19 



The only remainiiig correction required by [-K^'„],„ is that arising from the 

 fact that the angle between the standard Unes 14 and 43 is not exactiy 90". 

 To investigate this we bave made the observations of operation 7, which givo 

 us the excess over the samc distance on the scale of the four distances 

 marked a, h, c, d, in the figure. We shall designate thèse excesses by the 

 letters a, h, c, à. The first step is to correct a, h, c, d, by the aid of the 

 values [-K'„]^ , etc., already found. This will remove the ctfect of the division 

 errors already found, and gives corrected values a', h', c, d', coniputed by the 

 tormulae : 



c' = c - /7 {[zy^ + VK'^\^ - [A- 4, - \K,\y 

 d'^d- /T{[^i4 - [^'aiJu + [^"4 - L^"^ J43} 



(14) 



No matter what the angle between the lines 14 and 43 may bc, the follow- 

 ing relations ought to be rigorously satisfied : 



a = c' , h' = d', 



This is evident from the fact that the division error corrections ought to turu 

 the actual reseau Unes 14 and 43 into ideal straight lines accurately bisected 

 by each other. Of course the accumulated errors of observation prevent thèse 

 relations being rigorously satisfied. We therefore put: 



f _ i±.ù f _ ^' + ^ 



and then calculate the angle marked 90° + (ß in the figure by the formula : 



t\-f2 



(f^ = 



6or2 



X lO-^'osec r 



