9 
for the lightest powder to come to the surface. I have 
sometimes noticed, with regard to the tablets prepared as 
above, that portions which had been rubbed seemed per- 
ceptibly lighter than the undisturbed portion ; possibly this 
may be due to a slight excess of carbon on the upper surface, 
I also compared tint A with another consisting of 0A0G3 
grams carbon to 10 grams BaS0 4 , thus the quantity of 
carbon is a considerable multipie of that contained in tint A. 
The value of R got from the comparison differed considerably 
from* a value of R which I got by comparing A with B. At 
first I thought this was due to a failure in the theory ; after 
some time it occurred to me that the conditions of my ex- 
periments were not the same as the conditions of the theory. 
In the theory, I had supposed that the white was mixed 
with a perfect black, in the experiments the white had been 
mixed with a grey. 
Those surfaces which are popularly known as black, are 
in reality not black but grey. If we take such a surface, 
whether of black velvet or lamp black, aud hold an opaque 
object before it so as to intercept a portion of the incident 
light, a shadow will be found on the surface ; but it is evi- 
dent that a perfect black is incapable of receiving a shadow. 
Also, when I looked at a surface of lamp black through the 
colorimeter (consisting of a glass cylinder covered with black 
cloth, except a small aperture at the bottom) the lamp black 
surface appeared grey. The formula for the intensity of the 
residual whiteness, if we mix with grey, will not be the same 
as if we mixed with black. The formula will have to be 
altered as follows : suppose Wo the initial whiteness, after 
the addition of perfect black the residual whiteness will be 
W 0 R ra , but if the material added be grey, we must give back 
a quantity of white, which will be some fraction of the 
whiteness lost. Suppose p to be this fraction; also the 
whiteness lost will be W 0 — W 0 R"; so the quantity of white 
to be restored will be W 0 p(l — R w ) and the total whiteness 
