412

11.412 

.411 

.411

.411

11. 411

.410

.410 

.410

11.409

.409

.409

.408

11. 408

.407

.407

.407

11.407

.406

.405

.405

11.405

.404

.404

.403

11.403

.402

.401

.401

11.400

.399

.399

.398

11. 398

i<y

Inches

15. 218

.218

.218 

.218

15. 218

.217

.217

.217

15. 217 

.217 

.217

.217 

15. 216

.216 

.216 

.216

15. 215 

.215 

.215

.215

15. 214

.214

.213 

.213

15. 213

.212

.212

.211

15. 211

.210

.210

.209

15.208

.208

.207

.207

15.206

.205

.205

.204

15. 203

.202

.202

.201

15.200

.199

.199

.198

15. 197

15'

Inches

22.827

.827

.826 

.826

22. 826

.826

 .826

.826

22.826 

.825 

.825

.825

99 S9<» £t£i* OfiO

.824 

.824 

.824

22. 823 

.822 

.822

.822

22.821

.820

.820 

.820

22.819

.818

.817

.817

22. 816

.815

.814

.814

22. 813

.812

.811

.810

22.809

.808

.807

.806

22.805

.803

.803

.802

22.800

.799

.798

.797

22. 795

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

VA

 5

For latitude 0° ffl

WA

15

2M

6

For latitude 1° ^

WA

15

2M 

5

For latitude 2° ffi

1% 

15

2H

5

For latitude 3° ^

12H

15

Meridional 

distance

Inches

3.779

7.557

11. 336 

15. 115

18. 893

22. 672

3.779

7.557

11.336 

15. 115 

18. 893

22.672

3.779 

7.557 

11. 336 

15. 115 

18. 894 

22.672

3.779

7.658

11. 336 

15. 115

18. 894

22. 673

Ordinate 

of developed 

parallel

Inch

0.000

.000

.000 

.000

.000

.000

0.000

.000

.000 

.000 

.001

.001

0.000 

.000 

.000 

.001 

.001 

.002

0.000

.000

.001 

.001

.002

.003
52 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 2. Coordinates for the projection of maps, scale ^-sk^n Continued

Latitude 

of 

parallel

0 ,

3 00

05

10

15

20

25

30 

35

40

45

50

55

4 00 

05

10

15

20

22^ 

25

30

35

37^

40

45

60

52^

55

5 00

05

07 J^

10

15

20

22 J^

25

30

35

37^

40

45

60

62J^

55

6 00

Abscissas of developed parallel

Longitude interval

W

Inches

3.799

.799

.799 

.799

3.798

.798

.798 

.798

3.797 

.797 

.797 

.797

 -go

!796 

.796

.796

3.795 

.795 

.795

.794

3.794

.794

.793 

.793

3.793

.792

.792

.792

3.791

.791

.791

.791

3.790

.790

.789

.789

3.789

.788

.788

.788

3.787

.786

.786

.786

3.785

.785

.785

.784

3.784

5'

Inches

7.598

.598

.698 

.697

7.597

.596

!595

7.595 

.594 

.594 

.593

7 1OT

!592 

.592

.591

7.590 

 .590 

.589

.589

7.588

.587

.587 

.586

7.586

.585

.584

.584

7.583

.582

.582

.581

7.580

.579

.579

.578

7.577

.576

.576

.575

7.574

.573

.572

.572

7.671

.570

.570

.569

7.567

7*

Inches

11. 398

.397

.396 

.396

11. 395

.394

.394 

.393

11.392 

.391 

.391 

.390

11.389

.388 

.387

.387

11.386 

.385 

.384

.383

11. 382

.382

.380 

.380

11. 378

.377

.376

.376

11. 374

.373

' .372

.372

11.370

.369

.368

.367

11.366

.364

.363

.363

11.361

.359

.359

.358

11. 356

.355

.354

.353

11. 351

10'

Inches

15. 197

.196

.195 

.195

15. 193

.192

.191 

.191

15. 190 

.188 

.187 

.187

15. 185

.184 

.183

.182

15.181 

.179 

.179

.178

15. 176

.174

.174 

.173

15. 171

.169

.168

.168

15.166

.164

.163

.162

15.160

.158

.157

.156

15.154

.152

.151

.150

15. 148

.146

.145

.144

15. 142

.139

.138

.137

15. 135

15'

Inches

22. 795

.794

.793 

.792

22.790

.788

, .787 

.786

22.784 

.782 

.781 

.780

99 fit* 778 I/O

.776 

.775

.774

22.771 

.769 

.768

.767

22:764

.762

.760 

.759

22. 757

.754

.573

.751

22.749

.746

.745

.743

22.740

.737

.736

.734

22. 731

.728

.727

.725

22.722

.719

.717

.716

22.712

.709

.707

.706

22. 702

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

2J^

5

For latitude 3° ffi

12J£

15

2^

5 

For latitude 4° ffi

15

5

For latitude 5° ^ 

15

2^

5

For latitude 6° ffi

12^i

15

Meridional 

distance

Inches

3.779

7.558

11.336 

15. 115

18. 894

22.673

3.779

7.558 

11.337 

15. 115 

18.894 

22.673

3.779

7.558

11. 337 

15. 116 

18. 895 

22.674

3.779

7.558

11.337 

15. 116

18. 896

22.675

Ordinate 

of developed 

parallel

Inch

0.000

.000

.001 

.001

.002

.003

0.000

.000 

.001 

.002 

.002 

.003

0.000

.000

.001 

.002 

.003 

.004

0.000

.001

.001 

.002

.004

.005
FABLES FOR CONSTRUCTION 6P K)LYC6NiC PROJECTIONS

TABLE 2. Coordinates for the projection of maps, scale T^-g^ Continued

Latitude 

of 

parallel

0 /

6 00

05

07^ 

10

15

20

22M

25

30 

35

37}^

40

45 

60

55

7 00 

05 

07^

10

15

20

25 2

30

35

37^

40

45

50

52J/3

55

8 00

05

07M

10

15

20

22^

25

30

35

37H

40

45

50

52H

55

9 00

Abscissas of developed parallel

Longitude interval

W

Inches

3.784

.783

.783 

.783

3.782

.781

.781

.781

3.780 

.779

.779

.779

Q »77O O. I to

.778 

.777 

.777

3.776 

.776 

.775

.775

3.774

.774

.773 

.773

3.772

.771

.771

.771

3.770

.769

.769

.768

3.768

.767

.766

.766

3.765

.765

.764

.764

3.763

.762

.762

.761

3.760

.760

.759

.758

3.758

5'

Inches

7.567

.566

.566 

.565

7.564

.563

.562

.561

7.660 

.559

 1.558

.558

7.556 

.555 

.554 

.554

7.552 

.551 

.550

.550

7.648

.547

.546 

.546

7.544

.543

.542

.541

7.540

.538

.538

.537

7.535

.534

.533

.532

7.531

.529

.528

.527

7.526

.524

.523

.522

7.521

.519

.518

.517

7.516

7*

Inches

11.351

.349

.349 

.348

11. 346

.344

.343

.342

11.340 

.338

.338

.337

11.335 

.333 

.332 

.331

11.329 

.327 

.326

.325

11.323

.321

.319 

.318

11. 316

.314

.313

.312

11.310

.307

.306

.305

11.303

.301

.299

.298

11.296

.294

.292

.291

11.289

.286

.285

.284

11.281

.279

.277

.276

11. 274

Iff

Inches

15. 135

.133

.131 

.130

15.128

.125

.124

.123

15. 121 

.118

.117

.115

15. 113 

.110 

.109 

.108

15. 105 

.102 

.101

.100

15.097

.094

.093 

.091

15.088

.085

. .084

.083

15.080

.077

.075

.074

15. 071

.068

.066

.064

15.061

.058

.056

.055

15. 052

.048

.047

.045

15.042

.038

.037

.035

15.032

15'

Inches

22.702

.699

.697 

.695

22.692

.688

.686

.685

22.681

.677

.675

.673

99 tifit fifiQ DUo

.665 

.664 

.662

22.658 

.653 

.651

649

22.645

.641

.639 

.637

22.633

.628

.626

.624

22.619

.615

.613

.610

22.606

.601

.599

.597

22. 592

.587

.585

.582

22.577

.573

.570

.568

22.563

.558

.555

.653

22.547

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

2J^

5

For latitude 6° ^

12)^

15

2H

5

For latitude 7° ^

12i/

15

5 

For latitude 8° ^

12^2 

15

5 2

For latitude 9° ^

12J^j

15

Meridional 

distance

Inches

3.779

7.558

11.337 

15. 116

18. 896

22. 675

3.779

7.559

11. 338 

15. 117

18. 896

22. 676

3.779 

7.559 

11.338 

15. 118 

18. 897 

22. 677

3.780

7.559

11. 339 

15. 118

18. 898

22. 678

Ordinate 

of developed 

parallel

Inch

0.000

.001

" .001 

.002

.004

.005

0.000

.001

.001 

.003

004 u\n

.006

0.000 

.001 

.002 

.003 

.005 

.007

0.000

.001

.002 

.003

.005

.008
54 TABLES TOE CONSTRUCTION OF POLYCON1C PROJECTIONS 

TABLE 2. Coordinates for the projection of maps, scale -s-gfaTf~~Continued

Latitude

of 

parallel

0 /

9 00

05

07^ 

10

15

20

22^

25

30 

35

. 40

50 

55

10 00 

05 

07}^

10

15

20

 2&A

' 25

30

35

yjy

40

45

50

52^

55

11 00

05

07^

10

15

20

22}<

25

30

35

37 y

40

45

50&iy

55

12 00

Abscissas of developed parallel

Longitude interval

W

Inches

3.758

.757

.757 

.756

3.755

.754

.754

.753

3.753 

.752 

.751 

.751

!749 

.748 

.748

3.747 

.746 

.746

.745

3.744

.743

.743 

.742

3.741

.740

.740

.739

3.738

.737

.737

.736

3.735

.734

.733

.733

3.732

.731

.730

.730

3.729

.727

.727

.726

3.725

.724

.724

.723

3.722

5'

Inches

7.516

.514

.513 

.512

7.511

.509

.508

.507

7.505 

.503 

.502 

.502

1498 

.497 

.496

7.494 

.492 

.491

.490

7.488

.486

.485 

.484

7.482

.480

.479

.478

7.476

.474

.473

.472

7.470

.468

.467

.466

7.464

.461

.460

.459

7.457

.455

.454

.453

7.450

.448

.447

.446

7.444

7*

Inches

11. 274

.271

.270 

.268

11.266

.263

.262

.260

11.258 

.255 

.254 

.252

11 249

!245 

.244

11. 241 

.238 

.237

235

11.232

.229

.228 

.226

11.223

.220

.219

.217

11. 214

.211

.210

.208

11.205

.202

.200

.199

11. 195

.192

.191

.189

11. 186

.182

.181

.179

11. 176

.172

.171

.169

11. 165

10'

Inches

15.032

.028

.026 

.025

15. 021

.018

.016

.014

15. 010 

.007 

.005 

.003

14.999 

.996 

.994 

.992

14.988 

.984 

.982

080

14.976

.973

.971 

.969

14.965

.961

.959

.956

14.952

.948

.946

.944

14.940

.936

.934

.931

14.927

.923

.921

.919

14. 914

.910

.908

.905

14.901

.896

.894

.892

14.887

15'

Inches

22.547

.542

.540 

.537

22.532

.526

.524

.521

22.516 

.510 

.507 

.505

22. 499 

.493 

.491 

.488

22. 482 

.476 

.473

.470

22. 465

.459

.456 

.453

22. 447

.441

.438

.435

22.429

.422

.419

.416

32.410

.404

.400

.397

22. 391

.384

.381

 .378

22. 371

.365

.361

.358

22. 351

.345

.341

.338

22. 331

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

For latitude 9°

2M

5

ioH

12J<£

15

For latitude 10°

For latitude 11°

iy-i

5

15

VA 

5

15 2

For latitude 12°

2^

5

ioH

12M

15

Meridional 

distance

Inches

3.780

7.559

11. 339 

15. 118

18. 898

22. 678

3.780

7.560

11. 340 

15. 119 

18. 899 

22. 679

3.780 

7.560 

11. 340 

15.120 

18.901 

22.681

3.780

7.561

11. 341 

15. 121

18. 902

11.682

Ordinate 

of developed 

parallel

Inch

0.000

.001

.002 

.003

.005

.008

0.000

001

!(X)2 

.004 

.006 

.009

0.000 

.001 

.002 

.004 

.006 

.009

0.000

.001

.003 

.005

.007

.010
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 55

TABLE 2. Coordinates for the projection of maps, scale TS$-QTS Continued

Latitude 

of 

parallel

0 ,

12 00

05

10

15

20

22 J^

25

30 

35

40

45 

50 

52^ 

55

13 00 

05 

07^

10

15

20

25

30

35.

37J^

40

45

50

52Mi

55

14 00

05

07V£

10

15

20

22V£

25

30

35

37M

40

45

60

52^

55

15 00

Abscissas of developed parallel

Longitude interval

W

Inches

3.722

.721

.720 

.720

3.718

.717

.717

.716

3.715 

.714 

.713

.712

3 71 1 . i 11

.710 

.709 

.709

3.708 

.706 

.706

.705

3.704

.703

.702 

.701

3.700

.699

.698

.697

3.696

.695

.694

.693

3.692

.691

.690

.689

3.688

.687

.686

.685

3.684

.683

.682

.681

3.680

.678

.670

.677

3.676

5'

Inches

7.444

.441

.440 

.439

7.437

.434

.433

.432

7.430 

.427 

.426

.425

7 499

!420 

.419 

.418

7.415 

.413 

.411

.410

7.408

.405

.404 

.403

7.400

.397

.396

.395

7.392

.390

.388

.387

7.384

.382

.380

.379

7.376

.374

.372

.371

7.368

.365

.364

.363

7.360

.357

.356

.354

7.351

w

Inches

11. 165

.162

.160 

.159

11. 155

.152

.150

.148

11. 145 

.141 

.139

.137

11. 134

.130 

.128 

.126

11. 123 

.119 

.117

.115

11.111

.108

.106 

.104

11.100

.096

.094

.092

11.088

.084

.082

.080

11. 077

.072

.070

.068

11.064

.060

.058

.056

11. 052

.048

.046

.044

11.040

.035

.033

.031

11. 027

HX

Inches

14.887

.883

.880 

.878

14. 873

.869

.866

.864

14.859 

.855 

.852

.850

14.845

.840 

.838 

.835

14. 830 

.825 

.823

.820

14.815

.810

.808 

.805

14.800

.795

.792

.790

14.784

.779

.777

.774

14. 769

.763

.761

.758

14. 752

.747

.744

.742

14. 736

.731

.728

.725

14. 719

.714

.711

.708

14. 702

15'

Inches

22.331

.324

.321 

.317

22.310

.303

.300

.296

22.289 

.282 

.278

.275

22. 267

.260 

.256 

.253

22. 245 

.238 

.234

.230

22. 223

.215

.211 

.208

22.200

.192

.188

.184

22. 177

.169

.165

.161

22.153

.145

.141

.137

22.129

121

.116

.112

22.104

.096

.092

.088

22. 079

.071

.066

.062

22.054

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

For latitude 12°

2J<£

5

SA

12)/£

15

For latitude 13°

2H

5

15

For latitude 14°

5 2 

15

For latitude 15°<

»A

5

SA

12J^

15

Meridional 

distance

Inches

3.780

7.561

11. 341

15. 121

18.902

22. 682

3. 781

7.561

11. 342 

15. 123 

1O. IS fiftl U\JO

22.684

3.781 

7.562 

11. 343 

15. 124 

18. 905 

22. 686

3.781

7.562

11. 344 

15. 125

18.907

22.688

Ordinate 

of developed 

parallel

Inch 

0.000

.001

.003 

.005

.007

.010

0.000

.001

.003 

.005 

.008

.011

0.000 

.001 

.003 

.005 

.008 

.012

0.000

.001

.003 

.006

.009

.012
TABLES FOR CONSTRUCTION OF POLTCONlC PROJECTIONS

TABLE 2. Coordinates for the projection of maps, scale ?-STSTSTS~~Continued

Latitude 

of 

parallel

 o /

15 00

05

10

15

20

25 2

30 

35 

37^ 

40

,r

50

52^ 

55

16 00

05 

07^

10

15

20

25 2

30

35

37/^

40

45

50

52^

55

17 00

05

07 J^

10

15

20

22)^

25

30

35

37J^

40

45

50

52J^

55

18 00

Abscissas of developed parallel

Longitude interval

2*

Inches

3.676

.674

.673 

.673

3.671

.670

. 669 

.668

3.667 

.665 

.665 

.664

3.662

.661

.660 

.659

3.658

.656 

.656

.655

3.653

.652

.651 

.650

3.649

.647

.646

.646

3.644

.642

.642

.641

3.639

.638

.637

.636

3.634

.633

.632

.631

3.629

.628

.627

.626

3.624

.623

.622

.621

3.619

5'

Inches

7.351

,-. 348

.347 

.346

7.343

.340

.'S37

7.334 

.331 

.329 

.328

7 S2 r>

!322

.320 

.319

7.316

.313 

'.311

.310

7.307

.304

.302 

.301

7.297

.294

.293

.291

7.288

.285

.283

.282

7.278

.275

.274

.272

7.269

.265

.264

.262

7.259

.256

.254

.252

7.249

.246

.244

.242

7.239

7MInches

11. 027

.023

.020 

.018

11. 014

.010

.007 

!005

11.001 

10. 996 

.994 

.992

10. 987

.983

.981 

.978

10. 974

.969 

.967

.965

10. 960

.956

.953 

.951

10. 946

.942

.939

.937

10.932

.927

.925

.922

10.918

.913

.910

.908

10.903

.898

.896

.893

10.888

.883

.881

.878

10.873

.868

.866

.863

10.858

*

Inches

14. 702

.697

.694 

.691

14. 685

.679

.677 

.674

14.668 

.662 

.659 

.656

14 At. A'lft OOl/

.644

.641 

.638

14. 632

.626 

.623

.620

14. 614

.607

.604 

.601

14. 595

.589

.586

.582

14. 576

.570

.567

.563

14. 557

.551

.547

-.544

14.538

.531

.528

.524

14. 518

.511

.508

.505

14. 498

.491

.488

.484

14. 478

15'

Inches

22. 054

.045

.041 

.037

22.028

.019

.015 

.010

22.002 

21. 993 

.988 

.984

91 07 1\ 4L, y/o

.966

.962 

.957

21. 948

.939 

.934

.930

21. 920

.911

.907 

.902

21. 893

.883

.878

.874

21.864

.855

.850

.845

21.835

.826

.821

.816

21.806

.796

,792

, .787

21. 777

.767

.762

.757

21. 747

.737

.732

.727

21. 716

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

For latitude 15° <

2V£

5

10^

12/^

15

For latitude 16°

VA

5 

15 2

For latitude 17°

*A 

5

ioM

15 '2

For latitude 18°

PA

5

10^

12J^

15

Meridional 

distance

Inches

3.781

 7. 562

11. 344 

15. 125

18.907

22.688

3.782

7.563 

11. 345 

15. 126 

18. 908 

22.690

3. 782 

7.564

11. 346 

15.128

18. 910 

22. 692

3.782

7.565

11. 347 

15.129

18. 912

22.694

Ordinate 

of developed 

parallel

Inch

0.000

.001

.003 

.006

.009

.012

0.000

.001 

.003 

.006 

.009 

.013

0.000 

.002

.003 

.006

.010 

.014

0.000

.002

.004 

.006

.010

.015
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 57 

TABLE 2. Coordinates for the projection of maps, scale %-sfa-Q Continued

Latitude 

of 

parallel

o /

18 00

05

WA 

10

15

20

22>£

25

30

35

37^

40

45 

50 

62^ 

55

19 00 

05 

07^

10

15

20

WA 

25

30

35

37J^

40

45

50

52^

55

20 00

05w*A

10

15

20

22^

25

30

35

WA

40

45

50WA

55

21 00

Abscissas of developed parallel

Longitude interval

2H'

Inches

3.619

.618

.617 

.616

3.614

.613

.612

.611

3.609 

.607

' .606

.606

O. 1 KMUvrr

.602 

.601 

.600

3.598 

.597 

.596

w, . uou

3.593

.591

.590 

.589

3.588

.586

.585

.584

3.582

.580

.579

.578

3.576

.575

.574

.573

3.571

.569

.568

.567

3.565

.563

.562

.561

3.559

.557

.556

.555

3.553

5'

Inches

7.239

.235

.234 

.232

7.228

.225

.223

.222

7.218 

.215

.213

,211

7 It 9oa £uO

.204 

.202 

.200

7.197 

.193 

.192

 io\J ion

7.186

.182

.181 

.179

7.175

.171

.170

.168

7.164

.100

.158

.157

7.153

.149

.147

.145

7.141

.138

.136

.134

7.130

.126

.124

.122

7.118

.114

.112

.110

7.107

7H'

Inches

10.858

.853

.850 

.848

10.843

.838

.835

.832

10.827 

.822

.819

.817 

10.811

.806 

.803 

.801

10. 795 

.790

.787

.785

10. 779

.774

.771 

.768

10.763

.757

.754

.752

10. 746

.741

.738

.735

10.729

.724

.721

.718

10. 712

.706

.704

.701

10.695

.689

.686

.683

10. 678

.672

.669

.666

10.660

KX

Inches

14.478

.471

.467 

.464

14. 457

.450

.447

.443

14.436 

.429

.426

.422 

14. 415

.408 

.404 

.401

14. 394 

.387 

.383

.379

14. 372

.365

.361 

.358

14.350

.343

.339

.335

14.328

.321

.317

.313

14.306

.298

.294

.290

14.283

.275

.271

.268

14.260

.252

.248

.244

14.237

.229

. . 225

.221

14.213

15'

Inches

21. 716

.706

.701 

.696

21. 686

.675

. 670

.665

21.654 

.644

.639

.633 

21. 623

.612 

.607 

.601

21. 591 

.580 

.574

.569

21.558

.547

.542 

.536

21. 525

.514

.509

.503

21.492

.481

.475

.470

21. 458

.447

.441

.436

21. 424

.413

.407

.401

21.390

.378

.372

.367

21.355

.343

.337

.331

21.320

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

For latitude 18°

VA

5

7M 

10

12K

15

For latitude 19°

For latitude 20°

VA

5

1Yi 

10

1 01/ \iy-i

15

2K 

5 

7K 

10 

12^ 

15

For latitude 21°

VA

5

7H 

10

12^

15

Meridional 

distance

Inches

3.782

7.565

11. 347

15.129

18. 912

22. 694

3.783

7

CCO 

. ODO

11. 348 

15. 131

18. 914

22.697

3.783 

7.566 

11.350 

15. 133 

18. 916 

22. 699

3.784

7.567

11. 351 

15. 135

18.919

22. 702

Ordinate 

of developed 

parallel

Inch

0.000

.002

.004 

.006

.010

.015

0.000

fitV) 

 UVA

.004 

.007

.011

.015

0.000 

.002 

.004 

.007 

.011 

.016

0.000

.002

.004 

.007

.012

.017
58 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 

TABLE 2. Coordinates for the projection of maps, scale %-S$TSTI~~Continued

Latitude 

of 

parallel

0 /

21 00

05

07^ 

10

15

20

25

30 

35

40

45 

50

55

22 00

05

10

15

20

25

30

35

87!^

40

45

50

62^

55

23 00

05

10

15

20

22^

25

30

35

37K

40

45

50

52^

65

24 00

Abscissas of developed parallel

Longitude interval

W

Inches

3.553

.551

.550 

.549

3.547

.545

.544 

.543

3.541 

.539 

.538 

.537

3.535

.533

'.532

.531

3.529

.527

.526

.525

3.523

.521

.520 

.519

3.517

.514

.513

.512

3.510

.508

.507

.506

3.504

.502

.501

.499

3.497

.495

.494

.493

3.491

.489

.487

.486

3.484

.482

.481

.480

3.477

5'

Inches

7.107

.103

.101 

.099

7.095

.091

.089 

.087

7.083 

.079 

.077 

.075

7.070

.066

.064

.062

7.058

.054

.052

.050

7.046

.042

,039 

.037

7.033

.029

.027

.025

7.020

.016

.014

.012

7.008

.003

.001

6.999

6.995

.990

.988

.986

6.982

.977

.975

.973

6.968

.964

.962

.959

6.955

w

Inches

10. 660

.654

.651 

.648

10. 642

.636

. 633 

.630

10. 624 

.618 

.615 

.612

10.606

.600

.596

.593

10. 587

.581

.578

.575

10. 569

.562

.559 

.556

10. 550

.543

.540

.537

10. 531

.524

.521

.518

10.511

.505

.502

.498

10. 492

.485

.482

.479

10.472

.466

.462

.459

10. 452

.446

.442

.439

10. 432

10'

Inches

14. 213

.205

.201 

.197

14. 189

.181

.177 

.173

14. 165 

.157 

.153 

.149

14. 141

.133

.129

.125

14. 116

.108

.104

.100

14.091

.083

.079 

.075

14.066

.058

.054

.049

14.041

.032

.028

.024

14.015

.007

.002

13. 998

13. 989

.981

.976

.972

13. 963

.954

.950

.945

13. 937

.928

.923

.919

13. 910

15'

Inches

21.320

.308

.302 

.296

21.284

.272

. 266 

.260

21. 248 

.236 

.230 

.224

21 211

!l99

.193

.187

21. 174

.162

.156

.150

21. 137

.125

.118 

.112

21.099

.087

.080

.074

21.061

.049

.042

.036

21.023

.010

.003

20.997

20.984

.971

.964

.958

20.945

.931

.925

.918

20.905

.892

.885

.878

20. 865

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

For latitude 21°

y/i

5

10^

12J^

15

For latitude 22°

VA

6 

15 2

For latitude 23°

*Yi

5 f

SA

15

For latitude 24°

»A

5

10^

12}^

15

Meridional 

distance

Inches

3.784

7.567

11.351 

15. 135

18. 919

. 22.702

3.784

7.568 

11. 352 

15. 136 

18. 921 

22. 705

3. 785

7.569

11.354 

15. 138

18. 923

22. 708

3.785

7.570

, 11. 355 

15. 140

18. 926

22. 711

Ordinate 

of developed 

parallel

Inch

0.000

.002

.004 

.007

.012

.017

0.000

.002 

.004 

.008 

.012 

.017

0.000

.002

.004 

.008

.012

.018

0-001

.002

.005 

.008

.013

.019
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 59

TABLE 2. Coordinates for the projection of maps, scale Continued

Latitude 

of 

parallel

0 /

24 00

05

07>£ 

10

15

20

22^

25

30 

35

37^ 

40

45 

50 

52^ 

55

25 00 

05 

07^

10

15

20

22^ 

25

30

35

37H

40

45

50

55^

oo

26 00

05

07M

10

15

20

22^

25

30

35

37H

40

45

60

52M

55

27 00

Abscissas of developed parallel

Longitude interval

2H'

Inches

3.477

.475

.474 

.473

3.471

.468

.467

.466

3.464 

.462

.460 

.459

3.457 

.455 

.454 

.452

3.450

.448 

.447

AAK 

, ' no

3.443

.441

.440 

.438

3.436

.434

.432

.431

3.429

.426

.425

.424

3.422

.419

.418

.417

3.414

.412

.411

.409

3.407

.405

.403

.402

3.400

.397

.396

.395

3.392

5'

Inches

6.955

.950

.948 

.946

6.941

.937

.935

.932

6.928 

.923

.921 

.919

6.914 

.909 

.907 

.905

6.900 

.895 

.893

.891

6.886

.881

.879 

.877

6.872

.867

.865

.862

6.858

.853

. 850

.848

"6.843

.838

.836

.834

6.829

.824

.821

.819

6.814

.809

.807

.804

6.799

.794

.792

.789

6.784

7H'

Inches

10. 432

.426

.422 

.419

10. 412

.405

. 402

.398

10.392 

.385

.381 

.378

10.371 

.364 

.361 

.357

10! 350 

.343 

.340

.336

10.329

.322

.318 

.315

10. 308

.301

.297

.294

10. 286

.279

.276

.272

10.265

.258

.254

.250

10. 243

.236

.232

.228

10. 221

.214

.210

.206

10. 199

.191

.188

.184

10. 176

10'

Inches

13.910

.900

.896 

.892

13. 883

.874

.809

.865

13. 856 

.846

.842 

.837

iq QOQ lo. 040 

.819 

.814 

.810

13.800 

.791 

.786

.782

13. 772

.703

.758 

.753

13. 744

.734

.730

.725

13. 715

.706

.701

.696

13. 686

.677

if>72

.667

13. 657

.648

.643

.638

13. 628

.618

.613

.608

13. 598

.588

.584

.579

13. 569

15'

Inches

20. 865

.851

.845 

.838

20.824

.811

.804

.797

20. 783 

.770

.763 

.756

90 fAj> 749 t^.ti

.728 

.721 

.714

20.700 

.686 

.679

.672

20. 658

.644

.637 

.630

20. 616

.602

.594

.587

20. 573

.559

.551

.544

20. 530

.515

.508

.501

20. 486

.471

.464

.457

20. 442

.427

.420

.412

20. 398

.383

.375

.368

20. 353

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

2K

5

For latitude 24° < ^

12H

15

lYi

5

For latitude 25° ^

15

m

2J4

5

For latitude 26° ^

12H

15

2M

5

For latitude 27° ^

12M

15

Meridional 

distance

Inches

3.785

7.570

11.355 

15. 140

18. 926

22. 711

3.786

7 / . Uf ^711

11.357 

15. 142

18. 928 

22. 714

3.780 

7. 572 

11. 358 

15. 144 

18. 931 

22. 717

3.787

7.573

11.360 

15. 147

18. 934

22. 720

Ordinate 

of developed 

parallel

Inch

0.001

.002

.005 

.008

.013

.019

0.001

.002

.005 

.008

.013 

.019

0.001 

.002 

.005 

.009 

.014 

.020

0.001

.002

.005 

.009

.014

.020

6243° 2<
60 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 2. Coordinates for the projection of maps, scale j Continued

Latitude 

of 

parallel

0 /

27 00

05

10 a

15

20

22^

25

30 

35

37J-3

40

45 

50

55 i

28 00 

05 

07^

.10

15

20

25 2

30

35

37]^

40

45

50

52]/£

55

29 00

05

07 ]/'

10

15

20

25 2

30

35

37Jx

40

45

50

52^

Abscissas of developed parallel

Longitude interval

2/2'

Inches

3.392

.390

.388 

.387

3.385

.382

.381

.380

3.377 

.374

.373

.372

3. 369 

.367 

.365 

.364

3.362 

.309 

.308

ocn

, QUO

3.354

.351

.350 

.349

3.346

.343

.342

.341

3. 338

.335

.334

.333

3.330

.327

.326

.325

3. 322

.319

.318

.317

3.314

.311

.310

.308

3.306

.303

.302

55 . 300

30 00 3.298

5'

Inches

6.784

.779

.777 

.774

6.769

.764

.762

.709

6. 754. 

.749

.746

. 744

6.739

.734 

.731 

.728

6.723

.718 

.715

.713

6.708

.702

.700 

.697

6.692

.687

.084

.081

6.676

.671

.668

.666

6.660

.655

.652

.649

6. 644

.639

.636

.033

6.628

.622

.620

.617

6. 611

.000

.603

.601

6.595

1Y!

Inches

10. 176

. 169

. 105 

.101

10.154

.146

.142

.139

10. 131. 

. 123

.120

.116

10. 108 

.100 

.096 

.093

10. 085 

.077 

.073

.009

10. 061

.054

.000 

.046

10. 038

.030

.026

.022

10. 014

.006

.002

9.998

9.990

.082

.978

.974

9.966

.958

.954

.950

9.942

.934

.929

.925

9.917

.909

.905

.901

9.893

10'

Inches

13. 569

.559

.553 

.548

13. 538

.528

.523

.518

13. 508 

.498

.493

.488

13. 477 

. .407 

.402 

.467

13. 446 

.436 

.431

.426

13.415

.405

.400 

.394

13. 384

.373

.368

.303

13. 352

.342

.336

.331

.13. 320

.310

.304

.299

13. 288

.277

.272

.267

13. 256

.245

.239

.234

13. 223

.212

.207

.201

13. 190

10'

Inches

20. 353

.338

.330 

.323

20. 308

.292

.285

.277

20. 262 

.247

.239

.231 

on 91 ft

£,\J, &1\J

.201 

.193 

.185

20.170 

.154 

.146

.139

20.123

.107

.099 

.092

20. 076

.000

.052

.044

20. 028

.012

.004

19. 996

19.980

.904

.906

.948

19. 932

.916

.908

.900

]9.884

.867

.859

.851

19. 835

.818

.810

.802

19. 785

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

For latitude 27°

V/2

5

10*

12)^

15

For latitude 28°

For latitude 29°

2M

5

12V£

15

5 2 

15 2

For latitude 30°

y/2

5

10**

12}/£

15

Meridional 

distance

Inches

3.787

7.573

11. 360 

15. 147

18. 934

22. 720

3.787

7.574

11.302 

15. 149

18. 936

22.723

3.788 

7.575 

11.363 

15. 151 

18. 939 

22. 727

3.788

7. 577

11. 365 

15. 153

18. 942

22. 730

Ordinate 

of developed 

parallel

Inch

0.001

.002

.005 

.009

.014

.020

0.001

002

ioos

.009

.014

.021

0.001 

.002 

.005 

.009 

.015 

.021

0.001

.002

.005 

.010

.015

.022
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 61 

TABLE 2. Coordinates for the projection of maps, scale Tsfav Continued

Latitude 

of 

parallel

0 /

30 00

05

07K 

10

15

20

25

30

35

37J3

40 

45

50 

55 2

31 00 

05 

07/2

10

15

20

22^ 

25

30

35

37^

40

45

50

52//£

55

32 00

05

07^

10

15

20

22 ^A

25

30

35

37M

40

45

50

52^

.55

33 00

Abscissas of developed parallel

Longitude interval

W

Inches

3.298

.295

.293 

.292

3.289

.286

.285 

.284

 3.281

.278

.277

.275 

O. 3 979 61 ft

.270 

.268 

.267

3.264 

.201 

.200

.258

3.255

.253

.251 

.250

3.247

.244

.242

.241

3.238

.235

.234

.232

3.229

.220

.225

.224

3.221

.218

.216

.215

3.212

.209

.207

.206

3.203

.200

.198

.197

3.194

5'

Inches

6.595

.589

.587 

.584

6. 578

.573

.570 

.567

6.562 

.556

.553

.551 

6.545

.539 

.536 

.534

6.528 

.522 

.519

.517

6.511

.505

.502 

.499

6.494

.488

.485

.482

6.476

.470

.468

.465

0.459

.453

.450

.447

6.441

.435

.432

.429

6.424

.418

.415

.412

6.406

.400

.397

.394

6.388

7*

Inches

9. 893

.884

.880 

.876

9.868

. 859

.855 

.851

9.843 

.834

.830

.826 

9.817

.809 

.805 

.800

9.792 

.783 

.779

.775

9.766

.758

.753 

.749

9.740

.732

.727

.723

9.714

.706

.701

.697

9.688

.679

.675

.671

9.662

.653

.649

.644

9.635

.020

.622

.617

9.008

.600

.595

.591

9.582

10'

Inches

13. 190

.179

.174 

.168

13.157

.146

.140 

. 135

13. 123 

.112

.107

.101 

13. 090

.078 

.073 

.067

13. 056 

.044 

.039

033

13. 022

.010

.004 

12. 999

12. 987

.976

.970

.964

12. 953

.941

.935

.929

12. 918

.906

.900

.894

12. 882

.871

.865

.859

12. 847

.835

.829

.823

12.811

.799

.793

.787

12. 775

15'

Inches

19. 785

.769

.760 

.752

.19. 735

.719

.710 

.702

19.685 

.668

.000

.652 

19. 635

.618 

.609 

.601

19. 584 

.567 

.558

ECA 

. UUU

19. 532

.515

.507 

.498

19. 481

.464

.455

.446

19. 429

.411

.403

.394

19. 376

359

'.350

.341

19.324

.307

.297

.288

19.271

.253

.244

.235

19. 217

.199

.190

.181

19.163

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

V/'>

5 \

For latitude 30°' ty*

J2J^ 15 *

W5 "

For latitude 31° ^

12V*! 15 "

5 * 

For latitude 32° ^~

15 2

2*5 "

For latitude 33° ffi

15 i2y>"

Meridional 

distance

Inches

3.788

7.577

11.305 

15. 153

18. 942

22. 730

3.789

7. 578

11.367

15. 156

18.945

22. 734

3.789 

7.579 

11. 369 

15. 158 

18. 948 

22. 737

3.790

7.580

11.370 

15.161

18. 951

22. 741

Ordinate 

of developed 

parallel

Inch

0.001

.002

.005 

.010

.015

.022

0.001

.002

.005

.010

.015

.022

0.001 

.002 

.000 

.010 

.016 

.022

0.001

.003

.006 

.010

.016

.023
62 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 2. Coordinates for the projection of maps, scale YH-&TT Continued

Latitude 

of 

parallel

0 ,

33 00

05

07^ 

10

15

20

22^

25

30 

35

37^

40

45 

50 

52^ 

55

34" 00 

05 

07^

10

15

20

25 2

30

35

37^

40

45

50

52}/

55

35 00

05

07jx

10

15

20 iiy

25

30

35yiy,

40

45

50

52J/

55

36 00

Abscissas of developed parallel

Longitude interval

W

Inches

3.194

.191

.189 

. .188

3.185

.182

.180

.179

3.176 

.173

.171

.170

3.167 

.164 

.162 

.160

3.157 

.154 

.153

3.148

.145

.143 

.142

3.139

.136

.134

.132

3.129

.126

.125

.123

3.120

.117

.115

.114

3.110

.107

.106

.104

3.101

.098

.096

.094

3.091

.088

.086

.085

3.081

5'

Inches

6.388

.382

.379 

.376

6. 370

.364

.361

.358

6.351 

.345

.342

.339

6.333 

.327 

.324 

.321

6.315 

.309 

.305

QQO

6.296

.290

.287 

.284

6.277

.271

.268

.265

6.259

.252

.249

.246

6.240

.233

.230

.227

6.221

.214

.211

.208

6.202

.195

.192

.189

6.182

.176

.173

.169

6.163

7*

Inches

9.582

.573

.568 

.564

9.554

.545

.541

.536

9.527 

.518

.513

.509

!491 

.486 

.481

9.472 

.463 

.458

.453

9.444

.435

.430 

.426

9.416

.407

.402

.397

9.388

.379

.374

.369

9.360

.350

.345

.341

9.331

.321

.317

.312

9.302

.293

.288

.283

9.273

.264

.259

.254

9.244

10'

Inches

12. 775

.763

.757 

.751

12. 739

.727

.721

.715

12. 703 

.691

.685

.679

12. 666 

.654 

.648 

.642

12.629 

.617 

.611

f-fic 

» DUO

12. 592

.580

.574 

.567

12. 555

.542

.536

.530

12. 517

.505

.498

.492

12. 480

.467

.460

.454

12. 441

.429

.422

.416

12. 403

.390

.384

.377

12. 365

.352

.345

.339

12. 326

15' ,

Inches

19. 163

.145

.136 

.127

19.109

.091

.082

.073

19.054 

.036

.027

.018

18. 999 

.981 

.972 

.963

18. 944 

.926 

.916

. 907

18. 888

.870

.860 

.851

18.832

.814

.804

.795

18. 776

.757

.748

.738

18. 719

.700

.691

.681

18. 662

.643

.633

.624

18. 605

.585

.576

.566

18.547

.528

.518

.508

18. 489

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

2J<6

5

For latitude 33° ffi

\.iy<i

15

V/2

5

For latitude 34° 1^

12J/4

15

5 

For latitude 35° ffi

15

2H

5

For latitude 36° ffl

123^

15

Meridional 

distance

Inches

3.790

7.580

11. 370 

15. 161

18. 951

22. 741

3.791

7.581

11. 372 

15.163

18.954

22. 745

3.791 

7.583 

11. 374 

15. 166 

18. 957 

22. 748

3.792

7.584

11. 376 

15. 168

18. 961

22. 752

Ordinate 

of developed 

parallel

Inch

0.001

.003

.006 

.010

.016

.023

0.001

.003

.006 

.010

.016

.023

0.001 

.003 

.006 

.010 

.016 

.023

0.001

.003

.006 

.010

.016

.024

\
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 63

TABLE 2. Coordinates for the projection of maps, scale ^-B^TTII Continued

Latitude 

of 

parallel

0 /

36 00

05

 07M 

10

15

20

22^

25

30 

35

37H

40

45 

50 

52M 

55

37 00 

05 

07^

10

15 

20

22K 

25

30

35

37M

40

45

50

52^

55

38 00

05

07H

10

15

20

22M

25

' 30

35

37H

40

45

50

52M

55

39 00

Abscissas of developed parallel

Longitude interval

2K'

Inches

3.081

.078

.077 

.075

3.072

.068

.067

.065

3.062 

.059

.057

055

3

M1)

* V/u£

.049 

' .047 

.045

3.042 

.039 

.037

flOC 

. Uuu

3.032 

.029

.027 

.025

3.022

.019

.017

.015

3.012

.009

.007

.005

3.002

2.998

.997

.995

2.992

.988

, .986

.985

2.982

.978

.976

.974

2.971

.968

.966

.964

2.961

5'

Inches

6.103

.156

.153 

.150

6.143

.137

.134

.130

6.124 

.117

.114

.111

6. 104 

!097 

.094 

.091

6.084 

.077 

.074

.071

6.064 

.057

.054 

.051

6.044

.037

.034

.031

6.024

.017

.014

.010

6.004

5.997

.993

.990

5.983

.976

.973

.969

5.963

.956

052

C-349

5.942

.935

.932

.928

5.921

7W

Inches

9.244

.235

.230 

.225

9.215

.205

.200

.195

9.186 

.176

.171

.166

9.156 

.146 

.141 

.136

9.126 

.116 

.111

.106

9.096 

.086

.081 

.076

9.066

.056

.051

.046

9.036

.026

.021

.015

9.005

8.995

.990

.985

8.975

.964

.959

.954

8.944

.934

.928

.923

8.913

.903

.897

.892

8.882

10'

Inches

12.326

.313

.306 

.300

. 12. 287

.274

.267

.261

12. 248 

.234

.228

.221

19 Oflfi

\.£i. ZUO

.195 

.188 

.182

12. 168 

.155. 

