M 



scalarlj bj t>, it reduces to 



(31, ë) + (3)?, é) =- O 



or 



A [aiOi] = — il/s 



In order to determine the mean error of M,, we remark that of 

 all fhe lines through in Rn t is that which makes the smallest 

 angle with ^. The error of Ms therefore depends for the most part 

 on the error in the components Mt of ^^^ in the direction f. We 

 may consequently write 



m. e. of Ms = m e. of Mt X cos ((^, r) = g cos {^, t) 

 or 



f 5 z= s [d/T/] =z e 



Oil 



\/W]'. 



=-.e]/[ök']\ 



hence 



^A 



— 8 



[ftiOi] [aiOi] 



Since 



M, — Mt [öixi] = [7I//,T/,]' . [(7/T/] 

 we have 



Mn 



Oh 



A = 



M. 



or, putting 



Oh 



|/[(JA^] 

 Oh 



l/[(T/rJ' = [Maö/J, 



[«/(J/] 



. Mk 



— ph 



Introducing 

 P' 



[aiöi\ 

 A=- [phMh]', 

 1 _^A- _ W] 

 9A~ ^' " 



X=z 



, r^ 



Q' 



[aidi] 



, 2 



[aiOi]'' 

 R' 



= [pk^y 





[öt(7/] 



We ai-rive at 



ahX + Ar + YhZ + ... =1?/. (A = iv.^O 



«„ .jX + f^n+j^ -h r"+j-^ + . . = (j = 1,...V) 



[aipi] = 1 , [/^ipi] z= , [y,>>/] = ,... 



From these 7i -\- v -\- N equations we can solve the 7i-\-v unknown 

 quantities pi {i = 1 ... ii -{- v) and the jYauxiliary quantities X, Y,Z,... 



The quantity — = [«/(^l' in question is also found as follows 

 9A 



