REDUCTION OF TEIANGULATION. 



67 



fulfill these conditions is that known as the method of Least Squares. It is 

 unnecessary to explain the theory of this method, but only to show how it 



is applied in the class of cases under consideration, which can best be 

 done by tracing a case through. There are here three equations of condi- 

 tions, as follows: 



(1) a+b— g— 1".52 -0 



(2) d + e — h+ 1".71 -0 



(3) ./' + g + c + h— 0". 14 = 



in which the letters represent, not, as in the diagram, angles, but unknown 

 corrections to the angles. The coefficient of each of these corrections is 

 unit}-. Arrange them in tabular form, the numbers at the top referring to 

 the equations, thus forming what is called a table of correlates. Now mul- 

 tiply each coefficient by itself and every other in the same horizontal line, 

 and sum them. There result three normal equations, as follows: 



b 1 



'l 

 / 



3. -l.Olte -1".52 = 



3 OOy -l.Ote ; 1".71 = (l 

 -l.0Ow-l.Wi/ (-4. OOz — 0". 14 n 



