Adams. — On Triangulatiou by Least Squares. 203 



Column No. 4 gives the sums of the angles (seconds only) 

 of columns Nos. 2 and 3. 



With these angles (from column 4) the triangles are 

 calculated, and the following results are obtained : — 



Comparing the bearing and length of the side P. 3 P as 

 obtained from the two sets of triangles, we have — 

 220° 09' 19-7" 310890 links ; and 



220° 09' 24-7" 31093-3 „ 



giving differences of 5" and 4 - 3 links. 



The application of the ordinary adjustment, resulting as it 

 does in these differences, is therefore very unsatisfactory, and 

 the question arises as to whether it is desirable in this and 

 in similar cases to adopt some further adjustment to the 

 observed angles so as to eliminate the discrepancies shown 

 above. 



Before discussing the further adjustment it may be as well 

 to remark that the ordinary procedure would be to adopt the 

 mean values of the bearing and distance of P P 2 . None of 

 the other sides, however, would receive any correction ; con- 

 sequently if the calculation is repeated, using the mean value 

 of P P 2 as base, an entirely different set of values will be 

 obtained for all the other sides of the triangles. 



As the need for further adjustment is obvious, the method 

 of applying it will now be indicated. 



II. The Least-square Adjustment. 

 The problem to be solved is : Given the observed angles 

 of the four triangles, corrected as shown in I., by applying 

 one-third of the error of each triangle to each angle, what 

 further corrections must be made to these angles so as to 

 eliminate the discrepancies found above ? 



