824 PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
given. The diffusion of one gas into another has been explained by Maxwell ; but 
what has not, so far as I know, been explained is, that there should result a current 
from the side of the denser to that of the lighter gas. Indeed, from the manner 
in which these phenomena have been for the most part described, it would appear 
that the importance of this current has been overlooked ; for, owing to the fact that 
a larger volume of the lighter gas passes, the phenomena are generally described as 
if the current were from the lighter to the denser gas. 
These phenomena of transpiration, like those already considered, may be shown to 
follow" directly from the theory. But as has been already mentioned in Art. 73, in 
order to completely adapt the equations of transpiration to the case of tw T o or more 
gases, it would be necessary to commence by considering the case of two or more 
systems of molecules having different molecular weights, after the manner adopted by 
Maxwell.* Such an adaptation of the equations is too long to be included in this 
paper; but it may be seen from the equations, as they have already been deduced, that 
these particular phenomena would, and in some cases do, follow. 
Suppose that the gas on the two sides of the plate is at the same pressure and tem¬ 
perature, but that there is a difference in molecular constitution as air and hydrogen. 
Thus when the condition has become steady there will be a gradual variation of the 
molecular condition of the gas through the plate; in this case r is constant and p is 
constant, but the mean value of M varies. 
If we take M : and M 3 (as the molecular masses of the two systems of molecules), and 
consider a case in which M x differs but very slightly from M 3 , equation (98) becomes 
0^5 .< u4 > 
where M is the mean mass of the molecules, or if p x and p. 2 are the densities of the 
two gases 
M = — Ml ^ ' 
M 2 p 1 +M 1 p 3 
(Pi + Pi)- 
Whence, putting ^i=^, N 2 = ^r, 
y; Pt + Pa 
1 ~~ n 1+ n 3 • 
And since the pressure and temperature are constant 
N.+N^N 
where N is constant throughout the gas. 
* Phil. Trans., 1867. 