.148

.142

12, 128 

.115

.108 

.102

12.088

.075

.068

.061

12. 048

.034

.027

.021

12.007

11. 994

.987

.980

11. 966

.953

.946

.939

11. 925

.911

.905

.898

11.884

.870

.863

.856

11.842

15'

Inches

18. 489

.469

.459 

.450

18. 430

.411

.401

.391

.371 

.352

.342

.332

1 Q Q1O lo. oil

.292 

.282 

.272

18. 252 

.233 

.223

91 3 

. £iG

18. 193 

.172

.162 

.152

18. 132

.112

.102

.092

18. 072

.051

.041

.031

18. Oil

17.990

.980

.970

17. 949

.929

.919

.908

17. 888

.867

.857

.846

17. 826

.805

.795

.784

17. 763

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

2H

5

For latitude 36° ffi

12H

15

2M

5

For latitude 37° .^

12H

15

VA 

5

For latitude 38° < ^

12H

15

2M 

5

For latitude 39° . ffi

12H

15

Meridional 

distance

Inches

3.792

7.584

11.376 

15. 168

18. 961

22. 752

3.793

7.585

11. 378 

15. 171

18. 964

22. 756

3.793 

7.587 

11.380 

15. 173 

18. 967 

22. 760

3.794 

7.588

11. 382 

15. 176

18. 970

22. 764

Ordinato 

of developed 

parallel

Inch

0.001

.003

.000 

.010

.016

.024

0.001

.003

.006 

.011

.017

.024

0.001 

.003 

.006 

.011 

.017 

.024

0.001 

.003

.000 

.011

.017

.024
64 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 2. Coordinates for the projection of maps, scale ^-J-^TJ Continued

Latitude 

of 

parallel

0 /

39 00

05

10 2

15

20

22^

25

30 

35

37^

40

45 

50

55 2

40 00 

05

10 2

15

20

25 2

30

35

37^

40

45

50

52J-3

55

41 00

05

07^

10

15-

20

22^

25

30

35

37M

40

45

50

52J^

55

42 00

Abscissas of developed parallel

Longitude interval

2*

Inches

2.961

.957

.955 

.954

2.950

.947

.945

.943

2.940 

.936

.934

.933

2 929 

!926 

.924 

.922

2.918 

.915 

.913

.911

2.908

.904

.902 

.901

2.897

.893

.892

.890

2.886

.883

.881

.879

2.875

.872

.870

.868

2.864

.861

.859

.857

2.854

.850

.848

.846

2.843

.839

.837

.835

2.832

5'

Inches

5.921

.914

.911 

.907

5.900

.893

.890

.886

5.879 

.872

.869

.865

5.858 

.851 

.848 

.844

5.837 

.830 

.826

.823

5.816

.808

.805 

.801

5.794

.787

.783

.780

5.773

.765

.762

.758

5.751

.744

.740

.736

5.729

.722

.718

.714

5.707

.700

.696

.692

5.685

.678

.674

.670

5.663

W

Inches

8.882

.871

.866 

.861

8.850

.840

.835

.829

8.819 

.808

.803

.798

o 707

O. (O(

.777 

.771 

.766

8.755 

.745 

.739

.734

8.723

.713

.707 

.702

8.691

.680

.675

.670

8.659'

.648

.643

.637

8.620

.615

.610

.605

8.594

.5,83

.577

.572

8.561

.550

.544

.539

8.528

.517

.511

.506

8.495

I*

Inches

11. 842

.828

.821 

.814

11. 800

.786

.779

.772

11. 758 

.744

.737

.730

11.716 

.702 

.695 

.688

11. 674 

.660 

.652

.645

11. 631

.617

.610 

.603

11.588

.574

.567

.559

11.545

.531

.523

.516

11. 502

.487

.480

.473

11. 458

.444

.436

.429

11. 414

.400

.392

.385

11. 370

.356

.348

.341

11. 326

15'

Inches

17. 763

.743

.732 

.722

17. 701

.680

.669

.659

17. 638 

.617

.606

.595

17. 574 

.553 

.543 

.532

17. 511 

.489 

.479

.468

17. 447

.425

.414 

.404

17. 382

.361

.350

.339

17.318

.296

.285

.274

17. 253

.231

.220

.209

17. 187

.165

.154

.143

17. 122

.100

.089

.078

17. 056

.033

.022

.011

16.989

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

For latitude 39°

2/^

5

10^

12}^

15

For latitude 40°

For latitude 41°

2H

5

12!/

15

5 

15

For latitude 42°

2y2

5

loH

12J/2

15

Meridional 

distance

Inches

3.794

7.588

11.382 

15. 176

18.970

22. 764

3.795

7. 589

11. 384 

15. 179

18. 974

22. 768

3.795 

7.591 

11. 386 

15. 181 

18. 977 

22. 772

3.796

7.592

11.388 

15. 184

18. 980

22. 776

Ordinate 

of developed 

parallel

Inch

0.001

.003

.006 

.011

.017

.024

0.001

.003

.006 

.011

.017

.025

0.001 

.003 

.006 

.011 

.017 

.025

0.001

.003

.006 

.011

.017

.025
TABLES FOR CONSTRUCTION OF BOLYCONIC PROJECTIONS 65

TABLE 2. Coordinates for the projection of maps, scale 7-sinrff Continued

\

Latitude 

of 

parallel

0 /

42 00

05

07^ 

10

15

20

22 IX

25

30 

35

37^

40

45 

50 

f>VA 

55

43 00 

05 

07^

10

15

20

22^ 

25

30

35

WA

40

45

50

52^

55

44 00

05

07/^

10

15

20

22^

25

30

35

3%

40

45

50

52]^

55

45 00

Abscissas of developed parallel

Longitude interval

W

Inches

2.832

.828

.826 

.824

2.820

.817

.815

.813

2.809 

.806

.804

.802

2.798 

.794 

.792 

.791

2.787 

.783 

.781

. 779

2. 775

.772

.770 

.768

2.764

.700

.758

.756

2. 753

.749

.747

.745

2.741

.737

.735

.733

2.730

.726

.724

.722

2.718

.714

.712

.710

2.706

.703

.701

.699

2.695

5'

Inches

5.663

.656

.652 

.648

5.641

.633

.630

.626

5.619 

.611

.607

.604

. 5. 596 

.589 

.585 

.581

5.574 

.506 

.502

cro

. OOo

5. 551

.543

.540 

.536

5.528

.520

.517

.513

5.505

.498

.494

.490

5.482

.475

.471

.467

5.459

.452

.448

.444

5.436

.428

.424

.421

5.413

.405

.401

.397

5.389

7*

Inches

8.495

.483

.478 

.472

8.461

.450

.445

.439

8.428

.417

.411

.405

!383 

. 377 

.372

8. 300 

.349 

.343

.338

8. 320

.315

.309 

.304

8.292

.281

.275

.269

8.258

.246

.241

.235

8.223

.212

.200

.200

8.189

.177

.171

.166

8.154

.142

.137

.131

8. 119

.108

.102

.096

8.084

10'

Inches

11. 326

.311

.304 

.297

11. 282

.267

.259

.252

11. 237 

.222

. 215

.207

H. 

I ltt409

.177 

.170 

.162

11. 147 

.132 

.124

.117

11. 102

.087

.079 

.071

11.056

.041

.033

.026

11.011

10. 995

.988

.980

10. 965

.949

.942

.934

10. 918

.903

.895

.888

10. 872

.857

.849

.841

10. 826

. .810

.802

.794

10. 779

15'

Inches

16. 989

.967

.956 

.945

16. 923

.900

.889

.878

16. 856

fi'W 

. oM

.822

.811

1 A *7QQ

ID. IOO

.766 

.754 

.743

16. 721 

.698 

.087

.675

16. 653

.630

. 619 

.607

16.584

.562

.550

.539

16. 516

.493

.481

.470

16.447

.424

.412

.401

16. 378

.355

.343

.331

16. 308

. .285

.273

.262

16. 238

.21.5

.203

.192

16. 16S

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

2J/J

5

For latitude 42°' il^

l2J/£

15

<2\/2

5

For latitude 43° ffi

]2jx

15

5 ^ 

For latitude 44° A^

15 2

2^

5

For latitude 45° ffi

12J^

15

Meridional 

distance

Inches

3.796

7. 592

11.388 

15.184

18. 980

22. 776

3. 797

7.593

11.390 

15.187

18. 984

22. 780

3.797 

7.595 

11. 392

15. 189 

18. 987 

22.784

3.798

7.596

11.394 

15. 192

18.990

22. 788

Ordinate 

of devel 

oped 

parallel

Inch

0.001

.003

.006 

.011

.017

.025

0.001

.003

.006 

.011

.017

.025

0.001 

.003 

.006

.011 

.017 

.025

0.001

.003

 .006 

.011

. 017

.025

.

-

i
66 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 2. Coordinates for the projection of maps, scale ^-g^^ Continued

Latitude 

of 

parallel

O 1

45 00

05

10 2

15

20

22 J^

25

30 

35

37H

40

45 

50

55 2

46 00 

05

10 2

15

20

25 2

30

35

37H

40

45

50

y%y,

55

47 00

05

07^

10

15

20

W/<

25

30

35

37^

40

45

50

52^

55

48 00

Abscissas of developed parallel

Longitude interval

W

Inches

2.695

.691

.689 

.687

2.683

.679

.677

.675

2.671 

.667

.665

.663

2

CCQ . OUtf

 .655 

.653 

.651

2.647 

.643 

.641

OQQ

2.635

.631

.629 

.627

2.623

.619

.617

.615

2.611

.607

.605

.603

2.599

.595

.593

.591

2.587

.583

.581

.579

2.575

.571

.569

.567

2.563

.559

.557

.555

2.550

5'

Inches

5.389

.382

.378 

.374

5.366

.358

.354

.350

5.342 

.334

.330

.327

'.311 

.307 

.303

5.295 

.287 

.283

. 279

5.271

.263

.259 

.255

5.247

.239

.235

.231

5.223

.215

.211

.207

5.199

.191

.187

.182

5.174

.166

.162

.158

5.150

.142

.138

.134

5.125

.117

.113

.109

5.101

w

Inches

8.084

.072

.066 

.061

8.049

.037

.031

.025

8.014 

.002

7.996

.990

7.978 

.966 

.960 

.954

7.942 

.930 

.924

. 918

7.906

.894

.888 

.882

7.870

.858

.852

.846

7.834

.822

.816

.810

7.798

.786

.780

.774

7.762

.749

.743

.737

7.725

.713

.707

.700

7.688

.676

.670

.664

7.651

10'

Inches

10. 779

.763

.755 

.747

10. 732

.716

.708

.700

10. 685 

.669

.661

.653

10. 637 

.621 

.613 

.606

10.590 

.574 

.566

eeo 

. OOo

10. 542

.526

.518 

.510

10. 494

.478

.470

.462

10. 446

.430

.422

.413

10. 397

.381

.373

.365

10. 349

.332

.324

.316

10.300

.284

.275

.267

10. 251

.235

.226

.218

10.202

15'

Inches

16. 168

.145

.133 

.121

16.098

.074

.062

.051

16.027 

.003

15. 991

.980

15. 956 

.932 

.920 

.908

15. 884 

.861 

.849

QO7 * OO*

15. 813

.789

.777 

.765

15. 741

.717

.705

.693

15. 669

.644

.632

.620

15. 596

.572

.560

.547

15.523

.499

.486

.474

15. 450

.425

.413

.401

15. 376

.352

.339

.327

15. 303

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

For latitude 45°

2K

5

ioM

12H

15

For latitude 46°

For latitude 47°

iy<i

5

12H

15

5 2 

15

For latitude 48°

5 2

10^

12}^

15

Meridional 

distance

Inches

3.798

7.596

11. 394 

15. 192

18. 990

22. 788

3.799

7.597

11. 396 

15. 195

18. 994

22. 792

3.799 

7.599 

11. 398 

15. 197 

18. 997 

22. 796

3.800

7.600

11.400 

15. 200

19. 000

22. 800

Ordinate 

of developed 

parallel

Inch

0.001

.003

.006 

.011

.017

.025

0.001

.003

.006 

.011

.017

.025

0.001 

.003 

.006 

.011 

.017 

.025

0.001

.003

.006 

.011

.017

.025
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 67

TABLE 2. Coordinates for the projection of maps, scale t-g-^-g-~~Continued

Latitude 

of 

parallel

0 /

48 00

0510 2

15

20

22H

25

30 

35

40 2

60 

55 "

49 00 

05

10

15

20

25

30

35

37M

40

45

50

52V£

55

60 00

05

07^

10

15

20

22J^

25

30

35

37J^

40

45

50

52J^

55

51 00

Abscissas of developed parallel

Longitude interval

W

Inches

2.550

.546

.544 

.542

2.538

.534

.532

.530

2.526 

.522 

.519

.517

9 ft, UiO 113

.509 

.507 

.505

2.501 

.497 

.494

4Q2

2.488

.484

.482 

.480

2.476

.471

.469

.467

2.463

.459

.457

.455

2.450

.446

.444

.442

2.438

.433

.431

.429

2.425

.421

.418

.416

2.412

.408

.406

.403

2.399

5'

Inches

5.101

.093

.088 

.084

5.076

.068

.064

.060

5.051 

.043 

.039

.035

5.026 

.018 

.014 

.010

5.001 

4.993 

.989

08 1 . DOu

4.976

.168

.964 

° .960

4.951

.943

.939

.934

4.926

.918

.913

.909

4.901

.892

.888

.884

4.875

.867

.862

.858

4.850

.841

.837

.833

4^824

.815

.811

.807

4.798

7*

Inches

7.651

.639

.633 

.627

7.614

.602

.596

.589

7.577 

.565 

.558

.552

7.540 

.527 

.521 

.515

7.502 

.490 

.483

.477

7.465

.452

.446 

.439

7.427

.414

.408

.402

7.389

.376

.370

.364

7. 351

.338'

.332

.326

7.313

.300

.294

.287

7.274

.262

.255

.249

7.236

.223

.217

.210

7.197

vy

Inches

10. 202

.185

.177 

.169

10. 152

.136

.128

.119

10. 103 

.086 

.078

.070

10. 053 

.036 

.028 

.020

10.003 

9.986 

.978

Q7A 

. yt\j

9.953

.936

.928 

.919

9.902

.886

.877

.869

9.852

.835

.827

.818

9.801

.784

.776

.767

9.750

.733

.725

.716

9.699

.682

.674

.665

9.648

.631

.622

.614

9.596

15'

Inches

15. 303

.278

.266 

.253

15. 228

.204

.191

.179

15. 154 

.129 

.117

.104

15. 079 

.055 

,042 

.030

15.005 

14. 979 

 ,967

Q(\4

14. 929

.904

.892 

.879

14. 854

.829

.816

.803

14. 778

.753

.740

.727

14. 702

.676

.664

.651

14. 625

.600

.587

.574

14. 549

.523

.510

.498

14. 472

.446

.433

.420

14. 395

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

2M

5

For latitude 48°. ff*

12J/, 15 "

2H

For latitude 49° ^

15 2

5 2 

For latitude 50° ffi

15

»A

5

For latitude 51° ffi

12J^

15

Meridional 

distance

Inches

3.800

7.600

11.400 

15. 200

19.000

22.800

3.801

7.601

11.402 

15. 203 

19 004

22l 804

3.801 

7.603 

11.404 

15. 205 

19. 007 

22. 808 '

3.802

7.604

11.406 

15. 208

19.011

22. 812

Ordinate 

of developed 

parallel

Inch

0.001

.003

.006 

.011

.017

.025

0.001

.003

.006 

.011 

.017

.025

0.001 

.003 

.006 

.011 

.017 

.025

0.001

.003

.006 

.011

.017

.024
68 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 3. Coordinates for the projection of maps, scale yYiTff

Latitude of

parallel

0 /

0 00

02J^

03^

0507 y^

10

nM

12/^

15"Ml

18M

20

22^ 

25

27>i

30 

32!^

33% 

35

37J^

40

42)! " 45

48M

50

55 2

56^

57M

1 00

02j^

03M

05

07^

10

ll/^ i2y<

15

17/2

18M

20

22/^

25

26^

27^

30

32J/

33%

35

37^

40

41J^

42^

45

47H

48Jj

50

52^

55

56 J^

5%

2 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.306

.306

.306

.306

.306

2.306

.306

.306

.306

.306

.306

2.306

.306 

.306 

.306

.306

2.306 

.306

one

 oUO

.306

.306

2.306

.306 

.306

.306

.305

.305

2.305

.305

.305

.305

.305

2.305

.305

.305

.305

.305

2.305

.305

.305

.305

.305

.305

2.305

.305

.305

.305

.305

2.305

.305

.305

.305

.305

2.305

.305

.305

.305

.305

.305

2.305

.304

.304

.304

.304

2.304

Inches

2.882

.882

.882

.882

.882

2.882

.882

.882

.882

.882

.882

2.882

.882 

.882 

.882

.882

2.882 

.882

OOO

. oo/

.882

.882

2.882

.882 

.882

.882

.882

.882

2.882

.882

.882

.882

.882

2.882

.882

.882

.882

.882

2.882

.882

.881

.881

.881

.881

2.881

.881

.881

.881

.881

2.881

.881

.881

.881

.881

2.881

.881

.881

.881

.881

.881

2.881

.881

.881

.881

.880

2.880

Inches

5.764

.764

.764

.764

.764

5.764

.764

.764

.764

. 764

.764

5.764

.764 

.764 

.764

.764

5.764 

.764

'.764

.764

5.764

.764 

.764

.764

.764

.764

5.764

.764

.764

.763

.763

5.763

.763

.763

.763

.763

5.763

.763

.763

.763

.763

.763

5.763

.763

.763

.762

.762

5.762

.762

.762

.762

.762

5.762

.762

.762

.762

.761

.761

5.761

.761

.761

.761

.761

5.761

3«'

Inches

8.646

.646

.646

.646

.646

8.646

.646

.646

.646

. 646

.646

8.646

.646 

.646 

.646

.646

8.646 

.646

!646

.646

8.646

.646 

.646

.646

.646

.646

8.645

.645

.645

.645

.645

8.645

.645

.645

.645

.645

8.645

.645

.644

.644

.644

.644

8.644

.644

.644

.644

.644

8.643

.643

.643

.643

.643

8.643

.643

.643

.642

.642

.642

8.642

.642

.642

.642

.641

8.641

5'

Inches

11. 529

.529

.529

.529

.529

11. 529

.528

.528

.528

.528

.'528

11. 528

.528 

.528 

.528

.528

11. 528 

.528

!-528

.528

11. 528

.528 

' .528

.528

.527

.527

11. 527

.527

.527

.527

.527

11.527

.527

.527

.527

.526

11. 526

.526

.526

.526

.526

.526

11. 525

.525

.525

.525

.525

11. 525

.524

.524

.524

.524

11.524

.524

.523

.523

.523

.523

11.523

.522

.522

.522

.522

11. 522

Inches

17. 293

.293

.293

.293

.293

17. 293

.293

.293

.293

.293

.293

17. 293

.293 

.292 

.292

.292

17. 292 

.292 

. 292

'.292

.292

17. 292

.292 

.291

.291

.291

.291

17. 291

.291

.291

.290

.290

17. 290

.290

.290

.290

.290

17. 289

.289

.289

.289

.288

.288

17.288

.288

.288

.287

.287

17.287

.287

.286

.286

.286

17.286

.285

.285

.285

.284

.284

17. 284

.284

.283

.283

.283

17. 282

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

For latitude 0°>

IJi

2J^

3M

5

6M

7/^i

10

15 2

For latitude 1°.

\ iM

2M

5 4

10 2

1 9V

15

For latitude 2°.

 1/4

2/2

5 *

6M

10 2

15 2

Meridional 

distance

Inches

2.863

5.725

8.588

11. 450

14. 313

17. 176

22. 901

28.626

34. 352

2.863

5.725 

8.588

11.451 

14. 313 

17. 176

22. 901

28. 626

34. 352

2.863

5.725

8.588

11. 451 

14. 313

17. 176

22. 901

28.627 

34. 352

Ordinate of developed

parallel

Inch

0.000

.000

.000

.000

.000

.000

.000

.000

.000

0.000

.000 

000

'.000 

.000 

.000 !ooi

001 !ooi

0.000

.000

.000

.000 

.000

.001

.001

.002 

.003

/
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 69

TABLE 3. Coordinates for the projection of maps, scate -arhnF Continued

Latitude of

parallel

0 /

2 00

02M

03M

05

07J/2

10UK

12/2

15

17/2

185*

20

22^

25 

MX WA

30WA

33M 

35 

37^

40 

41M 

42>/2 

45 

47J-3 

4SM

50

52^

55

56}£

57M

3 00

02^

03M

05

07^

10

UK

12M

15

171/1

ISM

20

22^

25

26>i

27^

30

32J/2

33%

35

37M

40

41}i

42>i

45

47M

48^

50

52^

55

56^

57M

4 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.304

.304

.304

. 304

.304

2.304

.304

.304

.304

.304

.304

2.304

.304

.304 

.304

.304

2.304

.303 oni

. oUo

.303 

.303

2.303 

.303 

.303 

.303 

.303 

.303

2

0AQ 

 Ol/O

.303

.303

.303

.303

2.303

.302

.302

.302

.302

2.302

.302

.302

.302

.302

.302

2.302

.302

.302

.302

.302

2.301

.301

.301

.301

.301

2.301

.301

.301

.301

.301

.301

2.301

.300

.300

.300

.300

2.300

1M'

Inches

2.880

.880

.880

.880

.880

2.880

.880

.880

.880

.880

.880

2.880

.880

.880 

.880

.880

2.879

.879

. 879 

!879 

.879

2.879 

.879 

.879 

.879 

.879 

.879

2 gyg

!879

.878

.878

.878

2.878

.878

.878

.878

.878

2.878

.878

.878

.878

.877

.877

2.877

.877

.877

.877

.877

2.877

.877

.877

.877

.876

2.876

.876

.876

.876

.876

.876

2.876

.876

.875

.875

.875

2.875

PA'

Inches

5.761

.761

.761

.760

.760

5. 760

.700

.760

.760

.760

.760

5.760

.759

.759 

.759

.759

5.759

.759

.759 

.758 

.758

5.758 

.758 

.758 

.758 

.757 

.757

5.757

.757

.757

-.757

.757

5.756

.756

.756

.756

.756

5.756

.755

.755

.755

.755

.755

5.755

.754

.754

.754

.754

5.754

.753

.753

.753

.753

5.753

.752

.752

.752

.752

.752

5.751

.751

.751

.751

.751

5.750

3M'

Inches

8.641

.041

.641

.041

.640

8.640

.640

.640

.040

.640

.639

8.639

-.639

.639 

.639

.639

8. 638

.638

. 638 

.638 

.037

8.637 

.637 

.637 

.637 

.636 

.636

8.636

.636

.635

.635

.635

8.635

.034

.634

.634

.634

8.033

.033

.633

.633

.632

.632

8.632

.632

.031

.631

.631

8.630

.630

.630

.030

.029

8.629

.629

.628

.628

.628

.027

8.627

.627

.626

.626

.626

8.625

5'

Inches

11. 522

.521

.521

.521

.521

11. 520

.520

.520

.520

.519

.519

11. 519

.519

.518 

.518

.518

11. 518

.517 

.517

.517 

.516

11. 516 

.516 

.516 

.515 

.515 

.515

11. 515

.514

.514

.513

.513

11. 513

.512

.512

.512

.512

11.511

.511

.511

.510

.510

.509

11. 509

.509

.508

.508

.508

11. 507

.507

.506

.500

.506

11. 505

.505

.505

.504

.503

.503

11. 503

.502

.502

.502

.501

11. 501

VA'

Inches

17. 282

.282

.282

.281

.281

17. 281

.280

.280

.280

.279

.279

17. 279

.278

.278 

.277

.277

17. 276

.276

.276 

.275 

.275

17. 274 

.274 

.274 

.273 

.272 

.272

1 J. 7 ( . LI 979£i

.271

.271

.270

.270

17. 269

.269

.268

.268

.267

17. 267

.266

.266

.265

.204

.264

17. 264

.263

.262

.262

.262

17. 261

.260

.200

.259

.258

17. 258

.257

.257

.256

.255

.255

17. 254

.254

.253

. 20^

.252

17. 251

Ordinates ofileveloped parallel and 

meridional distances

Latitude and longitude intervals

/

f 1H

2M

3M

5

For latitude 2°< CM

7/2

10ny-i

15

nuO1X iy>.

OR/ A%

5

For latitude 3°. 6M 

7/2

10

12/2

,15

{ VAVA

3% 

5 

For latitude 4°' 6M 

7^ 

10

WA

15

Meridional 

distance

Inches

2. 803

5.725

8.588

11.451

14.313

17. 170

22. 901

28. 627

34. 352

2.863

6 725

8^588

11.451

14.314 

17. 176

22. 902

28. 627

34. 353

2. 863

5. 726

8.588 

11. 451 

14.314 

17. 177 

22. 902 

28. 028 

34. 353

Ordinate of developed 

parallel

Inch

0.000

.000

.000

.000

.000

.001

.001

.002

.003

0.000

000 !ooo

.000

.001 

.001

.002

.003

. vu:l nftd

0.000 

.000

.000 

.001 

.001 

.001 

.002 

.004 

.005
70 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 3. Coordinates for the projection of maps, scale -s^-gT, Continued

Latitude of

parallel

0 1

4 00

02H

03^

05

07^

' 10

UK

12H

15

17}^

18M

20

22^

25 

26K

27M

30

32^

O03>/ 0074

35 

37^i

40 

41K 

42^ 

45 

47H 

48%

50

52^

55

56K

57>i

5 00

02^

03^

05

07^

10UK

12J^

15

17H

ISM

20

22H

25

26K

27^

30

32H

33M

35

37H

40

41K

42^

45

47M

48%

50

52H

65

56%

57M

6 00

AKscissas of developed parallel

Longitude interval

1'

/Tic/ses

2.300

.300

.300

.300

.300

2.300

.300

.300

.299

.299

.299

2.299

.299

.299 

.299

.299

2.299

.299

. 

9QQ 6ao

.298 

.298

2.298 

.298 

.298 

.298 

.298 

.298

0 OQQ

Z. 4t7O

.297

.297

.297

.297

2.297

.297

.297

.297

.297

2.296

.296

.296

.296

.296

.296

2.296

.296

.295

.295

.295

2.295

.295

.295

.295

.295

2.294

.294

.294

.294

.294

.294

2.294

.294

.293

.293

.293

2.293

IK'

Inches

2.875

.875

.875

.875

.875

2.875

.875

.874

.874

.874

.874

2.874

.874

.874 

.874

.873

2.873

.873

070

. o/o

.873 

.873

2.873 

.873 

.872 

.872 

.872 

.872

2

Q79

. O( -6

.872

.872

.872

.871

2.871

.871

.871

.871

.871

2.871

.870

.870

.870

.870

.870

2.870

.870

.869

.869

.869

2.869

.869

.869

.869

.868

2.868

.868

.868

.868

.868

.867

2.867

.867

.867

.867

.867

2.866

M

Inches

5.750

.750

.750

.750

.749

5.749

.749

.749

.749

.748

.748

5.748

.748

.747

.747

.747

5.747

.746

.746 

.746 

.746

5.745 

.745 

.745 

.745 

.744 

.744

5. 744

!744

.743

.743

.743

5.742

.742

.742

.742

.741

5.741

.741

.741

.740

.740

.740

5.739

.739

.739

.738

.738

5.738

.738

.737

.737

.737

5.736

.736

.736

.735

.735

.735

5.735

.734

.734

.734

.733

5.733

3%'

Inches

8.625

.625

.625

.625

.624

8.624

.624

.623

.623

.622

.622

8.622

.621

.621 

.621

.620

8.620

.619

. 

fi1Q Ola

.619 

.618

8.618 

.618 

.617 

.617 

.616 

.616

8.616

.615

.615

.615

.614

8.614

.613

.613

.613

.612

8.612

.611

.611

.610

.610

.609

8.609

.609

.608

..608

.607

8.607

.606

.606

.606

.605

8.604

.604

.604

.603

.603

.602

8.602

.601

.601

.600

.600

8.599

5'

Inches

11. 501

.500

.500

.500

.499

11. 498

.498

.498

.497

.496

.496

11. 496

.495

.495 

.494

.494

11. 493

.493

. 4Q9 rtojS

.492 

.491

11.491 

.490 

.490 

.489 

.489 

.488

11. 488

.487

.486

.486

.486

11. 485

.484

.484

.484

.483

11. 482

.482

.481

.480

.480

.479

, 11.479

.478

.477

.477

.477

11. 476

.475

.475

.474

.473

11.473

.472

.472

.471

.470

.470

11.469

.468

.468

.467

.467

11. 466

7M'

Inches

17. 251

.250

.250

.249

.248

17. 247

.247

.247

.246

.245

.244

17. 244

.243

.242 

.241

.241

17.240

.239

OQQ £OO

.238 

.237

17. 236 

.235 

.235 

.234 

.233 

.232

n

ooo

. fitjil

.231

.230

.229

.229

17. 227

.226

.226

.225

.224

17.223

.222

.222

.221

.220

.219

17.218

.217

.216

.215

.215

17. 214

.213

.212

.211

.210

17.209

.208

.208

.206

.205

.204

17.204

.203

.201

.201

.200

17. 199

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

f IK

2K

3%

5

For latitude 4° 6M

7H

10

12H

15

IK

2H

3K

5

For latitude 5°' 6^ 

7H

10i9L<; "72

15

IK 

2H

3M 

5 

For latitude 6°' 6Ji 

?H 

10 

. 12H 

15

Meridional 

distance

Inches

2.863

5.726

8.588

11.451

14. 314

17. 177

22. 902

28. 628

34. 353

2.863

5.726

8.589

11.451

14. 314 

17. 177

22. 903

28.629

34.354

2.863 

5.726

8.589 

11.452 

14. 315 

17. 178 

22.904 

28.630 

34. 356

Ordinate of developed 

parallel

Inch

0.000

.000

.000

.001

.001

.001

.002

.004

.005

0.000

.000

.000

.001

.001 

.002

.003

.005

.007

0.000 

.000

.000 

.001 

.001 

.002 

.003 

.005 

.008
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 71

TABLE 3. Coordinates for the projection of maps, scale -sri^ Continued

Latitude of

parallel

0 ,

6 00

02 J^

03%

05

07J/£

10

11%

12J^

15

18%

20 

22^

25 

26%

27V6

30

33%

35

. 40 

41%

45 * 

48^

50

55

56%

7 00

02>£

03%

05o?y

1011%

15

17V<

18J(

2022 y

25

26%

27V3

30

32V

335<

35

37^

40

41%

42^

45

47Vl

48%

50

52V3

55

56%

57V*

8 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.293

.293

.293

.293

.293

2.292

.292

.292

.292

!292

2.292 

.292

.291 

.291

.291

2.291 

.291

.291

.291 

.290

2.290 

.290 

.290

.290 

.290 

.290

2.289

.289

.289

.289

.289

2.289

.288

.288

.288

.288

2.288

.288

.288

.287

.287

.287

2.287

.287

.287

.286

.286

2.286

.286

.286

.286

.285

2.285

.285

.285

.285

.285

.284

2.284

.284

.284

.284

.284

2.284

1%'

Inches 

2.866

.866

.866

.866

.866

2.866

.865

.865

.865

QfiK

. ODO

.865

2.865 

.864

.864 

.864

.864

2.864 

.863

ono

. oOo

.863 

.863

2.863 

.863 

.863

.862 

.862 

.862

2.862

.862

.861

.861

.861

2.861

.861

.860

.860

.860

2.860

.860

.859

.859

.859

.859

2.859

.858

.858

.858

.858

2.858

.857

.857

.857

.857

2.857

.856

.856

.856

.856

.856

2.855

.855

.855

.855

.855

2.854

*

Inches

5.733

.732

.732

.732

.732

5.731

.731

.731

.730

!730

5.729 

.729

.728 

.728

.728

5.727 

.727

* 797 141

.727 

.726

5.726 

.725 

.725

.725 

.724 

.724

5.724

.723

.723

.722

.722

5.722

.721

.721

.721

.720

5.720

.719

.719

.718

.718

.718

5.717

.717

.716

.716

.716

5.715

.715

.714

.714

.714

5.713

.713

.713

.712

.711

.711

5.711

.710

.710

.709

.709

5.709

3%'

Inches

8.599

.599

.598

.598

.597

8. 597

.596

.596

.595

.595 

.594

8. 594 

.593"

.593 

.592

.592

8.591 

.590

KQA

!590 

.589

8.588 

.588 

.588

.587 

.586 

.586

8.585

.585

.584

.583

.583

8.582

.582

.581

.581

.580

8.579

.579

.578

.578

.577

.577

8.576

.575

.575

.574

.574

8.573

.572

.572

.571

.570

8.570

.569

.569

.568

.567

.567

8.566

.565

.565

.564

.564

8.563

5'

Inches

11.466

.465

.464

.464

.463

11. 462

.462

.461

.460

.460 

.459

11.459 

.458

.457 

.456

.466

11.455 

.454

. 453

.453 

.452

11.451 

.451 

.450

.449 

.448 

.448

11.447

.446

.445

.445

.444

11.443

.442

.442

.441

.440

11.439

.439

.438

.437

.436

.435

11.435

.434

.433

.432

.432

11.431

.429

.429

.428

.427

11. 426

.426

.425

.424

.423

.422

11.422

.421

.419

.419

.418

11.417

«-

Inches

17. 199

.197

.197

.196

.195

17. 193

.193

.192

.191

1 fifi

. loy 

.189

17. 188 

.187

.185 

.185

.184

17. 182 

.181

Ififi

 loU

.180

.178

17. 177 

.176 

.175

.174 

.172 

.172

17. 171

.169

.168

.167

.166

17. 165

.163

.162

.162

.160

17. 159

.158

.157

.156

.154

.153

17. 152

.151

.149

.148

.147

17. 146

.144

.143

.143

.141

17. 139

.138

.138

.136

.134

.133

17. 133

.131

.129

.128

.127

17. 126

Ordinetes of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

2X2

3%

5

For latitude 6° < 6%

7V6

10

.15 2

1%

3%r

For latitude 7° 6%

io/2

12K 

U5

1%

2i^

3M 

5 

For latitude 8° < 6%

10 2

15

Meridional 

distance

Inches

2.863

5.726

8.589

11.452

14.315

17. 178

22. 904

28. 630

3,4. 356

2.863

5.726 

8.589 

1.1.452

14.315 

17.179

22. 905

28.631 

34. 357

2.863

5.726

8.590 

11.453 

14.316

17. 179 

22. 9C6 

28. 632 

34. 359

Ordinate of developed 

parallel

Inch

0.000

.000

.000

.001

.001

.002

.003

.005

.008

0.000

.000 

.001

!002

IVY) . \J\J£t

.004

.006 

.009

0.000

.000

.001 

.001 

.002

.003 

.005 

.007 

.010
72 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 

TABLE 3. Coordinates for the projection of maps, scale yri'B-ff Continued

Latitude of

parallel

0 /

8 00

02^

03%

05

Ql]/2

10

UK\iy-i

15

18%

20

22^

25 

26K

27H

30

33«$/ 35'

40 

41K 

42^ 

45

48%

50

55 2

56J^

57M

9 00

02^

03M

05

07J^

10UK

12Ji

15

nAl

18%

20

22 J^

25

26J4

27H

30

32^

33%

35

37M

40

41K

42}^

45

47^

48%

50

52^

55

56M

57}^

10 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.284

.283

.283

.283

.283

2.283

.282

.282

.282

.282 

.282

2.282

.282

.282 

.282

.282

2.281

.280 

.280

.280 

.280

2.280 

.279 

.279 

.279 

.279 

.279

2.279

.278

.278

.278

.278

2.278

.277

.277

.277

.277

2.276

.276

.276

.276

.276

.275

2.275

.275

.275

.275

.275

2.274

.274

.274

.274

.273

2.273

.273

.273

.273

.272

.272

2.272

.272

.271

.271

.271

2.271

« 

Inches

2.854

.854

.854

.854

.853

2.853

.853

.853

.853

.852 

.852

2.852

.852

.851 

.851

.851

2.851

.850

!sso

.850

2.849 

.849 

.849 

.849 

.848 

.848

2.848

.848

.848

.847

.847

2.847

.847

.846

.846

.846

2.846

.845

. 845

.845

.845

.844

2.844

.844

.844

.843

.843

2.843

.843

.842

.842

.842

2.841

.841

.841

.841

.840

.840

2.840

.840

.839

.839

.839

2.839

* 

Inches

5.709

.708

.708

.707

.707

5.706

.706

.706

.705

.704 

.704

5.704

.703

.703 

.702

.702

5.701

.701 

.700

.700 

.699

5.699 

.699 

.698 

.698 

.697 

.697

5.696

.696

.695

.695

.694

5.694

.693

.693

.692

.692

5.691

.691

.690

.690

.089

.689

5.688

.688

.687

.687

.686

5.686

.685

.685

.684

.684

5.683

.683

.682

.682

.681

.680

5.680

.679

.679

.678

.678

5.677

3%'

Inches

8.563

.562

.561

.561

.560

8.559

.559

.558

.558

.557 

.556

8.556

. 555

.554 

.553

.553

8.552

.551

.551 

.550 

.549

8.548 

.548 

.547 

.546 

.545 

.545

8.545

.544

 .543

.542

.542

8.541

.540

.539

.539

.538

8. 537

. 536

.536

.535

. 534

.533

8. 533

.532

.531

.530

.530

8.529

.528

.527

. 527

.526

8.524

.524

.523

.522

.521

.521

8.520

.519

.518

.518

.517

8.516

5'

Inches

11. 417

.416

.415

.415

.414

11. 412

.412

.411

.410

.409 

.408

11. 408

.406

.405 

.405

.404

11. 403

.402

.401 

.400 

.399

11. 398 

.397 

.397 

.395 

.394 

.393

11. 393

.391

.390

. 3S9

.389

11.388

.386

.386

.385

.384

11. 382

.382

.381

.380

.378

.378

11. 377

. 376

. 374

.373

. 373

11. 37.1

.370

.369

.369

.307

11.366

.365

.365

.383

.362

.361

11. 360

.359

.357

.357

.350

11.355

w

Inches

17. 126

.124

.123

.122

.120

17. 119

.118

.117

. 115

.113 

.112

17. Ill

.110

.108 

.107

.100

17.104

.102

.101 

.100 

.099

17. 097 

.096 

.095 

.093 

.091 

.090

17. 089

.087

.035

.084

.083

17. 081

.079

.078

.077

.075

17. 073

.072

.0?!

