i 



— =[;v,']'=[M«',X+/:?/J>yAi^+...)]'=A'[/)/,«/J'+r[y>/,/?/J+Z[/)/,^ 



Returning lo tlic original variables x,y,z,..., we derive from 



A 



Villi oi'] 



firstly 



^A 



and 



Further, putting 



pu — ku —ry— ' V"^j — ^''^^J -rr, 



the n -\- r -\- ^V equations pass into 



fill 

 a,,^; 5 + ^'u+pi f '\-+.;? -f . . . = , (,; = L . . . r) 



[,,;/.-,] r^l. [/'//V]— «>, [.v/.v]=zO, ..., 



whence 





Exami)le : 2 equations of observation, with 2 \ariables and 1 

 condition. The nnil-\ectors a and b determine a plane Ji\{X'=2), 

 the plane of the \ariables. This plane cuts the jdane of observation 

 R„{-n = 2) in the line qN-A^^ — v = ^), ^vllich thus coincides with 

 the line f. The line OP is drawn in the plane A'„ peri»endicular to 

 9Ar_,(t). Through the extremity M of the vector -iJ^t a line is drawn 

 parallel to ÖP; this line cuts the plane Un of the variables in J/'. 

 Tiie vector ^f^P ^-//^ PO is the correction-vector ^ . OJ/' is resolved 

 in the directions a and b into the components O A = ^^1 and 0B=^'^\ 

 The lengths of these lines represent the most probable values of the 

 variables A and B. 



The line FQ is perpendicular to the plane A\v and meets the 

 normal 7t. (line of condition), erected in () on R^, in tiie point Q. 



The vector OQ is called Jt'. 



oo 

 o o 



Proceedings Royal Acad. Amsterdam. Vol. XVil. 



