192 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
we have, writing k T for D T /D 12 , as in § 14, 
( 19 - 04 ) m = ^ 
\i\ 2 
2 a t r\ m 
3 , ■. Po'-'tA- 
Ai Ao 
Thus we may write (I9‘0l) in the form 
(19'05) »<*! = 
We may notice that there is an interesting analogy between this equation and the 
ordinary equation of continuity 
< 19 ' 06 > t = 
which refers the rate of concentration of matter in a volume element to the differential 
rate of transfer of matter across its extent. In the case of diffusion, the opposing 
inter-diffusing streams carry equal numbers of molecules in opposite directions, but 
while the energy of molecular agitation is the same for either group of molecules, the 
kinetic energy of diffusion is different, owing to the different masses with the same 
velocity of diffusion ± (u' Q , v' 0 , w\). It is, I imagine, to this cause that the thermal 
flux of diffusion is due, though the suggestion is only tentative and does not affect 
the accuracy of (19'05) one way or the other. It is clear, however, that if the 
velocity of diffusion is such as to cause a concentration of the more massive molecules 
in any region, at the expense of the lighter molecules (since the total number v 0 is not 
affected by diffusion), the temperature of the region will rise, k T being positive (§ 14); 
this readily follows from a comparison of (19'05) and (19'06). From our discussion 
of the magnitude of k T in § 14, it appears that the specific energy of diffusion is 
greater the greater the difference in mass and size between the molecules, as we 
should expect. 
§ 20. Appendix on the Inequality of Temperature between the Component 
Gases. 
’[Added June 2, 1916d\ 
Up to the end of § 3 the equations of this paper take account of the possibility of 
a difference of temperature (as defined in § 1 (c)) between the component gases. 
After that point it is virtually assumed that T' 0 is zero. We will now briefly 
consider what modification must be made in order to cover the general case. 
It is clear from (3T5l) that the component gases have different temperatures only 
when the ratio of the two gases, by volume, is changing with time. Consequently in 