.069

.067

.066

17. 065

.063

.061

.060

.059

17. 057

.055

.054

.053

.051

17. 049

.048

.047

.045

.043

.041

17. 040'

.038

.036

.035

.034

17. 032

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

IK

3%

5

For latitude 8° . 6K

7/^

10

.15 2

IK

«S/

5

For latitude 9° < CJ4

10

1 2lyfi

.15

f IK

2y*2

3% 

5 

For latitude 10° < 6%

7X2

10 

15 2

Meridional 

distance

Inches

2.863

5.726

8.590

11.453

14. 316

17. 179

22.906

28. 632

34. 359

2. 883

5.727

8.590

11.453

14.317 

17. 180

22. 907

28. 634

34. 360

2.864

5. 727

8.591 

11. 4.54 

14. 318 

17. 181 

22. 908 

28. 635 

34. 362

Ordinato of developed 

parallel

Inch

0.000

.000

.001

.001

.002

.003

.005

.007

.010

0.000

. 000

001 !ooi

.002

Ano 

. uuo

.005

.008

.012

0.000

. 000

.001 

.001 

.002 

.003 

.006 

.009 

.013
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 73

TABLE 3. Coordinates for the projection of maps, scale ^-rifty Continued

Latitude of

parallel

o /

10 00

02H

03%

05

07J/<

10

11%

15

17M

18%

20

22^

25 

26%

27M

30 

32^

33% 

35

40

41%

45

48%

50

52^

55

56%

11 00

02H

03%

05

07^

10

11%

12J/2

15

17}^

18%

20

22^

25

26%

30

32H

33%

35

37^

40

41%

42^

45

47H

48%

50

52^

55

56%

57J3

12 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.271

.271

.270

.270

.270

2.270

.270

.269

.269

.269

.269

2.269

.268

.268 

.268

.268

2.267 

.267

.267 

.266

2.266

.266 

.266

.266 

.265

.265

2.265

.265

.264

.264

.264

2.264

.263

.263

.263

.263

2.262

.262

.262

.262

.261

.261

2.261

.261

.260

.260

.260

2.260

.259

.259

.259

.259

2.258

.258

.258

.258

.257

.257

2.257

.257

.256

.256

.256-

2.256

1%'

Inches

2.839

.838

.838

.838

.83S

2.837

.837

.837

.836

.836

.836

2.836

.835

.835 

.835

.835

2.834 

.834

!S33 

.233

2.833

.832 

.832

.832 

.832

.831

2.831

.831

.830

.830

.830

2.830

.829

.829

.829

.828

2.828

.828

.828

.827

.827

.827

2.826

.826

.825

.825

.825

2.825

.824

.824

.824

.823

2.823

.823

.823

.822

.822

.822

2.821

.821

.820

.820

.820

2.820

*

Inches

5.677

.677

.676

.676

.675

5.674

.674

.674

.673

.672

.672

5.671

.671

.670 

.670

.669

5.668 

.668

.'667 

.666

5.665

.665 

.665

.664 

.663

.663

5.662

.661

.661

.660

.660

5.659

.658

.658

.657

,657

5.656

.655

.655

.654

.653

.653

5.653

.652

.651

.651

.650

5.649

.648

.648

.648

.647

5.646

.646

.645

.644

.643

.643

5.643

.642

.641

.640

.640

5.639

3%'

Inches

8.516

.515

.514

.514

.513

8.512

.511

.510

.509

.508

.508

8.507

.506

.505 

.504

.504

8.503 

.501

Wll

. OUl

.500 

.499

8.498

.497 

.497

.496 

.495

.494

8.493

.492

.491

.490

.490

8.489

.487

.487

.486

.485

8.484

.483

.483

.481

.480

.480

8.479

.478

.476

.476

.475

8.474

.473

.472

.471

.470

8.469

.468

.468

.466

.465

.465

8.464

.463

.461

.461

.460

8.459

5'

Inches

11. 355

.353

.353

.352

.350

11. 349

.348

.347

.346

.344

.344

11. 343

.341

.340 

.339

.338

11. 337 

.335

.334

.334 

.332

11. 331

.330 

.329

.328 

.326

.325

11. 324

.323

.321

.320

.320

11. 318

.317

.316

.315

.313

11.312

.311

.310

.308

.307

.306

11. 305

.304

.302

.301

.300

11.299

.297

.296

.295

.294

11. 292

.291

.290

.289

.287

.286

11.285

.283

.282

.281

.280

11. 278

w

Inches

17. 032

.030

.029

.027

.025

17. 023

.022

.021

.019

.016

.115

17. 014

.012

.010 

.009

.007

17. 005 

.003

!ooi

16. 998

16. 996

.«95 

.994

.991 

.989

.988

16. 987

.984

.982

.981

980

16. 977

.975

.974

.972

.970

16. 968

.966

.965

.963

.960

.959

16. 958

.955

.953

.952

.950

16. 948

.945

.944

.943

.940

16. 938

.937

.935

.933

.930

.929

16.928

.925

.923

.921

.920

16. 917

Ordmates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

 ¥

3%

5

For latitude 10°< 6%1^/i

10

12J/2

15

f 1%

Q3/

K

For latitude 11°. 6%10 2

1 ^\/

15

1%

2^2

3%

5 

For latitude 12°< 6%

10

15

Meridional 

distance

Inches

2.864

5.727

8.591

11.454

14. 318

17. 181

22. 908

28.635

34. 362

2.864

5.727

8. 591

11.455

14. 319

17 1 Qty 

ll. lot

22. 910

no £o, Ou «Q7 /

34. 365

2.864

5.728

8.592

11.456 

14. 320

17.183 

22. 911

28.639 

34. 367

Ordinato of developed 

parallel

Inch

0.000

.000

.001

.001

.002

.003

.006

.009

.013

0.000

000

'002 001

!(X)2 

004 !ooo

.010

.014

0.000

.000

.001

.002 

.003

.004 

.007

.011 

.015
74 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 

TABLE 3. Coordinates for the projection of maps, scale -niftf Continued

Latitude of 

parallel

0 /

12 00

02^

03M

05

07H

10

11^

\iy<t

15

UK

20

25 2 

26^

30

33j|

35 

37^

40

45 2 

48j|

50

55 2

56^

57K

13 00

02^

03%

0507A1

10

llji

12^

15\iy\

18J<

20

22K

25

26J-;

27X

30

323/

33^

35

37J/

40

41J/

42J^

45

47J/

48^

50

52J/

55

56y

57^

14 00

Abscissas of developed parallel

Longitude interval

1'

IncAes

2.256

.255

.255

.255

.255

2.254

.254

.254

.254

.253 

.253

2.253 

.252

.252 

.252 

.252

2.251 

.251

251

!251 

.250

2.250 

.250 

.250 

.249 

.249 

.249

2.248

.248

.248

.248

.247

2.247

.247

.246

.246

.246

2.246

.245

.245

.245

.244

.244

2.244

.244

.243

.243

.243

2.242

.242

.242

.242

.241

2.241

.241

.240

.240

.240

.239

2.239

.239

.238

.238

.238

2.238

« 

Inches

2.820

.819

.819

.819

.818

2.818

.818

.817

.817

. 816 

.816

2.816 

.816

.815 

.815 

.815

2.814 

.814

.814

.813 

.813

2.812 

.812 

.812 

.812 

.811 

.811

2.811

.810

.810

.809

.809

2.809

.808

.808

.808

.807

2.807

.807

.806

.806

.805

.805

2.805

.804

.804

.804

.804

2.803

.803

.802

.802

.802

2.801

.801

.801

.800

.800

.799

2.799

.799

.798

.798

.798

2.797

*

Inches

5.639

.638

.638

.637

.637

5. 636

.635

.635

.634

.633 

.633

5.632 

.631

.630 

.630 

.629

5.629 

.628

.627

.627 

.626

5.625 

.624 

.624 

.623 

.622 

.622

5.621

.620

.619

.619

.618

5.618

.617

.616

.616

.615

5.614

.613

.613

.612

.611

.610

5.610

.609

.608

.608

.607

5.606

.605

.605

.604

.603

5.602

.602

.601

.600

.599

.599

5.598

.597

.596

.596

.595

5.594

3M'

Inches

8.459

.457'

.457

.456

.455

8.453

.453

.452

.451

.449 

.449

8.448 

.447

.445 

.445 

.444

8.443 

.441

441

!440 

.439

8.437 

.437 

.436 

.435 

.433 

.433

8.432

.430

.429

.428

.428

8.426

.425

.424

.423

.422

8.421

.420

.419

.418

.416

.416

8.415

.413

.412

.411

.411

8.409

.408

.407

.406

.405

8.403

.402

.402

.400

.399

.398

8.397

.396

.394

.394

.393

8.391

5'

Inches

11.278

.276

.276

.275

.273

11. 271

.270

.270

.268

. 266 

.265

11.264 

.262

.261 

.260 

.259

11. 257 

.255

!253 

.252

11.250 

.249 

.248 

.246 

.244 

.243

11.242

.241

.239

.238

.237

11. 235

.233

.232

.231

.229

11. 227

.226

.226

.224

.222

.221

11.220

.218

.216

.215

.214

11. 212

.210

.209

.208

.206

11.204

.203

.202

.200

.198

.197

11. 196

.194

.192

.191

.190

11. 188

W

Inches

16. 917

.915

.913

.912

.910

16. 907

.906

.904

.902

.899 

.898

16. 896 

.894

.891 

.890

.888

16. 886 

.883

QQ1

. ool

.880 

.877

16. 875 

.873 

.872 

.869 

.866 

.865

16.864

.861

.858

.857

.855

16. 852

.850

.848

.847

.844

16. 841

.840

.838

.835

.833

.831

16. 830

.827

.824

.823

.821

16. 818

.815

.814

.812

.809

16. 806

.805

.803

.800

.797

.796

16. 795

.792

.789

.787

.786

16. 782

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

l^i

2/^

3M

5

For latitude 12°' 6^

7Ji

10

12/^

15

IK&A 3M

6

For latitude 13°' 6K

7J/2

10

12V^

15

lg

5* 

For latitude 14°< 6H10 2

15 2

Meridional distance

Inches

2.864

5.728

8.592

11.456

14. 320

17. 183

22. 911

28, 639

34. 367

2.864

5.728 

8. 592 

11.456

14. 321 

17. 185 

22.913

98 AA1 ^O. OIL

34. 370

2.864 

5.729

8.593 

11. 457 

14. 322 

17. 186 

22. 915 

28.644 

34.372

Ordinate of developed 

parallel

Inch

0.000

.000

.001

.002

.003

.004

.007

. .011

.015

0.000

.000 

.001

.'003 

.004 

.007

.011

.017

0.000 

.000

.001 

.002 

.003 

.004 

.008 

.012 

.018
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 75 

TABLE 3.- Coordinates for the projection of maps, scale j^ggo Continued

Latitude of

parallel

0 /

14 00

02M

03%

05

(fiYi

10

n/4

12//i

15

17/2

18%

20

22X2

25

28 J4

27M

30

33 %

35

37^

40

42^ 

45 

47^

50

52^

55

56 J4

57^

15 00

02H

03%

05

07H

10

11J4

izy

15

17M

18J4

20

22^

25

26M

27^

30

32H

33J^

35

37H

40

41J^

423^

45

47}/<

48%

50

52)^

55

56}<

57^

16 00

Abscissas of developed parallel

Longitude interval

1'

/7>cfte»

2.238

.237

.237

.237

.236

2.236

.236

.236

.235

.235

.235

2.234

.234

.234

.233

.233

2.233

.232

.232

.232

.232

2.231 

.231 

.231 

.230 

.230 

.230

2.229

.229

.229

.228

.228

2.228

.227

.227

.227

.220

2.226

.226

.225

.225

.225

.224

2.224

.224

.224

.223

.223

2.222

.222

.222

.222

.221

2.221

.220

.220

.220

.219

.219

2.219

.218

.218

.218

.217

2.217

*e

Inches

2.797

.797

.796

.796

.796

2.795

.795

.795

.794

.794

.793

2.793

.792

.792

.792

.791

2.791

.790

.790

.790

.789

2.789 

.789 

.788 

.788 

.787 

.787

2.787

.786

.786

.785

.785

2.785

.784

.784

.783

.783

2.782

.782

.782

.781

.781

.780

2.780

.780

.779

.779

.779

2.778

.777

.777

.777

.776

2.776

.775

.775

.775

.774

.774

2.773

.773

.772

.772

.772

2.771

2H'

Inches

5.594

.593

.593

.592

.591

5.590

.590

.589

.588

.587

.587

5.586

.585

.584

.583

.583

5.582

.581

.580

.580

.579

5.578 

.577 

.577 

.576 

.574 

.574

5.573

.572

.571

.571

.570

5.569

.568

.568

.567

.566

5.565

.564

.564

.563

.562

.561

5.560

.559

.558

.558

.557

5.556

.555

.554

.554

.553

5.552

.551

.550

.549

.548

.548

5.547

.546

.545

.544

.544

5.542

« 

Inches

8.391

.390

.389

.388

.387

8.385

.384

.384

.382

.381

.380

8 379

.377

.376

.375

.374

8.373

.371

.370

.370

.368

8.366 

.366 

.365 

.363 

.362 

.361

8.360

.359

.357

.356

.355

8.354

.352

.351

.350

.349

8.347

.346

.346

.344

.342

.341

8:341

.339

.337

.336

.336

8.334

.332

.331

.331

.329

8.327

.326

.326

.324

.322

.321

8.320

.319

.317

.316

.315

8.314

5'

Inches

11. 188

.186

.185

.184

.182

11. 180

.179

.178

.176

.174

.173

11. 172

.170

.168

.167

.166

11. 164

.162

.161

.160

.157

11. 155 

.154 

.153 

.151 

.149 

.148

11.147

.145

.143

.141

.140

11. 138

.136

.135

.134

.132

11. 130

.129

.127

.125

.123

.122

11. 121

.119

.116

.115

.114

11. 112

.110

.109

.107

.105

11. 103

.102

.101

.098

.096

.095

11.094

.092

.089

.088

.087

11.085

7H'

Inches

16. 782

.780

.778

.776

.773

16. 770

.769

.767

.764

.761

.760

16. 758

.755

.752

.750

.749

16. 745

.742

.741

.739

.736

16. 733 

.731 

.730 

.727 

.723 

.722

16. 720

 .717

.714

.712

.711

16. 707

.704

.703

.701

.698

16. 694

.693

.691

.688

 .685

.683

16. 681

.678

.675

.673

.671

16. 668

.665

.663

.661

.658

16. 654

.653

.651

.648

.644

.643

16. 641

.637

.634

.632

.631

16. 627

Ordinatos of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1/4

2J^

3%

5

For latitude 14°' 6K

7/^

10

12}^

15

1MOL^

3%

5

For latitude 15°' 6)4 10 2

\iYi

15

1M

2X2 

3% 

5 

For latitude 16°' 6%

10 ^

15

Meridional 

distance

Inches

2.864

6.729

8.593

11.457

14. 322

17. 186

22. 915

28. 644

34. 372

2.865

5.729

8.594

11.458

14. 323

17. 188

22. 917

28. 646

34. 375

2.865

5.730 

8.595 

11.459 

14. 325 

17. 189 

22. 919 

28. 649

34. 379

Ordinate of developed 

parallel

Inch

0.000

.000

.001

.002

.003

.004

.008

.012

.018

0.000

.001

.001

.002

.003

.005

.008

.013

.019

0.000

.001 

.001 

.002 

.003 

.005 

.009 

.014

.020

6243° 29 6
76 TABLES FOR CONSTRUCTION OF POLYCONlC PROJECTIONS

TABLE 3. Coordinates for the projection of maps, scale ^ Continued

Latitude ol

parallel

0 /

16 00

02^

03%

05

(flY

10

11% i2y

15

I//'1

18%

20 

22^

25 

26%yiy-i

30 

32}^

35* 

37H

40

45 2 

47^ 

48%

50

55 2

56%

57K

17 00

02^

03%

05

07^

10

11%

12/*t

15

17H

18%

20

22^*

25

26%

27^i

30

32J^

33%

35

37H

40

41%

42^

45

47H

48%

50

52^

55

56%

57^

18 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.217

.216

.216

.216

.216

2.215

.215

.215

.214

.214

.213

2.213 

.213

.212 

.212

.212

2.211 

.211 

.211

.210 

.210

2.209 

.209 

.209 

.208 

.208 

.208

2.208

.207

.207

.206

.206

2.206

.205

.205

.205

.204

2.204

 .203

.203

.203

.202

.202

2.202

.201

.201

.200

.200

2.200

.199

.199

.199

.198

2.198

.197

.197

.197

.196

.196

2.196

.195

.195

.194

.194

2.194

.« 

Inches

2.771

.771

.770

.770

.769

2.769

.709

.708

.768

.767

.767

2.767 

.706

.765 

.705

.765

2.764 

.764

. 763 

.763 

.762

2.762 

.762 

.761 

.761 

.760 

.760

2. 7KQ Ida

.759

.758

.758

.758

2.757

.756

.756

.756

.755

2.755

.754

.754

.753

.753

.752

2.752

.751

.751

.751

.750

2.750

.749

.749

.748

.748

2.747

.747

.746

.746

.745

.745

2.745

.744

.743

.743

.743

2.742

* 

Inches

5.542

.541

.541

.540

.539

5.538

.537

.537

.535

.534

.534

5.533 

.532

.531 

.530

.530

5.528 

.527 

527

'.526 

.525

5.524 

.523 

.522 

.521 

.520 

.519

6.519

.518

.516

.516

.515

5.514

.513

.512

.512

.510

5.509

.509

.508

.507

. 505

.505

5.504

.503

.502

.501

.500

5.499

.498

.497

.497

.495

5.494

.494

.493

.492

.490

.490

5.489

 .488

.486

.486

.485

5.484

3%'

Inches

8.314

.312

.311

.310

.308

8.307

.306

.305

.303

.301

.301

8.300 

.298

.296 

.295

.294

8.293 

.291

290 

!2S9 

.287

8.286 

.285 

.284 

.282 

.280 

.279

8

97Q . £itO

.276

.275

.274

.273

8.271

.269

.268

.207

.266

8.264

.263

.262

.260

.258

.257

8.256

.254

.253

.252

.251

8.249

.247

.246

.245

.243

8.241

.240

.239

.237

.235

.235

8.234

.232

.230

.229

.228

8.226

5'

Inches

11. 085

.083

.081

.080

.078

11. 076

.074

.073

.071

.069

.067

11. 066 

.004

.062 

.000

.059

11. 057 

.054

053 

!052 

.050

11.047 

.046 

.045 

.043 

.040 

.039

n

AQQ 

. Uoo

.035

.033

.032

.030

11.028

.026

.024

.023

.021

11. 018

.017

.016

.013

.011

.010

11.008

.006

.003

.002

.001

10. 998

.996

.995

.993

.991

10. 988

.987

.986

.983

.981

.979

10. 978

.976

.973

.972

.970

10. 968

7*

Inches

16. 627

.624

.622

.620

.617

16. 613

.612

.610

.606

.603

.601

16. 599 

.596

.592 

.590

.589

16. 585 

.582

.580 

.578 

.575

16. 571 

.569 

.567 

.564 

. 560 

.558

16. 557

.553

.549

.547

.546

16.542

.538

.536

.535

.531

16. 527

.526

.524

.520

.516

.514

16. 512

.509

.505

.503

.501

16. 498

.494

.492

.490

.486

16.482

.481

.479

.475

.471

.469

16. 467

.463

.459

.458

.456

16.452

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

1%

3%

5

For latitude 16°' 6%

7/^

10

15

1%

3% 

5

For latitude 17°' 6%

10 2

iglX

15

1%

3% 

5 

For latitude 18° 6%

10 2

15

Meridional 

distance

Inches

2.865

5.730

8.595

11. 459

14. 325

17. 189

22. 919

28.649

34. 379

2.865

5.730

8.595 

11. 461

14. 326

it i7 - 1Q1 lEfl

22.921

28.652

34. 382

2.865 

5.731

8.596 

11.462 

' 14.327 

17. 193 

22.923 

28.654 

34. 385

Ordinate of developed 

parallel

Inch

0.000

.001

.001

.002

.003

.005

.009

.014

.020

0.000

.001

.001 

.002

.004 

.005

!009

.014

.021

0.000 

.001

.001 

.002 

.004 

.006 

.010 

.015 

.022
TABLES FOE CONSTRUCTION OF POLYCONIC PROJECTIONS 77

TABLE 3. Coordinates for the projection of maps, scale g-n Continued

Latitude of

parallel

0 ,

18 00

02^

03X

05

07H

10UK

VIK

15

17H

18%

20

22^

25 

20K

27^

30

32^

33% 

35 

37>£

40 

41K 

42K 

45 

47M 

48%

50

62M

55

56K

57^

19 00

02^

03%

05

07H

'10

UK

12tf

15

17^

18%

20

22J-S

25

26K

27H

30

32^

33%

35

37K

40

41K

423^

45

47M

48%

50

52H

55

56K

57>i

20 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.194

. 193

.193

.193

.192

2.191

. 191

.191

.190

.190

.190

2.189

.189

.188 

.188

.188

2.187

.187

.186 

.186

2.185 

.185 

.185 

.184 

.184 

.183

o i oq /. loo

.183

.182

.182

.181

2.181

.180

.180

.180

.179

2.179

.178

.178

.178

.177

.177

2.177

.176

.175

.175

.175

2. 174

.174

.173

.173

.173

2.172

.172

.172

.171

.170

.170

2.170

' .169

.169

.168

.168

2.167

IK'

Inches

2.742

.741

.741

.741

.740

2.739

.739

.739

.738

.737

.737

2.737

.736

.735 

.735

.735

2. 734

.733

.733 

.733 

.732

2.731 

.731 

.731 

.730 

.729 

.729

2. 729

^728

.727

.727

.727

2.726

.725

.725

.725

.724

2.723

.723

.723

.722

.721

.721

2.721

.720

.719

.719

.719

2.718

.717

.717

.716

.716

2.715

.715

.714

.714

.713

.713

2.712

.712

.711

.710

.710

2.709

2H'

Inches

5.484

.483

.482

.481

.480

5.479

.478

.477

.476

.475

.474

5.474

.472

.471 

.470

.470

5.468

.467

466 

.466 

.464

5.463 

.462 

.462 

.460 

.459 

.458

5.458

.456

.455

.454

.454

5.452

.451

.450

.449

.448

5.447

.446

.445

.444

.443

.442

5. 441

.440

.438

.438

.437

5. 436

. 434

.434

.433

.431

5. 430

.429

.429

.427

.426

.425

' 5. 424

.423

.422

.421

.420

5.419

3%'

Inches

8.226

.224

.223

.222

.220

8.218

.217

.216

.214

.212

.211

8.210

.208

.206 

.205

.204

8.202

.200

199 

!l98 

.196

8.194 

.193 

.192 

.190 

.188 

.187

8

1 Qfl

. 1OO

.184

.182

.181

.180

8. 178

.176

.175

.174

.172

8.170

.169

.168

.166

.164

.163

8.162

.160

.158

.157

.156

8.154

.151

.150

.149

.147

8.145

.144

.143

.141

.139

.138

8.137

.135

.m

.131

.130

8.128

5'

Inches

10. 968

.965

.964

. 963

.960

10. 958

.956

.955

.952

. 950

.948

10. 947

.944

.942 

.941

.939

10. 037

.934 O'jo

. «'uo

.931 

.929

10. 926 

.925 

.923 

.921 

.918 

.917

10.915

.913

.910

.908

.907

10. 904

.902

.900

.899

.896

10. 893

.892

.891

.888

'.885

.884

10. 883

.880

.877

.876

.874

10. 871

.869

.867

.866

.863

10. 860

.859

.857

.855

.852

.850

10.849

.846

.843

.842

.840

10. 838

7J/2'

Inches

16.452

.448

.446

. 444

.440

16.436

.434

.432

.428

.424

.423

16. 421

.417

.413 

.411

.409

16. 405

.401 Qfin . 0\)\)

.397 

.393

16. 389 

.387 

.385 

.381 

.377 

.375

16. 373

.369

.305

.363

.361

16. 357

.353

. 350

.348

.344

16. 340

.338

.336

.332

.328

.326

16. 324

.320

.315

.313

.311

16. 307

.303

.301

.299

.294

16. 290

.288

.286

.282

.278

.276

16. 273

.269

.265

.263

.261

16. 256

Ordinates of developed parallel and 

meridional distances

Latitude and longitude Intervals

/

IK

2M

3%

5

For latitude 18°' 6K

VA

10

12K

U5

f Ik

n\jf &71

3%

5

For latitude 19° 6K 

7K

10

19L<C it'/l

15

:iK 

VA

3% 

For latitude 20° 6K

m10 

12X 

15

Meridional 

distance

Inches

2. 865

5.731

8.596

11. 462

14. 327

17. 193

22.923

28.654

34. 385

2.866

5 711 

. ioi

8.597

11.403

14. 329 

17. 194

22. 926

28.657

34. 389

2.866 

5.732

8.598 

11.464 

14. 330 

17. 196 

22. 929 

28.661 

34. 393

Ordinato of developed 

parallel

Inch

0.000

.001

.001

.002

.004

.006

.010

.015

.022

0.000

001 !ooi

.003

.004 

.006

.010

.016

.023

0.000 

.001

.002 

.003 

.004 

.006 

.011 

.017 

.024
78 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 3. Coordinates for the projection of maps, scale -grifT; Continued

Latitude of

parallel

0 /

20 00

02M

03k

05

07^

10

Ilk

12J*

15

nAl

18k

20 

22H

25 

26k 

27K

30 

32M

33k

35 

37K

40 

41k 

42H 

45 

47^ 

48k

50

52y2

55

56k

57>£

21 00

02M

03M

05

07H

10

Ilk

12M

15

17H

18k

20

223-3

25

26k

27}^

30

32H

33k

35

37%

40

41k

42M

45

473-3

48k

50

523-3

55

56k

571-3

22 00

Abscissas of developed parallel

Longitude interval

1'

Jncftes

2.167

.167

.167

.166

.166

2.165

.165

.165

.164

.163

.163

2.163 

.162

.162 

.161 

.161

2.161 

.160

160

!l59 

.159

2.158 

.158 

.158 

.157 

.156 

.156

O 1 *fi £,. 100

.155

.155

.154

.154

2.154

.153

.153

.152

.152

2.151

.151

.150

.150

.149

..149

2.149

.148

.147

.147

.147

2.146

.146

.145

.145

.144

2.144

.144

.143

.143

.142

.142

2.141

.141

.140

.140

.140

2.139

ik'

Inches

2.709

.709

.708

.708

.707

2.707

.706

.706

.705

.704

.704

2.704 

.703

.702 

.702 

.701

2.701 

.700

7Oft

. l\J\J

.699 

.699

2.698 

.697 

.697 

.696 

.696 

.695

2.695

.694

.693

.693

.693

2.692

.691

.691

.690

.690

2.689

.688

.688

.687

.687

.686

2.686

.685

.684

.684

.684

2.683

.682

.682

.681

.681

2.680

.679

.679

.678

.677

.677

2.677

.676

.675

.675

.674

2.674

2H'

Inches

5.419

.417

.417

.416

.414

5.413

.412

.412

.410

. 409

.408

5. 407 

.406

.404 

.404 

.403

5. 401 

.400

QQQ * oyy 

.399 

.397

5.396 

.395 

,.394 

.393 

.391 

.390

5.390

.388

.387

.386

.385

5.384

.382

000

. OO*

.381

.379

5.378

.377

.376

.375

.373

.372

5.372

.370

.369

.368

.367

5.366

.364

.363

.363

.361

5.359

.359

.358

.356

.355

.354

5.353

.352

.350

.349

.349

5.347

i

3k'

Inches

8.128

.126

.125

.124

.122

8.120

.119

.117

.115

.113

.112

8.111 

.109

.107 

.105 

.104

8.102 

.100

.099

.098 

.096

8.093 

.092 

.091 

.089 

.087 

.086

8.085

.082

.080

.079

.079

8.076

.073

.072

.071

.069

8.067

.066

.064

.062

.060

.059

8.058

.055

.053

.052

.051

8.048

.046

.045

.044

.042

8.039

.038

.037

.035

.032

.031

8.030

.028

.025

.024

.023

8.021

5'

Inches

10. 838

.835

.833

.832

.829

10. 826

.825

.823

.820

.817

.816

10. 815 

.812

.809 

.807 

.806

10. 803 

.800

. 7QQ /yy 

.797 

.794

10. 791 

.790 

.788 

.785 

.782 

.781

10. 779

.776

.773

.772

.770

10. 768

.764

.763

.762

.759

10. 756

.754

.752

.749

.746

.745

10. 743

.740

.737

.736

.734

10. 731

.728

.727

.725

.722

10. 719

.717

.716

.713

.710

.708

10. 707

.703

.700

.699

.697

10. 694

73/2'

Inches

16. 256

.252

.250

.248

.243

16.239

.237

.235

.231

.226

.224

16. 222 

.217

.213 

.211 

.209

16. 204 

.200 JQQ

. iyo 

.196 

.191

16. 187 

.185 

.182 

.178 

.174 

.171

16. 169

.165

.160

.158

.156

16. 151

.147

.145

.142

. .138

16. 133

.131

.129

.124

.120

.117

16. 115

.111

.106

.104

.102

16.097

.092

.090

.088

.083

16. 078

.076

.074

.069

.065

.062

16.060

.055

.051

.048

.046

16.041

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

f Ik

VA

3k

5

For latitude 20° 6k

7M

10

12M Us

f ik

2H 

3k 

5

For latitude 21°' 6k 

7A 1

10

1 Ol>(i l*n Us

Ik y/i

3k 

5 

For latitude 22°' 6k 

7M 

10

12H

15

Meridional 

distance

Inches

2.866

5.732

8.598

11. 464

14. 330

17. 196

22.929

28.661

34. 393

2.866

5.733 

8.599 

11. 466

14. 332 

17. 198 

22. 931

28. 664

34. 397

2.867 

5.733

8.600 

11.467 

14. 334 

17.201 

22. 934 

28.668 

34. 401

Ordinate of developed 

parallel

Inch

0.000

.001

.002

.003

.004

.006

.011

.017

.024

0.000

.001 

.002 

nno . UUo

.004 

.006 

.011

ftlft

 Ul(>

.025

0.000 

.001

.002 

.003 

.005 

.007 

.012 

.018 

.026
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 79

TABLE 3. Coordinates for the projection of maps, scale -s^fao Continued

Latitude of

parallel

0 1

22 00

02V£

03%

05

07H

10

11%

12H

15

17 /^

18%

20

22^

25 

20%

27^

30

32^

33% 

35

40 

41% 

42^ 

45

48%

60

52^

55

56%

57H

23 00

02J>£

03%

05

07H

10

11%

12J^

15

17H

18%

20

22H

25

26%

27 Yi

30

32^

33%

35

37^

40

41%

42^

45

47}^

48%

50

52^

55

56%

57^

24 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.139

.138

.138

.138

.137

2.136

.136

.136

.135

.134

.134

2.134

.133

.133 

.132

.132

2. 131

.131

.130 

.130 

.129

2.129 

.128 

.128 

.127 

.127 

.126

2 126

!l25

.125

.124

.124

2.123

.123

.123

.122

.122

2.121

.121

.120

.120

.119

.119

2.118

.118

.117

.117

.116

2.116

.115

.115

.114

.114

2.113

.113

.112

.112

.111

.111

2.110

.110

.109

.109

.108

2.108

1%'

Inches

2.674

.673

.072

.072

.071

2.670

.670

.670

.669

.668

.668

2.667

.666

.666 

.665

.665

2. 664

.603

.003 

.662 

.662

2.661 

.600 

.660 

.659 

.658 

.658

2

f.KQ 

. uOo

.657

.656

.656

.655

2.654

.654

.653

.653

.652

2. 651

.651

.650

.649

.649

.648

2.648

.647

.646

.646

.645

2.645

.644

.643

.643

.642

2.641

.641

.640

.640

.639

.638

2.638

.637

.636

.636

.635

2.634

2M'

Inches

5.347

.346

.345

.344

.342

5.341

.340

.339

.338

.336

.335

5.334

.333

.331 

.331

.330

6.328

.327

'.325 

.323

5.322 

.321 

.320 

.319 

.317 

.316

5. 315

.314

.312

.311

.310

5.309

.307

.306

.306

.304

5.302

.301

.301

.299

.297

.297

5.296

.294

.292

.292

.291

5.289

.287

.287

.286

.284

5.282

.282

.281

.279

.277

.277

5.276

.274

.272

.271

.271

5.269

3%'

Inches

8. 021

.018

.017

.016

.014

8.011

.010

.009

.006

.004

.003

8.002

7.999

.997 

.996

.995

7.992

.990

.989 

.987 

.985

7.983 

.981 

.980 

.978 

.975 

.974

7 /. 073 y/o 

.970

.968

.967

.966

7.963

.961

.960

. .958

.956

7.953

.952

.951

.948

.946

.945

7.944

.941

.939

.937

.936

7.934

.931

.930

.929

.926

7.924

.922

.921

.919

.916

.915

7.913

.911

.908

.907

.906

7.903

5'

Inches

10. 694

.691

.690

.688

.685

10. 682

.680

.678

.675

.672

.671

10. 669

.666

.663 

.661

.659

10. 656

.053

fiEO

. DO*

.650 

.647

10.043 

.042 

.640 

.637 

.634 

.632

10. 631

.627

.624

.622

.621

10. 618

.014

.013

.011

.608

10. 605

.603

.601

.598

.595

.593

10. 591

.588

.585

.583

.581

10. 578

.575

.573

.571

.568

10. 565

.563

.561

.558

.555

.553

10. 551

.548

.545

.543

.541

10. 538

«-

Inches

10. 041

.037

.034

.032

.027

16. 022

.020

.018

.013

.008

.006

16. 003

15. 999

.994 

.992

.989

15. 984

.980

.977 

.975 

.970

15. 965 

.963 

.900 

.956 

.951 

.948

15. 946

.941

.936

.934

.931

15. 926

.921

.919

.917

.912

15.907

.904

.902

.897

.892

.890

15. 887

.882

.877

.875

.872

15. 867

.862

.860

.857

.852

15. 847

.845

.842

.837

.832

.830

15. 827

.822

.817

.814

.812

15.807

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

3%

5

For latitude 22° 6%

7J^

10

12J/S

.15

1MO \.£

3%

5

For latitude 23°' 6%

10j2jx

,15

2H

3% 

5 

For latitude 24° 6%

10 2

,15 2

Meridional 

distance

Inches

2.867

5.733

8.600

1 1. 467

14. 334

17. 201

22. 934

28.668

34. 401

2.86?

5.734

8.601

11.468

14. 336 

17. 203

22. 937

28.672

34. 405

2.867 

5.735

8.602 

11.470 

14.338 

17.205 

22.940 

28.675 

34. 410

Ordinate of developed 

parallel

Inch

0.000

.001

.002

.003

.005

.007

. 012

.018

.026

0.000

.001

.002

.003

.005 

.007

.012

.019

.027

0.000 

.001

.002 

.003 

.005 

.007 

.012 

.019 

.028
80 TABLES FOR CONSTRUCTION OF'POLYCONIC PROJECTIONS 

TABLE 3. Coordinates for the projection of maps, scale -grinr Continued

Latitude of

parallel

0 /

24 00

02H

03K

05

07H

10

UK

12H

15

17H

18K

20

22H

25 

26K

WA

30

32^

33K 

35 

37^

40 

41K 

42^ 

45 

47H 

48K

cnOU

52M

55

56 K

67H

25 00

02^

03%

05

07^

10

UK

12J4

15

17J4

18tf

20

22H

25

26K

27J-3

30

32^

33K

35

37M

40

41K

42^

45

47J-S

48Ji

50

52}^

55

56^

57M

26 CO

Abscissas of developed parallel

Longitude interval

1'

Inches

2.108

.107

.107

.106

.105

2.105

.104

' .104

.103

.103

.102

2.102

.101

.101 

.100

.100

2.099

.099

.098 

.098 

.097

2.097 

.096 

.096 

.095 

.095 

.094

9 X. ntu utrl

.093

.092

.092

.092

2.091

.090

.090

.090

.089

2.088

.088

.087

.087

.086

.086

2.085

.085

.084

.083

.083

2.082

.082

.081

.081

.080

2.079

.079

.079

.078

.077

.077

2.077

.076

.075

.075

.074

2.074

W

Inches

2.034

.634

.633

.633

.632

2.631

.631

.630

.629

.629

.628

2.628

.628

.626 

.625

.625

2.624

.623

flOQ

. DAO

.622 

.622

2:521

.620 

.620 

.619 

.618 

.618

2.617

.616

.615

.615

.615

2.614

.613

.612

.612

.611

2.610

.610

.609

.608

.608

.607

2.607

.606

.605

.604

.604

2.603

.602

.602

.601

.600

2.599

.599

.598

.598

.597

.596

2.596

.595

.594

.593

.593

2.592

VA'

Inches

5.269

.267

.266

.265

.264

5. 262

.261

.260

.259

.257

.256

5. 255

.254

.252 

.251

.250

5.248

.247

.246 

.245 

.243

5.241 

.241 

.240 

.238 

.236 

.235

5.234

.233

.231

.230

.229

5.227

.226

.225

.224

.222

5.220

.219

.219

.217

.215

.214

5.213

.211

.210

.209

.208

5.206

.204

.203

.202

.201

5.199

.198

.197

.195

.193

.192

5.192

.190

.188

.187

.186

5.184

3%'

Inches

7. 903

.901

.899

.898

.896

7.893

.892

.891

.888

.885

.884

7.883

.880

.878 

.876

.875

7.872

.870

QAQ . ooy 

.867 

.865

7.862 

.861 

.859 

.857 

.8.54 

.853

7. 852

.849

.846

.845

.844

7.841

.838

.837

.836

.833

7.830

.829

.828

.825

.822

.821

7.820

.817

.814

.813

.812

7.809

.806

.805

.804

.801

7.798

.797

.795

.793

.790

.789

7.787

.785

.782

.781

.779

7.776

5'

Inches

10. 538

.534

.533

.531

.527

10. 524

.522

.521

.517

.514

.512

10. 510

.507

.504 

.502

.500

10. 497

.493

.491 

.490 

.486

10. 483 

.481 

.479 

.476 

.472 

.471

10.469

.465

.462

.460

.458

10. 455

.451

.449

.448

.444

10.441

.439

.437

.433

.430

.428

10. 426

.423

.419

.417

.416

10.412

.408

.407

i405

.401

10. 398

.396

.394

.390

.387

.385

10.383

.379

.376

.374

.372

10. 369

7H'

Inches

15. 807

.802

.799

.796

.791

15. 786

.784

.781

.776

.771

.768

15. 766

.760

.755 

.753

.750

15. 745

.740 707 . lot

.735 

.729

15. 724 

.722 

.719 

.714 

.708 

.706

15. 703

.690

.693

.690

.687

15. 682

.677

.674

.672

.666

15. 661

.658

.656

.650

.645

.642

15.640

.634

.629

.626

.623

15. 618

.613

" .610

.607

.602

15. 596

.594

.591

.585

.580

.577

15. 575

.569

.564

.561

.558

15.553

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

f IK

VA

3K

5

For latitude 24° < 6K

7^

10

12M Us

IK

2K"IM "/4

5

For latitude 25° < 6Kn\/ 1/2

10

12J$

,15

IK 

2^

3M 

5 

For latitude 26°' 6K 

VA 

10 

12J$ 

,15

Meridional 

distance

Inches

2.867

5.735

8.602

11. 470

14. 338

17. 205

22. 940

28.675

34. 410

2.868

5.736

8.604

11.471

14. 340 

17. 207

22. 943

28. 679

34. 415

2.868 

5.736

8.605 

11.473 

14. 342 

17. 210 

22. 946 

28.683 

34. 419

Ordinate of developed 

parallel

Inch

0.000

.001

.002

.003

.005

.007

.012

.019

.028

0.000

.001

.002

.003

. 005 

.007

.013

.020

.029

0.000 

.001

.002 

.003 

.005 

.007 

.013 

.021 

.030
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 81

TABLE 3. Coordinates for the projection of maps, scale -g-rirTT Continued

Latitude of

parallel

0 ,

26 00

02^

03%

05

07^

10

11%

12X2

15

18%

20 

22H

25 

26%

30

33% 

35

40 

41%

45 2 

48%

50

52H

55

50%

57^

27 00

02Jx

03%

05

07%

10

11% \iy<

15171/1

18%

20iiy,

25

26%

27X2

30

32^

33%

35

37^

40

41%

45

47J-3

48%

50

52X

55

56%

57%

28 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.074

.073

.073

.072

.072

2.071

.070

:070

.069

.069 

.068

2.068 

.067

.066 

.066

.066

2.065 

.064

.064 

.063 

.063

2.062 

.061 

.061

.060 

.060 

.059

2 059

!058

.058

.057

.057

2.056

.055

.055

.054

.054

2.053

.052

.052

.051

.051

.050

2.050

.049

.048

.048

.047

2.047

.046

.046

.045

.044

2.044

.043

.043

.042

.041

.041

2.041

.040

.039

.039

.038

2.037

1%'

