226 



WRIGHT AND VAN ORSTRAND : MINERAL ANALYSES 



origin as an observed point but this assumption seems in the 

 present instance unnecessary and incorrect in principle. 



To obtain the required solution let the equations be put in the 

 form 



Piyi-fnpiXl=PiVi, P2y2-'mp2X2=P2V2, . . Pnyn-mPnXn=PnVn(2) 



in which yi,?;2 . • . ^n are the respective residuals or the dif- 

 ferences between the observed values (2/1,2/2, . . . y^) and the 

 computed values {y\, y'2, . . ?/'„); pi,p2, . . Pn are arbitrary 

 weights assigned to the corresponding observation equations. 

 By making now the sum of the weighted squares of the residuals 

 (PiVi^ + P2%^ + . . . + PnVj) a minimum we obtain the best 

 possible solution of the equation for m, namely, 



m = 



PlX^yl + p2X2y2 + 



r PnXnyn 



PlXl^ + P2X2^ + 



an expression which reduces to 



m = 



xiyi + X2y2 + 



+ PnXj 



+ Xnyn 



Xi" ~p Xo I 



r Xn 



(3) 



Pn) to be as- 



when we assume that the weights (pi, p2, . . . 

 signed to the observation equations are all unity. 



To apply this method to the analysis cited by Schaller we ascer- 

 tain first the mol numbers (Column 2) by dividing the weight 



* Considered as (Agj) and (Cuj) respectively. Sum = 0.3975 



