GANNETT.] 
REDUCTION TO CENTER. 
11 
In the use of this formula, proper attention should be paid to the 
signs of sin (Q+y) and sin y\ for the first term will be positive only 
when (Q+y) is less than 180° (the reverse with sin y)\ D being the 
distance of the right-hand object, the graduation of the instrument 
running from left to right. 
r being relatively small, the lengths of D and G are approximately 
computed with the angle Q. 
The following quantities must be known in addition to the measured 
angles in order to find the correction for reducing to center: 
1. The angle measured at the instrument, P, between the center of 
the signal or station, C, and the first-observed station to the right of 
it, A. 
2. The distance from the center of the instrument to the center of 
the station = r. 
3. The approximate distances, D, G, etc., from the station occupied 
to the stations observed. The latter may l)e computed from the 
uncorrected angles. 
Example: Reduction to center from P to C. 
Constants: a. c. log sin 1" =5. 31443 
log feet to log meters =9. 48402 
log constant (for any station) 
^'=G.5 feet: log- 
log constant for this station 
4. 79845 
==0.81291 
5. 61136 
log sin angle 
a. c. log distance 
log r + constant 
log correction 
correction to direction 
Angle 
Q-Y 
(CPA) 
23° 40' 
9. 6036 
5. 8954 
5.6114 
0. 6104 
4^^ 08 
Angle 
Y 
(BPC) 
37°14' 
or 322° 46' 
9. 7818 
5. 8162 
5. 6114 
0. 7094 
correction to angle B P A=4^^08 -f r/M2=9^^20. 