Inches

2.592

.591

.591

.590

.589

2.588

.588

.588

.587

CQC .080 

.585

2.585 

.584

.583 

.582

.582

2.581 

.580

.580 

.579 

.578

2.577 

.577 

.576

.575 

.575 

.574

2.574

.573

.572

.571

.571

2.570

.569

.568

.568

.567

2.566

.566

.565

.564

.563

.563

2.562

.561

.560

.560

.559

2.558

.557

.557

.556

.555

2.554

.554

.553

.553

.552

.551

2.551

.550-

.549

.548

.548

2.547

w

Inches

5.184

.182

.182

.181

.179

5. 177

.176

.175

.173

.171 

.170

5.170 

.168

.166 

.165

.164

5.162 

.160

!l58

. .157

5.155 

.154 

.153

.151 

 .149 

.148

5.147

.145

.143

.142

.141

5.140

.138

.137

.136

.134

5.132

.131

.130

.128

.126

.125

5.124

.122

.121

.120

.119

5.117

.115

.114

.113

.111

5.109

.108

.107

.105

.103

.102

5.101

.100

.097

.096

.095

5.093

3%'

Inches

7.776

.774

.772

.771

.768

7.765

.764

.763

.760

.757 

.756

7.754 

.752

.749

.747

.746

7.743 

.740 

739

!738 

.735

7.732 

. .731 

.729

.726 

.724 

.722

7.721

.718

.715

.714

.712

7.709

.707

.705

.704

.701

7.698

.697

.695

.692

.689

.688

7.687

.684

.681

.679

.678

7.675

.672

.671

.669

.666

7.663

.662

.660

.658

.655

.653

7.652

.649

.646

.644

.643

7.640

5'

Inches

10. 369

.365

.363

.361

.358

10.354

.352

.350

.346

'.341

10. 339 

.335

.332 

.330

.328

10.324 

.321

'J1Q

. oiy 

.317 

.313

10. 309 

.307 

.306

.302 

.298 

.296

10.294

.291

.287

.285

.283

10. 279

.275

.274

.272

.208

10. 264

.202

.260

.256

.253

.251

10.249

.245

.241

.239

.237

10. 233

.229

.228

.226

.222

10. 218

.216

.214

.210

.206

.204

10. 202

.198

.195

.193

.191

10. 187

W

Inches

15. 553

.547

.545

.542

.536

15.531

.528

.525

.520

.514 

.511

15. 509 

.503

.498 

.495

.492

15. 486 

.481 

.478

.475 

.470

15. 464 

.461 

.458

.453 

.447 

.444

i c 441 J.0, ^trtl

.436

.430

.427

.424

15.419

.413

.410

.407

.402

15. 396

.393

.390

.385

.379

.376

15. 373

.367

.362

.359

.356

15.350

.344

.341

.338

.333

15.327

.324

.321

.315

.309

.306

15.304

.298

.292

.289

.286

15.280

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

f 1%

2,4

3%

5

For latitude 26°' 6%

7//£

10

12//£

15

1%OL^

3% 

5

For latitude 27°' 6%

10 2

i OLji

,15

1% 

2X2

3% 

5 

For latitude 28°< 6%

10 2

15 2

Meridional 

distance

Inches

2.868

5.736

8.605

11. 473

14. 342

17. 210

22. 946

28.683

34. 419

2.869

5 707 

. iOi

8.606 

11. 475

14. 344 

17. 212

22.949

28.687

34.424

2.869 

5,738

8.607 

11. 478 

14. 346

17. 215 

22.953 

28.691 

34.429

Ordinate of developed 

parallel

Inch

0.000

.001

.002

.003

.005

.007

.013

.021

.030

0.000

001

!(K)2 

.003 ioos

.008

!014

.021

.031

0.000 

.001

.002 

.003 

.005

.008 

.014 

.022 

.031
82 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 

TABLE 3. Coordinates for the projection of maps, scale -sT-J-g-B Continued

Latitude of

parallel

0 /

28 00

02^

03%

05

07K

10

11M

Wi

15

17H

m

20

22^

25 

26& "HYi

30

32^

OQ3/ A&%

35 

37H

40 

41% 

42>I 

45 

MYi 

48%

50

52H

55

56&

57K

29 00

02}/2

03%

05

07J/S

10

MM

12^

15

17^

18%

20

22^

25

26%

27J^

30

32M

33%

35

37M

40

41%

42H

45

47M

48%

50

523^

55

56%

57^

30 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.037

.037

.036

.036

.035

2.034

.034

.033

.033

.032 

.031

2.031

.030

.029 

.029

.029

2.028

.027

. 097 \j£il

.026 

.025

2.025 

.024 

.024 

.023 

.022 

.022

 2. 021

.021

.020

.019

.019

2.018

.017

.017

.017

.016

2.015

.015

.014

.013

.012

.012

2.012

.011

.010

.010

.009

2.008

.008

.007

.007

.006

2.005

.005

.004

.003

.003

.002

2.002

.001

.000

.000

1.999

1.998

W

Inches

2.547

.546

.545

.545

.544

2.543

.542

.542

.541

.540 

.539

2.539

.538

.537 

.536

.536

2. 535

.534

cqq

. Ooo

.533 

.532

2.531 

.530 

.530 

.529 

.528 

.527

2.527

.526

.525

.524

.524

2.523

.522

.521

.521

.520

2.519

.518

.518

.517

.516

.515

2.515

.514

.513

.512

.512

2.511

.509

.509

.508

.507

2.506

.506

.505

.504

.503

.503

2.502

.501

.500

.500

.499

2.498

2K'

Inches

5.093

.091

.090

.089

.088

5. 085

.085

.084

.082

.080 

.079

5.078

.076

.074 

.073

.072

5.070

.068

067 

!066 

.064

5.062 

.061 

.060 

.058 

.056 

.055

5. 054

.052

.050

.049

.048

5.046

.044

.043

.042

.039

5. 037

.036

.035

.033

.031

.030

5.029

.027

.025

.024

.023

5.021

.019

.018

.017

.015

5.013

.012

.011

.009

.007

.006

5.005

.003

.000

4.999

.998

4.996

3%'

Inches

7.640

.637 :

.636

.634

.631

7.628

.627

.625

.622

.619 

.618

7.616

.613

.610 

.609

.607

7.604

.601

. 

fifiA OUU

.598 

.596

7.593 

.591 

.590 

.586 

.583 

.582

7.580

.577

.574

.573

.571

7.568

.565

.564

.502

.559

7. 556

.555

.553

.550

.547

.545

7.544

.541

.538

.536

.535

7.532

.529

.527

.525

.522

7.519

.518

.516

.513

.510

.508

7.507

.504

.501

.499

.497

7.494

5'

Inches

10. 187

.183

.181

.179

.175

10. 171

.169

.167

.163

.159 

.157

10. 155

.151

.147 

.145

,143

10. 139

.135

1 Q3

. loo

. 131 

.127

10. 123 

.121 

.119 

.115 

.111 

.109

10. 107

.103

.099

.097

.095

10. 091

.087

.085

.083

.079

10. 075

.073

.071

.067

.063

.001

10. 059

.055

.050

.048

.046

10. 042

.038

.036

.034

.030

10. 026

.024

.022

.017

.013

.011

10.009

.005

.001

9.999

.997

9.992

7K'

Inches

15. 280

.274

.271

.268

.262

15. 256

.254

.251

.245

.239 

.236

15. 233

.227

.221 

.218

.215

15. 209

.203 

. 200

.197 

.191

15. 185 

.182 

.179 

.173 

.167 

.164

15. 161

.155

.149

.146

.143

15. 137

.131

.127

.125

.118

15. 112

.109

.106

.100

.094

.091

15. 088

.082

.076

.073

.069

15. 063

.057

.054

.051

.045

15. 039

.035

.032

.026

.020

.017

15. 014

.007

.001

14. 998

.995

14. 989

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

V/2

3%

5

For latitude 28°' 6%

VA

10

WA

15

( 1%Ol/ lYi

3%

5

For latitude 29° 6% 

VA

10

12H

15

1% 

VA3%

5 

For latitude 30°' 6% 

VA

10 

12^

15

Meridional 

distance

Inches

2.869

5.738

8.607

11. 476

14. 346

17. 215

22.953

28. 691

34. 429

2.869

c 700 

o. /oy

8. 609

11. 478

14. 348 

17. 217

22. 956

28. 696

34. 434

2.870 

5.740

8.611 

11. 480 

14. 350 

17. 220 

22.960 

28.700 

34. 440

Ordinate of developed 

parallel

Inch

0.000

.001

.002

.003

.005

.008

.014

.022

.031

0.000

.001

.002

.004

.006

ftftS 

. uvo

.014

AOO 

. \j£t£i

.032

0.000 

.001

.002 

.004 

.006 

.008 

.015 

.023 

.033

0
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 83

TABLE 3. Coordinates for the projection of maps, scale -jri-sir Continued

Latitude of

parallel

0 /

30 00

02H

03%

05

07K

10

Ilk

12J^

15

171^

18%

20

25

27^

30

32H

35 * 

37^

40

45 

48%

50

55

56k

57}^

31 00

02H

03%

05

07Ji

10

Ilk

12}-£

15

17J£

18%

20

22^

25

26k

27^

30

32^

33%

35

37J^

40

41k

42^

45

47H

48%

50

52^

55

66k

57^

32 00

Abscissas of developed parallel

Longitude interval

1'

Inches

1.998

.998

.997

.997

.996

1.995

.995

.994

.993

.993

.992

1.992 

.991

.990 

.990

.989

1.988

.988

.987 

.987 

.986

1.985 

.985 

.984 

.983 

.982 

.982

1.982

.981

.980

.979

.979

1.978

.977

.977

.976

.976

1.975

.974

.974

.973

.972

.972

1.971

.970

.969

.969

.969

1.968

.967

.967

.966

.965

1.964

.964

.963

.963

.962

.961

1.961

.960

.959

.959

.958

1.957

Ik'

Inches

2.498

.497

.497

.496

.495

2.494

.493

.493

.492

.491

.490

2.490 

.489

.488 

.487

.487

2.486

.484

.484 

.483 

.482

2.481 

.481 

.480 

.479 

.478 

.478

2.477

.476

.475

.474

.474

2.473

.472

.471

.471

.469

2.468

.468

.467

.466

.465

.465

2.464

.463

.462

.461

.461

2.460

.459

.458

.458

.456

2.455

.455

.454

.453

.452

.451

2.451

.450

.449

.448

.448

2.447

w

Inches

4.996

.994

.993

.992

.990

4.988

.987

.986

.984

.982

.981

4.979 

.977

.975 

.974

.973

4.971

.969

QAft

. yoo 

.967 

.965

4.963 

.961 

.960 

.958 

.956 

.955

4 954

!952

.'950

.949

.948

4.945

.943

.942

.941

.939

4.937

.936

.935

.932

.930

.929

4.928

.926

.924

.923

.921

4.919

.917

.916

.915

.913

4.911

.910

.908

.906

.904

.903

4.902

.900

.897

.896

.895

4.893

« 

Inches

7.494

.491

.490

.488

.485

7.482

.480

.479

.476

.472

.471

7.469 

.466

.463 

.461

.460

7.457

.453

452 

.'450 

.447

7.444 

.442 

.441 

.437 

.434 

.433

7 431

!428

.425

.423

.421

7.418

.415

.413

.412

.408

7.405

.403

.402

.399

.395

. .394

7.392

.389

.386

.384

.382

7.379

.376

.374

.373

.369

7.366

.364

.363

.359

.356

.354

7.353

.349

.346

.345

.343

7,340

5'

Inches

9.992

.988

.986

.984

.980

9.976

.974

.971

.967

.963

.961

9.959 

.955

.950 

.948

.946

9.942

.938

.936 

.934 

.929

9.925 

.923 

.921 

.916 

.912 

.910

9.908

.904

.899

.897

.895

9.891

.886

.884

.882

.878

9.874

.871

.869

.865

.861

.858

9.856

.852

.848

.845

.843

9.839

.834

.832

.830

.826

0.821

.819

.817

.813

.808

.806

9.804.

.799

.795

.793

.790

9.786

w

Inches

14. 989

.982

.979

.976

.970

14. 964

.960

.957

.951

.945

.942

14. 033 

.932

.926 

.923

.919

14.913

.907

903 

.'894

14. 888 

.884 

.881 

.875 

.868 

.865

14. 862

.856

.849

.846

.843

14. 836

.830

.827

.823

.817

14. 810

.807

.804

.797

.791

.787

14. 784

.778

.771

.768

.765

14.758

.752

.748

.745

.739

14. 732

.729

.725

.719

.712

.709

14.706

.699

.692

.689

.686

14. 679

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

Ik

3%

5

For latitude 30° > 6k

7M

10

12)^

15

VAC\\/

3% 

5

For latitude 31°' 6k

10

12V*S

15

*¥

3% 

5 

For latitude 32° 6k

10

12H 

15

Meridional 

distance

Inches

2.870

5.740

8.611

11.480

14. 350

17. 220

22. 960

28.700

34. 440

2.870

5,741

8.611 

11.482

14. 352 

17 223

22! 963

28. 704

34. 445

2.871 

5.742

8.613 

11.483 

14. 355 

17. 225 

22. 967 

28.709 

34. 450

Ordinate of developed 

parallel

Inch

0.000

.001

.002

.004

.006

.008

.015

.023

.033

0.000

.001

.002 

.004

.006 

008

!fll5

.023

.033

0.000 

.001

.002 

.004 

.006 

.008 

.015 

.024 

.034

«

0
84 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 

TABLE 3. Coordinates for the projection of maps, scale sxi'8'7 Continued

Latitude of

parallel

0 /

32 00

02 J^

03%

05

07H

10

11%

12/^

15

17/^

18%

20

25 

26%

27H

30

32^ oofty 66% 

35 

37^

40

42^ 

45

48%

50

52^

55

56%

57^

33 00

02^

03%

05

07M

1011%

12J^

15

' 17^6

18%

20

22H

25

2C%

27H

30

32^

33%

35

.37^

40

41%

42^

45

47H

48%

50

52^

55

56%

57^

34 00

Abscissas of developed parallel

Longitude interval

1'

Inches

1.957

.956

.956

.955

.955

1.954

.953

.953

.952

.951

.951

1.950 

.949

.948 

.948

.947

1.947

.946

'.945 

.944

1.943 

.942 

.942 

.941 

.940 

.940

1.939

.938

.937

.937

.937

1.936

.935

.934

.934

.933

1.932

.932

.931

.930

.929

.929

1.928

.927

.926

.926

.926

1.925

.924

.923

.923

.922

1.921

.921

.920

.919

.918

.918

1.917

.916

.915

.915

.915

1.914

1%'

Inches

2.447

.445

.445

.444

.443

2.442

.441

.441

.440

.439

.438

2.438 

.437

.435 

.435

.434

2.433

.432 

431

1431 

.430

2.429 

.428 

.428 

.426 

.425 

.425

2.424

.423

.422

.421

.421

2.420

.418

.418

.417

.416

2.415

.415

.414

.413

.412

.411

2.410

.409

.408

.408

.407

2.406

.405

.404

.404

.402

2.401

.401

.400

.399

.398

.397

2.397

.395

.394

.394

.393

2.392

«'

Inches

4.893

.891

.890

.889

.886

4.884

.883

..882

.880

.877

.876

4.875 

.873

.871 

.870

.869

4.866

.864

.863 

.862 

.860

4.857 

.856 

.855 

.853 

.851 

.849

4.848

.846

.844

.843

.841

4.839

.837

.836

.835

3 .832

4.830

.829

.828

.825

.823

.822

4.821

.819

.816

.815

.814

4.812

.809

.808

.807

.805

4.802

.801

.800

.798

.795

.794

4.793

.791

.789

.787

.786

4.784

3%'

Inches

7.340

.336

.335

.333

.330

7.326

.325

.323

 .320

.316

.315

7.313 

.310

.306 

.305

.303

7.299

.295 

.294

.293 

.289

7.286 

.284 

.283 

.279 

.276 

.274

7.272

.269

.266

.264

.262

7.259

.255

.254

.252

.249

7.245

.243

.242

.238

.235

.233

7.231

.228

.224

.223

.221

7.218

.214

.212

.211

.207

7.204

. .202

.200

.197

.193

.191

7.190

.186

.183

.181

.179

7.176

5'

Inches

9.786

.782

.779

.777

.773

9.768

.766

.764

.759

.755

.753

9.751 

.746

.742 

.739

.737

9.733

.728

.726 

.724 

.719

9.715 

.712 

.710 

.706 

.701 

.699

9. 697

1692

.687

.685

.683

9.678

.674

.671

.669

.665

9.660

.658

.656

.651

.648

.644

9.642

.637

.633

.630

.628

9.623

.619

.617

.614

.610

9.605

.603

.600

.596

.391

.589

9.586

.'582

.577

.575

.572

9.568

« 

Inches

14. 679

.672

.669

.660

.659

44. 652

.649

.646

.639

.632

.629

14. 626 

.619

.612 

.609

.606

14. 599

.592 

. 589

'.585 

.579

14. 572 

.569 

.565 

.558 

.551 

.548

14. 545

.538

.531

.528

.524

14. 518

.511

.507

.504

.497

14. 490

.487

.483

.476

.470

.466

14. 463

.456

.449

.445

.442

14. 435

.428

.425

.421

.414

14. 407

.404

.400

.394

.387

.383

14. 380

.373

.366

.362

.358

14. 352

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

3%

5

For latitude 32°' 6%

7jl

10

15

1%

3% 

5

For latitude 33°' 6%

10 2

I OlX

15

1%

3% 

5 

For latitude 34°' 6%

10 

15

Meridional 

distance

Inches

2.871

5.742

8.613

11.483

14. 355

17. 225

22. 967

28. 709

34. 450

2.871

5. 743

8.614 

11. 485

14. 357 

17.228

22. 971

28.714

34. 456

2.872 

5.744

8.615 

11. 487 

14. 359 

17. 231 

22. 974 

28.718 

34. 462

Ordinate of developed 

parallel

Inch

0.000

.001

.002

.004

.006

.008

.015

.024

.034

0.000

.001

.002 

.004

.006 

.009

.015

.024

. 035

0.000 

.001

.002 

.004 

.006 

.009 

.016 

.024 

.035

5'
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 85 

TABLE 3. Coordinates for the projection of maps, scale -gri^Ti Continued

Latitude of 

parallel

0 /

34 00

02^

03%

05

07^

10

11%

15

17J^

38%

20

22J/2

25 

26% 

W/2

30

32^

33% 

35 

37^

40 

41% 

42^ 

45 

47H 

48%

50

55 2

56%

35 00

02H

03%

05

07J/2

10

11%

15 2

17H

18%

20

22^

25

26%

30

32V£

33%

35yiAl

40

41%

45 ^

47M

48%

50

52V4

55

56%

57^

36 00

Abscissas of developed parallel

Longitude interval

1'

Inches

1. 914

.913

. 9.1.2

.912

.911

1.910

.909

.909

.908

.907

.900

1.906

.905

.904 

.904 

.903

1.902

.901 

901

!900 

.899

1.898 

.898 

.897 

.897 

.896 

.895

1 895

!894

.893

.892

.892

1.891

.890

.889

.889

.888

1.887

.886

.886

.885

.884

.884

1.883

.882

.881

.881

.880

1.879

.878

.878

.877

.876

1.875

.875

.874

.873

.872

.872

1.871

.870

.869

.869

.869

1.868

1%'

Inches

2.392

.391

.390

.390

.388

2.387

.387

.386

.385

.384

.383

2.383

.381

.380 

.380 

.379

2.378

.377

* 17A 01 \)

.375 

.374

2.373 

.373 

.372 

.371 

.370 

.369

2.368

.367

.366

.365

.365

2.364

.362

.362

.361

.360

2.359

.358

.357

.356

.355

.354

2.354

.353

.352

.351

.350

2.349

.348

.347

.347

.345

2.344

.344

.343

.342

.341

.340

2.339

.338

.337

.336

.336

2.334

2tf

Inches

4.784

.782

.780

.779

.777

4.775

.773

.772

.770

.767

.766

4.765

.763

.760 

. 759 

.758

4.756

.753

!751 

.749

4.746 

.745 

.744 

.741 

.739 

.738

4.737

.734

.732

.731

.729

4.727

.725

.724

.722

.720

4.717

.716

.715

.713

.710

.709

4.708

.705

.703

.702

.701

4.698

.696

.694

.693

.691

4.688

.687

.686

.684

.681

.680

4.679

.676

.674

.673

.671

4.669

3%'

Inches

7.176

.172

.171

.169

.165

7.162

.160

.158

.155

.151

.149

7.148

.144

.141 

.139 

.137

7.133

.130

.126 

.123

7.119 

.117 

.116 

.112 

.109 

.107

7.105

.101

.098

. 095

.094

7.091

.087

.085

.083

.079

7.076

.074

.073

.069

.065

.064

7.062

.058

.054

.053

.051

7.047

.044

.042

.040

.036

7.033

.031

.029

.025

.022

.020

7.018

.014

.011

.009

.007

7.003

5'

Inches

9.568

' . 563

.561

. 558

.554

9.549

.547

.544

.540

.535

.533

9.530

.525

.521 

.518 

.516

9. 511

.507

!502 

.497

9.492 

.490 

.488 

.483 

.478 

.476

9.473

.468

.464

.461

.459

9.454

. 449

!445

.439

9.435

.433

.430

.425

.420

.418

9.416

.411

.406

.404

.401

9.396

.391

.389

.387

.382

9.377

.374

.372

.367

.362

.360

9.357

.352

.348

.345

.343

9.338

7K'

Inches

14. 352

.345

.341

.338

.331

14.324

.320

.316

.309

.302

.299

14. 295

.288

.281 

.278 

.273

14. 267

.260 

. 256

!246

14. 239 

.235 

.231 

.224 

.217 

.213

14. 210

.203

.196

.192

.188

14. 181

.174

.170

.167

.160

14. 152

.149

.145

.138

.131

.127

14. 124

.116

.109

.105

.102

14. 094

.087

.083

.080

.073

14. 065

.002

.058

.051

.043

.040

14. 036

.029

.021

.018

.014

14.007

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

3%

5

For latitude 34° 6%

1]/i

10

12J^

15

1%

3%

For latitude 35° 6%10 2

1 oiy

15

1%

3% 

5 

For latitude 36° 6%

10 

12^ 

15

Meridional 

distance

Inches

2.872

5.744

8.615

11.487

14. 359

17.231

22. 974

28. 718

34. 462

2.872

5.745

8.617

11.489

14. 362 

17. 234 

22. 978

9fi £O. 791 1 £G

34. 467

2.873 

5.745

8.618 

11.491 

14.364 

17.237 

22. 982 

28.728 

34. 473

Ordinate of developed

parallel

Inch

0.000

.001

.002

.004

.006

.009

.016

.024

.035

0.000

.001

.002

. 004 !ooo

.009 

.016

AOC . mo

.030

0.000 

.001

.002 

.004 

.006 

.009 

.016 

.025 

.036
86 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 3. Coordinates for the projection of maps, scale g-yi's-iy Continued

Latitude of 

parallel

0 /

36 0002 y% 03%

05

07K

10

nK

12K

15

17^

18K

20

25 2

27>i

30

33% 

35

40

41K 

42^ 

45

48%

50

Wi

55

56}^ &A1

37 00

02H

03^

05

07H

10UK

12M

15

17}^

18%

20

22H

25

26}^

27^

30

32^

33%

35

37^

40

41K

42 J^

45

47}<

48%

50

52^

55

56K

57J^

38 00

Abscissas of developed parallel

Longitude interval

1'

Inches

1.868

.867

.866

.866

.865

1.864

.863

.863

.862

.861

.860

1.860 

.859

.858 

.857

.857

1.856

.855

'.854 

.853

1.852

.851 

.851 

.850 

.849

.848

1.848

.847

.846

.845

.845

1.844

.843

.842

.842

.841

1.840

.839

.839

.838

.837

.836

1.836

.835

.834

.833

.833

1.832

.831

.830

.830

.829

1.827

.827

.826

.825

.824

.824

1.823

.822

.821

.821

.820

1.819

IK'

Inches

2.334

.333

.333

.332

.331

2.330

.329

.328

.327

.326

.325

2.325 

.323

.322 

.321

.321

2.320

.318

01 Q

. olo 

.317 

.316

2.315

.314 

.313 

.312 

.311

.310

2.310

.308

.307

.306

.306

2.305

.303

.303

.302

.301

2.300

.299

.298

.297

.296

.295

2.295

.293

.292

.291

.291

2.289

.288

.288

.287

.286

2.284

.284

.283

.282

.280

.280

2.279

.278

.277

.276

.275

. 2. 274

2H'

Inches

4.669

.666

.665

.664

.661

4.659

.658

.657

.654

652

.650

4.649 

.647

.644 

.643

.642

4.639

.637

noc

. OoO

.634 

.632

4.629

.628 

.627 

.624 

.622

.621

4.619

.617

.614

.613

.612

4.609

.607

.605

.604

.602

4.599

.598

.597

.594

.592

.590

4.589

.587

.584

.583

.581

4.579

.576

.575

.574

.571

4.569

.567

.566

.564

.561

.560

4.558

.556

.553

.552

.551

4.548

3%'

Inches

7.003

.000

6.998

.996

.992

6.989

.987

.985

.981

.977

.976

6.974 

.970

.966 

.964

.963

6.959

.955 

953

!951 

.948

6.944

.942 

.940 

.936 

.933

.931

6.929

.925

.921

. 919

.918

6.914

.910

.908

.906

.902

6.899

 .897

.895

.891

.887

.885

6.884

.880

.876

.874

.872

6.868

.864

.863

.861

.857

6.853

.851

.849

.845

.841

.840

6.838

.834

.830

.828

.826

6.822

5'

Inches

9.338

.333

.330

.328

.323

9.318

.316

.313

.308

.303

.301

9.298 

.293

.288 

.286

.283

9.278

.273

. 971 fit 1

.268 

.264

9.259

.256 

.254 

.249 

.243

.241

9.238

.233

.228

.226

.223

9.218

.213

.211

.208

.203

9.198

.196

.193

.188

.183

.181

9. 178

.173

.168

.165

.163

9.158

.153

.150

.148

.142

9.137

.135

.132

.127

.122

.119

9.117

.112

.107

.104

.101

9.096

W

Inches

14. 007

13. 999

.996

.992

.984

13. 977

.973

.970

.962

.955

.951

13. 947 

.940

.933 

.929

.925

13. 918

.910

'.903 

.895

13. 888

.884 

.880 

.873 

.865

.862

13. 858

.850

.843

.839

.835

13. 828

.820

.816

.813

.805

13. 797

.794

.790

.782

.775

.771

13. 767

.759

.752

.748

.744

13. 737

.729

.725

.721

.714

13. 706

.702

.698

.691

.683

.679

13. 675

.668

.660

.656

.652

13. 644

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

IK

3%

5

For latitude 36°' 6K

7/^

10

12)^

15

f IK

91/J

3M 

5

For latitude 37°' 6M

10 2

,15

IK

2/^

3%

5 

For latitude 38°' 6M

10 2

15 2

Meridional 

distance

Inches

2.873

5.745

8.618

11.491

14.364

17. 237

22. 982

28. 728

34. 473

2.873

5.746

8.620 

11. 493

14. 366 

17.240

22. 986

28. 733

2.874

5.747

8.621

11. 495 

14. 369 

17. 242 

22. 990

28.738

34. 485

Ordinate of developed

parallel

Inch

0.000

.001

.002

.004

.006

.009

.016

.025

.036

0.000

. nmUUJ.

.002

!ooe

AAQ

. UUW

.016

.025 

.036

0.000

.001

.002

.004 

.006 

.009 

.016

.025

.037
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 87 

TABLE 3. Coordinates for the projection of maps, scale -grifff Continued

Latitude of

parallel

0 ,

38 0002 y

WK

05

07H

10iiK

15

17}^

18J4

20.

 22V*

25 

26J^

27^

30

32H

35 *

/ 6

40 

41K 

42^ 

45 

47X2

50

52^

55

60}^

6%

39 00

02^

05*

07J4

10UK

12M

15

17M

18J4

20

22H

25

26K

30

32H

35 *

37^

40

41K

42^

45

47^

48J4

50

52^

6556H

MM

40 00

Abscissas of developed parallel

Longitude interval

1'

Inches

1.819

.818

.818

.817

.816

1.815

.815

.814

.813

.812

.812

1.811

.810

.809 

.808

.808

1.807

.806

.'805 

.804

1.803 

.802 

.802 

.801 

 .800 

.799

1.798

.797

.790

.796

.795

1.794

.793

.793

.792

.791

1.790

.790

.789

.788

.787

.786

1.786

.785

.784

.783

.783

1.782

.781

.780

.779

.778

1.777

.777

.776

.775

.774

..774

1.773

.772

.771

.770

.770

1.769

IK'

Inches

2.274

.273

' .272

.272

.270

2.269

.268

.268

.266

.265

.264

2.264

.262

.261 

.260

.260

2.259

.257

.'256 

.255

2.253 

.253 

.252 

.251 

.249 

.249

2.248

.247

.245

.245

.244

2.243

.242

.241

.240

.239

2.238

.237

.236

.235

.234

.233

2.232

.231

.230

.229

.228

2.227

.226

.225

.224

.223

2.222

.221

.220

.219

.218

.217

2.216

.215

.214

.213

.212

2.211

Inches

4.548

.546

.544

.543

.540

4.538

. 537

.535

.533

.530

.529

4.527

.525

.522 

.521

.520

4.517

.515

C] Q

. 010

.512 

.509

4.507 

.505 

.504 

.501 

.499 

.498

4.496

 .494

.491

.490

.488

4.486

.483

.482

.480

.478

4.475

.474

.473

.470

.467

.466

4.465

.462

.459

.458

.457

4.454

.451

.450

.449

.446

4.443

.442

.441

.438

.435

.434

4.433

..430

.427

.426

.425

4.422

Inches

6.822

.818

.816

.814

.811

6.807

.805

.803

.799

.795

.793

6.791

.787

.783 

.781

.780

6.776

.772 

.770

.708 

.764

6.760 

.758 

.756 

.752 

.748 

.746

6.744

.740

.736

.734

.732

6.729

.725

.723

.721

.717

6.713

.711

.709

.705

.701

.699

6.697

.693

.689

.687

.685

6.681

.677

.675

.673

.669

6. 665

.663

.661

.657

.653

.651

6.649

.645

.641

.639

.637

6.633

5'

Inches

9. 096

.091

.089

.086

.081

9.076

.073

.071

.005

.060

.058

9.055

.050

.045 

.042

.039

9.034

.029

.026 

.024 

.019

9.013 

.011 

.008 

.003 

8.998 

.995

8.992

.987

.982

.979

.977

8.971

.966

.964

.961

.956

8.950

.948

.945

.940

.934

.932

8.929

.924

.919

.916

.913

8.908

.903

.900

.897

.892

8.887

.884

.881

.876

.871

.868

8.865

.860

.855

.852

.849

8.844

Inches

13. 644

.636

.633

.629

.621

13.614

.010

.606

.598

.590

.580

13. 582

.575

.507 

.503

.559

13. 551

.544

.540 

.536

.528

13. 520 

.516 

.513 

.504 

.497 

.493

13. 489

.481

.473

.469

.465

13. 457

.449

.445

.441

.433

13. 425

.422

.418

.410

.402

.398

13. 394

.386

.378

.374

.370

13. 362

.354

.350

.346

.338

13. 330

.326

.322

.314

.306

.302

13. 298

.290

.282

.278

.274

13. 266

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

iK

2}^

354

5

For latitude 38° 6)4

7H

10

12V<2

15

IK

OT^J

3V

5

For latitude 39° i 6J4 

7H

10

12V6

15

IK

2]/£

5 * 

For latitude 40°' OH

10 

12M 

15

Meridional 

distance

Inches

2.874

5. 747

8.621

11.495

14. 369

17. 242

22. 9<JO

28.738

34. 485

2.874

5.748

8.623

11. 497

14. 371 

17. 245

22. 994

9fi *O. 7<T! <4O

34. 491

2.875

5.749

8.624 

11.49!) 

14. 374 

17. 248, 

22.998 

28. 748 

34. 497

Ordiuate of developed

parallel

Inch

0.000

.001

.002

.004

.006

.009

.016

.025

.037

0.000

001

!(K)2

.004

.006

ftfiQ 

. \J\Ju

.010

.026

.037

0.000

.001

.002 

.004 

.006 

. .009 

.017 

.026 

.037

o.
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 

TABLE 3. Coordinates for the projection of maps, scale -griTf Continued

Latitude of

parallel

0 /

40 00

02!^

03^

05

07.H>

10iiM

12.M2

15

17JX

18M

20

22/2

25 

26M

27^

30

33 % 

35

40 

45

rn

iJ\J

55 2

56 Ji

WA

41 00

02 Yi

03Ji

05dfiYi

10

11/4

12^

15

17J^

18%

20

22^

25

26 Ji

27K

30

32^

35 *

37J^

40

41M

42^

45

47^

50

52^

55

56/^

573^

42 00

Abscissas of developed parallel

Longitude interval

1'

/ ncAes

1.769

.768

.767

.767

.765

1.764

.764

.763

.702

.761

.761

1.760

.759

.758 

.757

.757

1.756

!755

. 754 

!754 

.753

1.751 

.751 

.750 

.749 

.748 

.748

1.747

.746

.745

.744

.744

1.743

.742

.741

.740

.739

1.738

.738

.737

.736

.735

.734

1.734

.733

.732

.731

.731

1.729

.728

.728

.727

.726

1.725

.724

.724

.723

.722

.721

1.721

.719

.718

.718

.717

1.716

1M'

Inches

2.211

.210

.209

.208

.207

2.206

.205

.204

.203

.202

.201

2.200

.199

.197 

.197

.196

2.195

.193

1QO . iuo

.192 

.191

2.189 

.189 

.188 

.180 

.185 

.184

2.184

.182

.181

.180

.180

2.178

.177

.176

.176

.174

2.173

.172

.171

.170

.169

.108

2.107

.166

.165

.164

.163

2.162

.100

.100

.159

.158

2.156

.156

.155

 .153

.152

.151

2.151

.149

.148

.147

.146

2.145

K

Inches

4.422

.419

.418

. 416

.414

4.411

.410

.408

.406

.403

.402

4.400

.398

.395 

.394

.392

fe

4.389

.387

qor

. oJSO

.384 

.381

4.379 

.377 

.376 

.373 

.370 

.369

4.368

.305

.362

.361

.360

4.357

.354

.353

.351

.348

4.346

.344

.343

.340

.337

.336

4.335

.332

.329

.328

.326

4.324

.321

.319

.318

.315

4.313

.311

.310

.307

.304

.303

4.301

.297

.296

.294

.293

4.290

* 

Inches

0.033

.629

.627

.625

.621

6.617

.615

.012

.609

.605

.602

6.600

.596

.592 

.590

.588

6.584

.580

C-TQ

. O/o

.576 

.572

6.568 

.566 

.564 

.560 

.556 

.554

6.551

.547

.543

.541

.539

6.535

.531

.529

.527

.523

6.519

.517

.514

.510

.506

.504

6.502

.498

.494

.492

.490

6.485

.481

.479

.477

.473

6.469

.467

.465

.460

.456

.454

6.452

.448

.444

.442

.439

6.435

5'

Inches

8.844

.838

.836

.833

.828

8.822

.819

.817

.811

.806

.803

8.801

.795

.790 

.787

.784

8.779

.773

.771 

.708 

.703

8.757 

.754 

.752 

.746 

.741 

.738

8.735

.730

.724

.722

.719

8.713

.708

.705

.702

.697

8.691

.689

.686

.680

.675

.672

8.669

.664

.658

.656

.653

8.647

.642

.039

.636

.631

8.625

.622

.619

.614

.608

.606

8.603

.597

.592

.589

.586

8.580

* 

Inches

13. 266

. 258

.254

.250

.241

13. 233

.229

.224

.217

.209

.205

13. 201

.193

.185 

.181

.177

13. 168

.100

.158 

.152 

.144

13. 130 

.132 

.128 

.119 

.111 

.107

13. 103

.095

.087

.083

.078

13. 070

.062

.058

.054

.045

13. 037

.033

.029

.021

.012

.008

13. 004

12. 996

.987

.983

.979

12. 971

.963

.958

.954

.946

12. 938

.933

.929

.921

.913

.908

12.904

.896

.887

.883

.879

12. 871

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

iM

&A

3%

5

For latitude 40° 6M

7/4

10

123^

15

iMov/

or/ 5 4

For latitude 41°. 6J4

10 2

i ov/f>

15

IM

3j|

5 

For latitude 42°' 6^

10 2

15

Meridional 

distance

Inches

2.875

5.749

8.624

11. 499

14. 374

17. 248

22. 998

28. 748

34. 497

2.875

. 5. 750

8.020

11. 501

14. 370 

17. 252

23. 002

28. 753

34. 503

2.876 

5.751

8.627 

11.503 

14. 379 

17. 255 

23.006 

28.758 

34. 509

Ordinate of developed 

parallel

Inch

0.000

.001

.002

.004

. .006

.009

.017

.026

.037

0.000

flfll

!002

.004

.006 

.009

.017

.020

.037

0.000 

.001

.002 

.004 

.007 

.009 

.017 

.026 

.038
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 89 

TABLE 3. Coordinates for the projection of maps, scale -STASIS~~Continued

Latitude of

parallel

0 /

42 00

02}^

03%

05

07k

10

Ilk

15

171^

18%

20 

22^

25 

26k

30

33% 

35 

37k

40

42)| 

45 

47^ 

48%

50

52H

55

56k

57^

43 00

02V*i

03%

05

10

Ilk12 y<i

15

17 !/5

18%

20

22 J^

25

26k

27^

30

32^

33%

35

37^

40

4lk

42^

45

48%

50

52^

55

56k

44 00

Abscissas of developed parallel

Longitude interval

1'

Inches

1.716

.715

.714

.714

.713

1.712

.711

.711

.709

.708

.708

1.707 

.706

.705 

.704

.704

1.703

.701 

.701

.700 

.699

1.698 

.697 

.697 

.090 

. 695 

.694

1.693

.092

.691

.691

.690

1.689

.688

.687

.687

.686

1.684

.684

.683

.682

.681

.680

1.680

.679

.677

.677

.676

1.675

.674

.673

.673

.672

1.671

.670

.669

.668

.667

.666

1.666

.665

.664

.663

.662

1.661

Ik'

Inches

2.145

.144

.143

.142

.141

2.140

.139

.138

.137

.135

.135

2.134 

.132

.131 

.130

.130

2:i28

.127 

.126

.125 

.124

2.123 

.122 

.121 

.120

.118 

.118

2.117

.115

.114

.113

.113

2.111

.110

.109

.108

.107

2. 105

.105

.104

.103

.101

.100

2.100

.098

.097

.096

.095

2.094

.093

.092

.091

.090

2.088

.087

.087

.085

.084

.083

2.082

.081

.080

.079

.078

2.077

«

Inches

4.290

.287

.286

.285

.282

4.279

.278

.276

.273

.271

.269

4.268 

.265

.262 

.201

.259

4. 256

.254

!251 

. 248

4.245 

.244 

. 242 

.239 

.237 

.235

4. 234

.231

.228

.227

1225

4.222

.220

.218

.217

.214

4.211

.210

.208

.205

.202

.201

4.199

.197

.194

.192

.191

4.188

.185

.184

.182

.179

4.176

.175

.173

.171

.168

.166

4.165

.162

.159

.158

.156

4.153

3%'

Inches

6.435

.431

.429

.427

.423

6.418

.416

.414

.410

.406

.404

6.402 

.397

.393 

.391

.388

6. 385

.380

 J7Q

. O/o

.376 

.372

6. 368 

.366 

.363 

.359 

.355 

.353

6. 351

.346

.342

.340

.338

6.334

.329

.327

.325

.321

6. 310

.314

.312

.308

.303

.301

6.299

.295

.291

.289

.286

6.282

.278

.275

.273

.269

6.265

.262

.260

.256

.252

.249

6.247

.243

.239

.236

.234

6.230

5'

Inche.s

8.580

.575

.572

.569

.564

8.558

.555

.552

.547

.541

.538

8.535 

.530

.524 

. 521

. 519

8.513

.507

'. 502 

.496

8. 490 

.437 

. 485 

.479 

.473 

.470

8.408

. 402

.456

.453

.450

8.445

.439

.436

.433

.428

8.422

.419

.416

.410

.405

.402

8.399

.393

.387

.385

.382

8.376

.370

.307

.364

.359

8.353

.350

.347

.341

.336

.333

8.330

.324

.318

.315

.312

8.307

7*4'

