7 
than Herschel’s reasoning : — Suppose we have a column of 
any length, conceive it divided anywhere into two lengths* 
x and y , by an imaginary plane. Let I 0 he the initial 
intensity of light ; after penetrating the column x we shall 
have 
l x = I 0 (j)(x). 
But if light of intensity I* penetrate a column of length 
y , the transmitted light will be or by substitution 
1 000*00(2/)* This will be the intensity after penetrating the 
whole column, since the length of the column is x+y, the 
emergent light will also be expressed by I 0 (j)(x+y), equating 
these two expressions lor the same quantity there results 
<p(oc)(f)(y) = <p(x + y ). 
It is well known that this functional equation is satisfied 
by an exponential form. 
I may also take this opportunity to correct some errors 
in Colorimetry, part II., contained in vol. XIX. of the 
Proceedings. 
c. c. 
Page 41 line 31 for 6000 read 6014. 
,, „ 32 insert “nearly” before the theoretical column. 
43 ,, 20 for 600 read 6000. 
„ „ 23 for 6682 read 6652. 
46 „ 20 for 17*9 read 9. 
„ „ 22 for 5-2 read 5*1. 
,, „ 26 for former read “latter” and for latter “former. n 
„ „ 27 for 1600 (17+^) = 2400 x21 -2 read 
1600 (21-2 + x) = 2400 x 17. 
“On the Intensity of Light that has been transmitted 
through an Absorbing Medium in which the Density of the 
Colouring Matter is a function of the distance traversed,” by 
James Bottomley, B.A., D.Sc. 
In previous papers it has been supposed that the absorb- 
ing matter was uniformly distributed throughout the 
