ANGULAR SURVEYING 65 



In a transit survey in which the angular measurements, 

 though sufficiently great to be considered, are small as com- 

 pared with the error of closure, the formulas for the correc- 

 tions of the ranges are 



and Ct = ~ X r 



in which Sg and St have the same significance as before; r is the 

 corresponding range to be corrected; and S r is the arithmet- 

 ical sum of the ranges of one kind, either latitude or longitude. 



In a transit survey in which the angles are measured accu- 

 rately the balancing is done by correcting the lengths of the 

 sides, due consideration being given to the following principles: 



Principle I. Measurements made either up or down a slope 

 are likely to be too long as compared with measurements made 

 under similar conditions on level ground. 



Principle n. Error in chaining is more likely to occur in 

 lines measured over rough ground or under unfavorable condi- 

 tions than in lines measured over smooth ground and under favor- 

 able conditions. 



These principles may serve as a guide in balancing a transit 

 survey, an operation that must be done by trial, as no exact 

 method has yet been devised. 



Accuracy of Angular Measurements. 

 The accuracy of the measurements of the 

 angles of a closed survey can be checked 

 by one of the following methods, depend- 

 ing on the method used in measuring the 

 angles. 



1. When the angles are measured 

 directly, the sum 5 of the interior angles 

 of a polygon of sides is given by the 

 formula 5=180 o x(M _ 2) FIG. 6 



It should be borne in mind, in applying this formula, that 

 reentrant angles, as that at A, Fig. 6, are greater than 180. 

 The angle A should be called 260, not 100. The sum of 