Inches

12. 871

.862

.858

.854

.845

12. 837

.833

.829

.820

.812

.807

12. 803

.795

.786 

.782

.778

12. 769

.761

. 7^7 tot 

.752 

.744

12. 735 

.731 

.727 

.718 

.710 

.706

12. 701

.693

.684

.680

.676

12. 667

.659

.654

.050

.641

12. 633

.629

.624

.616

.607

.603

12. 598

.590

.581

.577

.573

12. 564

.555

.551

. 547

.538

12. 529

.525

.521

.512

.503

.499

12. 495

.486

.477

.473

.468

12. 460

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

Ik

3%

5

For latitude 42°. 6k

7M

10

15

flk

3%

For latitude 43°. 6k

10 2

1 '^V1^

15

f Ik

3% 

7 

For latitude 44°< 5k

10 

15

Meridional 

distance

Inches

2.876

5.751

8.627

11.503

14. 379

17. 255

23. 006

28. 758

34. 509

2.870

O* c 7=9 104

8.629 

11.505

14. 382 

17. 258

23. 010

28. 763

34. 515

2.877 

5.753

8.630 

11. 507 

14. 384 

17. 261 

23.014 

28. 768 

34. 521

Ordinate of developed 

parallel

Inch

0.000

.001

.002

.004

.007

.009

.017

.026

.038

0.000

001

'.002

!007 

 

ftftQ \AJo

.017

.026

.038

0.000 

.001

.002 

.004 

.007 

.009 

.017 

.026 

.038
90 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 3. Coordinates for the projection of maps, scale g-ri's-Tr Continued

Latitude of

parallel

0 /

44 00

02^

03%

05

07H

10

11%

12}<2

15

18%

20 

22^

25 

26%

27^

30 

32^

Qoa/ 33%

35

40

41%

45 

47^

48%

50

55

56%

57K

45 00

02^

03^

05

07H

10

11%

12/^

15

17J4

18%

20

22^

25

26%

27^

30

32H

33%

35

37^

40

41%

42^

45

47^

48%

50

52j<j

55

56%

46 00

Abscissas of developed parallel

Longitude interval

1'

Inches

1.661

.660

.660

.659

.658

1.657

.656

.656

.654

.653 

.653

1.652 

.651

.650 

.649

.648

1.647 

.646 

.645

.645 

.644

1.643

.642 

.641

.640 

.639

.639

1.638

.637

.636

.635

.634

1.633

.632

.631

.631

.630

1.629

.628

.627

.626

.625

.624

1.624

.622

.621

.621

.620

1.619

.618

.617

.616

.615

1.614

.613

.613

.612

.611

.610

1.609

..608

.607

.606

.606

1.605

1%'

Inches

2.077

.075

.074

.074

.072

2.071

.070

.069

.068

.066 

.066

2.065 

.064

.062 

.061

.061

2.059 

.058 

.057

.056 

.055

2.053

.052 

.052

.050 

.049

.048

2.047

.046

.044

.044

.043

2.041

.040

.039

.038

.037

2.036

.035

.034

.033

.031

.030

2.030

.028

.027

.026

.025

2.024

.022

.021

.021

.019

2.018

.017

.016

.015

.013

.012

2.012

.010

.009

.008

.007

2.006

w «-

Inches > Inches

4.153 6.230

.150 : .226

. 149 . 223

.147 .221

. 145 . 217

4.142

.140

.139

.136

.133 

.131

4.130 

.127

.124 

.123

.121

4.118 

.115 

.114

.112 

.109

4.106

.105 

.104

.101 

.098

.096

4.095

.092

.089

.087

.086

4.083

.080

.078

.077

.074

4.071

.070

.068

.065

.062

.061

4.059

.056

.053

.052

.050

4.047

.044

.043

.041

.038

4.035

.034

.032

.029

.026

.025

4.023

.020

.017

.016

.014

4.011

6.212

.210

.208

.204

.199 

.197

6.195 

.191

.186 

.184

.182

6.177 

.173 

.171

.169 

.164

6.160

.158 

.155

.151 

.146

.144

6.142

.138

.133

.131

.129

6.124

.120

.118

.115

.111

6.107

.105

.102

.098

.093

.091

6.089

.084

.080

.078

.075

6.071

.066

.064

.062

.057

6.053

.051

.048

044

.039

.037

6.035

.030

.026

.024

.021

6.017

5'

Inches

8.307

.301

.298

.295

.289

8.283

.280

.277

.272

. 266 

.263

8.260 

.254

.248 

.245

.242

8.236 

.231

!225 

.219

8.213

.210 

.207

.201 

.195

.192

8.189

.184

.178

.175

.172

8.166

.160

.157

.154

.148

8.142

.139

.136

.130

.124

.121

8.118

.112

.106

.103

.100

8.094

.088

.085

.082

.076

8.070

.067

.065

.059

.053

.050

8.047

.040

.034

.031

.028

8.022

7K-'

Inches

12. 460

.451

.447

.442

.434

12. 425

.420

.416

.407

.399 

.394

12. 390 

.381

.372 

.369

.364

12. 355 

.346 

.341

.337 

.328

12. 319

.315 

.311

.302 

.293

.289

12. 284

.275

.266

.262

.258

12. 249

.240

.235

.231

.222

12. 213

.209

.204

.195

.186

.182

12. 177

.168

.160

.155

.151

12. 142

.133

.128

.124

.115

12. 106

.101

.097

.088

.079

.074

12. 070

 .061

.052

.047

.043

12. 034

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

3%

5

For latitude 44°' 6%

7J^

10

12H

15

1%

3% 

5

For latitude 45° 6%

10

 1 2J/

15

'1%

2/2

3%

5 

For latitude 46°' 6%

10

15

Meridional 

distance

Inches

2.877

5.753

8.630

11. 507

14. 384

17.261

23. 014

28.768

34.521

2.877

K 7CC U. fOU

8.632

U CAQ 

. OUu

14. 387 

17. 264

23.018

no 770 ZO. (id

34. 527

' 2.878

5.756

8.633

11.511 

14. 389

17. 267 

23. 022

28. 778 

34. 534

Ordin ate ofde- . veloped 

parallel

Inch

0.000

.001

.002

.004

.007

.009

.017

.026

.038

0.000

.001

.002

!007 

.009

.017

.026

.038

0.000

.001

.002

.004 

.007

.009 

.017

. 026 

.038
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 91

TABLE 3. Coordinates for the. projection of maps, scale -gT&s-s Continued

Latitude of

parallel

0 /

46 00

03%

05

07^

10

Yi]A 15 "

m

20

22/^

25

26%

27^

30

32^

33%

35

37^

40

W/2

45 

48%

50

52)^

55

56%

57H

47 00

02^

03%

05

07^

10

11)4

12M

15

17J4

18%

20

22 J^

25

26%

27M

30

32V

33%

35

37^

40

41%

42^

45

47M

48%

50

52^

55

56%

57^

48 00

Abscissas of developed parallel

Longitude interval

1'

Inches

1.605

.603

.603

.602

.601

1.600

.599

.598

.597

.596

.595

1. 595

.594

.592

.592

.591

1.590

.589

.588

.588

.586

1.585 

.584 

.584 

.583 

.581 

.581

1.580

.579

.578

.577

.577

1.575

.574

.574

.573

.572

1.570

.570

.569

.568

.567

.566

1.565

.564

.563

.562

.562

1.561

.559

.559

.558

.557

1.556

.555

.554

.553

.552

.551

1. 551

.549

.548

.548

.547

1.546

1%

Inches

2. 006

.004

.003

.003

.001

2.000

1, 999

.998

.997

.995

.994

1.994

.992

.990

.990

.989

1. 987

.986

.985

.984

.983

1.981 

.981 

.980 

.978 

.977 

.976

1.975

.974

.972

.971

. .971

1.969

.968

.967

.966

.965

1.963

.962

.962

.960

.958

.958

1.957

.955

.954

.953

.952

1. 951

.949

.948

.948

.946

1. 945

.944

.943

.941

.940

.939

1.938

.937

.935

.934

.934

1.932

21/2

Inches

4.011

.008

.007

.005

.002

3.999

.998

.996

.993

.990

.989

3.987

.984

.981

.979

.978

3.975

.972

.970

.969

.966

3.963 

.961 

.960 

.957 

.954 

.952

3.951

.948

.944

.943

.941

3.938

.935

.934

.932

.929

3.926

.925

.923

.920

.917

.915

3.914

.911

.908

.906

.905

3.901

.898

.897

.895

.892

3.889

.888

.886

.883

.880

.878

3.877

.874

.871

.869

.867

3.864

3%

Inches

6.017

.012

.010

.008

.003

5.999

.996

.994

.990

.985

.983

5.981

.976

.972

.969

.967

5.962

.958

.956

.953

.949

5.944 

.942 

.940 

.935 

.930 

.928

5. 926

.921

.917

.914

.912

5.908

.903

.901

.898

.894

5.889

.887

.885

.880

.875

.873

5.871

.866

.861

.859

.857

5.852

.848

.845

.843

.838

5.834

.831

.829

.824

.820

.817

5. 815

.810

.806

.803

.801

5.796

5'

Inches

8.022

.016

.013

.010

.004

7.998

.995

.992

.986

.980

.977

7.974

.968

.962

.959

. 956

7.950

.944

.941

.938

.932

7.926 

.923 

.919 

.913 

.907 

.904

7.901

.895

.889

.8S6

.883

7.877

.871

.868

' .864

.858

7.852

.849

.846

, .840

! .834

' .831

7.828

.821

.815

.812

.809

7.803

.797

.794

.791

.784

7.778

.775

.772

. 766

.760

.757

7.753

.747

.741

.738

.735

7.729

7^

Inches

12. 034

.025

.020

.016

.007

11.998

.993

.988

.979

.970

.966

11. 961

.952

.943

.938

.934

11.925

.916

.911

.907

.897

11. 888 

.884 

.879 

.870 

.861 

.856

11. 852

.843

. 8u3

.829

.824

11.815

.806

.801

.797

.788

11. 778

.774

.769

.760

.751

.746

11. 741

.732

.723

.718

.714

11. 704

.695

.691

.686

.677

11. 667

. 663

.658

.649

. 639

. 635

11. 630

.621

.612

.607

.602

11. 593

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

2^

3%

5

For latitude 46°' 6%

10 7^"

12M

15

1%

2V4

3%

5

For latitude 47°' 6%7Mi

10

IVA

15

1%

For latitude 48°' 6% 

10 ^

15 ^

Meridional 

distance

Inches

2.878

5.756

8. 633

11.511

14. 389

17. 267

23. 022

28. 778

34. 534

2.878

5.757

8.635

11.513

14. 392 f

17.270

23. 026

28. 784

34. 540

2. 879

5. 758 

8.636 

11. 515 

14. 394 

17. 273 

23. 030 

28. 789

34. 546

Ordinate of developed

parallel

Inch

0.000

.001

.002

.004

.007

.009

.017

.026

.038

0.000

.001

.002

.004

.007

.009

.017

.026

.038

0.000

.001 

.002 

.004 

.007 

.009 

.017 

.026

.038

6243° 2
92 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 3. Coordinates for the projection of maps, scale ^r^-sn~~Continued

Latitude of

parallel

0 /

48 00

02H

03%

05oiAl

10UK

15

17V^

18%

20 

22^

25 

26%

30

32K

35 * 

37^

40 

41K

45 

47^ 

48%

50

52^

55

56%

57^

49 00

§iy<i

03%

05

07^

10UK

15 2

17K

18%

20

22M

25

26%

27K

30

32J^

33%

35

37^

40

41%

42^

45

47^

48%

50

52M

55

5S^

50 00

Abscissas of developed parallel

Longitude interval

1'

Inches

1.546

.544

.544

.543

.542

1.541

.540

.540

.538

.537

.536

1. 536 

.534

.533 

.533

.532

1.531

.529

!528 

.527

1.526 

.525 

.524 

.523 

.522 

.521

1.521

.519

.518

.518

.517

1.516

.514

.514

.513

.512

1.511

.510

.509

.508

.507

.506

1.505

.504

.503

.502

.502

1.500

.499

.498

.498

.497

1.495

.495

.494

.493

.492

.491

1.490

.489

.488

.487

.486

1.485

IK'

Inches

1.932

.931

.930

.929

.927

1.926

.925

.924

.923

.921

.920

1.920 

' .918

.917 

.916

.915

1.913

.912

.910 

.909

1.907 

.906 

.905 

.904 

.902 

.902

1.901

.899

.898

.897

.896

1.894

.893

.892

.891

.890

1.888

.887

.887

.885

.883

.883

1.882

.880

.879

.878

.877

1.875

.874

.873

.872

.871

1.869

.868

.867

.866

.864

.863

1.863

.861

.860

.859

.858

1.856

«

Inches

3.864

.861

.860

.858

.855

3.852

.850

.849

.846

.842

.841

3.839 

.836

.833 

.831

.830

3.827

.824

!820 

.817

3.814 

.813 

.811 

.808 

.805 

.803

3.802

.798

.795

.794

.792

3.789

.786

.784

.783

.780

3.776

.775

.773

.770

.767

.765

3.764

.760

.757

.756

.754

3.751

.748

.746

.745

.741

3.738

.737

.735

.732

.729

.727

3.725

.722

.719

.717

.716

3.713

3M'

Inches

5. 796

.792

.789

.787

.782

5.778

.775

.773

.768

. 764

.761

5.759 

.754

.750 

.747

.745

5.740

.735

7OO

. too

.731 

.726

5.721 

.719 

.717 

.712 

.707 

.705

5.702

.698

.693

.691

.688

5.684

.679

.676

.674

.669

5.665

.662

.660

.655

.650

.648

5.646

.641

.636

.634

.631

5.626

.622

.619

.617

.612

5.607

.605

.602

.598

.593

.591

5.588

.583

.578

.576

.574

5.569

5'

Inches

7.729

.722

.719

.716

.710

7.704

.701

.697

.691

.685

.682

7.679 

.672

.666 

.663

.660

7.654

.647

.644 

.641 

.635

7.628 

.625 

.622 

.616 

.610 

.606

7.603

.597

.591

.587

.584

7.578

.572

.569

.565

.559

7. 553

.550

.546

.540

.534

.531

7.527

.521

.515

.511

.508

7.502

.496

.492

.489

.483

7.476

.473

.470

.464

.457

.454

7.451

.444

.438

.435

.432

7.425

Inches

11. 593

.583

.579

.574

.565

11. 555

.551

.546

.537

.527

.523

11. 518 

.509

.499 

.494

.490

11. 480

.471

.466 

.462 

.452

11. 443 

.438 

.433 

.424 

.414 

.410

11. 405

.395

.386

.381

.376

11. 367

.358

.353

.348

.339

11. 329

.324

.320

.310

.301

.296

11.291

.281

.272

.267

.262

11. 253

.243

.238

.234

.224

11. 215

.210

.205

.195

.186

.181

11. 176

.167

.157

.152

.147

11. 138

 Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

2^i

3%

5

For latitude 48° 6%

7}<£

10

12}^

15

1%

2V*?

3% 

5

For latitude 49° 6%

10 2

1 Ol^

15

1%

5 * 

For latitude 50° 6%

10 ' 2

.15

Meridional 

distance

Inches

2.879

5.758

8.636

11.515

14. 394

17. 273

23. 030

28.789

34. 546

2.879

5 7CQ . toy

8.638 

11.517

14. 397 

17. 276

23. 034

28. 794

34. 552

2.880 

5.760

8.639 

11. 519 

14. 399 

17. 279 

23. 039 

28. 799 

34. 558

Ordinate of developed 

parallel

Inch

0.000

.001

.002

.004

.007

.009

.017

.026

.038

0.000

.001

.002

.'007

. nno uuy

.017

.026

.037

0.000 

.001

.002 

.004 

.006 

.009 

.017 

.026 

.037
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 93

TABLE 3. Coordinates for the projection of maps, scale J^J-Q ~~ Continued

Latitude of

parallel

0 /

50 00

02H

03%

05

07^

10

UK

12H

15

18M

20

25 

26K

30

32H

33% 

35

40 

41K 

42^ 

45 

47M 

48M

 iO

52>3

55

56K

51 00

02^

03%

05

10

UK

15

17H

18%

20

22}^

25

26K

30

Wi

33%

35

37j^

40

41K

42H

45

47V

48%

50

52J^

55

56K

NYz

52 00

Abscissas of developed parallel

Longitude interval

1'

Inches

1.485

.484

.483

.482

.481

1.480

.479

.479

.477

.476

.475

1.475 

.473

.472 

.471

.471

1.470

.408

'.467 

.466

1.464 

.464 

.463 

.462 

.461 

.460

1 459

!458

.457

.456

.455

1.454

.453

.452

.451

.450

1.449

.448

.447

.446

.445

.444

1.444

.442

.441

.440

.440

1.438

.437

.436

.436

.434

1.433

.432

.432

.430

.429

.428

1.428

.426

.425

.425

.424

1.423

IK'

Inches

1.856

.855

.854

.853

.851

1.850

.849

.848

.847

.844

1.843 

.842

.840 

.839

.839

1.837

.835

Qor

. OOU

.834 

.832

1.830 

.830 

.829 

.827 

.826 

.825

1 824

!822

.821

.820

.819

1.818

.816

.815

.814

.813

1.811

.810

.809

.808

.806

.805

1.804

.803

.801

.800

.800

1.798

.796

.795

.795

.793

1.791

.791

.790

.788

.786

.786

1.7,45

.783

.781

.781

.780

1.778

w

Inches

3.713

.709

.708

.706

.703

3.700

.698

.697

.693

.690 

.688

3.687 

.684

.680 

.679

.677

3.674

.671

.669 

.667 

.664

3.661 

.659 

.658 

.655 

.051 

.650

3.648

.645

.642

.640

.638

3.635

.632

.630

.628

.625

3.622

.620

.619

.615

.612

.611

3.609

.606

.602

.601

.599

3.596

.593

.591

.589

' .586

3.583

.581

.579

.576

.573

.571

3.570

.566

.563

.561

.560

3.556

* 

Inches

5.569

.564

.562

.559

.554

5.550

.547

.545

.540

coc .000

.533

5.530 

.525

.521 

.518

.516

5.511

.506 

. 504 !soi

.496

5.491 

.489 

.487 

.482 

.477 

.474

5.472

.467

.462

.460

.457

5.453

.448

.445

.443

.438

5.433

.431

.428

.423

.418

.416

5.413

.408

.404

.401

.399

5.394

.389

.386

.384

.379

5.374

.372

.369

.364

.359

.357

5.354

.349

.344

.342

.339

5.334

5'

Inches

7.425

.419

.416

.412

.406

7.399

.396

.393

.387

ion 

. oou

.377

7.374 

.367

.361 

.358

.354

7.348

.341

ono

. GOO

.335 

.328

7.322 

.319 

.316 

.309 

.303 

.299

7.296

.290

.283

.280

.277

7.270

.264

.200

.257

.250

7.244

.241

.237

.231

.224

.221

7.218

.211

.205

.201

.198

7.192

.185

.182

.178

.172

7.165

.162

.159

.152

.146

.142

7.139

.132

.126

.123

.119

7.113

W

Inches

11. 138

.128

.123

.118

.109

11.099

.094

.090

.080

.070 

.065

11. 061 

.051

.041 

.036

.031

11. 022

.012 

. 007

.002 

10. 993

10. 983 

.978 

.973 

.964 

.954 

.949

10. 944

.934

.925

.920

.915

10. 905

.895

.890

.886

.876

10. 866

.861

.856

.846

.837

.832

10. 827

.817

.807

.802

.797

10. 787

.778

.773

.768

.758

10. 748

.743

.738

.728

.718

.713

10.709

.699

.689

.684

.679

10. 669

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

HK

2H

3%

5

For latitude 50° < 6K

7Ms

10

12M

15

IK

2V^

3%c

For latitude 51° < 6K

10

12V^ 15 i

IK

3%2 

5 

For latitude 52°' 6K

10 2

15 2

Meridional 

distance

Inches

2.880

5.760

8.639

11.519

14. 399

17. 279

23. 039

28. 799

34. 558

2.880

5.761

8.641 

11.521

14. 402 

17. 282

23. 043

28. 804

34. 564

2.881 

5.762

8.643 

11. 523 

14. 404 

17. 285 

23. 046 

28. 809 

34. 570

Ordinate of developed 

parallel

Inch

0.000

.001

.002

.004

.006

.009

.017

.026

.037

0.000

.001

.002 

004

!006 

.009

.016

.026

.037

0.000 

.001

.002 

.004 

.006 

.009 

.016 

.025 

.037
94 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale ^i-crFo

Latitude of

parallel

0 /

0 00

02^

03%

05

07^

10

11%

12H

15

17^

18%

20yp/i

25 

26%

27^

30

32^

33% 

35 

37M

40 

41% 

42H 

45 

47^ 

48%

50

52K

55

56%

57H

1 00

02^ 

03%

05

07H

10

11%

12^

15

17^

18%

20

22>S

25

26%

27^

30

32J4

33M

35

37M

4041i/ ^tl?4

42J4

45

47H

48%

50

52>i

55

56%

57>i

2 00

Abscissas of developed parallel

Longitude interval

1'

Inches

3.043

.043

.043

.043

.043

3.043

.043

.043

.043

.043

.043

3.043

.043

.043 

.043

.043

3.043

.043

.043 

.043 

.043

3.043 

.043 

.043 

.043 

.043 

.043

3

/viq

. \r±o

.043

.043

.043

.043

3.043

.043 

.043

.043

.043

3.043

.043

.043

.043

.043

.043

3.043

.043

.0-13

.043

.043

3.042

.042

.042

.042

.042

3.042

.042

.042

.042

.042

.042

3.042

.042

.042

.042

.042

, 3.042

1%'

Inches

3.804

.804

.804

.804

.804

3.804

.804

.804

.804

.804

.804

3.804

.804

.804 

.804

.804

3.804

.804

804 

.'804 

.804

3.804 

.804 

.804 

.804 

.804 

.804

3.804

.804

.804

.804

.804

3.804

.804 

2 .804

.804

.804

3.804

.804

.804

.803

.803

.803

3.803

.803

.803

.803

.803

3.803

.803

.803

.803

.803

3.803

.803

.803

.803

.803

.802

3.802

.802

.802

.802

.802

3.802

2^'

Inches

7.609

.609

.609

.609

.609

7.609

.609

.609

.609

.609

.609

7.609

.609

.609 

.609

.609

7.609

.608

.608 

.608 

.608

7.608 

.608 

.608 

.608 

.608 

.608

7.608

.608

.608

.608

.608

7.608

.608 

.607

.607

.607

7.607

.607

.607

.607

.607

.607

7.607

.607

.606

.606

.606

7.606

.606

.606

.606

.606

7.606

.605

.605

.605

.605

.605

7.605

.605

.605

.604

.604

7.604

3%'

Inches

11.413

.413

.413

.413

.413

11. 413

.413

.413

.413

.413

.413

11. 413

.413

.413 

.413

.413

11. 413

' .413 

. rtlO ill 1*

.413 

.413

11.412 

.412 

.412 

.412 

.412 

.412

11. 412

.412

.412

.412

.412

11.411

.411 

.411

.411

.411

11.411

.411

.411

.410

.410

.410

11. 410

.410

.410

.410

.409

11. 409

.409

.409

.409

.409

11. 408

.408

.408

.408

.408

.407

11. 407

.407

.407

.407

.407

11. 406

5'

Inches

15. 217

.217

.217

.217

.217

15. 217

.217

.217

.217

.217

.217

15. 217

.217

.217 

.217

.217

15. 217

.217

.217 

.217 

.217

15. 217 

.210 

.216 

.216 

.216 

.216

15. 216

.216

.216

.215

.215

15. 215

.215 

.215

.215

.215

15. 214

.214

.214

.214

.214

.214

15. 213

.213

.213

.213

.213

15. 212

.212

212

.212

.211

15. 211

.211

.211

.210

.210

.210

15. 210

.209

.209

.209

.209

15. 208

7H'

Inches

22. 826

.826

.826

.826

.826

22. 826

.826

.826

.826

.826

.826

22. 826

.826

.826 

.826

.826

22. 826

.825

DOC

. O/D

.825 

.825

22. 825 

.825 

.825 

.824 

.824 

.824

99 till, S9d O£rt

.824

.823

.823

.823

22. 823

BOQ 

. OiO

.822

.822

.822

22. 822

.821

.821

.821

.820

.820

22. 820

.820

.819

.819

.819

22. 819

.818

.818

.818

.817

22. 817

.816

.816

.816

.815

.815

22. 815

.814

.814

813

.813

22. 812

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%VA

3%

5

For latitude 0° < 6%

VH

10

12M

15

1%

VA

3%

5

For latitude 1° < 6% 

7K

10

WA

15

1% 

2X2

3% 

5 

For latitude 2° 6% 

lYi 

10 

12^ 

,15

Meridional 

distance

Inches

3.779

7.557

11. 336

15. 114

18. 893

22. 672

30. 229

37. 786

45. 344

3.779

7.557

11.336

15. 115

18. 893 

22. 672

30. 229

37. 787

45. 344

3.779 

7.557

11.336 

15. 115 

18. 893 

22. 672 

30.229 

37. 787 

45.344

Ordinate of developed 

parallel

Inch

0.000

.000

.000

.000

.000

.000

.000

.000

.000

0.000

.000

.000

000 !ooo

.000

.001

.001

.002

0.000 

.000

.000 

.000 

.001 

.001 

.001 

.002 

.003 \
TABLES FOR CONSTRUCTION OF POLYCONTC PROJECTIONS 95

TABLE 4. Coordinates for the projection of maps, scale -j^-J-g-j Continued

Latitude of

parallel

0 /

2 00<BH

03%

05

07^

10

11%

123/2

15

ny>

18%

20 

22K 

25 

26% 

273-3

30

33% 

35

40

41% 

45/2

48%

50

62M

55

56%

3 00

02H

03%

05

073^

10

11%

15

17}^

18%

20

22^

25

26%

30

32J^

33%

35

37/4

40

41%

45

47M

48%

50

52%

55

66%

573^

4 00

Abscissas of developed parallel

Longitude interval

1'

/nc/ies

3.042

.042

.042

.041

.041

3.041

.041

.041

.041

.041

.041

3.041 

.041 

.041 

.041 

' .041

3.041 

.041

rvn

. Urtl

.040 

.040

3.040

.040 

.040 

.040 

.040

.040

3.040

.040

.039

.039

.039

3.039

.039

.039

.039

.039

3.039

.039

.039

.039

.039

.038

3.038

.038

.038

.038

.038

3.038

.038

.038

.038

.037

3.037

.037

.037

.037

.037

.037

3.037

.037

.036

.036

.036

3.036

ii/C' *?*

Inches

3.802

.802

.802

.802

.802

3.802

.802

.802

.801

.801

.801

3.801 

.801 

.801 

.801 

.801

3.801 

.801

QA1 . olU

.801 

.800

3.800

.800 

.800 

.800 

.800

.800

3.800

.800

.799

.799

.799

3.799

.799

.799

.799

.799

3.799

.799

.798

.798

.798

.798

3.798

.798

.798

.798

.798

3.797

.797

.797

.797

.797

3.797

.797

.796

.796

.796

.796

3.796

.796

.796

.795

.795

3.795

Inches

7.604

.604

.604

.604

.604

7.603

.603

.603

.603

.003

.603

7. 602 

.602 

.602 

.602 

.002

7.602 

.601 

.601

.601 

.601

7.601

.600 

.600 

.600 

.600

.600

7.600

.599

.599

.599

.599

7.598

.598

.598

.598

.598

7.597

.597

.597

.597

.596

.596

7.596

.596

.595

.595

.595

7.595

.594

.594

.594

.594

7.593

.593

.593

.593

.592

.592

7.592

.591

.591

.591

.591

7.590

Inches

11. 406

.406

.406

.406

.405

11. 405

.405

.405

.404

.404

.404

11. 404 

.403 

.403 

.403 

.403

11.402 

.402 

.402

.402 

.401

11.401

.401 

.400 

.400 

.400

.400

11.399

.399

.398

.398

.398

11. 398

.397

.397

.397

.396

11. 396

.396

.395

.395

.394

.394

11. 394

.393

.393

.393

.393

11. 392

.391

.391

.391

.390

11. 390

.390

.389

.389

.388

.388

11.388

.387

.387

.386

.386

11. 386

5' o

Inches

15. 208

.208

.208

.207

.207

15. 207

.206

.206

.206

. 205

.205

15. 205 

.205 

.204 

.204 

.204

15. 203 

.203 

. 202

.202 

.202

15.201

.201 

.201 

.200 

.200

.'199

15. 199

.198

.198

.198

.197

15/197

.196

.196

.196

.195

15. 195

.194

.194

.193

.193

.192

15. 192

.191

.191

.190

.190

15. 189

.189

.188

.188

.187

15. 187

.186

.186

.185

.184

.184

15. 184

.183

.182

.182

.181

15. 181

w

Inches

22.812

.812

.812

.811

.811

22. 810

.810

.809

.809

.808 1

.808

22. 808 

.807 

.806 

.806 

.805

22. 805 

.804 

.804

.803 

.802

22. 802

.801 

.801 

.800 

.799

.799

22. 799

.798

.797

.796

.796

22. 795

.794

.794

.794

.793

22. 792

.791

.791

.790

.789

.788

22. 788

.787

.786

.786

.785

22. 784

.783

.782

.782

.781

22. 780

.779

.779

.778

.777

.776

22. 776

.774

.773

.773

.772

22. 771

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

( 1%

23i

3%

5

For latitude 2°. 6%7 i/.

10

15 ^

f 1%

3% 

5 

For latitude 3°< 6%

10 i

15

[1%

23/2

3%

5 

For latitude 4°< 6%

io/2

15

Meridional 

distance

Inches

3.779

7.557

11.336

15. 115

18. 893

22. 672

30. 229

37. 787

45. 344

3.779

7 f . OO/ ^^T

11.336 

15. 115 

18. 894 

22. 673 

30. 230

37.788 

45. 345

3.779 

7.558

11. 337

15. 115 

18. 894 

22. 673 

30. 231

37. 788 

45. 346

Ordinato of developed

parallel

Inch

0.000

.000

.000

.000

.001

.001

.001

.002

.003

0.000

.000

.000 

.001 -.001

.001 

.002

.004 

.005

0.000 

.000

.000

.001 

.001 

.002 

.003

.005 

.007
96 TABLES FOR CONSTRtJCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale Continued

Latitude of

parallel

0 /

4 00

02^

03%

05

07M

10

ll/^ \iy

15

17)4 

18%

20

25 2 

26%

27^

30

33%

35

40

41%

45 2 

47^

48%

50

55 2

56% yiy-i

5 00

02J^

03%

05

07 J4

10

11%

12/-<j

15

17M

18%

20

22M

25

26%

27>i

30

32J4

33%

35

37K

40

41%

42K

45

47H

48%

60

52^

55

66%

57.J4

6 00

Abscissas of developed parallel

Longitude interval

1'

Inches

3.036

.036

.036

.036

.036

3.036

.035

.035

.035

fiqc

. UOO

.035

3.035 

.035 

.035 

.034 

.034

3.034 

.034

034

!034 

.034

3.033

.033 

.033

.033 

.033

.033

3.033

.033

.032

.032

.032

3.032

.032

.032

.032

.031

3.031

.031

.031

.031

.031

.031

3.030

.030

.030

.030

.030

3.030

.029

.029

.029

.029

3.029

.029

.029

.028

.028

.028

3.028

.028

.027

.027

.027

3.027

1%'

Inches

3.795

.795

.795

.795

.795

3.794

.794

.794

.794

.794 

.794

3.794 

.793 

.793 

.793 

.793

3.793 

.793

. 792

!792 

.792

3.792

.792 

.792

.791 

.791

.791

3.791

.791

.790

.790

.790

3.790

.790

.790

.790

.789

3.789

.789

.789

.789

.788

.788

3.788

.788

.787

.787

.787

3.787

.787

.787

.786

.786

3.786

.786

.786

.785

.785

.785

3.785

.785

.784

.784

.784

3.784

PA'

Inches

7.590

.590

.590

.590

.589

7.589

.589

.588

. .588

. 588 

.587

7.587 

.587 

.586 

.586 

.586

7.585 

.585

CQC

. ooo 

.585 

.584

7.584

.584 

.583

.583 

.582

.582

7.582

.581

.581

.581

.580

7.580

.580

.579

.579

.579

7.578

.578

.578

.577

.577

.576

7.576

.575

.575

.575

.574

7.574

.573

.573

.573

.572

7.572

.572

.571

.571

.570

.570

7.570

.569

.568

.568

.568

 7.567

3%'

Inches

11. 386

.385

.385

.385

.384

11. 383

.383

.383

.382

QQ1

. Ool

.381

11. 381 

.380 

.380 

.379. 

.379

11. 378 

.378 377

!377 

.376

11. 376

.375 

.375

.374 

.374

.373

11. 373

.372

.371

.371

.371

11. 370

.369

.369

.369

.368

11. 367

.367

.366

.366

.365

.364

11. 364

.363

.362

.362

.362

11. 361

.360

.360

.359

.359

11.358

.357

.357

.356

.355

.355

11.354

.354

.353

.352

.352

11.351

5'o

Inches

15. 181

.180

.180

.179

.178

15. 178

.177

 .177

.176

.175 

.175

15. 174 

.174 

.173 

.172 

.172

15. 171 

.170

.170

.169 

.168

15. 167

.167 

.167

.166 

.165

.164

15.164

.163

.162

.161

.161

15. 160

.159

.159

.158

.157

15. 157

.156

.155

.154

.153

.153

15. 152

.151

.150

.149

.149

15. 148

.147

.146

.146

.145

15. 144

.143

.143

.141

.140

.140

15. 139

.138

.137

.136

.136

15. 135

«f

Inches

22. 771

.770

.769

.769

.768

22. 766

' .766

.765

.764

.763 

.762

22. 762 

.760 

.759 

.758 

.758

22.756 

.755

fee

'.754 

.753

22. 751

.751 

.750

.748 

.747

.746

22. 746

.744

.743

.742

.741

22. 740

.739

.738

.737

.736

22. 734

.733

.733

.731

.730

.729

22. 728

.726

.725

.724

.723

22. 722

.720

.720

.719

.717

22. 716

.715

.714

.712

.710

.710

22. 709

.707

.705

.705

.704

22. 702

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

2M

3%

5

For latitude 4°' 6%

7/^

10

,15 2

f 1%

3% 

5 

For latitude 5°< 6%

10 2

15

U%

21^

3%

5 

For latitude 6° 6%

10 2

15 2

Meridional 

distance

Inches

3.779

7.558

11. 337

15. 115

18. 894

22.673

30.231

37. 788

45. 346

3.779

7.558 

11. 337 

15. 116 

18.894 

22. 674 

30.231'

37. 789 

45. 347

3.779

7.558

11. 337

15. 116 

18. 895

22. 674 

30.233

37. 791

45. 349

Ordinate of developed 

parallel

Inch

0.000

.000

.000

.001

.001

.002

.003

.005

.007

0.000

.000 

.001 

.001 

.001 

.002 

.004

.006 

.009

0.000

.000

.001

.001 

.002

.003 

.005

.007

.010
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 97 

TABLE 4. Coordinates for the projection of maps, scale -z-jfojTs Continued

Latitude of

parallel

0 /

6 00

02^

05 *

07^

10

UKv&A

15

18$

20

25 

WA

30 

32^

35* 

37^

40

45

47^

50

52^

55

56K

57^

7 00

02^

03J4

05

07^

10

11}^ \iy

15

17/"i

18^

20

22^

25

26K

30

32^

33$4

35

37^

40

41K

42^

45

47H

48%

5052J-I

65

56K

57>^

8 00

Abscissas of developed parallel

Longitude interval

1'

Inches

3.027

.027

.027

.027

.026

3.026

.026

.026

.026

AOK .1)25 

.025

3.025 

.025

.025 

.024 

.024

3.024 

.024

.024

.024 

.023

3.023

.023 

.023

.023

.022

.022

3.022

.022

.021

.021

.021

3.021

.021

.021

.020

.020

3.020

.020

.020

.019

.019

.019

3.019

.019

.018

.018

.018

3.018

.017

.017

.017

.017

3.017

.016

.016

.016

.016

.015

3.015

.015

.015

.015

.014

3.014

Inches

3.784

.783

.783

.783

.783

3.783

.782

.782

.782 

. 789 IO*

.781

3.781 

.781

.781 

.781 

.780

3.780 

.780

780

!779 

.779

3.779

.779 

.778

.778

.778

.778

3.778

.777

.777

.777

.777

3.776

.776

.776

.776

.775

3.775

.775

.774

.774

.774

.774

3.773

.773

.773

.773

.772

3.772

.772

.771

.771

.771

3.771

.770

.770

.770

.769

.769

3.769

.769

.768

.768

.768

3.768

Ol^C' lYi,

Inches

7.567

.567

.566

.566

.566

7.565

.565

.564

.564

CfiO

. 000

.563

7.563 

.502

.561 

.561 

.561

7.560 

.560

.559

.559 

.558

7.558

.557 

.557

.556

.556

.555

7.555

.554

.554

.553

.553

7.552

.552

.551

.551

.550

7.550

.549

.549

.548

.548

.547

7.547

.546

.546

.545

.645

7.544

.543

.543

.543

.542

7.541

.541

.540

.540

.539

.439

7.538

.537

.537

.536

.536

7.535

Inches

11. 351

.350

.350

.349

.348

11. 348

.347

.347

.346

.345 

.344

11. 344 

.343

.342 

.342 

.341

11. 340 

.339

.339

.338 

.337

11. 336

.336 

.335

.335

.334

.333

11. 333

.332

.331

.330

.330

11. 329

.328

.327

.327

.326

11. 325

.324

. .323

.322

.321

.321

11. 320

.319

.318

.318

.317

11. 316

.315

.315

.314

.313

11.312

.311

. 311

.310

.308

.308

11. 307

.300

.305

.305

.304

11. 303

5'

Inches

15. 135

.134

.133

.132

.131

15. 130

.129

.129

.128

.126

15. 125 

.124

.123 

.122 

.122

15. 120 

.119

. 118 no

.118 

.117

15. 115

.115 

.114

.113

.111

.111

15. 110

.109

.107

.107

.106

15. 105

.103

.103

.102

.101

15. 099

.099

.098

.097

.095

.095

15. 094

.093

.091

.090

.090

15. 088

.087

.080

.085

.084

15. 082

.082

.081

.079

.078

.077

15. 070

.075

.073

.073

.072

15. 070

,

Inches

22. 702

.700

.699

.699

.697

22. 695

.694

.093

.691

. 690 

.689

22. 688 

.686

.684 

.683 

.682

22.681 

.679

.678

.677 

.675

22. 673

.672 

.071

.609

.667

.660

22. 065

.663

.661

.600

.059

22. 657

.055

.654

. 653

.651

22. 649

.648

.647

.645

.643

.642

22. 641

.640

.637

.035

.034

22. 632

.630

.629

.028

.626

22. 024

.023

.621

.619

.617

.616

22. 615

.612

.610

.609

.608

22. 606

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

i

IKlYi

3M

5

For latitude 6°< 6K"lYi

10

,15

IK

5 *

For latitude 7°' 6K

10 2

,15

IK

5 

For latitude 8°< 6K

10 2

15 2

Meridional 

distance

Inches

3.779

7.558

11.337

15. 116

18. 895

22. 674

30. 233

37. 791

45. 349

3.779

7. 558

11.338 

15.117

18. 896 

22. 675 

30. 234

37. 792 

45. 351

3.779 

7.559

11.338

15. 118 

18.897

22. 670

30. 235

37. 794

45. 353

Ordinate of developed

parallel

Inch

0.000

.000

.001

.001

.002

.003

.005

.007

.010

0.000

.000

.001 

001

!002 

.003 

.005

.008 

.012

0.000 

.000

.001

.001 

.002

.003

.006

.010

.014
98 TABLES FOE CONSTRUCTION OF POLYCONIC PROJECTIONS 

TABLE 4. Coordinates for the projection of maps, scale -j-^tstf Continued

Latitude of

parallel

0 ,

8 00

02^

03%

05

WA

10

11%

12^

15

17^

18%

20 

22^

25 

26%

"ilY-i.

