10 
GEOGRAPHIC TABLES AND FORMULAS. 
[BULL. 234. 
REDUCTIOIS^ TO CEJ^TER. 
In %. 2 let 
P = place of instrument; 
C= center of station; 
Q= measured angle at P between two objects, A and B; 
?/ = angle at P between and the left-hand object, B; 
7'= distance CP; 
C' = unknown and required angle at C; 
D = distance AC; 
(/' and D must be reduced to same unit, usually meters.) 
G = distance BC; 
A = angle at A between P and C; 
B= angle at B between P and C. 
Fig. 2.— Reduction to center. 
Then, from the relation between the parts of the triangle, 
G : r :: sin ?/ : sin B; 
hence 
. „ 7' sin y 
sm B= Y^' 
As the angles at A and B are very small, their sines may be reg^arded 
as equal to A sin 1" and B sin 1", respectively; hence 
and 
B = (mseconds)g:^^^^ 
^-W.-t £)sini'' Gsinl" 
