GANNETT.] 
REDUCTION TO CENTER. 
11 
In the use of this formula, proper attention should be paid to the 
signs of sin (Q+//) and sin y\ for the first term will be positive only 
when (Q+//) is less than 180° (the reverse witlr sin ?/); I) 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 Gr 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 be 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) 
7'= 6. 5 feet: log 
log' constant for this station 
4. 79845 
:0. 81291 
5. 61136 
Angle 
Q-Y 
(CPA) 
23° 40' 
log sin angle 9. 6036 
a. c. log distance 5. 3954 
log /' f constant 5. 6114 
log correction 0. 6104 
correction to direction 4. 08" 
Angle 
(BPC) 
37°14' 
or 322° 4G" 
9. 7818 
5. 3162 
5. 6114 
0. 7094 
5. 12" 
correction to angle B P A =4. 08" +5. 12 // =9 // . 20 
