66 ANGULAR SURVEYING 



the measured angles should satisfy the formula within about 

 2 min. per angle. 



2. When the deflection method is used each deflection 

 angle, being the angle made by a side with the prolongation 

 of the preceding, is an exterior angle of the polygon. The 

 sum of all these angles should be equal to 360, within the 

 limits mentioned above. 



SPECIAL PROBLEMS 



SUPPLYING OMISSIONS 



When, in surveying a closed field, omissions occur in the 

 notes, they may in certain cases be supplied by computation. 

 It must then be assumed that the remaining field notes are 

 exactly correct; consequently, there are no means of balancing 

 the work and all errors are thrown into the part or parts sup- 

 plied. The following are the cases when it is possible to sup- 

 ply omissions by calculations: 



1. When only one side is deficient, that is, when the bear- 

 ing or the length, or both, are missing, the ranges of that course 

 may be determined from the equations 



t x +S t = 



and g x +S g = 



in which t x and g x are, respectively, the latitude and the longi- 

 tude range of the deficient side, and S t and S g are, respectively, 

 the algebraic sums of the latitude ranges and longitude ranges 

 of the known sides. . 



Prom these equations, t x = S t and g x = S g . Then the 

 bearing G x and length l x of the deficient side may be calcu- 

 lated by the formula 



and 



Since two angles correspond to a given tangent, in finding 

 G x two solutions are possible. The one to use may be deter- 

 mined by the signs of the ranges. 



