the point A we scale the distance PiA on the loca- 



and the distance PcA on the preliminary, * 

 obtaining the station and plus for A via each of 

 the two lines. We now have of the triangle 

 PiPiA the given side PiP (taken from the field 

 notes of preliminary), the given ant 



scaled sides PiA and PsA, and one scaled 

 angle, APiPi. All the scaled quantities are af- 

 fected by the errors of scaling, which are large 

 compared with field errors, and it is evident that 

 our values for the five parts of the triangle are 

 mathematically inconsistent, since any three parts 

 <-h Include one side) of a triangle determine 

 the other parts. The ; A hen the field 



party has located to A, and found they do not 

 check on the preliminary within several feet, they 

 have no means of telling how much of the error is 

 due to surveying and how much to scaling. In 

 this case the surveying checks the scaling, but 

 there practically Is no check on the field work. 



BY CALCULATION. By this method we scale 

 only so many parts of the triangle Pil'sA as will, 

 together with the given part or parts, determine 

 the size and shape of the triangle. Side PiP and 

 angle PtPsA are known from the preliminary 

 notes. If. then, we scale the angle PsPiA we shall 

 have values for three parts of the triangle, f 

 which we can compute the sides' PiA and PsA. 

 These five parts of the triangle two given, one 

 scaled and two computed are mathemath 

 consistent; and when the location party arrives at 

 A and find they do not exactly check on the pre- 

 liminary, they know that the error Is all charge- 

 able to field work (assuming that no errors have 

 been made in computing). In this case the field 

 k is really checked. Of he error may 



be In running the preliminary or the location, or 



probably In both. T! 

 veylng on both line* t nl A. If * 



.-. ithln the limit of error permit 

 the location Is re-run (using the same notes), and 

 If this In found to be i 



step Is to re-run the pt If 



the error Is r. It must be f" 



In the office work computations or 

 note*. It cannot be due to scaling. 



