(156) 
The angular displacements whereby ABC is brought 
to A’ B’ C’ are accordingly 
; C— A 
0, — Sin & COS nl, 
de — Sin & sin 2 nt, 
x C— A 
8; — tan À Sin a cos nl. 
Further the variation of latitude is 
C — A 
d'A = SIN & Sin nl. 
Since in our figure the angle 
; C — A 
ACRIS £7 — 90 OP 7 + nt, 
it follows from the approximate treatment of the sphe- 
rical triangle C/CP or ICP that the angle 9% between the 
astronomical and geographical meridians at the point P 
1s given by 
sin «& C — A 
d'y — COS —— nt (*). 
À cos À A (0) 
() The following are the rigorous formulæ for ôÀ and ÔY : 
sin (À + ÔÀ) = sin À cos « — cos À sin « sin %o, 
TS lan & COS ®o 
KT cos à + tana sin À sin vo 
