24 ON THE METHOD OF LEAST SQUARES. 



In consequence of the relations 



2/*a=l, 2/*5 = 0, &c.=0, 

 the new system of equations will be 



= &c. 



(C). 



These p equations determine \, X 2 ,... X,, and thus in virtue of 

 (B) the values of ^ /v p n become known. Finally as 



x will be completely determined. 



Now let us recur to the original equations of condition stated 

 in the last paragraph. 



&c. - 7 ^ 



.- F 



&c. = &c. 

 e = ac 



F n J 



From this system we deduce a new one, containing p equations. 

 The first of these is got by multiplying equations (a) by 



r| > p > & c -> an d adding the results : the second by using the 

 factors j~ , ~, &c.: and so on as before. The resulting system 



1 **^S 



will be, neglecting all errors, 



&c. 



= &c. 



