522 



VAN ORSTRAND AND WRIGHT: MINERAL ANALYSES 



are in no way related to the other errors of the system. Sys- 

 tematic errors of the kind Wells describes are readily detected 

 and easily separated from the random errors of the system by 

 an application of any of the equations (5) to (8) inclusive; but 

 preferably by means of equation (7) for the reason that it is more 

 easily interpreted, and that, except for certain special cases, 

 there is no adequate reason for assigning the weights imposed 

 by the remaining equations. Both constant and systematic 

 errors may be evaluated by means of equation (9), and, if it is 

 desired to impose the condition that the smn of the adjusted values 

 equals 100, we include equation (11) with equations (9) and solve 

 in the usual manner. 



To illustrate the method, let us take the data used in the papers 

 referred to above. Substituting the values from columns (1) and 

 (2) in equations (10) and putting the weights equal to unitv, we find 



a = 0.030 m = 0.04964G. 



The theoretical value of w is 



m = 



100 



2009.61 



= 0.049761, 



hence there are systematic errors proportional to the difference of these 

 two quantities. Multiplying the difference (w/ — m ^ 0.000115) by 

 the successive values of x, we obtam the values in column (5) which 

 represent the probable systematic errors of the system. 



The probable constant error is a = 0.030. Referring to figure 1, 

 we see that a = 00' , and m is the tangent of the angle which the ad- 

 justed line makes with the x axis. Hence it follows that the ordi- 



