VAN ORSTRAND AND WRIGHT: MINERAL ANALYSES 



517 



x = theoretical weight number 

 y = observed weight percentage 

 y' = computed weight percentage 

 1^ = y — y' = residual 

 p = weight of the observation. 



The quantity p is an abstract, number indicating the relative 

 value or worth of an observation in comparison with other ob- 

 servations. The arithmetic mean of n observations, for ex- 

 ample, is supposed to be worth n times as much as a single ob- 

 servation; its weight would therefore be n times the weight of a 

 single observation. 



Adopting first the observation equations 



^^1 = y\ (weight pi) 



mx2 = 2/2 (weight pa) 



\ 



(1) 



mx„ = ?/„ (weight p„) ^ 

 we obtain the least square solution 



Pl-'Cl?/! + P2^22/2 + • • • +VnXnyn 



^i = 2 , 2 , 



in which the residuals (vi, V2, . . 

 dition 



PlXi^l + P2X'22J2 + • • 



Some special cases in which the weights are simple functions of 

 X are the following: 



+ VnXn 



(2) 



t;,J are subject to the con- 



+ VnXnK = 0. ... (3) 



m = 



m = 



m = 



m 