30

32J^

33% 

35 

37^

40 

41% 

42}| 

45yiVi

48%

50

52}i

55

56%

57>i

9 00

02^

03%

05

07^

10

11%

12J4

15

WA

18%

20

22}^

25

26% 27A1

30

32J^

33%

35

37^

40

41%

42>i

45

XlYi

48%

50

52^

55

56%

57>£

10 00

Abscissas of developed parallel

Longitude interval

1'

Inches

3.014

.014

.014

.013

.013

3.013

.013

.013

.012

.012

.012

3.012 

.011

.011 

.011

.011

3.010

.010

.010 

.010 

.009

3.009 

.009 

.009 

.008 

.008 

.008

3.008

.007

.007

.007

.007

3.006

.006

.006

.006

.005

3.005

.005

.005

.004

.004

.004

3.003

.003

.003

.003

.002

3.002

.002

.001

.001

.001

3.001

.000

.000

.000

2.999

.999

2.999

.999

.998

.998

.998

2.998

1%'

Inches

3.768

.767

.767

.767

.766

3.766

.766

.766

.765

.765

.765

3.764 

.764

.764 

.764

.763

3.763

.762

. 762 

.762 

.762

3.761 

.761 

.761 

.760 

.760 

.760

3 7fin . iDU

.759

.759

.758

.758

3.758

.757

.757

.757

.757

3.756

.756

.756

.755

.755

.755

3.754

.754

.753

.753

.753

3.753

.752

.752

.752

.751

3.751

.750

.750

.750

. 749

.749

3.749

.748

.748

.748

.748

3. 747

Ol "

lyi

Inches

7.535

.534

.534

.534

.533

7. 532

.532

.531

.531

.530

.529

7. 529 

.528

.527 

.527

.527

7.526

.525

. 525 

.524 

.523

7.522 

.522 

.522 

.521 

.520 

.520

7. 519

.518

.517

.517

.517

7. 516

.515

.514

.514

.513

7.512

.512

.511

.510

.510

.509

7.509

.508

.507

.506

.508

7.505

.504

.504

.503

.502

7. 501

.501

.501

.500

.499

.498

7.498

.497

.496

.495

 .495

7.494

o- / /

o/.^

Inches

11. 303

.302

.301

.300

.299

11. 298

.298

.297

.296

.295

.294

11. 293 

.292

.291 

.290

.290

11. 289

.287

OQ7

. LQi

.286 

.285

11. 284 

.283 

.282 

.281 

.280 

.279

11. 279

.277

.276

.275

.275

11. 274

.272

.272

.271

.270

11. 26S

.208

.267

.266

.264

.264

11. 263

.262

.260

.260

.259

11. 258

.256

.256

.255

.254

11. 252

.251

.251

249

.248

.247

11. 247

.245

.244

243

.242

11. 241

Inches

15. 070

.069

.068

.067

.066

15. 064

.063

.063

.061

.059

.059

15. 058 

.056

.055 

.054

.053

15. 051

.050

.049 

.048 

.047

15. 045 

.044 

.043 

.042 

.040 

.039

1 i\ OQQ J.O. UOo

.036

.035

.034

.033

15.031

.030

.029

.028

.026

15.024

.024

.023

.021

. 019

.018

15. 017

.016

.014

.013

.012

15.010

.008

.007

.007

.005

15. 003

.002

.001

14. 999

.997

. 996

14. 995

.993

.992

.991

.990

14. 988

~Y-i

Inches

22. 606

.603

.602

.601

.599

22. 596

.595

.594

.592

. 589

.588

22. 587 

.585

.582 

.581

.580

22. 577

.575

.574 

.572 

.570

22. 567 

.506 

.565 

.562 

.560 

.559

22. 557

.555

.552

.551

.550

22. 547

.545

.543

.542

.539

22. 537

.535

.534

.531

.529

.527

22. 526

.523

.521

.519

.518

22. 515

.513

.511

.510

.507

22. 504

.503

.502

.499

.496

.494

22. 493

.490

.487

.486

.485

22. 482

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

f 1%

2M

3M

5.

For latitude 8° 6%

m10

12H

,15

{ 1%

2H

3% 

5

For latitude 9° 6% "lYi

10

12H

,15

1% 

2H

3% 

5 

For latitude 10° 6% 

7M 

10 

12^ 

15

Meridional 

distance

Inches

3.779

7.559

11. 338

15. 118

18. 897

22. 676

30. 235

37. 794

45. 353

3.780

7.559

11. 339 

15. 118

18. 898 

22. 678

30. 237

37. 796

45. 356

3.780 

7.560

11. 339 

15. 119 

18. 899 

22. 679 

30. 238 

37. 798 

45. 358

Ordinate of developed

parallel

Inch

0.000

.000

.001

.001

.002

.003

.006

.010

.014

0.000

.000

.001 

.002

.003 

.004

.007

.011

.015

0.000 

.000

.001 

.002 

.003 

.004 

.008 

.012 

.017
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 99

TABLE 4. Coordinates for the projection of maps, scale 77-0-57 Continued

Latitude of

parallel

0 /

10 00

02 J^

03%

05

07M

1011%

15

1' 7*

18%

20

25 ^ 

26%

27^

30

32s/

35 4

40 

41%

45 2 

48%2

50

65

66%

11 00

02^

03%

0507*4

10

11%

12}^

15

17V*

18%

20

22 J*<

25

26%

30

32}^

33%

35

37H

40

41%

42^

45

47H

48%

50

52^

65

66%

67J^

12 00

Abscissas of developed parallel

Longitude interval

1'

/ncAes

2.998

.997

.997

.997

.996

2.996

.996

.996

.995

.995

.995

2.995 

.994

.994 

.994

.993

2.993

.993

!992 

.992

2.991 

.991 

.991 

.990 

.990 

.990

2.990

.989

.989

.989

.988

2.988

.988

.987

.987

.987

2.986

.986

.986

.985

.985

.985

2.985

.984

.984

.983

.983

2.983

.982

.982

.982

.982

2.981

.981

.981

.980

.980

.979

2.979

.979

.978

.978

.978

2.977

1%'

Inches

3.747

.747

.746

.746

.746

3.745

.745

.745

.744

.744

.743

3.743 

.743

.742 

.742

.742

3.741

.741

.740 

.740 

.740

3.739 

.739 

.739 

.738 

.738 

.737

3.737

.737

.736

.736

.735

3.735

.734

.734

.734

.733

3.733

.733

.732

.732

.731

.731

3.731

.730

.730

. .729

.729

3.728

.728

.728

.727

.727

3.726

.726

.726

.725

.725

.724

3.724

.724

.723

.723

.722

3.722

«

Inches

7.494

.493

.493

.492

.491

7.490

.490

.489

.488

.487

.487

7.486 

.485

.484 

.484

.483

7.482

.481

.481 

.480 

.479

7.478 

.478 

.477 

.476 

.475 

.475

7.474

.473

.472

.471

.471

7.470

.469

.468

.468

.467

7.466

.465

.465

.463

.462

.462

7.461

.460

.459

.459

.458

7.457

.456

.455

.455

.454

7.453

.452

.451

.450

.449

.449

7.448

.447

.446

.445

.445

7.444

3%'

Inches

11. 241

.239

.239

.238

.237

11. 235

.234

.234

.232

.231

.230

11. 229 

.228

.226 

.226

.225

11. 223

.222

.221 

.220 

.219

11. 217 

.216 

.216 

.214 

.213 

.212

11. 211

.210

.208

.207

.206

11. 205

.203

.202

.202

.200

11. 199

.198

.197

. .195

.194

.193

11. 192

.190

.189

.188

.187

11. 186

.184

.183

.182

.181

11. 179

.178

.177

.176

.174

.173

11. 172

.171

.169

.168

.167

11. 165

5'

Inches

14. 988

.986

.985

.984

.982

14. 980

.979

.978

.976

.974

.973

14. 972 

.970

.968 

.967

.966

14. 964

.962

(101

. UO-l

.960 

.958

14.956 

.955 

.954 

.952 

.950 

.949

14 (U8 l:t. trco

.946

.944

.943

.942

14. 940

.938

.937

.936

.933

14. 931

.930

.929

.927

.925

.924

14. 923

.921

.918

.917

.916

14.914

.912

.911

.910

.907

14. 905

.904

.903

.901

.899

.897

14. 896

.894

.892

.891

.889

14. 887

W

Incites

22. 482

.479

.478

.476

.473

22. 470

.469

.467

.464

.461

.460

22. 459 

.456

.452 

.451

.450

22. 447

.444

.442 

.440 

.437

22. 435 

.433 

.431 

.428 

.425 

.424

22. 422

.419

.416

.414

.413

22. 410

.406

.405

.403

.400

22. 397

.395

.394

.390

.387

.386

22. 384

.381

.378

.376

.374

22. 371

.368

.366

.364

.361

22. 358

.356

.354

.351

.348

.346

22. 344

.341

.338

.336

.334

22. 331

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

IK

3%

5

For latitude 10° 6K

7</2

10

12/-2

15

1%

2!/£

3%

For latitude 11°' 6%

10 2

i 91 /

,15

US3% 

5 

For latitude 12° 6%

io/2

,15

Meridional 

distance

Inches

3.780

7.560

11. 339

15. 119

18. 899

22. 679

30. 238

37. 798

45. 358

3.780

7. 560

11. 840 

15. 120

18. 900 

22. 680

30. 240

37. 801

45. 361

3.780

7.561

11. 341 

15. 121 

18. 902 

22. 682 

30. 243 

37. 804 

45. 364

Ordinnto of developed 

parallel

Inch

0.000

.000

.001

.002

.003

.004

.008

.012

.017

0.000

no i . \J\JL

.001

Ann 

. UUi

.003

!oos

mi . U1O

019

0.000 

.001

.001 

.002 

.004 

.005 

.009 

.014 

.020

»
100 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale -ZT&TTTS Continued

Latitude of

parallel

0 /

12 00

02^

03%

05

07^

10

ll/^

12J-<

15

17J-6

18%

20

25 2

yiy.

30 

32H

33%

35

40 

41%

45 2 

47^ 

48%

50

WA

55

56%

57^

13 00

wAl

03%

05

07^

10

11%

^12)^

15

17J^

18%

20

22^

25

26%

27J-i

30

323^

33%

35

37H

40

41%

42J-3

45

47V6

48%

50

52^

55

66%

67^

14 00

Abscissas of developed parallel

Longitude interval

1'

JncAes

2. 977

.977

.977

.977

.976

2.976

.975

.975

.975

.974

.974

2.974 

.973

.973 

.973

.972

2.972 

.971

.971

.971 

.970

2.970 

.970 

.969 

.969 

.968 

.968

2.968

.967

.967

.967

.966

2.966

.966

.965

.965

.965

2.964

.964

.964

.963

.963

.962

2.962

.961

.961

.961

.960

2.960

.959

.959

.959

.958

2.958

.958

.957

.957

.956

.956

2.956

.955

.955

.954

.954

2.954

1%'

Inches

3.722

.721

.721

.721

.720

3.719

.719

.719

.718

.718

.717

3.717 

.717

.716 

.716

. 715

3.715 

.714

.714

.714 

.713

3.712 

.712 

.712 

.711 

.711 

.710

3.710

.709

.709

.708

.708

3.708

.7,07

.707

.706

.706

3.705

.705

.704

.704

.703

.703

3.703

.702

.701

.701

.701

3.700

.699

.699

.699

.698

3.697

.697

.697

.696

.695

.695

3.695

.694

.693

.693

.693

3.692

w

Inches

7.444

.442

.442

.441

.440

7.439

.438

.438

.437

.435

.435

7.434 

.433

.432 

.431

.431

7.430 

.428

.428

.427 

.426

7.425 

.424 

.424 

.422 

.421 

.421

7.420

.419

.417

.417

.416

7.415

.414

.413

.413

.411

7.410

.409

.409

.408

.406

.406

7.405

.404

.402

.402

.401

7.400

.398

.398

.397

.396

7.395

.394

.393

.392

.391

.390

7.390

.388

.387

.386

.386

7.384

* 

Inches

11. 165

.164

.163

.162

.160

11. 158

.158

.157

.155

.153

.152

11. 151 

.150

.148 

.147

.146

11.144 

.143

.142

.141 

.139

11. 137 

.136 

.135 

.134 

.132 

.131

11. 130

.128

.126

.125

.124

11. 123

.121

.120

.1.19

.117

11.115

.114

.113

.111

.109

.108

11. 107

.106

.104

.103

.102

11.100

.098

.097

.096

.094

11. 092

.091

.090

.088

.086

.085

11. 084

.082

.080

.079

.078

11. 076

5'

Inches

14.887

.885

.884

.883

.880

14. 878

.877

.876

.873

.871

.870

14. 869 

.866

.864 

.863

.862

14. 859

.857

.856

.854 

.852

14. 850

.848 

.847 

.845 

.842 

.841

14.840

.837

.835

.834

.832

14. 830

.828

.826

.825

.823

14.820

.819

.818

.815

.813

.811

14. 810

.807

.805

.804

.802

14.800

.797

.796

.795

.792

14. 790

.788

.787

.784

.782

.780

14. 779

.776

.774

.772

.771

14. 769

« 

Inches

22. 331

.327

.326

.324

.320

22. 317

.315

.313

.310

.306

.305

22. 303 

.299

.296 

.294

.292

22.289 

.285

.283

.281 

.278

22. 274 

.273 

.271 

.267 

.264 

.262

22. 260

.256

.252

.251

.249

22. 245

.241

.240

.238

.234

22. 230

.228

.226

.223

.219

.217

22. 215

.211

.207

.205

.204

22.200

.196

.194

.192

.188

22.184

.182

.180

.176

.172

.170

22. 169

.165

.161

.159

.157

22. 153

Ordinates of developed parallel 

and, meridional distances

Latitude and longitude intervals

,

IJi

2H

3%

5

For latitude 12°' 6%71^

10

12}^

15

1%Q] /

3% 

5

For latitude 13°' 6%

10

12V£

15

2$

3% 

5 

For latitude 14°< 6%10 2

15 2

Meridional 

distance

Inches

3.780

7.561

11. 341

15. 121

18. 902

22.682

30. 243

37.804

45.364

3.781

7 'Sfil

ll! 342

15 122

is! 903

30! 245

37. 806

45. 367

3.781 

7.562

11. 343 

15.124 

18. 905 

22.686 

30. 247 

37.809 

45. 371

Ordinate of developed 

parallel

Inch

0.000

.001

.001

.002

- .004

.005

.009

.014

.020

0.000 nni UUl

.001

IY19 

. uv/z

.004

nnc 

. UUO

.010

.015

.022

0.000 

.001

.002 

.003 

.004 

.006 

.010 

.016 

.023
TABLES FOE CONSTRUCTION OF POLYCONIC PROJECTIONS 101

TABLE 4. Coordinates for the projection of maps, scale Tzfav Continued

Latitude of

parallel

0 /

14 00

02H

03%

05

07^

10

11%

15

17^

18^

20 

22^

25 

26%

27H

30

33^

35

40 

41% 

42^ 

45

48%2

50

52^

65

56%

57^

15 00

02M>

03%

05

07M

10

11%

12^

15

17J>*

18%

20

22j^

25

26%

30

32>i

33%

35

37^

40

41%

42)^

45

47H

48%

50

52^

55

56%

16 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.954

.953

.953

.953

.952

2.952

.951

.951

.950

.950

.950

2.949 

.949

.948 

.948

.948

2.947

.947

!946 

.946

2.945 

.944 

.944 

.944 

.943 

.943

2.943

.942

.942

.941

.941

2.940

.940

.940

.939

.939

2.938

.938

.938

.937

.936

.936

2.936

.935

.935

.934

.934

2.934

.933

.933

.932

.932

2.931

.931

.931

.930

.929

.929

2.929

.928

.928

.927

.927

2.926

1%'

Inches

3.692

.691

.691

.691

.690

3.689

.689

.689

.688

.687

.687

3.687 

.686

.685 

.685

.685

3.684

.683

.683 

.683 

.682

3.681 

.681 

.681 

.680 

.679 

.679

3.678

.678

.677

.677

.676

3.676

.675

.675

.674

.673

3.673

.672

.672

.671

.671

.670

3.670

.669

.668

.668

.668

3.667

.666

.666

.665

.665

3.664

.664

.663

.662

.662

.661

3.661

.660

.659

.659

.659

3.658

*

Inches

7.384

.383

.382

.381

.380

7.379

.378

.378

.376

.375

.374

7.373 

.372

.371 

.370

.369

7.368

.367

.366 

.365 

.364

7.362 

.362 

.361 

.360 

.358 

.358

7 357

'.355

.354

.353

.353

7.351

.350

.349

.348

.347

7.345

.345

.344

.343

.341

.340

7.340

.338

.337

.336

.335

7.334

.332

.332

.331

.329

7.328

.327

.326

.325

.323

.322

7.322

.320

.319

.318

.317

7.31C

3%'

Inches

11. 076

.074

.073

.072

.070

11. 068

.067

.066

.064

.062

.061

11. 060 

.058

.056 

.055

.054

11. 052

.050

. 049 

!046

11.044 

.043 

.042 

.039 

.037 

.036

11. 035

.033

.031

.030

.029

11. 027

.025

.024

.023

.020

11.018

.017

.016

.014

.012

.011

11.009

.007

.005

.004

.003

11.001

10. 999

.997

.996

.994

10. 992

.991

.990

.987

.985

.984

10.983

.981

.978

.977

.976

10. 974

5'

Inches

14. 769

.766

.764

.763

.760

14. 758

.756

.755

.752

.750

.748

14. 747 

.744

.741 

.740

.739

14. 736

.733

!730 

.728

14. 725 

.723 

.722 

.719 

.717 

.715

14. 714

.711

.708

.707

.705

14. 702

.700

.698

.697

.694

14. 691

.689

.688

.685

.682

.681

14. 679

.676

.673

.672

.670

14. 668

.665

.663

.662

.659

14. 656

.654

.653

.650

.647

.645

14.644

.641

.638

.636

.635

14.632

7HInches

22. 153

.149

.147

.145

.141

22. 137

.135

.132

.128

.124

.122

22. 120 

.116

.112 

.110

.108

22.104

.100

AQQ

. UVo

.096 

.091

22. 087 

.085 

.083 

.079 

.075 

.073

99 ft ft. \JI 11711

.066

.062

.060

.058

22. 054

.049

.047

.045

.041

22. 036

.034

.032

.028

.023

.021

22. 019

 .014

.010

.008

.006

22.001

21. 997

.995

.993

.988

21.984

.981

.979

.975

.970

.968

21. 966

.961

.957

.954

.952

21. 948

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

i

1%

3%

5

For latitude 14° 6%I^A

10

15

1M

2J/2 

3% 

5

For latitude 15° 6%

10 2

121^

15

1%

3% 

5 

For latitude 16°' 6%

10 2

15 ^

Merid 

ioual 

distance

Inches

3.781

7,562

11, 343

15, 124

18. 905

22. 686

30.247

37. 809

45. 371

3.781

7.562 

11.344 

15. 125

18. 906 

22. 687

30. 250

37.813

45. 375

3.781 

7.563

11.345 

15. 126 

18.908 

22. 690 

30. 253 

37.816 

45. 379

Ordinato of developed 

parallel

Inch

0.000

.001

.002

.003

.004

.006

.010

.016

.023

0.000

.001 

.002 

.003

.005 

.006

.011

.017

.025

0.000 

.001

.002 

.003 

.005 

.007 

.012 

.018 

.026
102 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale ix-fr-ff-o Continued

Latitude of

parallel

0 /

16 00

02H

03M

05

07^

10

UK

15

17V^

18%

20

22^

25

27}|

30

32H

35 4

40

42}| 

45 

47^ 

48%

50

52H

55

56^

57^

17 00

02^

03%

05

07^6

10

UK

12}^

15

17H ISM

20

22Ji

25

26M

30

32^

33%

35

37^

40

41K

42^

45

47^

48%

50

52^

55

56K

67H

18 00

Abscissas of developed parallel

Longitude interval

1'

Jncftes

2.926

.926

.925

.925

.925

2.924

.924

.923

.922

.922

.921

2.921

.921

.920 

.920

.920

2.919

.918

.918 

1918 

.917

2.916 

.916 

.916 

.915 

.915 

.914

2.914

.913

.913

.912

.912

2.911

.911

.910

.910

.909

2.909

.908

.908

.907

.907

.906

2.906

.905

.905

.904

.904

2.904

.903

.903

.902

.902

2.901

.901

.900

.900

.899

.899

2.898

.898

.897

.896

.896

2.895

IK'

Inches

3.658

.657

.657

.656

.656

3.655

.655

.654

.653

.653

.652

3. 652

.651

.650 

.650

.649

3.649

.648 

. 648

.647 

.646

3.646 

.645 

.645 

.644 

.643 

.643

o A42

!642

.641

.640

.640

3.639

.638

.638

.638

.637

3. 636

.636

.635

.634

.634

.033

3.633

.632

.631

.631

.630

3.629

.629

.628

.628

.627

3.626

.626

.625

.624

.624

.623

3.623

.622

.621

.621

.620

3.619

W

Inches

7.316

.314

.314

.313

.311

7. 310

.309

.308

.307

.305

.304

7.304

.302

.300 

.300

.299

7.297

.296 

.295

.294 

.293

7.291 

.290 

.290 

.288 

.286 

.286

7.285

.283

.282

.281

.280

7.278

.277

.276

.275

.274

7.272

.271

.270

.269

.267

.266

7.265

.264

.262

.261

.260

7.259

.257

.256

.255

.254

7.252

.251

.251

.249

.247

.246

7.245

.244

.242

.241

.240

7.239

* 

Inches

10. 974

.972

.970

.969

.967

10. 965

.964

.962

.960

.958

.957

10. 955

.953

.951 

.950

.948

10. 946

.944

!941 

.939

10. 937 

.936 

.934 

.932 

.930 

.928

10 927

>J25

.922

.921

.920

10. 918

.915

.914

.913

.910

10. 908

.907

.906

.903

.901

.899

10. 898

.896

.893

.892

.891

10. 888

.886

.884

.883

.881

10. 878

.877

.876

.873

.871

.869

10. 868

.866

.863

.862

.861

10. 858

5'

Inches

14.632

.629

.627

.626

.623

14. 620

.618

.617

.614

.610

.609

14. 607

.604

.601 

.599

.598

14. 595

.592

'. 589 

.585

14. 582 

.581 

.579 

.576 

.573 

.571

14. 570

.566

.563

.562

.560

14. 557

.554

.552

.550

.547

14. 544

.542

.541

.537

.534

.532

14. 531

.528

.524

.523

.521

14. 518

.514

.513

.511

.508

14.504

.503

.501

.498

.494

.493

14. 491

.488

.484

.483

.481

14. 477.

« 

Inches

21. 948

.943

.941

.938

.934

21. 929

.927

.925

.920

.916

.913

21.911

.907

.901 

.899

.897

21. 892

.888

QO c

. ooD

.883 

.878

21. 874 

.871 

.869 

.864 

.859 

.857

21 855

!850

.845

.842

.840

21. 835

.830

.828

.826

.821

21. 816

.813

.811

.806

.801

.799

21. 796

.791

.786

.784

.781

21. 777

.772

.769

.766

.762

21. 757

.754

.752

.747

.741

.739

21. 736

.731

.726

.724

.721

21.716

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1/4

2/^

3%

5

For latitude 16° 6M

7/^

10

12}^

15

IKrti>

3Y5 *

For latitude 17°. 6J4

10

1 914 15 "

IK

5 * 

For latitude 18°' 6K

10

15 2

Meridional 

distance

Inches

3.781

7.563

11. 345

15. 126

18. 908

22. 690

30. 253

37.816

45. 379

3.782

7.564

11.346

15.128

18.910

99 LL. fiQ9 \J\3L

30. 256

37. 820

45. 384

3.782 

7.565

11.347 

15.129 

18.912 

22. 694 

30. 259 

37. 824 

45. 388

Ordinatc of developed 

parallel

Inch

0.000

.001

.002

.003

.005

.007

.012

.018

.026

0.000

. 

flmUUl

.002

003

'.005 

.007

.012

.019

.028

0.000 

.001

.002 

.003 

.005 

.007 

.013 

.020 

.029
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 103 

TABLE 4. Coordinates for the projection of maps, scale -y^-^-s~~Continued

Latitude of

parallel

0 ,

18 00

03%

05

10

UK

15

\lYi

18%

20

22}<£

25

26K

27J^

30

33%

35

37^

40

41K 

42%

45

47J^

48%

60

55 2

56K

57^

19 00

02^

03%

05

07^

10UK

15

17/^

18%

20

22 Ji

25

26K

27^

30

32^

33%

35

37^

40

41K

42^£

45

47^

48%

50

52^

55

56K

20 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.895

.895

.894

.894 

.893

2.893

.892

.892

.891

.891

.890

2.890

.889

.889

.888

.888

2.887

.887

.886

.886

.885

2.884

.884 

.884

.883

.882

.882

2

QOO

. oo^I

.881

.880

.880

.879

2.879

.878

.878

.877

.877

2:876

.875

.875

.874

.874

.873

2.873

.872

.872

.871

.871

2.870

.809

.809

.869

.868

2.867

.867

.866

.866

.865

.865

2.864

.863

.863

.802

.862

2.861

IK'

Inches

3.619

.018

.618

.618 

.617

3.016

.016

.615

.614

.613

.613

3.612

.612

.611

.610

.610

3. 009

.608

.608

.607

.606

3. 606

.605 

.605

.604

.603

.602

3.602 

.601

.600

.600

.599

3.598

.598

.597

.597

.596

3.595

.594

.594

.593

.592 '.59"2

3.591

.590

.589

.589

.588

3.588

.587

.586

.586

.585

3.584

.583

.583

.582

.581

.581

3.580

.579

.578

.578

.577

3-570

2W

Inches

7.239

.237

.236

.235 

.234

7.232

.231

.230

' .228

.227

.226

7.225

.223

.222

.221

.220

7.218

.216

.215

.215

.213

7.211

.210 

.209

.208

.206

.205

7 204

!200

.199

.199

7.197

.195

.194

.193

.191

7.190

.189

.188

.186

.184

.183

7.182

.181

.179

.178

.177

7.175

.173

.172

.171

.169

7.168

.167

.166

.164

.162

.161

7.160

.158

.156

.150

.155

7.153

3%'

Inches

10. 858

.855

.854

.853 

.850

10. 848

847

.845

.843

.840

.839

10.837

.835

.832

.831

.830

10. 827

.824

.823

.822

.819

10. 817

815 

.814

.811

.809

.807

10. 800 

.803

.801

.799

.798

10. 795

.793

.791

.790

.787

10. 784

.783

.782

.779

.776

.775

10. 774

.771

.768

.766

.765

10. 703

.760

.758

.757

.754

10. 751

.750

.749

.746

.743

.742

10. 740

.738

.735

.733

.732

10. 729

5'

Inches

14. 477

.474

.472

.471 

.467

14. 404

.462

.460

.457

.453

.452

14. 450

.447

.443

.441

.440

14. 436

.433

.431

.429

.426

14. 422

.420 

.419

.415

.411

.410

14. 408 

.404

.401

.399

.397

14. 394

.390

.388

.386

.383

14. 379

.377

.376

. 372

.368

.367

14. 365

.361

.357

.356

.354

14. 350

.346

.345

. 343

.339

14. 335

.333

.332

.328

.324

.322

14. 321

' .317

.313

.311

.309

14. 305

W

Inches

21.716

.711

.708

.706 

.701

21. 696

.693

.090

.085

.080

.678

21. 075

.070

.605

.662

.659

21.654

.649

.646

.044

.038

21.033

.029 

.628

.623

.617

.615

21.012 

.607

.601

.598

.596

21. 591

.585

.582

.580

.574

21. 509

. 560

.563

.558

.553

.550

21. 547

.542

.536

.533

.531

21. 525

.520

.517

. 514

.508

21. 503

.500

.497

.492

.486

.484

21. 481

.475

.469

.467

.464

21. 458

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

IK

2J<J

3%

5 

For latitude 18°' 6K

7^<j

10

12J<j

15

IK

2/^i

3%

5

For latitude 19° OK

10 iy>"

12J^

15

IKiy<i

3%

5

For latitude 20° OK

10

15

Meridional 

distance

Inches

3.782

7. 565

11.347

15. 129 

18.912

22. 694

30. 259

37. 824

45. 388

3.783

7. 505

11.348

15.131

18.914

22. 697

30. 202

37. 828

45. 393

3.783

7. 500

.11.350

15. 133

18. 916 

22. 699

30. 205

37. 832

45. 398

Ordinato of developed 

parallel

Inch

0.000

.001

.002

.003 

.005

.007

.013

.020

.029

0.000

.001

.002

.003

. 005

.008

.014

.021

.031

0.000

.001

.002

.004

.000 

.008

.014

.022

.032
104 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale -^^-^is Continued

Latitude of

parallel

o /

20 00

02H

03%

05

07^

10

11%

12M

15

17H

18%

20

22^

25

26%

27^

30

32J^

33% 

35 

37M

40 

41% 

42M 

45 

47H 

48%

50

52^

55

56%

S7M

21 00

02H

03%

05

07X

1011%

12H

15

17J/2

18%

20

22J/2

25

26%

27H

30

32^

33%

35

37H

40

41%

WA

45

47^

48%

50

52J^

55

56%

57^

22 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.861

.860

.860

.860

.859

2.858

.858

.857

.857

.856

.855

2.855

.854

.853

.853

.853

2.852

.851

ORl

 oOJ.

.850 

.850

2.849 

.848 

.848 

.847 

.847 

.846

2. 846

.845

.844

.844

.843

2.843

.842

.841

.841

.840

2.839

.839

.839

.838

.837

.837

2.836

.835

.835

.834

.834

2.833

.832

.832

.831

.831

2.830

.829

.829

.828

.827

.827

2.827

.826

.825

.825

.824

2.823

1%'

Inches

3.576

.575

.575

.574

.574

3.573

.572

.572

.571

.570

.569

3.569

.568

.567

.566

.566

3.565

.564

KflO

 Ouo

.563 

.562

3.561 

.561 

.560 

.559 

.558 

.558

3

KC7 

. OOi

.556

.555

.555

.554

3.553

.552

.552

.551

.550

3.549

.549

.548

.547

.546

.546

3.545

.544

.543

.543

.542

3.541

.540

.540

.539

.538

3.537

.537

.536

.535

.534

.534

3.533

.532

.531

.531

.530

3.529

mr

Inches

7.153

.151

.150

.149

.147

7.145

.144

.143

.141

.139

.139

7.138

.136

.134

.133

.132

7.130

..128

.127 

.126 

.124

7.122 

.121 

.120 

.118 

.116 

.115

7.114

.112

.110

.110

.108

7.106

.004

.104

.103

.101

7.099

.098

.097

.095

.093

.092

7.091

.089

.087

.086

.085

7.083

.081

.080

.078

.076

7.074

.073

.072

.070

.068

.067

7.066

.064

.062

.061

.060

7.058

3%'

Inches

10. 729

.726

.725

.723

.721

10.718

.713

.715

.712

.709

.708

10. 706

.703

.701

.699

.698

10. 695

.692

flQA 

 \ty\j

.689 

.686

10. 683 

.682 

.680 

.677 

.674 

.673

10. 672

.669

.666

.664

.663

10. 660

.657

.655

.654

.651

10. 648

.646

.645

.642

.639

.637

10. 636

.633

.630

.628

.627

10.624

.621

.619

.618

.615

10. 612

.610

.609

.606

.602

.601

10. 599

.596

.593

.592

.590

10. 587

5'

Inches

14. 305

.302

.300

.298

.294

14. 290

.288

.287

.283

.279

.277

14. 275

.271

.267

.265

.264

14. 260

.256

.254 

.252 

.248

14. 244 

.242 

.240 

.237 

.233 

.231

14. 1*. 99Q &£itj

.225

.221

.219

.217

14. 213

.209

.207

.205

.201

14. 197

.195

.193

.189

.185

.183

14. 181

.177

.173

.171

.169

14. 165

.161

.159

.157

.153

14. 149

.147

.145

.141

.137

.135

14. 133

.128

.124

.122

.120

14. 116

1W

Inches

21. 458

.452

.450

.447

.441

21. 436

.433

.430

.424

.418

.416

21. 413

.407

.401

.398

.395

21. 390

.384

001

. Ool

.378 

.372

21. 366 

.363 

.361 

.355 

.349 

.346

91 £i\.. 34.3 OtO

.337

.331

.328

.325

21. 319

.313

.311

.308

.302

21.296

.294

.290

.284

.278

.275

21. 272

.266

.260

.257

.254

21. 248

.242

.239

.235

.229

21. 223

.220

217

.211

.205

.202

. 21. 199

.193

.187

.183

.180

21. 174

Ordinates of developed parallel and 

meridional distances

Latitude and longitude interval

/

1%

2H

3%

5

For latitude 20°' 6%

7^

10

12H

15

f M

VA

3%

5

For latitude 21° 6%

7M

10

12H

15

1% 

2H

3% 

5 

For latitude 22°i 6%

7/2

10 

12H

15

Meridional

distance

Inches

3.783

7.566

11. 350

15. 133

18.916

22. 699

30. 265

37. 832

45. 398

3.784

7.567

11.351

15. 134

18.918

22. 702

30. 269

37. 837

45. 403

3.784 

7.568

11. 352 

15. 136 

18. 921 

22. 705 

30. 272 

37. 841 

45.409

Ordinate 

of developed 

parallel

Inch

0.000

.001

.002

.004

.006

.008

.014

.022

.032

0.000

.001

.002

.004

.006

.008

.015

.023

.033

0.000 

.001

.002 

.004 

.006 

.009 

.015 

.024 

.035
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 105

TABLE 4. Coordinates for the projection of maps, scale Continued

Latitude of 

parallel

0 ,

22 00

(MA

0354

05

07^

10

11/4

12M

15

18$

20

25

30

33%

35 

37^

40

42^ 

45 

47H

50

62^

55

66}^ yiy-i

23 00

02%

03%

05

07H

10

11}^

12V6

15

17V4

1854

20

22}/£

25

26}i

27H

30

32V*>

33 J4

35

37H

40

41J4

42}i

45

47^

50

52M

55

56M

24 00

Abscissas of developed parallel

Longitude interval

1'

JncAes

2.823

.822

.822

.822

.821

2.820

.819

.819

.818

!817

2.817 

.816 

.815 

.815 

.814

2.813 

.812

Ot rt

.'811 

.811

2.810 

.809 

.809 

.808 

.807 

.807

2.806

.806

.805

.804

.804

2.803

.802

.802

.801

.800

2.800

.799

.799

.798

.797

.797

2.796

.795

.794

.794

.793

2.793

.792

.791

..791

.790

2.789

.789

.788

.787

.786

.786

2.786

.785

.784

.783

.783

2.782

IK'

Inches

3.529

.528

.527

.527

.526

3.525

.524

.524

.523

t U44 199

.521

3.521 

.520 

.519 

.518 

.518

3.517 

.515

.515

.514 

.513

3.512 

.512 

.511 

.510 

.509 

.509

3.508

.507

.506

.505

.505

3.504

.503

.502

.502

..501

3.499

.499

.498

.497

.496

.496

3.495

.494

.493

.492

.492

3.491

.490

.489

.489

.487

3.486

.486

.485

.484

.483

.482

3.482

.481

.480

.479

.479

3.477

2H'

Inches

7.058

.056

.055

.054

.052

7.050

.049

.048

.040

.044 

.043

7.041 

.039 

.037 

.036 

.035

7.033 

.031

.030

.029 

.027

7.025 

.024 

.022 

.020 

.019 

.017

7.016

.014

.012

.011

.010

7.008

.005

.004

.003

.001

6.999

.998

.997

.995

.992

.991

6.990

.988

.986

.985

.984

6.981

.979

.978

.977

.975

6.973

.972

.970

.968

.966

.965

6.964

.962

.959

.958

.957

6.955

3^'

Inches

10. 587

.584

.582

.581

.578

10. 575

.573

.572

.568

. 565 

.564

10. 562 

. 559 

.556 

.554 

.553

10. 550 

.546

.545

.543 

.540

10. 537 

.535 

.534 

.530 

.527 

.526

10. 524

.521

.518

.516

.515

10. 511

.508

.506

.505

.502

10. 498

.497

.495

.492

.489

.487

10. 485

.482

.479

.477

.475

10. 472

.469

.467

.466

.462

10. 459

.457

456

.452

.449

.447

10. 446

.442

.439

.437

.436

10. 432

5'

Inches

14. 116

.112

.110

.108

.104

14. 100

.097

.095

.091

i085

14. 083 

.079 

.074 

.072 

.070

14. 066 

.062

060

.'058 

.053

14. 049 

.047 

.045 

.041 

.036 

.034

14. 032

.028

.024

.021

.019

14. 015

.011

.009

.006

.002

13. 998

.996

.994

.989

.985

.983

13. 980

.976

.972

.969

.967

13. 963

.958

.956

.954

.950

13. 945

.943

.941

.937

.932

.930

13. 928

.923

.919

.916

.914

13. 910

7H'

Inches

21. 174

.168

.165

.162

.156

21. 149

.146

.143

.137

.131 

. .128

21. 124 

.118 

.112 

.109 

.105

21. 099 

.093

.090

.087 

.080

21. 074 

.071 

.067 

.061 

.055 

.051

21. 048

.042

.035

.032

.029

21. 023

.016

.013

.010

.003

20. 997

.994

.990

.984

.977

.974

20. 971

.964

.957

.954

.951

20. 944

.938

.934

.931

.925

20. 918

.915

.911

.905

.898

.895

20. 891

.885

.878

.875

.871

20.865

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

For latitude 22°

IV

2vt

gsx

5

714

10

15

For latitude 23°<

\M

5 4 

6M

10 2

15

For latitude 24°.

1%

5 *

10 

15

Meridional 

distance

Inches

3.784

7.568

11. 352

15. 136

18. 921

22. 705

30. 272

37. 841

45. 409

3.784

7.569 

11.354 

15. 138 

18. 923 

22. 707 

30. 276

37. 846 

45.415

3.785 

7.570

11. 355 

15. 140 

18. 925 

22. 710 

30. 280 

37. 851 

45. 421

Ordinate of developed

parallel

Inch

0.000

.001

.002

.004

.006

.009

.015

.024

.035

0.000

.001 

.002 

.004 

.006 

.009 

.016

.025 

.036

0.000 

.001

.002 

.004 

.006 

.009 

.016 

.020 

.037
106 TABLES FOR CONSTEUCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale -2-%^-$ Continued

Latitude of

parallel

0 /.

