PROPERTIES OF MATTER EST THE GASEOUS STATE. 
823 
According to the experiments, it appears that as the density diminishes, — approaches 
to unity; but owing to the impossibility of measuring the exact difference on the two 
sides of the plate this determination is not very definite. 
c 
Result XI. refers to the thermal difference of pressure when - is large. 
s 
1 dr 
In this case 0 = 0, while -, —, and M are constant. 
t ax 
Equation (.99) becomes 
\ 1 dp 1 s 
A i + I j, * - 2?r - u (:)+ 
1 dr 
t dx 
( 112 ) 
in which f[zj ^ ias some finite value. 
In the limit, therefore, we may neglect mX. : , and we have 
a - c Il— JL A I f 
p dx 2tt r 3 '' J 
(11.3) 
And since sec - and c is constant 
P 
which is result XI. 
1 dp fl dr 
p dx p 2 t dx 
1 dr 
Since the coefficient of - — in equation (113) involves A,, which (Art. 98) depends 
on the nature of the gas, this equation indicates that different results would be 
obtained with different gases. 
And this appears still more in the case of intermediate pressures when m\, 2 on the 
left of equation (112) is important. 
These conclusions are according 1 to result XII., which therefore affords additional 
proof of the correctness of the conclusions in Art. 98 respecting the value of X. 
108. I have now shown how I was led to predict the experimental results, and how 
in every particular the experiments have verified the theory, both as regards transpi¬ 
ration under pressure and the thermal differences of pressure. This concludes the 
application of the theory to those experimental results of transpiration which w T ere 
revealed by the theory. * 
There remains, however, an important class of transpiration phenomena of which, 
as yet, no mention has been made. These are the phenomena of transpiration when 
the gas on the two sides of the plate differs in molecular constitution. 
Transpiration by a variation in the molecular condition of the gas. 
108 a. These phenomena are well known, and were experimentally investigated by 
Graham, but hitherto, I believe, no complete theoretical explanation of them has been 
5 N 
MDCCCLXXIX. 
