68 



A MANUAL OF TOPOGRAPHIC METHODS. 



These three equations involving throe unknown quantities, are then 

 solved by elimination, with results as follows: 



w — +.515 

 y=— .562 

 s = +.023 



These values can now be substituted in the table of correlates, columns 

 1, 2, 3; the algebraic sum of lines a, b, c, d, etc., giving corrections to the 

 angles a, b, c, d, etc. 



FIGURE ADJUSTMENT. 



The measurement of the angles having been executed by instruments 

 and methods much better than the needs of the map require, it is not ordi- 

 narily necessary to make any figure adjustment, further than an equal dis- 

 tribution of the error of each triangle among the three angles. 



Still, as the necessity for a more elaborate adjustment may arise, a 

 description of the method of applying the least square adjustment to geo- 

 metric figures in triangulation is here given, with a simple example of its 

 application. 



Each geometric figure in a system of triangulation is composed of a 

 number of triangles. The measured angles of each triangle should equal 

 180° plus the spherical excess. Each triangle, therefore, furnishes an equa- 

 tion of condition, which is known as an angle equation. The number of 

 angle equations in any figure is equal to the number of closed triangles 

 into which it can be resolved. But since certain of these are a consequence 

 of the others, the number of angle conditions which it is desirable to intro- 

 duce is less than the number of triangles. 



The number of angle equations in any figure is equal to the number 

 of closed lines in the figure plus one, minus the number of stations. Thus, 

 in a closed quadrilateral, the number of angle equations is 6 + 1 — 4 = 3. 



