6<) 



A MANUAL OF TOPOGRAPHIC METHODS. 



ical excess. The latter need be computed and subtracted from the sum of 

 the angles, however, only for the purpose of testing the accuracy of closure 

 of the triangle, as in the reduction the angles are treated as plane angles. 

 When the area of the triangle is large, the spherical excess in seconds (E) 

 should be computed by the equation: 



E — 



_S / 



siu 1 



where S ■=. the area of the triangle in square miles, and r the radius of 

 curvature of the eax-th in miles. When the triangle (being within the 

 United States) has an area less than 500 square miles, r may be assumed 

 as constant, and the spherical excess may be obtained by dividing the area 

 in square miles by 75.5. 



The next step is the adjustment of the angles'about the observing sta- 

 tion, or the station adjustment, as it is called. Referring to the diagram, 

 which represents the angles read at Walton station, in Kansas, it is seen that 

 eight angles were measured as follows — 



a Dunkard— Peabody 65 45 28.37 



b Peabody— Newt 31 47 58.50 



Obs. angle 



Sum 



g Dunkard— Newt (meas.) . 



Sum ... 

 h Township ( 



/ Bennett — Dunkard - . . 



g Dunkard — Newt 



c Newt— Township cor . 

 h Tp. corner.— Bennett. 



Sum . 



61 09 26. 17 



97 33 28.39 



79 32 06. 25 



121 41 59.05 



Station 

 adjust- 

 ment. 



Correc- 

 tion to 

 center. 



+. 02 +4. 67 



— . 49 +7. 40 



+. 02 —8. 17 



+ .50 -3.90 



Angles locally 



adjusted and 



reduced to 



center. 



61 09 30.86 



97 33 35.30 



79 31 58. 10 



121 14 55 74 



Of these a + b should — g, d + e should — h, audy/ + c + h + /should 

 r=360°. Thus are formed in this case three conditions affecting eight 

 unknown quantities. The method by which are found the corrections which 



