202 Transactions. — Miscellaneous. 



Example No. 1. — The Adjustment of Four Plane Tri- 

 angles. 



For the purposes of comparison with the usual method of 

 adjusting triangulation (in which one-third of the triangular 

 error is applied to each angle of the triangle) an easy example 

 is selected embracing the adjustment of four plane triangles. 



The side P 4 P in the figure is a side of the existing triangu- 

 lation, and is to be adopted as correct both in bearing and 

 length. From this side it is desired to extend the triangula- 

 tion so as to include the points P! P 3 and P 2 . The angles are 

 all observed, and are shown in column No. 2 of the schedule. 

 No observation was possible between Pj and P 3 . 



I. Adjustment as Four Separate Triangles. 



The angles in each triangle are adjusted by applying to 

 each angle one-third of the triangular error of the triangle. 



The adjustment is shown in the schedule in columns 

 1 to 4. 



In column 1 the names of the angles are entered as follows 

 (see figure) : — 



A, = P P x P 4 A 2 = P P 2 P x 

 B x = P x P 4 P B a = P 2 P t P 

 C, = P 4 P P t C 2 = P, P P 2 



A 3 = P P s P 2 A 4 = P P 4 P 8 

 B g = P 3 P 2 P B 4 = P 4 P 3 P 

 C 3 = P 2 P P 3 C 4 = P 8 P P 4 



Column No. 2 contains the observed angles. 

 In column No. 3 one-third of the triangular error of each 

 triangle is applied to each angle. 