24 00

02J/6

03%

05

07^

10

11% \iy

15

18%

20 

22%

25 

26%

27 A1

30 

32^

33% 

35

40 

41%

45 2 

47^ 

48%

50

52%

55

56%

25 00

02%

03M

05

07^

10

11%

12%

15

17H

18%

20

22^

25

26%

27J/2

30

32^

33%

35

37M

40

41%

42^

45

47^

48%

50

52%

55

56%

57^

26 00

Abscissas of developed parallel

Longitude interval

1'

Incftes

2.782

.781

.781

.780

.779

2.778

.778

.777

.777

. 776 

.775

2.775 

.774

.773 

.772

.772

2.771 

.770

.770 

.769 

.768

2.767 

.767 

.766 

.766 

.765 

.764

2.764

.763

.762

.761

.761

2.760

.759

.759

.758

.757

2.756

.756

.755

.754

.753

.753

2.753

.752

.751

.750

.750

2.749

.748

.747

.747

.746

2.745

.744

.744

.743

.742

.742

2.741

.740

.739

.739

.738

2.737

li '

Inches

3.477

.476

.476

.475

.474

3.473

.4.72

.472

.471

.470 

.469

3.468 

.467

.466 

.466

.465

3.464 

.463

.462 

.462 

.460

3.459 

.459 

.458 

.457 

.456 

.455

3.455

.454

.452

.452

.451

3.450

.449

.448

.448

.447

3.445

.445

.444

.443

.442

.441

3.441

.439

.438

.438

.437

3.436

.435

.434

.434

.432

3.431

.431

.430

.429

.428

.427

3.426

.425

.424

.423

.423

3.422

Inches

6.955

.953

.952

.950

.948

6.946

.945

.944

.941

.939 

.938

6.937 

.935

.932 

.931

.930

6.928 

.925

.924 

.923 

.921

6.919 

.917 

.916 

.914 

.912 

.911

6. 909

.907

.905

.904

.902

6.900

.898

.897

.895

.893

6.891

.890

.888

.886

.884

.882

6.881

.879

.877

.875

.874

6.872

.870

.868

.867

.865

6.862

.861

.860

.858

.855

.854

6.853

.850

.848

.847

.846

6.843

3%'

Inches

10. 432

.429

.427

.426

.422

10. 419

.417

.415

.412

.409 

.407

10. 405 

.402

.398 

.397

.395

10. 392

.388

. 386 

.385 

.381

10. 378 

.376 

.374 

.371 

.367 

.366

10. 364

.361

.357

.355

.354

10. 350

.347

.345

.343

.340

10. 336

.334

.333

.329

1325

.324

10. 322

.318

.315

.313

.311

10. 308

.304

.302

.301

.297

10. 294

.292

.290

.286

.283

.281

10. 279

.276

.272

.270

.268

10. 265

5'

Inches

13. 910

.905

.903

.901

.896

13. 892

.889

.887

.883

070 

. o/O

.876

13. 874 

.869

.864 

.862

.860

13. 855

.851

. 849 

!842

13. 837 

.835 

.833 

.828 

.823 

.821

13. 819

.814

.809

.807

.805

13.800

.796

.793

.791

.786

13. 781

.779

.777

.772

.767

.765

13. 763

.758

.753

.751

.748

13. 744

.739

.737

734

.729

13. 725

.722

.720

.715

.710

.708

13. 706

.701

.696

.694

.691

13. 686

Inches

20. 865

.858

.855

.851

.844

20. 838

.834

.831

.824

.817 

.814

20.811 

.804

.797 

.793

.790

20. 783 

.776

779

, I I O

.769 

.763

20.756 

.752 

.749 

.742 

.735 

.732

on ZU. 790 i £o

.721

.714

.711

.707

20.700

.693

.690

.686

.679

20. 672

.669

.665

.658

.651

.647

20.644

.637

.630

.626

.623

20. 616

.609

.605

.601

.594

20.587

.583

.580

.573

.565

.562

20.558

.551

.544

.540

.537

20.530

Ordiuates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1/4

2%

3%

5

For latitude 24° 6%

7/^

10

15 2

1MQV/

3% 

5

For latitude 25°' 6%

10 2

12^ 

15

(IK

3% 

5 

For latitude 26°' 6%

10

15 *

Meridional 

distance

Inches

3.785

7.570

11. 355

15. 140

18. 925

22. 710

30.280

37. 851

45. 421

3.786

7.571

11. 357 

15. 142

18. 928 

22. 713

30.284

37. 856 

45. 426

3.786

7 W> I, OI&

11.358 

15. 144 

18. 931 

22. 717 

30.289 

37. 861 

45. 433

Ordinate of developed

parallel

Inch

0.000

.001

.002

.004

.006

.009

.016

.026

.037

0.000

. 001

!002 

.004

.007 

.010

.017

.026 

.038

0.000

.001

.002 

.004 

.007 

.010 

.017 

.027 

.039
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 107

TABLE 4. Coordinates for the projection of maps, scale tfkisis~~Continued

Latitude of 

parallel

0 /

26 00

02^

03%

05

07H

10UK

15

18%

20 

22^

25 

26K

30

32^

33%

35

37^

40 

41K 

42^ 

45

48%

50

55 2

56K

27 0002 y<

03K

05

Q7/4

10

UK

15

17M

18%

20

25

26K

27H

30

yn/i 33%:

35

40

41K

42H

45

47}^

48%

50

55

56K

28 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.737

.736

.736

.735

.734

2.733

.733

.732

.731

.730 

.730

2.729

.728

.727 

.727

.727

2.726

.725

.724

.724

.723

2.722 

.721 

.721 

.720 

.719 

.718

2.718

.717

.716

.715

.715

2.714

.713

.712

.712

.711

2.710

.709

.709

.708

.707

.706

2.706

.705

.704

.703

.703

2.702

.701

.700

.700

.699

2.697

.697

.696

.696

.694

.694

2.693

.692

.691

.691

.690

2.689

IK'

Inches

3.422

.420

.420

.419

.418

3.417

.416

.416

.414

.413 

.412

3.412 

.411

.409 

.409

.408

3.407

.406

.405

.404

.403

3.402 

.401 

.401 

.400 

.398 

.398

3.397

.396

.395

.394

.393

3.392

.391

.390

.390

.388

3.387

.386

.386

.384

.383

.383

3.382

.381

.380

.379

.378

3.377

.376

.375

.374

.373

3.372

.371

.371

.369

.368

.367

3.367

.365

.364

.364

.363

3.362

w

Inches

6.843

.841

.840

.838

.836

6.833

.832

.831

.829

.826 

.825

6.824 

.821

.819 

.818

.816

6.814

.811

.810

.809

.807

6.804 

.803 

.802 

.799 

.797 

.795

6.794

.792

.789

.788

.787

6.784

.782

.780

.779

'.777

6.774

.773

.772

.769

.767

.765

6.764

.762

.759

.758

.756

6.754

.751

.750

.749

.746

6.744

.742

.741

.739

.736

.735

6.734

.731

.728

.'727

.726

6.723

3%'

Inches

10. 265

.261

.259

.258

.256

10. 250

.248

.247

.243

.239 

.237

10. 236 

.232

.228 

.226

.225

10. 221

.217

.215

.213

.210

10. 206 

.204 

.202 

.199 

.195 

.193

10. 191

.188

. 184

.182

.180

10. 176

.173

.171

.169

.165

10. 161

.159

.157

.154

.150

.148

10. 146

.142

.139

.137

.135

1Q. 131

.127

.125

.123

.119

10. 116

.114

.112

.108

.104

.102

10. 100

.096

.093

.091

.089

10. 085

5'

Inches

13. 686

.682

.679

.677

.672

13. 667

.665

.662

.657

.652 

.650

13. 647 

.643

.638 

.635

.633

13.628

.623

.620

.618

.613

13. 608 

.606 

.603 

.598 

.593 

.591

13. 588

.583

.578

.576

.573

13. 568

.563

.561

.558

.553

13. 548

.546

.543

.538

.533

.531

13.528

.523'

.518

.516

.513

13. 508

.503

.500

.498

.493

13. 488

.485

.482

.477

.472

.470

13. 467

. 462

.457

.454

.452

13.446

w

Inches

20. 530

.522

.519

.515

.508

20.500

.497

.493

.486

.478 

.475

20. 471 

.464

.456 

.453

.449

20.442

.434

.431

.427

.420

20. 412 

.408 

.405 

.397 

.390 

.386

20. 383

.375

. 368

.364

.360

20. 353

.345

.341

.338

.330

20. 323

.319

.315

.307

.300

.296

20. 292

.285

.277

273

.269

.20. 262

.254

.250

.247

.239

20. 231

.227

.224

.216

.208

.204

20.201

.193

.185

.181

.177

20.170

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

IK

3%

5

For latitude 26° 6K

7M

10

15

IK

3% 

5

For latitude 27° 6K

10 2

12^6

15

IK

2X2 

3% 

5 

For latitude 28°. 6K

10

15

Meridional distance

Inches

3.786

7.572

11. 358

15. 144

18. 931

22. 717

30. 289

37. 861

45. 433

3.787

7 573

ll! 360 

15. 146

18. 933 

22. 720

30.293

37. 867

45. 439

3.787

7.574 

11. 362 

15. 148 

18. 936 

22. 723 

30.297 

37. 872

45. 446

Ordlnate of developed 

parallel

Inch

0.000

.001

.002

.004

.007

.010

.017

.027

.039

0.000

001

^003 

004

!007 

.010

.018

.028

.040

0.000

.001 

.003 

.005 

.007 

.010 

.018 

.029

.041

6243° 29 8
108 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale -5-7-0TJU Continued

Latitude of 

parallel

0 /

28 00

02^

03%

05

07K

10

11%

15 2

17J/2

20

22)^

25 

26%

27^

30 

32H

33% 

35 

37^

40 

41%

45

48%

50

52^

55

56%

29 00

02^

03%

05

07^

10

11%

15 2

\iy,

18%

20

22V£

25

26%

30

32H

33%

35

37^

40

41%

42^

45

47^

48%

60

52^

55

56%

57J4

30 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.689

.688

.688

.687

.686

2.685

.685

.684

.683

. oo2

.681

2.681

.680

.679 

.678

.678

2.677 

.676

!675 

.674

2.673 

.672 

.671

.670 

.669

.669

2.668

.667

.666

.666

.665

2.664

.663

.662

.662

.661

2.660

.659

.659

.658

.657

.656

2.655

.654

.653

.653

.652

2.651

.650

.649

.649

.648

2.647

.646

.646

.644

.643

.643

2.642

.641

.640

.640

.639

2.638

1%'

Inches

3.362

.360

.360

.359

.358

3.356

.356

.355

.354

'JKO

. QUO

.352

3.351

.350

.349 

.348

.347

3.346 

.345

!343 

.342

3.341 

.340 

.339

.338 

.337

.336

3.335

.334

.333

.332

.331

3.330

.329

.328

.327

.326

3.325

.324

.323

.322

.321

.320

3.319

.318

.317

.316

.315

3.314

.313

.312

.311

.310

3.308

.308

.307

.306

.304

.304

3.303

.302

.300

.300

.299

3.297

w

Inches

6.723

.721

.719

.718

.715

6.713

.711

.710

.708

.705

.704

6.702

.700

.697 

.696

.694

6.692

.689

RCQ . DOO

.687 

.684

6.681 

.680 

.679

.676 

.673

.672

6.671

.668

.665

.664

.663

6.660

.657

.656

.655

.652

6.649

.648

.647

.644

.641

.640

6.639

.636

.633

.632

.630

6.628

.625

.624

.622

.620

6.617

.616

.614

.611

.609

.607

6.606

.603

.600

.599

.598

6.595

3%'

Inches

10. 085

.081

.079

.077

.073

10. 069

.067

.065

.061

.057

.055

10. 054

.050

.046 

.044

.042

10. 038 

.034 

032 !oso

.026

10. 022 

.020 

.018

.014 

.010

.008

30.000

.002

9.998

.996

.994

9.990

.986

.984

.982

.978

9.974

.972

.970

.966

.962

.960

9. 958

.954

.950

.948

.946

9.942

.938

.936

.933

.929

9.925

.923

.921

.917

.913

.911

9.909

.905

.901

.899

.897

9.892

5'

Inches

13. 446

.441

.439

.436

.431

13. 426

.423

.420

.415

.410

.407

13. 405

.399

.394 

. 392-

.389

13. 384 

.378 

. 376

.373 

.368

13. 363 

.360 

.357

.352 

.347

.344

13. 342

.336

.331

.328

.326

13.320

.315

.312

.309

.304

13. 299

.296

.293

.288

.283

.280

13. 277

.272

.266

.264

.261

13. 256

.250

.247

.245

.239

13. 234

.231

.228

.223

.217

.215.

13. 212

.206

.201

.198

.195

13. 190

7H'

Inches

20. 170

.162

.158

.154

.146

20. 138

.134

.131

.123

.115

.111

20. 107

.099

.091 

.086

.083

20. 076 

.068 

064

!C60 

.052

20. 044 

.0-10 

.036

.028 

.020

.016

20. 012

.004

19. 996

.992

.988

19. 980

.972

.968

.964

.956

19. 948

.944

.940

.932

.924

.920

19. 916

.908

.900

.896

.891

19. 883

.875

.871

.867

.859

19. 851

.847

.842

.834

.826

.822

19. 818

.810

.801

.797

.793

19. 785

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

3%

5

For latitude 2S°< 6%

7/^

10

15 2

1%

3%

5

For latitude 29°' 6%

o 2

15 2

1%

3% 

5 

For latitude 30°. 6%

10 2

,15

Meridional distance

Inches

3.787

7.574

11. 362

15. 148

18. 936

22. 723

30. 297

37. 872

45.446

3.788

7 1 . 01 IT'Su

U QftO 

. QUO

15. 151

18. 939 

22. 726

30. 302

37. 878 

45. 453

3.788

7.577

11. 365 

15. 153 

18. 942

22. 730 

30. 306

37. 884 

45. 460

Ordinate of developed 

parallel

Inch

0.000

.001

.003

.005

.007

.010

.018

.029

.041

0.000

.001 ioos

!oo7

.011

.019

.029 

.042

0.000 

.001

.003 

.005 

.007

.011 

.019

.030 

.043
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 109

TABLE 4. Coordinates for the projection of maps, scale Y^^ Continued

Latitude of

parallel

0 /

30 00

02J/3

03%

05

07^

10

11% \iy-i

15

18M

20 

22J/6 

25

27M

30

33% 

35

40

45 

47]^ 

48%

50

55 l

56%

57H

31 0002 y

03%

05

07^

10

11%

15 2

17}^

!8iN

20

22J/

25

26%

27^

30

32}/

33%

35

37J/

40

41%

42^

45

47V

48%

50

525/<

55

56%

57X

32 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2 6^8 !es7

.636

.636

.635

2.633

.633

.632

.631

.630 

.630

2.629 

.628 

.627 

.626

.626

2.625

.623

.'622 

.621

2.620 

.620 

.619 

.618 

.617 

.616

2.616

.615

.613

.613

.612

2.611

.610

.609

.609

.608

2.607

.606

.605

.604

.603

.603

2.602

.601

.600

.599

.599

2.597

.596

.596

.595

.594

2.593

.592

.592

.591

.589

.589

2.588

.587

.586

.585

.585

2.583

1%'

Inches

3.297

.296

.295

.295

.293

3.292

.291

.291

.289

!287

3.286 

.285 

.284 

.283

.282

3. 281

.279

!278 

.277

3.275 

.275 

.274 

.272 

.271 

.270

3.270

.268

.267

.266

.265

3.264

.263

.262

.261

.260

' 3. 258

.258

.257

.255

.254

.253

3.253

.251

.250

.249

.248

3.247

.245

.245

.244

.242

3.241

.240

.240

.238

.237

.236

3.235

.234

.232

.232

.231

3.229

Inches

6.595

.592

.591

.589

.587

6.584

.583

.581

.578

.576 

.574

6. 573 

.570 

.567 

.566

.564

6.562

.559

.557 

.556 

.553

6. 550 

.549 

.548 

.545 

.542 

.541

6.539

.536

.534

.532

.531

6.528

.525

.524

.522

.519

6.516

.515

.514

.511

.508

.506

6.505

.502

.499

.498

.496

6.494

.491

.489

.488

.485

6.482

.481

.479

.476

.473

.472

6.470

.467

.465

.463

.462

6.459

Inches

9.892

.888

.886

.884

.880

9.876

.874

.872

.867

.863 

.861

9.859

.855 

.851 

.849

.847

9.843

.838

Q*ifi

. ooO

.834 

.830

9.826 

.824 

.821 

.817 

.813 

.811

9.809

.805

.800

.798

.796

9.792

.788

.785

.783

.779

9.775

.773

.770

.766

.762

.760

9.757

.753

.749

.747

.745

9.740

.736

.734

.732

.727

9.723

.721

.719

.714

.710

.708

9.706

.701

.697

.695

.693

9.688

5'

Inches

13. 190

.184

.182

.179

.173

13. 168

.165

.162

.157

.151 

.148

13. 146 

.140 

.135 

.132

.129

13. 123

.118 

. 115

.112 

.106

13. 101 

.098 

.095 

.090 

.084 

.081

13. 078

.073

.067

.064

.061

13. 056

.050

.047

.044

.039

13. 033

.030

.027

.021

.016

.013

13. 010

.004

12. 999

.996

.993

12. 987

.981

.978

.976

.970

12. 964

.961

.958

.952

.947

.944

12. 941

.935

.929

.926

.923

12. 917

Inches

19. 785

.777

.772

.768

.760

19. 752

.748

.743

.735

.727 

.723

19. 719 

.710 

.702 

.698

.693

19. 685

.677 

.672

.668 

.660

19. 651 

.647 

.643 

.634 

.626 

.622

19. 618

.609

.601

.596

.592

19. 584

.575

.571

.566

.558

19. 549

.545

.541

.532

.524

.519

19. 515

.506'

.498

.493

.489

19. 481

.472

.468

.463

.455

19. 446

.442

.437

.429

.420

.416

19. 411

.402

.394

.389

.385

19. 376

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

3%

5

For latitude 30°' 6%

TYi

10

12J^

15

1%

3% 

5 

For latitude 31°< 6%

10 2

1 2V*i

15

W

3% 

5 

For latitude 32°' 6%

10 2

15 2

Meridional 

distance

Inches

3. 788

7.577

11. 365

15. 153

18. 942

22. 730

30. 300

37. 884

45. 460

3.789

7.578

11.367 

15. 155 

18. 945 

22. 733

30. 311

O7 QQA 0(. owu

45. 467

3.789 

7.679

11. 369 

15. 158 

18. 948 

22. 737 

30. 316 

37. 896 

45. 474

Ordinato of developed

parallel

Inch

0.000

.001

.003

.005

.007

.011

.019

.030

.043

0.000

.001

.003 

.005 

.008 

.011

.020

.031

.044

0.000 

.001

.003 

.005 

.008 

.011 

.020 

.031 

.045
110 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale -2^-5-5 Continued

Latitude of

parallel

0 /

32 00

02^

03%

05

07H

10

11%

12J^

15

17^

18%

20

22^

25 

26%

27K

30

32^

33% 

35yiy-i

40 

41^ 

42^ 

45 

47H 

48%

50

52^

55

56%

67>i

33 00

02^

03%

05

07^

10

11%

12}$

15

"«

18%

20

22M

25

26%

27^i

30

32^

33%

35

37^

40

41%

«fc

45

47^

48%

50

52^

55

56%

57^

34 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.583

.582

.582

.581

.580

2.579

.578

.678

.576

.575

.575

2.574

.573

.572 

.571

.571

2.569

.568

pno

. OOO

.567 

.566

2.565 

.564 

.562 

.562 

.561 

.560

O Rfif\ 6. OOU

.559

.557

.557

.556

2.555

.554

.553

.553

.551

2.550

.550

.549

.548

.547

.546

2.545

.544

.543

.542

.542

2.540

.539

.539

.538

.537

2.536

.535

.535

.533

.532

.531

2.531

.530

.528

.528

.527

2.526

1%'

Inches

3.229

.228

.227

.226

.225

3.224

.223

.222

.221

.219

.218

3.218

.216

.215 

.214

.213

3.212

.210

OAO . Z\Jt)

.209 

.207

3.206 

.205 

.204 

.203 

.201 

.201

3.200

.198

.197

.196

.195

3.194

.192

.192

.191

.189

3.188

.187

.186

.185

.183

.183

3.182

.180

.179

.178

.177

3.176

.174

.173

.173

.171

3.170

.169

.168

.167

.165

.164

3.163

.162

.160

.160

.159

3.157

2tf

Inches

6.459

.456

.454

.453

.450

6.447

.445

.444

.441

.438

.437

6.435

.432

.429 

.428

.426

6.423

.420

.419 

.417 

.415

6.412 

.410 

.409 

.406 

.403 

.401

6.400

!397

.394

.392

.391

6.388

.385

.383

.382

.379

6.376

.374

.373

.370

.367

.365

6.364

.360

.357

.356

.354

6.351

.348

.347

.345

.342

6.339

.338

.336

.333

.330

.328

6.327

.324

.321

.319

.318

6.315

3%'

Inches

9.688

.684

.681

.679

.675

9.671

.668

.666

.662

.657

.655

9.653

.649

.644 

.642

.640

9.635

.631

. 628 

.626 

.622

9.617 

.615 

.613 

.608 

.604 

.602

9. oyy HQQ

.595

.590

.588

.586

9.581

.577

.575

.572

.568

9.563

.561

.559

.554

.550

.548

9.545

.541

.536

.534

.532

9.527

.523

.520

.518

.513

9.509

.506

.504

.500

.495

.493

9.490

.486

.481

.479

.477

9.472

5'

Inches

12. 917

.912

.909

.906

.900

12. 894

.891

.888

.882

.876

.873

12. 871

.865

.859 

.856

.853

12.847

.841

OQO

. OOO

.835 

.829

12. 823 

.820 

.817 

.811 

.805 

.802

19 i£i. 7QQ IUU

.793

.787

.784

.781

12. 775

.769

.766

.763

.757

12. 751

.748

.745

.739

.733

.730

12. 727

,721

.715

.712

.709

12. 703

.697

.694

.691

.684

12. 678

.675

.672

.666

.660

.657

12.654

.648

.642

.638

.635

12. 629

7H'

Inches

19. 376

.367

.363

.359

.351

19. 341

.337

.332

.323

.315

.310

19. 306

.297

.288 

.284

.279

19. 270

.261

. 4*JI 957

.252 

.244

19. 235 

.230 

.226 

.217 

.208 

.203

19. 199

!l90

.181

.176

.172

19. 163

.154

.149

.145

.136

19. 127

.122

.118

.109

.100

.095

19. 091 ' '. 081

.072

.068

.063

19.054

.045

.040

.036

.027

19. 017

.013

.008

18. 999

.990

.985

18. 981

.972

.962

.958

.953

18.C44

Ordinatcs of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

VA

3%

5

For latitude 32°' 6%

7M

10

12>S

15

1%

2K

3%

5

For latitude 33° 6% 

7y2

10

12^

15

1% 

2X2

3% 

5 

For latitude 34°. 6%

7X 

10

12M 

15

Meridional 

distance

Inches

3.789

7.579

11. 369

15. 158

18.948

22. 737

30. 316

37. 896

45. 474

3.790

7.580

11.370

15. 160

18. 951 

22. 741

30. 321

37. 902

45. 481

3.791 

7.581

11. 372 

15. 162 

18. 954 

22. 744 

30. 326 

37. 908 

45. 489

Ordinate of developed 

parallel

Inch

0.000

.001

.003

.005

.008

.011

.020

.031

.045

0.000

.001

.003

.005

.008 

.011

.020

.032

.040

0.000 

.001

.003 

.005 

.008 

.011 

.021 

.032 

.046
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 111

TABLE 4. Coordinates for the projection of maps, scale yzlsTsti~~Continued

Latitude of

parallel

0 /

34 00

02^

03%

05

073^

10UK

12K ie

m

20

22^

26 

26%

27^

30

3234

If* 

37^

40 

41%

45 

48%

50

623^

65

66%

67^

35 00

02)^

03%

05

Q7X

1011%

15

173^

18%

20

223-i

25

26%

27H

30

323^

33%

35

WA

40

41%

423-3

45

47}^

48%

50

WA

55

56%

573^

36 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.526

.525

.524

.623

.622

2.621

.620

.520

.610

.617

.617

2.516

.615

.613 

.613

.612

2.611

.610

KAO . OUw

.608 

.507

2.506 

.505 

.505 

.603 

.502 

.502

2.501

.500

.498

.498

.497

2.496

.495

.494

.493

.492

2.491

.490

.490

.488

.487

.486

2.486

.484

.483

.482

.482

2.481

.479

.479

.478

.477

2.476

.475

.474

.473

.472

* .471

2.470

.469

.468

.467

.466

2.465

IK

Inches

3.157

.166.

.165

.164

.163

3.161

.160

.160

.148

.146

.146

3.146

.143

.142 

.141

.140

3.139

.137

. 136 

.136 

.134

3.132 

.132 

.131 

.129 

.128 

.127

0 JOB

!l25

.123

.122

.121

3.120

.118

.117

.117

.115

3.113

.113

.112

.110

.109

.108

3.107

.106

.104

.103

.102

3.101

.099

.098

.098

.096

3.094

.093

.093

.091

.089

.089

3.088

.086

.085

.084

.083

3.081

1tt

Inches

6.316

.312

.310

.308

.305

6.302

.301

.209

.296

.293

.291

6.290

.287

.284 

.282

.281

6.277

.274

!271 

.268

6.265 

.263 

.262 

.259 

.255 

.254

6.252

.249

.246

.244

.243

6.240

.237

.235

.233

.230

6.227

.225

.224

.221

.217

.216

6.214

.211

.208

.206

.205

6.202

.198

.197

.195

.192

6.189

.187

.185

.182

.179

.177

6.176

.172

.169

.168

.166

6.163

3H

Inches

0.472

.467

.465

.463

.468

0.463

.451

.440

.444

' .439

.437

9.435

.430

.425 

.423

.421

9.41C

.411

. 409 

.407 

.402

9.397 

.395 

.393 

.388 

.383 

.381

9.378

.374

.369

.367

.364

9.359

.355

.352

.350

.345

9. 341

.338

.336

.331

.326

.324

9.321

317

.312

.309

.307

9.302

.297

.295

.293

.288

9.283

.281

.278

.273

.268

.266

9.264

.259

.254

.252

.249

9.244

5'

Inches

12. 629

.623

.620

.617

.011

12. 605

.601

.598

.592

.586

.683

12. 680

.574

.567 

.664

.561

12. 555

.549

'.542 

..536

12. 530 

.527 

.523 

.517 

.511 

.508

12. 505

.498

.492

.489

.486

12. 479

.473

.470

.467

.460

12. 454

.451

.448

.44.1

.435

.432

12.428

.422

.416

.413

.409

12. 403

.397

.393

.390

.384

12. 377

.374

.371

.364

.358

.355

12. 352

.345

.339

.335

.332

12. 326

/H

Inches

18. 944

.935

.930

.925

.916

18. 907

.902

.898

.888

.879

.874

18. 870

.860

.861 

.846

.842

18. 832

.823

Q1 ft

. olo

.814 

.804

18. 795 

.790 

. .785 

.776 

.766 

.762

IS T\1 lo. t ijl

.747

.738

.733

.728

18. 719

.710

.705

.700

.691

18. 681

.676

.672

.662

.652

.648

IS. 643

.633

.624

.619

.614

18. 605

.595

.590

.585

.576

18. 566

.561

.556

.547

.537

.532

18. 527

.518

.508

.503

.498

18. 488

Ordinatcs of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

23/2

3%

6

For latitude 34°, 6%

73^

10

123^

15

1^

OlX

3%

6

For latitude 35°. 6%

10

123/2

15

IK

3% 

5 

For latitude 36°< 6%

10 2

15

Meridional 

distance

Inches

3.791

7.681

11. 372

15. 162

18. 954

22. 744

 30. 326

37. 908

46. 489

3.791

7.583

11. 374

15. 165

18. 957 

22. 748

30. 331

37. 914 

45. 496

3.792 

7.684

11. 376 

15. 168 

18. 960 

22. 752 

30. 336 

37. 921 

45.504

Ordinate of developed

parallel

Inch

0.000

.001

.003

.005

.008

.011

.021

.032

.046

0.000

.001 ioos

.005

.008 

.012

.021

. 033 

.047

0.000 

.001

.003 

.005 

.008 

.012 

.021 

.033 

.047
.112 TABLES FOB CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale 1-^-^-5 Continued

Latitude of

parallel

o /

36 00

02*

03^

05

07*

10

11*

12*

15

17*

18*

20

22*

25

26Ji

2V*

30

32*

35 * 

37*

40 

41* 

42* 

45

47* 

48%

50

52*

55

56Ji

57*

37 00

02*

03%

05

07*

10

11*

12*

15

17*

18*

20

22*

25

26*

27*

30

32*

33%

35

37*

40

41*

42*

45

47*

50

52*

55

56*

57*

38 00

Abscissas of developed parallo'

Longitude interval

1'

Inches

2.465

.464

.463

.463

.461

2.460

.459

.459

.457

.456

.455

2.455

 .453

.452

.451

.451

2.449

.448

447 

!447 

.446

2.444 

.444 

.443 

.442 

.440 

.440

2.439.

.438

.436

.436

.435

2.434

.432

.432

.431

.430

2.428

.428

.427

.426

.424

.424

2.423

.422

.420

.420

.419

2.418

.416

.416

.415

.414

2.412

.412

.411

.410

.408

.407

2.407

.405

.404

.403

.403

2.401

1*'

Inches

3.081

.080

.079

.078

.077

3.075

.074

.073

.072

.070

.069

3.068

.067

.065

.064

.063

3.062

.060

!059 

.057

3.055 

.054 

.054 

.052 

.050 

.050

0 /VIQ

!047

.045

.045

.044

3.042

.040

.040

.039

.037

3.035

.035

.034

.032

.030

.030

3.029

.027

.025

.025

.024

3.022

.020

.020

.019

.017

3.015

.014

.014

.012

.010

.009

3.009

.007

.005

.004

.003

3.002

2*'

Inches

6.163

.160

.158

.156

.153

6.150

.148

.147

.143

.140

.138

6.137

.134

.130

.129

.127

6.124

.120

!l!7 

.114

6.111 

.109 

.107 

.104 

.101 

.099

6.097

.094

.091

.089

.087

6.084

.081

.079

.077

.074

6.071

.069

.067

.064

.061

.059

6.057

.054

.051

.049

.047

6.044

.041

.039

.037

.034

6.031

.029

.027

.024

.020

.019

6.017

.014

.010

.009

.007

6.004

3*'

Inches

9.244

.239

.237

.234

.230

9.225

.222

.220

.215

.210

.208

9.205

.200

.195

.193

.190

9.186

.181

17(3

. I/O

.176 

.171

9.166 

.163 

.161 

.156 

.151 

.149

9.146

.141

.136

.134

.131

9.126

.121

.119

.116

.111

9.106

.104

.101

.096

.091

.089

9.086

.081

.076

.074

.071

9.066

.061

.059

.056

.051

9.046

.043

.041

.036

.031

.028

9.026

.021

.015

.013

. .010

9.005

5'

Inches

12. 326

.319

.316

.313

.306

12.300

.296

.293

.287

.280

.277

12. 274

.267

.260

.257

.254

12.247

.241

'.234 

.228

12. 221 

.218 

.215 

.208 

.201 

.198

12. 195

.188

.181

.178

.175

12.168

.162

.158

.155

.148

12. .142

.138

.135

.128

.121

.118

12. 115

.108

.101

.098

.095

12. 088

.081

.078

.075

.068

12.061

.058

.054

.048

.041

.Q38

12. 034

.027

.021

.017

.014

12. 007

7*'

Inches

18. 488

.479

.474

.469

.459

18. 450

.445

.440

.430

.420

.415

18. 410

.401

.391

.386

.381

18. 371

.361

oec

. ouu

.351 

.342

18. 332 

.327 

.322 

.312 

.302 

.297

18 -LO. 909 4iJ£l

.282

.272

.267

.262

18. 252

.242

.237

.232

.222

18. 212

.207

.102

.192

.182

.177

18. 172

.162

.152

.147

.142

18. 132

.122

.117

.112

.102

18. 092

.087

.082

.071

.061

.056

18. 051

.041

.031

.026

.021

18. Oil

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1*

2*

3%

5

For latitude 36°. 6K

7*

10

12*

15

1*

2*

3%

5

For latitude 37°' 6J£

7*

10

12*

15

1*

2*

5 * 

For latitude 38°. 6K

10 2

12* 

15

Meridional 

distance

Inches

3.792

7.584

11. 376

15.168

18. 960

22. 752

30. 336

37. 921

45. 504

3.793

7.585

11. 378

15. 170

18.964

22. 756

30. 341

37. 927

45. 512

3.793 

7.587

11.380 

15. 173 

18. 967 

22. 760 

30. 346 

37. 935 

45. 520

Ordinate of developed 

parallel

Inch

0.000

.001

.003

.005

.008

.012

.021

.033

.047

0.000

.001

.003

.005

.008

.012

.021

.033

..048

0.000 

.001

.003 

.005 

.008 

.012 

.021 

.034 

.048
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 113

TABLE 4. Coordinates for the projection of maps, scale -ST^THS Continued

Latitude of

parallel

0 ,

38 00

02^

03%

05

07^

10HK

15 2

17J^

w

20

22 J^

25

26K

30

33%

35

40

41K

45 i

yiy-i

48%

50

55 2

.66K

39 00

03%

05

OVA

10UK

15 2

18%

20

25

26K

27^

30

32^

33%

35

40

41K

45

WA

48%

50

65

56K

40 00

Abscissas of developed parallel

Longitude interval

.1'

Inches

2.401

.400

.399

!397

2.396

.395

.395

.393

.392

.391

2.391

.389

.388

.387

.386

2.385

.384

.383

.382 

.381

2.380

.379 

.378

.377

.375

.375

2.374 

.373

.371

.370

.370

2.368

.367

.366

.366

.364

2.363

.362

.361

.360

.359

.358

2.357

.356

.354

.354

.353

2.352

.350

.350

.349

.347

2.346

.345

.345

.343

.342

.341

2.340

.339

.338

.337

.336

2.335

IK'

Inches

3.002

.000

2.999

!997

2.995

.994

.993

.992

.990

.989

2.988

.986

.985

.984

.983

2.981

.980

.979

.978 

.976

2.974

.974 

.973

.971

.969

.968

2. 967 

.966

.964

.963

.962

2.961

.959

.958

.957

.955

2.954

.953

.952

.950

.948

.947

2.947

.945

.943

.942

.941

2.940

.938

.937

.936

.934

2.933

.932

.931

.929

.927

.926

2.925

.924

.922

.921

.920

2.918

w

Inches

6.004

.000

5.998

.997

.993

5.990

.988

.986

.983

.980

.978

5.976

.973

.969

.968

.966

5.963

.959

.957

.956 

.952

5.949

.947 

.945

.942

.938

.937 

O. n oil UtjO

.931

.928

.926

.924

5.921

.918

.916

.914

.911

5.907

.905

.904

.900

.897

.895

5.893

.890

.886

.884

.883

5.879

.876

.874

.872

.869

5.865

.863

.862

.858

.855

.853

5.851

.847

.844

.842

.840

5.837

3%'

Inches

9.005

.000

8.998

.995

.990

8.985

.982

.980

.975

.969

.967

8.964

.959

.954

.951

.949

8.944

.939

.936

.933 

.928

8.923

.921 

.918

.913

.908

.905

O QAO O, UV4

.897

.892

.889

.887

8.882

.876

.874

.871

.866

8.861

.858

.856

.850

.845

.842

8.840

.835

.829

.827

.824

8.819

.813

.811

.808

.803

8.798

.795

.792

.787

.782

.779

8.776

.777

.766

.763

.761

8.755

5'

Inches

12. 007

.000

11. 997

.993

.987

11. 980

.976

.973

.966

.959

.956

11. 952

.946

.939

.935

.932

11. 925

.918

 01 yio%

.911 

.904

11. 897

.894 

.891

.884

.877

.873 

11.870

.863

.856

.852

.849

11. 842

.835

.832

.828

.821

11.814

.811

.807

.800

.793

.790

11. 786

.779

.772

.769

.765

11.758

.751

.748

.744

.737

11. 730

.727

.723

.716

.709

.705

11. 702

.695

.688

.684

.681

11. 674

«r

Inches

18. Oil

.000

17. 995

.990

.980

17. 970

.965

.959

.949

.939

.934

17. 929

.918

.908

.903

.898

17.888

.877

Q7O 

. Q( &

.867 

.857

17. 846

.841 

.836

.826

.815

.810 

17. 805

.794

.784

.779

.774

17.763

.753

.748

.742

.732

17. 721

.716

.711

.701

.690

.685

17.680

.669

.658

.653

.648

17.638

.627

.622

.616

.606

17. 595

.590

.585

.574

.564

.558

17. 553

.542

.532

.526

.521

17. 510

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

IK

3%

5

For latitude 38°' 6K

7^A

10

12J^

15

IK

WA

3%

6

For latitude 39° 6K"tYi

10

12}^

15

IK

2K

3% 

5

For latitude 40°' 6K

10 2

15

Meridional 

distance

Inches

3.793

7.587

11. 380

15. 173

18. 967

 22. 760

30. 346

37. 935

45. 520

3.794

7.588

11. 382

15. 176

18. 970

22.764

30. 352

37.940

45. 527

3.795 

7.589

 11.384 

15. 178

18. 973 

22. 768

30. 357

37. 947

45. 536

Ordinate of developed 

parallel

Inch

0.000

.001

.003

.005'

.008

.012

.021

.034

.048

0.000

.001

.003

.005

.008

.012

.022

.034

.049

0.000 

.001

.003

!<X)9 

.012

.022

.034

.049
114 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale if o"ira Continued

Latitude of

parallel

0 /

40 00

02^

03^

05

07//3

10UK

15 2

18j|

20

25 2 

26K

27^

30

32^

33% 

35

40

41K 

42^ 

45

48%

50

52K

55

56K

57^

41 00

02^

03^

05

07H

10

iiK

15 2

\iy<i

18%

20

22J^

25

26/4

27^

30

32/^

33%

35

37^

40

41K

45

47^

50

52^

55

56K

57^

42 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.335

.333

.333

.332

.330

2.329

.328

.328

.326

.325 

.324

2.323 

.322

.321 

.320

.319

2.318

.316

ITi

. DIG

.315 

.313

2. 312

.311 

.310 

.309 

.308 

.307

2.306

.305

.303

.303

.302

2.300

.299

.298

.297

.296

2.295

.294

.293

.292

.290

.289

2.289

.287

.286

.285

.284

2.283

.281

.281

.280

.279

2.277

.276

.276

.274

.273

.272

2.271

.270

.268

.267

.267

2.265

,

Inches

2.918

.917

.916

.915

.913

2.911

.910

.910

.908

.906 

.905

2.904 

.902

.901 

.900

.899

2.897

.895

894 

!893 

.892

2.890

.889 

.888 

.886 

.884 

.884

2.883

.881

.879

.878

.877

2.875

.874

.873

.872

.870

2.868

.867

.866

.864

.863

.862

2.862

.859

.857

.856

.855

2.854

.852

.851

.850

.848

2.846

.845

.844

.843

.841

.840

2.839

.837

.835

.834

.833

2.831

,

Inches

5.837

.833

.831

.830

.826

5.823

.821

.819

.815

.812 

.810

5.808 

.805

.801 

.799

.798

5.794

.790

!787 

.783

5.780

.778 

.776 

.772 

.769 

.767

5.765

.762

.758

.756

.754

5.751

.747

.745

.744

.740

5.736

.734

.733

.729

.725

.724

5.722

.718

.714

.713

.711

5.707

.703

.702

.700

.696

5.692

.691

.689

.685

.681

.680

5.678

.674

.670

.669

.667

5.663

3%'

Inches

8. 755

.750

.747

.745

.739

8.734

.731

.729

.723

.718 

.715

8. 712 

.707

.702 

.699

.696

8.691

.686

!o80 

.675

8.670

.667 

.664 

.659 

.653 

.651

8.648

.642

.637

.634

.632

8.626

.621

.618

.615

.610

8.604

.602

.599

.594

.588

.585

8.583

.577

.572

.569

.566

8.561

.555

.552

.550

.544

8.539

.536

.533

.528

.522

.519

8.517

.511

. .506

.503

.500

8.494

ri

Inches

11. 674

.667

.663

.659

.652

11. 645

.642

.638

.631

.624 

.620

11.617 

.010

.602 

.599

.595

11. 588

.581

.577 

.574 

.567

11. 559

.556 

.552 

.545 

.538 

.534

11. 531

.523

.516

.512

.509

11. 502

.494

.491

.487

.480

11. 473

.469

.405

.458

.451

.447

11. 443

.436

.429

.425

.422

11.414

.407

.403

.400

.392

11. 385

.381

.378

.370

.363

.359

11. 356

.348

.341

.337

.333

11. 326

Inches

17. 510

.500

.494

.489

.479

17. 468

.462

. 457

.446

' .436 

.430

17. 425 

.414

.404 

.398

.393

17. 382

.371

. 366 

.361 

.350

17. 339

.334 

.328 

.317 

.306 

.301

17. 296

.285

.274

.269

.263

17. 252

.241

.236

.231

.220

17. 209

.203

.198

.187

.176

.171

17. 165

.154

.143

.138

.132

17. 121

.110

.105

.099

.088

17. 077

.072

.066

.055

.044

.039

17. 033

.022

.011

.006

.000

16. 989

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

IK

3%

5

For latitude 40°. 6%iy<i

10

15 2

IK

3% 

5

For latitude 41° 6M

10 2

1 2 V^

15

IK

5 *

For latitude 42° 6ji

7^2

10

15 i

Meridional 

distance

Inches

3.795

7.589

11. 384

15. 178

18. 973

22. 768

30. 357

37. 947

45. 536

3.795

7 590

ll! 386 

15. 181

18. 977 

22. 772

30. 362

*>7 QCQ ot. yoo

AK. K.AA ID. £)rr*t

3.796 

7.592

11. 388

15. 184 

18.980 

22. 776 

30. 367 

37. 960 

45. 551

Ordinate of developed

parallel

Inch

0.000

.001

.003

.005

.009

.012

.022

.034

.049

0.000

. 001 iocs

005

 009

!022

.034

0.000 

.001

.003

.006 

.009 

.012 

.022 

.034 

.050
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 115

TABLE 4. Coordinates for the projection of maps, scale IT&TFTF Continued

Latitude of

parallel

0 /

42 00

02H

03%

05

07/2

10

UK

15 2

17/2

1 QRX

20

22 J^

25

26K

30

33% 

35 

yiYi

40 

41K

45

48% 

50

62^

55

50K

57^

43 00

02H

03%

05

07M

10UK

15

171^

18%

20

22/

25

26K

27 Yi

30

32^

33%

35

37^

40

41K

45 2

47Jx

48%

60

62}X

55

66K

57)^

44 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.265

.264

.263

.262

.261

2.259

.259

.258

.256

.255

.254

2.253

.252

.250

.250

.249

2.247

.246

!244 

.243

2.241 

.241 

.240 

.238 

.237

.236 0 

2.235

.234

.232

.232

.231

2.229

.228

.227

.226

.225

2.223

.223

.222

.220

.219

.218

2.217

.210

.214

.213

.213

2.211

.2.10

.209

.208

.207

2.205

.204

.204

.202

.201

.200

2.199

.197

.196

.195

.194

2.193

IK'

Inches

2.831

.830

.829

.828

.826

2.824

.823

.822

.820

.819

.818

2.817

.815

.813

.812

.811

2.809

.807

ftfi?

