10 
GEOGRAPHIC TABLED AND FORMULAS. 
'BULL. 214. 
REDUCTION" TO CENTER. 
In fig. 2 let 
P= place of instrument; 
C = center of station; 
Q= measured angle at P between two objects, A and B; 
y=smg\e at P between C and the left-hand object, B; 
r= distance CP; 
C' = unknown and required angle at C; 
D = distance AC; 
(r and D must be" reduced to same unit, usually meters.) 
G= distance BC; and 
A = angle at A between P and C; 
B= angle at B between P and C. 
Fig. 2.— Reduction to renter. 
Then, from the relation between the parts of the triangle, 
G : r :: sin y : sin B; 
hence 
(jr 
As the angles at A and B are very small, they ma} r be regarded as 
equal to A sin 1" and B sin 1"; hence 
and 
B= (in seconds) *; s ? n ?„ 
Gr sin 1" 
C'-Q 4- ^ sinJQiy) _ r sin y 
^ ^ D sin 1" G sin 1"* 
