12 GEOGRAPHIC TABLES AND FORMULAS. [bull. 234. 
GKAPITTC^ RF.13ITCTION TO CF.IS^TER. 
Approximate closure errors of triangles may be tested in the field 
before distances have been computed by scaling- from the plot tlie 
distances between stations in miles and the perpendicular distance in 
feet from signal to line joining instrument and distant station. 
Then, since 1 foot at a distance of 10 miles subtends an angle of 1" 
(nearly), 
lenpfth of perpendicular in feet X 40 , • • t 
— - — ^ — ^^— , , ., = correction in seconds. 
number or miles 
Example: Station P. Correction for swing on line B P, 80 miles 
in length from instrument to signal 
_ 3.8 feet X -1:0 _ „ 
- 3^ - 5 .1, 
correction for swing on line A P, 25 miles in length, 
_2.6 feet X 40_ ,„ ,, 
~ 25 - ^ •^' 
and correction to angle B P A = Q to reduce from instrument to sig- 
nal = 5.1" + 4.2" = 9.3", agreeing closely with the exact compu- 
tation. 
APPROXIMATE SPHERK^AL EXCESS IN SECONDS. 
This may be o})tained ])y dividing the area of the triangle in square 
miles by 75.5. 
SOTATTIOX OF rKIA^GI.FS. 
Given two sides and included ano-le, to solve the trian^-le: 
Fig. 3.— Solution ol triaugle.s; two sides and included angle given. 
Let X be an auxiliary angle; then 
tan x=—') or log tan x=log a— log hj 
tan i (A-B)=:tan (r^-45^) tan i (A+B); 
i(A+B)+i(A-B)-A; 
i(A+B)-HA-B) = B; 
from which remaining parts can be computed. 
