Godfrey H. Thomson 
221 
and are now linear in h and c. We have now n linear equations in which 7 and s 
are known, h and c are required. If we insert any pair of values h and c into these 
?^ equations they will leave residuals v.,. If we were now to proceed to make 
S {Vo') a minimum, 
this would not effect our purpose. It is 2 {v^-) we wish to make a minimum, not 
1 {vi). If however we can find multipliers or weights M such that each 
Mv^ = (6) 
we can then make 2 {Mvi) a minimum. 
That is, we Can apply Least Squares to the equations (3), weighted with certain 
artificial weights M. The use of this device is Mliller's particular credit in this 
connexion. 
Clearly the residuals which may be regarded as errors in p, are connected 
with the residuals v.,, which may he regarded as erroi's in 7, by th(^ ecjuation 
1 
from equations (1) and (8). Therefore 
ilf=e-V/7r. 
Herein we can omit the tt since it is only the relative values of the Miiller weights 
which are of importance. These weights are given in most works on psychophysics, 
e.g. W. Brown, or Titchener, op. cit. 
The condition that 2 {v{-) should be a minimum has now become, that 2 (Mv.j-) 
should be a minimum. With this substitution, the Normal E<]uations (2) give 
[3[s']h-[Ms]c= [Msy]) 
-[Ms]h +[M]c =-[iV7] r 
the square brackets being the sign of summation used by Gauss, and still persisting 
in psychophysics in this connexion. The summation here is over the 71 equations. 
Thence we have 
_ [Ms][Msj]-[My] [Ms^] 
[M] [Ah^]-[Msy 
c ^ [Ms ] [iMsj] - [My] [iMs^] 
h [M][Msy]-[My][Ms] 
(4) The Probability of a Certain Category of Judgment. 
The Constant Process remained in this form from 1879 to 1909. It is very 
much mixed up with the psychological method of experimenting and collecting the 
data, so that frequently the name " Method of Right and Wrong Cases," really the 
name of a certain method of collecting data, has been used to include this mathe- 
