190 
UEOGKAPHIC TABLES AND FORMULAS. 
[Bull. '234. 
Table 22. — Geodetic Position Computations. 
TABLE OF LOGARITHMS OF FACTORS A, B, C, D, E, F, BASED TPON THE CLARKE SPHE- 
ROID OF 1866 AND THE METRIC SYSTEM, BETWEEN LATITUDES 0° AND 72°. 
[Extracted from reports of the U. S. Coast and Geodetic Survey.] 
CONSTANTS. 
(1 — 1'^ siii^ cp)^ 
A = 
a arc 1^ 
( 1 — e'^ sin^ gD) ^ 
^""a (1 — e^) arcr^ 
C = 
D = 
(1 — e^ sin'' cpY tan cp 
2a^ (1 — e') arcr^ 
f ^ sin <p cos q> arc 1^^ 
1 — e^ sin^ (p 
^ (l + 3tan=^ <p) (1-^'' sin'' cp) 
F = Jo sin </? cos*^ ^ arc"^ V^ 
^ (f arc V 
1 
^^8« (1-t'"'') arcP 
1 1 
^''^2d' {\ — e') arcr 
log a = 6. 804 698 57 
log/y==6.803 223 78 
ogt^'^ = 7.830 502 57 
= 8.509 726 56 
==8.512 676 15 
1.406 947 6 
log (f e^ arc rO =2.692 168 7 
log g^ = 5.612 45 
log (xVarc" 1^0 = 8-291 96 
Ratio adopted in this table is the Clarke value of the meter, namely, 1 meter = 
39.370432 inches. 
The formulas for the computation of the geodetic differences in latitude Acp, in 
longitude A\^ and in azimuth A a are as follows: 
i--A(p—8 cos a . B j-s^ sin"^ a . C'+-{8cp)'^ D—h . i^^ sin'^ a . E 
//A=.s sin a sec (p^ . A 
-^Acx=JX sin I {cp+cp') sec i {A(p)+{AXy F 
where 
r (p'--=(p^A(p 
\ /V=A-t z/A _ I f — <5(p=.§ cos a . B—i? sin'' a . C—h . .s'' sin" a . E 
I a^ = a-^Ja-^im •- also /i=s cos a . B 
For subordinate triangulation when tlie sides do not exceed say 25 kilometers, or 
about 15 statute miles, the term involving E in Aq) and the factor sec i {A(p), as 
well as the term involving Fin A a, may be omitted. 
