Mr Sang on Optimum Surveying. SSS 



the position of N. But, in practice, there are many sources 

 of minute error ; so that 

 a magnified view of the 

 point N may be this, in 

 which N may represent 

 the true position. Per- 

 pendiculars drawn from 

 N iijxjn the lines marked 

 A, B, C, &c. would re- 

 present the errors, in aim, 

 of the different traverse 

 lines ; and these perpen- 

 diculars divided by the distances of the stations would give the 

 angular errors. Let N a be one of these perpendiculars, the entire 



measure ofinaccuracy would be 2 ( ^ai ) • But at different sta- 

 tions accidental circumstances may have given peculiar chances 

 of precision (the methods of estimating these I shall treat of in 

 two succeeding papers) ; and hence, taking all circumstances in- 

 to account, the entire measure of inaccuracy will take the form 



where a is a quantity known from the field operations. We 

 have, then, so to determine N as that this integral may be the 

 least possible. 



Denoting hy x ,y ;x ^y ; &c., the rectangular co-ordinates 

 of the points A, B, &c., and by AN, BN, &;c., the bearings of 

 N, as seen from A, B, the value of the perpendicular N a 

 will be 



N a =3 (a-^ — Xj^) sin AN — (y^ — y^) cos AN 

 and hence, taking every cause of inaccuracy into account, the 

 best position of N will be found by solving the equations 

 . ^ sinAN' -sin AN. cos AN 



. ^ sin AN. COS AN, ^ Cos AN = . 



the solution of which will give o:^, y^. 

 In this inquiry I have supposed that the positions of the sta- 



