GANNETT.] 
Example: 
SOLUTIOK OF TEIANGLES. 
Given log a=4. 3666779 Given C (spherical angle) 21° 14' 51". 10 
Given log b=4. 2050498 Given i sph. exe. — .10 
13 
(1) tan a;=0. 1616281 
a;=55° 25' 25".41 
-45 
(5) Logtan (:c-45°)=10° 25' 25". 41=9. 2647291 
(6) Log tan 79 22 33 .00=0.7268100 
C (plane angle )= 21 14 54 .00 (2) 
180 
180°-C=A-fB=158 45 06 .00 (3) 
i (A+B)= 79° 22' 33". 00 (4) 
(7) 
9. 9915391 = tan i (A-B) 
44 26 
.90 
sum=A=123° 49' 03". 90 (8) 
difFerence=B= 34 56 02 .10 (9) 
(10) 
Check. 
log a =4. 3666779 
A=123° 49^ 03^^ 90 a. c. log sin A=0. 0804971 
B= 34 56 02 . 10 log sin B=:9. 7578749 
C= 21 14 54.00 log sin C=9. 5592012 
Sum =180 00 00 .00 
log c =4. 0063762 
log b =4. 2050499 
THREE-POII^T PROBIiEM. 
If three points, forming a triangle of which the sides and angles are 
known or can be computed, be visible from a fourth point, P, it is 
required to determine the position of P. 
Set up the theodolite at P and measure the two angles subtended by 
any two of the given sides. 
This problem is of use in cases where, the regular triangulation hav- 
ing been completed, additional points are required for the topographic 
survey, or are needed for special service. The angles should be care- 
fully measured, and in the computations the logarithms should be car- 
ried to seven places of decimals. 
Three cases of its application are given, as in others, such as when 
P falls upon one or another of the sides of the known triangle, or on 
the prolongation of either, the case resolves itself into the solution of 
a simple triangle with one side and the angles given; or the problem is 
indeterminate, as when P is situated on the circumference of the circle 
passing through the three known points — a contingenc}^ which rarely 
occurs. 
