116 
PROFESSOR AIRY ON AN INEQUALITY OF LONG PERIOD 
Section 20. 
Numerical calculation of the perturbation in latitude. 
. ( 9 ) 
65. The first of the terms found in the last section is — M . d 2, <p' f . cos 
{ 13 (n 1 1 + s') — 8 {nt + s) — 3 ts' — 0' — 0}. With respect to this term only, 
\ d 2 f. cos {13 (n t -{- s') — 8 (nt z) — 3 or' — 0'— 0} ; whence 
( 9 ) 
n' a Pd R , M a' 
r- 0 ' _ VLaL - 0 ' 4 - 
0 ~ U u> tfjt d 4 “ U + 
/x' <pj t d <p l 
— 8 (n t -f- s) — 3 zs — 0' — 6}. 
f -lsy-sn* (j/sm {13 (» 1 + 0 
And 
^7 — _ ]y[ ( \ e '3 qj f % s i n { 13 (ri t + s) — 8 (n t -f- s) — 3 vs — 0' — ; 
whence 
( 9 ) 
, , w r a' R - , . M a n , „ 
f = ® + = ® 3 /-c°s{13(»/ + s) 
— 8 (w / + s) — 3 ZS — — 0}. 
The Earth’s latitude, neglecting small terms, is <p' . sin (V / -f- s' — 0'). And 
from the expression above, sin {ri t -f s' — 0') = 
( 9 ) 
sin (n't + s'- 0') . - f3^ - ”^ 8w • ^ cos («'* + s' - 0') . si 
{13 (n't + s') — 8 (n t + s) - 3 nf — 0' — 
Multiplying this by the expression for <£>', and putting 0', <p\ for 0', O', in the 
small terms, we find for the latitude 
sm 
(9) 
M a' n' , j. . 
-7- • rnr-"87» • « 3 /- sm {12 (» < + 0 
— 8 (ft t 4“ s) — 3 73 -' — 0} 
O' . sin (n t + s'— 0') — 
and the last part, or the perturbation in latitude, is 
n' M ^ d 
~ 13»'-8m ‘ e ' 3 f’ * sin { 12 i n>t + 0 “ 8 (ft t + s) - 3 tar' - 
Similar expressions will be obtained from all the other terms. 