. oU/

.805 

.804

2.802 

.801 

.800 

.798 

.796

.795 

2.794

.792

.790

.790

.789

2.787

.785

.784

.783

.781

2.779

.778

.777

.775

.774

.773

2.772

.770

.768

.767

.766

2.764

.762

.761

.760

.758

2.756

.755

.754

.753

.751

.750

2.749

.747

.745

.744

.743

2.741

« 

Inches

5.663

.659

.657

.656

.652

5.648

.646

.644

.641

.637

.635

5.633

.630

.626

.624

.622

5.618

 . 615

nio

 OJ.O

.611 

.607.

5.604 

.602 

.600 

.596 

.592

.590 

5.589

.585

.581

.579

.577

5.574

.570

.568

.566

.562

5.558

.557

.555

.551

.547

.545

5.543

.539

.536

.534

.532

5.528

.524

.522

.520

.517

5'. 513

.511

.509

.505

.501

.499

5.498

.494

.490

.488

.486

5.482

3%'

Inches

8.494

.489

.486

.483

.478

8.472

.470

.467

.462

.456

.453

8.450

.444

.439

.436

.433

8.428

.422

.419 

.416 

.411

8.405 

.402 

.400 

.394 

.388

.386

8

OQO

. OOO

.377

.371

.369

.366

8.360

.355

.352

.349

.343

8.338

.335

.332

.326

.321

.318

8.315

.309

.304

.301

.298

8.292

.286

.284

.281

.275

8.269

.266

' .263

.258

.252

.249

8. 246

.241

.235

.232

.229

8.223

5

Inches

11. 326

.319

, .315

.311

.304

11. 296

.293

.289

.282

.274

.270

11. 267

.259

.252

.248

.244

11.237

.229

.226 

.222 

.215

11. 207 

.203 

.200 

.192

.184

.181 

11. 177

.169

.162

.158

.154

11. 147

.139

.136

.132

.124

11. 117

.113

.109

.102

.094

.090

11. 086

.079

.071

.068

.064

11. 056

.049

.045

.041

.033

11. 026

.022

.018

.010

.003

10.999

10. 995

.987

.980

.970

.972

10. 964

w

Inches

16. 989

.978

.972

.967

.956

16. 945

.939

.933

.922

.911

.906

16. 900

.889

.878

.872

.867

16. 855

.844

'. 833 

.822

16.811 

.805 

.799 

.788 

.777

.771 

16. 766

.754

.743

.737

.732

16. 721

.709

.704

.698

.687

16. 675

.670

.664

652

.641

.635

16. 630

.618

.607

.601

.596

16. 584

.573

.567

.561

.550

16. 538

.533

.527

.516

.504

.498

36.493

.481

.470

.464

.458

16. 447

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

 IK

'3%

5

For latitude 42°, 6K

7^2

10

12]/£

15

IK

3%

5

For latitude 43°< 6K

10 2

12V<2

15

IK

3% 

5 

For latitude 44° < 6K

7/2

10

,15 2

Meridional 

distance

Inches

3. 796

7.592

11. 388

15. 184

18. 980

22. 776

30. 367

37. 960

45. 551

3.797

7.593

11.390

15. 186

18. 983

22. 780

30. 373

37. 967

45. 560

3.797 

7.594

11. 392 

15. 189 

18. 987 

22. 784 

30. 378 

37. 974

45. 568

Ordlnate of developed 

parallel

Inch

0.000

.001

.003

.006

.009

.012

.022

.034

.050

0.000

.001

.003

.006

.009

.012

.022

.035

.050

0.000' 

.001

.003 

.006 

.009 

.012 

.023 

.035

.050
116 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale ^-f^TS Continued

Latitude of

parallel

0 '

44 00

02H

03k

05

07k

10

Hk

12}^

15

I'T* isk

20

22)^

25 

26k

27^

30

32H

33k 

35

40 

41k

45 

47H 

48k

50

52}$

55

56k

57^

45 00

02M

03k

05

07^

10

Hk

12/^

15

17M

18k

20

22^

25

26k

27J^

30

32^

33k

35

37k

40

41k

42^

45

47^

48k

50

52}£

55

56k

57^

46 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.193

.191

.191

.190

.188

2.187

.186

.185

.184

.182

.181

2.181

.179

.177 

.177

.176

2.174

.173

.171 

.170

2.168 

. .167 

.167 

.165 

.164 

.163

2.162

.160

.159

.158

.157

2.156

.154

.153

.153

.151

2.149

.149

.148

.146

.145

.144

2.143

.142

.140

.139

.139

2.137

.135

.134

.134

.132

2.131

.130

.129

.127

.126

.125

2.124

.123

.121

.120

.119

2.118

Ik'

Inches

2.741

-.739

.738

.737

.735

2.733

.732

.732

.730

.728

.727

2.726

.724

.722 

.721

.720

2.718

.716

.715 

.714 

.712

2.710 

.709 

.708 

.706 

.704 

.703

2.702

.701

.699

.698

.697

2.695

.'693

.692

.691

.689

2.687

.686

.685

' .683

.681

.680

2.679

.677

.675

.674

.673

2.671

.669

.668

.667

.665

2.663

.662

.661

.659

.657

.656

2.655

.653

.651

.650

.649

2.647

2^'

Inches

5.482

.478

.476

.475

.471

5.467

.465

.463

.459

.455

.453

5.451

.448

.444 

.442

.440

5.436

.432

. 430 

.428 

.424

5.420 

.419 

.417 

.413 

.409 

.407

5.405

.401

.397

.395

.393

5.389

.385

.383

.381

.378

5.374

.372

.370

.366

.362

.360

5.358

.354

.350

.348

.346

5.342

.338

.336

.334

.330

5.326

.324

.323

.319

.315

.313

5.311

.307

.303

.301

.299

5.295

3k'

Inches

8.223

.218

.215

.212

.206

8.200

.197

.195

.189

.183

.180

8.177

.171

.166 

.163

.160

8.154

.148

.145 

.142 

.137

8.131 

.128 

.125 

.119 

.113 

.110

8.107

.102

.096

.093

.090

8.084

.078

.075

.072

.066

8.061

.058

.055

.049

.043

.040

8.037

.031

.025

.022

.019

8.013

.007

.004

.001

7.996

7.990

.987

.984

.978

.972

.969

7.966

.960

.954

.951

.948

7.942

5'

Inches

10. 964

.957

.953

.949

.941

10. 934

.930

.926

.918

.911

.907

10. 903

.895

.887 

.884

.880

10. 872

.864

CAft

. sou 

.856 

.849

10. 841 

.837 

.833 

.825 

.818 

.814

10. 810

.802

.794

.790

.787

10. 779

.770

.767

.763

.755

10. 747

.743

.740

.732

.724

.720

10. 716

.708

.700

.696

.692

10. 685

.677

.673

.669

.661

10.653

.649

.645

.637

.629

.625

10. 621

.613

.605

.601

.597

10. 590

,*

Inches

16. 447

.435

.429

.424

.412

16. 401

.395

.389

.376

.366

.360

16. 354

.343

.331 

.325

.320

16. 308

.296

!285 

.273

16. 261 

.256 

.250 

.238 

.227 

.221

16.215

.203

.191

.186

.180

16. 168

.156

.150

.144

.133

16. 121

.115

.109

.097

.086

.080

16. 074

.062

.050

.045

.039

16. 027

.015

.009

.003

15. 991

15. 979

.973

.968

.956

.944

.938

15. 932

.920

.908

.902

.896

15. 884

Ordinates of developed parallel and 

meridional distances

Latitude and 

longitude intervals

,

Ik

3k

5

For latitude 44°' 6k

7M

10

12k

15

Ik

3k

5

For latitude 45°< 6k

10 2

I2i/

15

Ik 

2/^

3k 

5 

For latitude 46°' 6k

10 

15

Meridional 

distance

Inches

3.797

7.594

11. 392

15. 189

18, 987

22. 784

30. 378

37. 974

45. 568

3.798

7.596

11. 394

15. 192

18.990 

22. 788

30. 384

37. 980

45. 576

3.799 

7.597

11. 396 

15. 194 

18. 994 

22. 792 

30. 389 

37. 987 

45.484

Ordinate of developed 

parallel

Inch

0.000

.001

.003

.006

.009

.012

.022

.035

.050

0.000

.001

.003

.006

.009 

.012

.022

.035

.050

0.000 

.001

.003 

.008 

.009 

.012 

.022 

.035 

.050
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 117

TABLE 4. Coordinates for the projection of maps, scale -s^fa-a Continued

Latitude of

parallel

O 1

46 00

02^

03%

05

07>i

10

11%

12M

15

18%m

20

WA

25

MX

27H

30

32^

33% 

35 

37H

40 

41% 

42^ 

45 

47^ 

48%

CAou 

62^

65

56%

57J4

47 00

02J^

03%

05

07H

10UK

12>£

15

17M

18%

20

22H

25

26%

27M

30

32^

33%

35

37^

40

41%

42}^

45

47H

48%

50

52^

55

56%

57J^

48 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.118

.116

.116

.115

.113

2.112

.111

.110

.108

.107

.106

2.105

.104

.102

.101

.100

2.099

.097

.096 

.096 

.094

2.092 

.092 

.091 

.089 

.087 

.087

2

f\oa 

. USD

.084

.083

.082

.081

2.079

.078

.077

.076

.075

2.073

.072

.071

.070

.068

.067

2.066

.065

.063

.062

.062

2.060

.058

.058

.057

.055

2.053

.053

.052

.050

.049

.048

2.047

.045

.044

.043

.042

2.040

1%'

Inches

2.647

.645

.644

.643

.641

2.639

.638

.637

.635

.633

.632

2.631

.629

.627

.626

.625

2.623

.621

ftOA . b/U 

.619 

.617

2.615 

.614 

.613 

.611 

.609 

.608

2.607

.605

.603

.602

.601

2.599

.597

.596

.595

.593

2.591

.590

.589

.587

.585

.584

2.583

.581

.579

.578

.577

2.575

.573

.572

.571

.569

2.566

.566

.565

.563

.561

.560

2.559

.557

.555

.553

.552

2.550

2K'

Inches

5.295

.291

.289

.287

.283

5.279

.277

.275

.271

.267

.265

5.263

.259

.255

.253

.251

5.247

.243

.241 

.239 

.235

5.231 

.229 

.227 

.223 

.219 

.217

5. 215

.211

.207

.205

.203

5.199

.195

.192

.190

.186

5.182

.180

.178

.174

.170

.168

5.166

.162

.158

.156

.154

5.150

.146

.144

.142

.138

5.134

.131

.129

.125

.121

.119

5.117

.113

.109

.107

.105

5.101

3%'

Inches

7.942

.936

.933

.930

.924

7.918

.915

.912

.906

.900

.897

7.894

.888

.882

.879

.876

7.870

.864

.861 

.858 

.852

7.846 

.843 

.840 

.834 

.828 

.825

7 Q99 1. o&L

.816

.810

.807

.804

7.798

.792

.789

.786

.780

7.774

.771

.768

.763

.755

.752

7.749

.743

.737

.734

.731

7.725

.719

.716

.713

.706

7.700

.697

.694

.688

.682

.679

7.676

.670

.664

.660

.657

7.651

5'

Inches

10. 590

.582

.578

.574

.566

10. 558

.554

.550

.542

.534

.530

10. 526

.518

.510

.506

.502

10. 494

.486

.482 

.478 

.470

10.462 

.458 

.454 

.446 

.438 

.434

10. 429

.421

.413

. 109

.405

10. 397

.389

.385

.381

.373

10. 365

.361

.357

.349

.341

.336

10. 332

.324

.316

.312

.308

10. 300

.292

.288

.284

.275

10. 267

.263

.259

.251

.243

.239

10. 234

.226

.218

.214

.210

10. 202

7H'

Inches

15.884

.872

.867

.861

.849

15. 837

.831

.825

.813

.801

.795

15. 789

.777

.765

.759

.753

15. 741

.729

.723 

.717 

.705

15. 692 

.686 

.680 

.668 

.656 

.650

15.644

!632

.620

.614

.608

15. 596

.584

.577

.571

.559

15. 547

.541

.535

.523

.511

.505

15. 499

.486

.474

.468

.462

15. 450

.437

.431

.425

.413

15. 401

.394

.388

.376

.364

.358

15. 352

.339

.327

.321

.315

15. 302

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

1%

2H

3%

5

For latitude 46°' 6%

7K2

10

12M

15

1%

2^

3%

5

For latitude 47°.' 6%

IX

10

12>$

15

1% 

Wl 3% 

5 

For latitude 48°' 6%iy-i

10 

12^ 

15

Meridional 

distance

Inchen

3.799

7.597

11.396

15. 194

18. 994

22. 792

30. 389

37. 987

45.584

3.799

7.599

11. 398

15. 197

18. 997

22. 796

30. 394

37. 994

45. 592

3.800 

7.600

11.400 

15.200 

19.000 

22.800 

30.400 

38.001 

45. 600

Ordinate of developed 

parallel

Inch

0.000

.001

.003

.006

.009

.012

.022

.035

.050

0.000

.001

.003

.006

.009

.012

.022

.035

.050

0.000 

.001

.003 

.006 

.009 

.012 

.021 

.035 

.050
118 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 4. Coordinates for the projection of maps, scale TS^-O'UO- Continued

Latitude of

parallel

0 /

48 00

02^

05 4

07M

10

Ilk

15 2

17/^

18k

20

22^

25 

26k

30

33k 

35 

37^

40 

41k

42^ 

45

48k

50

SV/2

55

56k

49 00

02^

03k

05

07^

10

Ilk

15

17H

18k

20

22y2

25

26k

30

32^

33k

35

37H

40

41k

42^

45

47V*

48k

50

521/1

55

56k

57J3

50 00

Abscissas of developed parallel

Longitude interval

1'

Inches

2.040

.039

.038

.037

.035

2.034

.033

.032

.030

.029

.028

2.027

.025

.024 

.023

.022

2.020

.019

ftlfl

. Ulo 

.017 

.016

2.014 

.013 

.012 

.011 

.009 

.008

9 £1. fVY7 UUI

.006

.004

.003

.002

2.001

1.999

.998

.997

.996

1.994

.993

.992

.991

.989

.988

1.987

.986

.984

.983

.982

1.980

.979

.978

.977

.975

1.974

.973

.972

.970

.969

.968

1.967

.965

.964

.963

.962

1.960

Ik'

Inches

2.550

.548

.547

.546

.544

2.542

.541

.540

.538

.536

.535

2.534

.532

.530 

.'529

.528

2.526

.524 

. 523

!521 

.519

2.517 

.516 

.515 

.513 

.511 

.510

9 fit UUO VIQ

.507

.505

.504

.503

2.501

.499

.498

.497

.494

2.492

.491

.490

.488

.486

.485

2.484

.482

.480

.479

.478

2.476

.473

.472

.471

.469

2.467

.466

.465

.463

.461

.460

2.459

.457

.454

.453

.452

2.450

w

Inches

5.101

.097

.095

.093

.088

5.084

.082

.080

.076

.072

.070

5.068

.064

.060 

.058

.055

5.051

.047

OAK.

, UlU

.043 

.039

5.035 

.033 

.031 

.027 

.022 

.020

5.018

.014

.010

.008

.006

5.001

4.997

.995

.993

.989

4.985

.983

.981

.976

.972

.970

4.968

.964

.960

.957

.955

4.951

.947

.945

.943

.939

4.934

.932

.930

.926

.922

.920

4.918

.913

.909

.907

.905

4.901

3k'

Inches

7.651

.645

.642

.639

.633

7.626

.623

.620

.614

.608

.605

7.602

.596

.589 

.586

.583

7.577

.571

KCQ

, OOo

.564 

.558

7.552 

.549 

.546 

.540 

.533 

.530

7.527

.521

.515

.512

.508

7.502

.496

.493

.490

.483

7.477

.474

.471

.465

.458

.455

7.452

.446

.439

.436

.433

7.427

.420

.417

.414

.408

7.401

.398

.395

.389

.383

.379

7. 376

.370

.363

.360

.357

7.351

5'

Inches

10. 202

.193

.189

.185

.177

10. 169

.165

.160

.152

.144

.140

10. 136

.127

.119 

.115

.111

10. 103

.094 

noft . UoU

.086 

.078

10. 069 

.065 

.061 

.053 

.045 

.040

10. 036

.028

.020

.015

.011

10.003

9.995

.990

.986

.978

9.970

.965

.961

.953

.944

.940

9.936

.928

.919

.915

.911

9.902

.894

.890

.886

.877

9.869

.864

.860

.852

.843

.839

9.835

.826

.818

.814

.810

9.801

* 

Inches

15. 302

.290

.284

.278

.265

15. 253

.247

.241

.228

.216

.210

15. 204

.191

.179 

.173

.166

15. 154

.142

iqc

. lou

.129 

.117

15. 104 

.098 

.092 

.079 

.067 

.061

15. 054

.042

.029

.023

.017

15. 004

14.992

.986

.979

.967

14. 954

.948

.942

.929

.917

.910

14. 904

.891

.879

.872

.866

14. 854

.841

.835

.828

.816

14. 803

.797

.790

.778

.765

.759

14. 753

.740

.727

.721

.714

14. 702

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

/

Ik

2J/2

3k

5

For latitude 48°< 6k

7Mi

10

12M

15

Ik

21^ 3k

5

For latitude 49°' 6k

7X2

10

1 Ot/^

1*5

ik

3j|

5 

For latitude 50° ! 6k 10 2 

\iy-i,

15

Meridional 

distance

Inches

3.800

7.600

11. 400

15. 200

19.000

22.800

30.400

38. 001

45. 600

3.801

7.601

11. 402

15. 202

19.004 

22. 804

30. 405

38. 007

45. 608

3.801 

7.603

11.404 

15. 205 

19. 007 

22. 808 

30.411 

38. 014 

45. 617

Ordinate of developed 

parallel

Inch

0.000

.001

.003

.005

.009

.012

.022

.034

.050

6.000

.001

.003

.005

.009 

.012

.022

.034

. 049

0.000 

.001

.003 

.005 

.009 

.012 

.022 

.034 

.049
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 119

TABLE 4. Coordinates for the projection of maps, scale -^tair Continued

Latitude of

parallel

0 1

50 00

02 J.^

03%

05

07^

10

11%

15 2

17J^

V&A

20

25 2 

20%

30

33% 

35

373-3

40

41%

4234

45

47H

48%

50

52J4

55

50%

57J4

51 00

02H

03%

05

07%

10

11%

15 2

173^

18^

20

2234

25

20%

2734

30

323^

33%

35yiYi

40

41%

45

47J4

48%

50

5234

55

66%

57>i

52 00

Abscissas of developed parallel

Longitude interval

1'

Inches

1.960

.959

.958

.957

.955

1.953

.953

.952

.950

.948

.948

1.947 

.945

' .943 

.942

.942

1.940

.938

.937 

.936

.935

1.933

.932

.931

.930

.928

.927

1.926

.924

.923

.922

.921

1.919

.918

.917

.910

.914

1.912

.912

.911

.909

.907

.906

1.906

.904

.902

.901

.900

1.899

.897

.896

.895

.893

1.892

.891

.890

.888

.886

.885

1.885

.883

.881

.880

.879

1. 878

1%'

Inches

2.450

.448

.447

.446

.444

2.442

.441

.440

.438

.435

.434

2.433 

.431

.429 

.428

.427

2.425

.423

.422 

.420

.418

2.416

.415

.414

.412

.410

.409

2.408

.400

.403

.402

.401

2.399

.397

.390

.395

.393

2.390

.389

.388

.386

.384

.383

2.382

.380

.377

.376

.375

2.373

.371

.370

.369

.367

2.364

.363

.362

.360

.358

.357

2.356

.354

.352

.350

.349

2.347

W

Inches

4. 901

.896

.894

.892

.888

4.884

.882

.879

.875

.871

.869

4.867 

.802

.858 

.850

.854

4.850

.845

. 843 

.841

.837

4.833

.830

.828

.824

.820

.818

4.815

.811

.807

.805

.802

4.798

.794

.792

.790

.785

4.781

.779

.777

.772

.768

.766

4.764

.759

.755

.753

.751

4.746

.742

.740

.738

.733

4.729

.727

.725

.720

.716

.714

4.712

.707

.703

.701

.699

4.694

3%'

Inches

7.351

.344

.341

.338

.332

7.325

.322

.319

.313

.306

.303

7.300 

.293

.287 

.284

.281

7.274

.268

!261

.255

7.249

.246

.242

.230

.229

.226

7.223

.217

.210

.207

.204

7.197

.191

.188

.184

.178

7.171

.168

.165

.159

.152

.149

7.146

.139

.133

.129

.120

7.120

.113

.110

.107

.100

7.094

.090

.087

.081

.074

.071

7.068

.001

.055

.051

.048

7.042

5'

Inches

9.801

.793

.788

.784

.776

9.767

.763

.759

.750

.742

.737

9.733 

.725

.710 

.712

.708

9.699

.691

. 080 

.682

.074

9.665

.661

.656

.648

.639

.035

9.631

.622

.614

.609

.605

9.596

.588

.583

.579

.571

9.562

.558

.553

.545

.530

.532

9.528

.519

.510

.506

.501

9.493

.484

.480

.476

.467

9.458

.454

.450

.441

.432

.428

9. 424

.415

.406

.402

.397

9.389

1Y!

Inches

14. 702

.689

.683

.676

.664

14. 651

.645

.638

.625

.613

.606

14. COO

.587

.574 

.568

.561

14. 549

.536

. 529 

.523

.510

14. 498

.491

.485

.472

.459

.453

14. 446

.433

.420

.414

.408

14. 395

.382

.375

.369

.356

14. 343

.330

.330

.317

.304

.298

14. 291

.278

.265

.259

.252

14. 239

.226

.220

.213

.200

14. 187

.181

.174

.101

.148

.142

14. 135

.122

.109

.103

.090

14.083

Ordinates of developed parallel and 

meridional distances

Latitude and longitude intervals

,

f 1%

VA

3%

5

For latitude 50° 6%

734

10

1234

15

1%

3% 

5

For latitude 51°' 6%

10 2

12V^

15

Meridional

distance

Inches

3.801

7.603

11.404

15. 205

19.007

22. 808

30.411

38. 014

45. 617

3.802

7.604

11. 406

15. 208

19. 010 

22. 812

30. 410

38. 021

45. 025

Ordinato

of developed 

parallel

Inch

0.000

.001

.003

.005

.009

.012

.022

.034

.049

0.000

. 001

!(X)3 fin"; . uuu

.008 

.012

.022 fl'U . Uu'l

.049
TABLE 5. Coordinates of intersections of meridians and parallels and lengths of 

[For modified polyconic projection of map of the world, n

Latitude 

(°)

0- 1 

1- 2 

2- 3 

3- 4

(0-4)

4- 5 

5- 6 

6- 7

7- 8

(4-8)

8- 9 

9-10 

10-11 

11-12

(8-12)

12-13 

13-14 

14-15 

15-16

(12-16)

16-17 

17-18 

18-19 

19-20

(16-20)

Length 

of 

central 

meridian

110,498.2 

110, 498. 9 

110,500.3 

110,502.3

441, 999. 7

110, 505. 7 

110,509.1 

110, 513. 2 

110,518.0

442, 046. 0

110, 524. 4 

110, 530. 4 

110, 537. 2 

110, 544. 6

442, 136. 6

110, 554. 8 

110, 563. 4 

110, 572. 6 

110,582.4

442, 273. 2

110, 595. 4 

110, 606. 4 

110, 617. 9 

110, 630. 0

442, 449. 7

Meridian 1° from central meridian

Length 

of 

meridian

110,515.2 

110,515.8 

110,517.2 

110,519.3

442, 067. 5

110, 522. 5 

110,525.0 

110, 530. 0 

110,534.7

442, 113. 1

110, 540. 9 

110, 546. 9 

110, 553. 7 

110, 561. 1

442, 202. 6

110, 570. 7 

110, 579. 3 

110, 588. 6 

110, 598. 4

442, 337. 0

110, 610. 7 

110, 621. 7 

110, 633. 3 

110,645.4

442, 511. 1

X

(for lower 

latitude)

111,321.3 

111,253.9 

111,186.6 

111,119.3

111,051.9 

110,850.2 

110, 648. 5 

110,446.8

110, 245. 1 

109, 909. 9 

109, 574. 8 

109, 239. 6

108, 904. 4 

108, 437. 4 

107, 970. 3 

107, 603. 2

107, 036. 1 

106, 439. 3 

105, 842. 5 

105, 245. 7

Y 

(for lower 

latitude)

0.0 

16.9 

33.8 

50.7

67.6 

84.2 

100.7 

117.3

133.9 

149.8 

165.7 

181.7

197.6 

212.6 

227.5 

242.5

257. 5 

271.2 

284.9 

298.6

Meridian 2° from central m

Length 

of 

meridian

110, 565. 9 

110,566.6 

110,568.0 

110, 570. 0

442, 270. 5

110, 572. 8 

110, 576. 2 

110, 580. 2 

110, 585. 0

442, 314. 2

110,590.4 

110, 596. 4 

110, 603. 2 

110,610.6

442, 400. 6

110,618.6 

110, 627. 2 

110, 636. 4 

110, 646. 2

442, 528. 4

110, 656. 7 

110,667.7 

110,679.2 

110, 691. 4

442, 695. 0

'X 

(for lower 

latitude)

222, 642. 6 

222, 507. 9 

222, 373. 1 

222, 238. 4

222, 103. 7 

221, 700. 1 

221, 296. 6 

220, 893. 0

220, 489. 5 

219, 819. 0 

219, 148. 5 

218. 477. 9

217, 807. 3 

216, 873. 0 

215. 968. 7 

215, 034. 2

214, 069. 7 

212, 875. 9 

211,681.9 

210, 487. 9
TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS .121

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122 TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS

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2

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TABLES FOR CONSTRUCTION OF POLYCONIC PROJECTIONS 123

TABLE 6. Coordinates of intersections of meridians and parallels and lengths of 

meridians for each degree of latitude, in inches

[For modified polyconlc projection of map of the world, scale 1:1,000,000]

Latitude (°)

0-1 

1-2 

2-3 

3-4

(0-4)

4-5 

6-6 

6-7 

7-8

(4-8)

8-9 

9-10 

10-11 

11-12

(8-12)

12-13 

13-14 

14-15 

15-16

(12-16)

16-17 

17-18 

 18-19 

19-20

(16-20)

20-21 

21-22 

22-23 

23-24

(20-24)

24-25 

25-26 

26-27 

27-28

(24-28)

28-29 

29-30 

30-31 

31-32

(28-32)

32-33 

33-34 

34-35 

35-36

(32-36)

36-37 

37-38 

38-39 

39-40

(36-40)

Length of 

central 

meridian

4.350 

4.350 

4.350 

4.350

17. 400

4.351 

4.351 

4.351 

4.351

17.404

4,351 

4.352 

4.352 

4.352

17. 407

4.353 

4.353 

4.353 

4.354

17. 413

4. 354 

4.355 

4.355 

4.356

17. 420

4.356 

4.357 

4.357 

4.358

17.428

4.358 

4.359 

4.360 

4.360

17. 437

4.361 

4.362 

4.362 

4.363

17.448

4.364 

4.365 

4.365 

4.366

17.460

4.367 

4.368 

4.369 

4.369

17. 473

Meridian 1° from central 

meridian

Length of 

meridian

4.351 

4.351 

4.351 

4.351

17.404

5.351 

4.351 

4.352 

4.352

17. 406

4.352 

4.352 

4.353 

4.353

17. 410

4.353 

4.354 

4.354 

4.354

17. 415

4.355 

4.355 

4.356 

4.356

17.422

4.357 

4.357 

4.358 

4.358

17. 430

. 4. 359 

4.360 

4.360 

4.361

17.440

4.362 

4.362 

4.363 

4.364

17. 451

4.364 

4.365 

. 4.366 

4.367

17. 462

4.367 

4.368 

4.369 

4. 370

17. 474

X

(for 

lower latitude)

4.383 

4.380 

4.377 

4.375

4.372 

4.364 

4.356 

4.348

4.340 

4.327 

4.314 

4. 301

4.288 

4.269 

4.251 

4.232

4.214 

4.191 

4.167 

4.144

4.120 

4.092 

4.063 

4.035

4.006 

3.973 

3.939 

3.906

3.873 

3-834 

3.796 

3.758

3.720 

3.678 

3.635 

3.592

3.550 

3.503 

3.456 

3.409

Y 

(for 

lower latitude)

0.000 

.001 

.001 

.002

.003 

.003 

.004 

.005

.005 

.006 

.007 

.007

.008 

.008 

.009 

.010

.010 

.011 

.011 

.012

.012 

.013 

.013 

.014

.014 

.015 

.015 

.015

.016 

.016 

.017 

.017

.017 

.017 

.018 

.018

.018 

.018 

.019 

.019

Meridian 2° from central 

meridian

Length of 

meridian

4.353 

4.353 

4.353 

4.353

17. 412

4.353 

4.353 

4.354 

4.354

17. 414

4.354 

4.354 

4.354 

4.355

17. 417

4.355 

4.355 

4.356 

4.356

17. 422

4.357 

4.357 

4-357 

4.358

17.429

4.358 

4.359 

4.359 

4.360

17. 436

4.361 

4.361 

4.362 

4.362

17. 446

4.363 

4.364 

4.364 

4.365

17.456

4.366 

4.367 

4.367 

4.368

17.468

4.369 

4.369 

4.370 

4.371

17. 479

X

(for 

lower 

latitude)

8.765 

8.760 

8.755 

8.750

8.744 

8.728 

8.712 

8.697

8.681 

8.654 

8.628 

8.601

8.575 

8.538 

8.503 

8.466

8.428 

8.381 

8.334 

8.287

8.240 

8.183 

8.126 

8.069

8.012 

7.945 

7.878 

7.812

7.745 

7.669 

7.593 

7.516

7.440 

7.355 

7.270 

7.1$

7.099 

7.005 

6.911 

6.818

Y 

(for 

lower latitude)

0.000 

.003 

.005 

.008

.011 

.013 

.016 

.018

.021 

.024 

.026 

.029

.031 

.033 

.036 

.038

.041 

.043 

.045 

.047

.049 

.051 

.053 

.055

.057 

.059 

.060 

.062

.063 

.065 

.066 

.067

.069 

.070 

.071 

.072

.073 

.073 

.074 

.075

Meridian 3° from central 

meridian

/ength of 

meridian

4.356 

4.356 

4.356 

4.356

17. 424

4.357 

4.357 

4.357 

4.357

17.428

4.357 

4.357 

4.358 

4.358

17. 430

4.358 

4.359 

4.359 

4.359

17. 435

4.360 

4.360 

4.360 

4.361

17.441

4.361 

4.362 

4.362 

4.363

17.448

4.363 

4.364 

4.365 

4.365

17. 457

4.366 

4.366 

4. 367 

4.368

17. 467

4.368 

4. 369 

4. 370 

4.370

17. 477

4.371 

4. 372 

4. 372 

4. 373

17.488

X

(for 

lower 

latitude)

13. 148 

13. 140 

13. 132 

13.124

13. 116 

13. 092 

13. 069 

13.045

13. 021 

12. 981 

12. 942 

12. 902

12. 862 

12. 807 

12. 752 

12. 697

12.642 

12. 571 

12.501 

12. 430

12. 359 

12. 274 

12.188 

12. 103

12. 017 

11.917 

11.817 

.11. 717

11. 617 

11.502 

11.388 

11. 274

11. 159 

11. 032 

10.904 

. 10.776

10.648 

10.507 

10. 366 

10. 225

Y 

(for 

lower 

latitude)

0.000 

.006 

.012 

.018

.024 

.030 

.036 

.042

.047 

.053 

.059 

.064

.070 

.075 

.081 

.086

.091 

.096 

.101 

.106

.111 

.115 

.11.9 

.124

.128 

.132 

.135 

.139

.143 

.146 

.149 

.152

.155 

.157 

.159 

.162

.164 

.165 

.167 

.168

6243° 2<
124 TABLES FOB CONSTRUCTION OF POLYCONIC PROJECTIONS

TABLE 6. Coordinates of intersections of meridians and parallels and lengths of 

meridians for each degree of latitude, in inches Continued

Latitude (°)

4041 

41-42 

42-43 

43-44

(40-44)

44-45 

45-46 

46-47 

47-48

(44-48)

48-49 

49-50 

50-51 

51-52

(48-52)

52-53 

53-54 

54-55 

55-56

(52-56)

56-57 

57-58 

58-59 

59-60

(56-60) 

60

Length of 

central 

meridian

4.370 

4.371 

4.372 

4.373

17. 486

4.374 

4.374 

4.375 

4.376

17. 499

4.377 

4.378 

4.378 

4.379

17. 512

4.380 

4.381 

4.382 

4.382

17. 525

4.383 

4.384 

4.385 

4.385

17. 537

Meridian 1° from central 

meridian

Length of 

meridian

4.371 

4.371 

4.372 

4.373

17. 487

4.374 

4.375 

4.375 

4.376

17.500

4.377 

4.378 

4.379 

4.379

17. 513

4.380 

4.381 

4.382 

4.383

17. 526

4.383 

4.384 

4.385 

4.386

17. 538

X

(for 

lower 

latitude)

3.362 

3.311 

3.260 

3.209

3.158 

3.103 

3.048 

2.993

2.938 

2.880 

2.821 

2.762

2.704 

2.642 

2.580 

2.518

2.456 

2.392 

2.327 

2.262

2.197

Y

(for 

lower 

latitude)

0.019 

.019 

.019 

.019

.019 

.019 

.019 

.019

.019 

.019 

.019 

.019

.019 

.018 

.018 

.018

.018 

.017 

.017 

.017

.017

Meridian 2° from central 

meridian

Length of 

meridian

4.372 

4.373 

4.373 

4.374

17. 492

4.375 

4.376 

4.376 

4.377

17.504

4.378 

4.379 

4.379 

4.380

17. 516

4.381 

4.382 

4.383 

4.383

17. 529

4.384 

4.385 

4.385 

4.386

17.540

X

(for 

lower latitude)

6.724 

6.621 

6.519 

6.417

6.315 

6.205 

6.095 

5.985

v 5. 876 

5.759 

5.641 

5.524

5.407 

5.284 

5.160 

5.036

4.912 

4.783 

4. 653 

4.523

4.393

Y 

(for 

lower 

latitude)

0.075 

.076 

.076 

.076

.077 

.076 

.076 

.076

.076 

.076 

.075 

.075

.074 

.074 

.073 

.072

.071 

.070 

.069 

.068

.066

Meridian 3° from central 

meridian

Length of 

meridian

4.374 

4.374 

4.375 

4.376

17. 499

4.376 

4.377 

4.378 

4.379

17. 510

4.379 

4.380 

4.381 

4.382

17. 522

4.382 

4.383 

4.384 

4.384

17.533

4.385 

4.386 

4.386 

4.387

17.544

X

(for 

lower latitude)

10.084 

9.931 

9.778 

9.625

9.471 

9.307 

9.142 

8.977

8.812 

8.637 

8.461 

8.285

8.110 

7.924 

7.738. 

7.553

7.367 

7. 173 

6.978 

6.783

6.589

Y 

(for 

lower latitude)

0.170 

.170 

.171 

.172

.172 

.172 

.172 

.172

.171 

.170 

.169 

.168

.167 

.165 

.164 

.162

.160 

.157 

.155 

.152

.149
INDEX

Page 

Advantages of polyconic projection....... 1

Albers equal-area projection, suggested for

use._.......................... 27

Arc of meridian, approximate formula for

length on spheroid_._..--... 10 

computation of.___.______----- 9-14

developed arc on modified polyconic projection... ............-...-..---.. 38-41

formulas for developed arcs on modified

polyconic projection..___.. 38,40,41

rigid formulas for length on spheroid .. 13,14

Arc of parallel, computation of __..... 14-15

formula for length of...________ 15 

radius of_....____________ 16

Characteristics of polyconic projection....... 2

Choice of projection.....________.... 1

Clarke, Col. A. R., reference to_._____ 3,30 

Clarke spheroid of 1866, dimensions of....... 4

reference to..______-...___...- 3,4 

Clarke spheroid of 1880, comparison with

Hayford spheroid......_.__ 31

dimensions of._..°.............._..... 36

references to--....-......---.-.-... 30,31,36,38

Coast and Geodetic Survey publications, references to.... 2,3,4,8,10,17,21,25,26,28

Constants, in formulas for meridional arcs.12,14,39 

in formulas forz and y.____....___ 19,42

of generating ellipse.._...___._.-.-- 4 

Construction of American polyconic projection, by Bumstead plate, reference to.. --------_.-._------- 21

by Coast Survey method, reference to. .. 21,25 

by Geological Survey method, description

of.... - .....--. .---- 21-25

Construction of modified polyconic projection

of map of world, description of 31-35 

Conversion of meters on spheroid to inches on

map scale_._..__.__..-. 20 

Coordinates. See Rectangular coordinates. 

Curved meridians _....... ...... . 2,24

D

Disadvantages of polyconic projectionEccentricity of ellipse .... 

Elements of generating ellipse.

Page 

Factors, log A........................ 8,9,17,18,19

log B................................... 8,9,10

Formulas for American polyconic projection,

A M.......................... 10,13,14

A P...................................... 15

M....................................... 12

Pm~ ............................... 7,9

Pn..................................^.... 8,9

x..................................... 17,18,19

y..................................... 17,18,19

Formulas for modified poly conic projection

A M0 ............................ 40,41

A Mi..................................... 40,41

A Ma...............................

A M«...............................

Pm_ ___----.---__-_------.__-_.------

-..... ....-.-- 38,41

.............................. 40,41

.............................. 37

pa........................................ 37

x......................................... 41,42

y.. ...................................... 41,42

G

Geological Survey bulletins, references to_. 3, 

4,8,10,17,20,25 

H

Hassler, Ferdinand, polyconic projection

devised by...__________ 2 

Hayford spheroid, comparison with Clarke

spheroid_.. ........ 31

dimensions of...__...____ ___ 31

references to_______________ 3,30,38

Hinks, Arthur R., quoted................... 26,28

International Map Committee, reference

to......................... 25,26,28,30

International map sheets, above latitude 60°. 28 

junction of............____ __ 27

limits of._________________ 25 

numbering of...............__.___.. 26

Interpolation of projection tables for other

scales..__.__________ 25

Joining of sheets__......__________ 2,27

L

Lallemand, Charles, formulas of.... 30,38,40,41,42

Lambert conformal projection, reference to.. 27 

Latitude, geocentric._-..-....-.-.--------- 5

astronomical__.........__.......__ 5,9

Lomnicki, Antoni, suggestions by. -_ 26,29,30,37

125
126 INDEX

Page

M

Meridional arcs, approximate formula for

length on spheroid_ ....__ 10 

computation of - 9-14 

developed arc on modified polyconic

projection.... _... 38-41 

formulas for developed arcs on modified

polyconic projection.. __ 38,40,41 

rigid formulas for length on spheroid.._ 13,14 

Meter, legal value in the United States__ 4,8,20 

Modified polyconic projection of map of

world, construction of-..__... 31-35 

description of tables for..__ __... 29 

dimensions of spheroid used.. __ __.. 36 

drawing of developed parallels... __... 29 

general specifications..... ..-- 25,26

joining of sheets. _______ __... 27 

length of developed meridians.... ___ 38-41

order of computations...__....._... 37-38

nomenclature used in formulas.-.._..". 36 

radii of curvature___._...__--. 37 

rectangular coordinates..__ ........ 41-42

spheroid used...___________... 30 

standard parallels and meridians..._... 26 

subdivision of meridians into 1° lengths.. 40 

theory of................................ 35-42

O

Ordinates of developed parallel, method of

plotting-....-.---------.----.--. 23.33

Parallel, arc of, computation of... __ 14-15

arc of, formula for length of... ----- 15

radius of.____..__... ........ 16

Page

Parallels, method of drawing, on American

polyconic projection__ ___ 24 

method of drawing, on modified polyconic

projection.____________ 29 

Polyconic projection of 15' quadrangle. ___ 22 

Projection scale, -special type used by Geological Survey.._______.. 32

R

Radian, value of...______________ 9

Radius of curvature, meridional section_ 4,7,9,37 

normal section_____________ 4,8,9,37

Rectangular coordinates for American polyconic projection_______... 15-19 

analysis of formulas for x and y.......... 19

analysis of values of x and AP._____ 20 

approximate formulas for x and y........ 18,19

rigid formulas forz and y................ 17

Rectangular coordinates for modified polyconic projection_______ 41-42

approximate formulas for x and y........ 42

rigid formulas for i and y_.___:___ 41

Smithsonian Geographic Tables, references

to.............................. 3,4,8

Spheroid. See Clarke spheroid and Hayford 

spheroid.

Tangent cone, elements of. 

development of.___.

W

Woodward, R. S., reference, to

O