149 
hand denoting the light transmitted through the other 
cylinder. Each expression consists of two terms, the terms 
of the form 1(1 — m-yqt) denotes the white light transmitted, 
the term of the form pqtY denotes the excess of yellow ; 
this term we may call the effective yellow, for it is the only 
portion which produces the sensation of colour. Now sup- 
pose the light before passing through the cylinders to pass 
through a yellow screen, suppose the composition of the 
incident light after transmission through the screen to be 
pY + piB + pih, 
p being greater than p 1} say p = p 1 +r, so that the composi- 
tion of the light may be written 
Pil + rY, 
rY being the effective yellow after passing through screen. 
After using the screen the left hand expression of A would 
become 
I / o 1 (l - m x qt) + Yr - Yrm x qt + p x qtYfi. 
Since qt = q't', if we substitute eft' for qt in the last expres- 
sion, we shall get the light transmitted by the other cylinder 
after using a screen; hence if the columns be adjusted so as 
to produce equality of colour with white light, they will 
still be in adjustment if the light should become tinged 
with yellow. 
Let y x and y 2 denote the effective yellows in one of the 
cylinders with white incident light and with yellow light ; 
then we shall have 
y 1 = f iqYt 
y 2 = Yr - Yrniiqt + Y p X fiqt 
Now suppose the length of the column of coloured liquid to 
be altered a little so as to become £ + §£, let Sy x and Sy 2 de- 
note the alterations in the effective yellow in each case, then 
hy% = (Ypi \xq - Yrm x q)U 
tyi = Y pqU 
Hence 
<^2 ~ tyi= “ { Yrvthq + /JLqY(l - pi)}&5 
Therefore Sy is less than Sy 1} that is to say, we shall not see 
