VAN ORSTRAND AND WRIGHT: MINERAL ANALYSES 



519 



weights are defined by some inverse power of Xi (equations 5 

 and 6) , points near the origin will have weights approximately^ 

 equal to infinity, and the line will tend to pass through these 

 points while the more distant points will have practically no 

 influence in fixing the final .position of the line. In other words, 

 the assignment of a large weight presupposes that the actual 

 error of the weighted quantity is very small and that the ad- 

 justed line should therefore pass nearer to these points than to 

 other points in the system having smaller weights. The reverse 



Fig. 1 



is true when the weights are proportional to some direct power 

 of X (e.g. equation 8) . These and other conclusions follow from 

 the law that weights are to each other as the inverse squares of 

 the corresponding probable errors. 



Pl'P2-P 



l.A.i 



2 • 2 • 2 



ri 7-2 r 



(12) 



Another method of adjustment on the basis of 100 in which 

 the constant ratio m is not taken into account consists in writing 

 the observation equations in the fonn: 



(weight Pi) 1 



zi = Vi 



Z2 = Z/2 



(weight P2) 



i 



(13) 



Zn = y» (weight p„) J 



