nOO 



The yj)a<'0 joining' oa-v >vitli /»\ is here the |)hant' -S'.v ■ Tl»e plane 



Fig. 2. 

 erected in O perpendicnlar to ?•, intersects S\\ in the line e, which 

 therefore is perpendicnhir to 53 and .5v. So A and .1/ are projected 

 on i in the same point As- 



The normal plane A A^ M of e cuts t in a point T. the distance 

 of which to amounts 1o Mt (with mean error h). The mean error 

 fs of .4., thns has the value bs=:: ^ cos {^,t), and that of A the value 



M = 



^s ("OS (é, t) 



V. The errors (residuals) of J/,, J/,, . . J A» are A', A',, . . Kn resp. 

 The sum of their squares is [A'^^'J = A"^ 



For the case that no equations of condition are given, ii must be 

 perpendicular to Rx- So ^ may dispose of a space of?? — iV^ dimen- 

 sions ((he normal space of Rn)- Hence .5v has n^N components, 

 all with the same mean value a. Consequently 



K' = {n—N) X £' 

 hence 



= 1 /i^ 



[/ n — N' 



In case r conditions are imposed. ^ may dispose of the space S 

 of n -\- V — ^V dimensions. Consequently S\ now has // -|- v — S 

 components, all with a moan value e. In this case we have therefore 





