﻿IN THE METHOD OF LEAST SQUARES. 203 



able error of tlie same quantity obtained with the employment of the exact coefficients 

 bv less than — of that error. 



1250 



We shall, however, for the present confine our attention to a direct comparison be- 

 tween the results of the solutions I., II., and III., and retain in each the exact coeffi- 

 cients of the original equations, adopting the constants A, C, D, E, F = 1.0, and 



JB = 1000.0, and for the factors a /3 a somewhat ruder system of representation, 



especially in II., than that upon which the previous discussions have been based. 



If we employ the limits (28), (29), we find that the most favorable equations are (1), 

 (5), (7), and (10), and the least favorable (2), (4), (8), (11). Applying (III.) in the 

 particular form to which it is limited in (28) and (29), we shall omit (2), (4), (8), and 

 (11), as iueffijctive in the final equations for dL. (1), (5), (7), and (10) give 



(P) = 1 X 0.8= + 1 X 1.7- + 1 X 1.0' + 1 X 0.7- = 5.0000, 

 and (2), (4), (8), and (11), 



(p) = 1 X 0.03' + 1 X O.OP + 1 X 0.08' + 1 X 0.01" = 0.0075. 



(P) 66-" 



According to (28), we must have, in this case, 



^100 . 



in order to preserve the equivalency of (II.) and (III.), if the original equations (2), 

 (4), (8), and (11) are omitted in forming the final equation for d L. "We may, then, 

 adopt the following system of factors. 



dL. 



