164 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
(§) The fourth term represents the increase of heat which ordinary physics regards 
as due to conduction, together with a term due to diffusion which has not, so far 
as I know, been hitherto recognised in either ordinary physics or the kinetic theory. 
These two terms are discussed in detail in the next section of this chapter. 
(c) Conduction of Heat and the Thermal Flux of Diffusion. 
If there is no mass motion the equation of energy takes the form 
(1217) P.C.|E = i2r 0 M' 0 (X ! -X 2 )-i 2 
and in the last term we will now substitute from (5 "2 5), with the result 
(I2d8) Po C v ^ = iz^'otXx-X,) 
0 RT 
0T 
+ 9^2 — —j- | 2 r (i/ 1 a r + i' 2 a_ r ) + B 0 — 2 (r 1 /3 r + ^_ r ) 
dx 
It is convenient to eliminate £' 0 by means of (3*15), and on so doing (12‘18) 
becomes transformed into 
(12-19) p 0 C.= j2k 0 m' 0 (X,—X 2 ) 
+ 
d_ RT 
dx J 
2r (v 1 a. r + v 2 ct_ r ) 
a , 
u 'o + 9 R 0 2 (r 1 /3 r +i/ 2 /3_ r ) 
- 9 2r (na r + r 3 a_ r ) 
a 0 1 
If we suppose that no diffusion is taking place, so that (u' 0 , v' 0 , w' 0 ) are all zero, 
and compare (12’19) with Fourier’s equation of conduction of heat in a gas at 
rest, i.e ., with 
(12 ' 20> 
we obtain the following equation for the coefficient of thermal conduction 3-:— 
(12-21) & = iB, {£ M,+ ,J3_ r ) - & 2 r ( w. + >v*_,)} . 
J l i a o i J 
9 
From (12’19) we perceive also that the motion of inter-diffusion is accompanied 
by a flow of heat, which is proportional to the velocity of diffusion, and also depends 
on the temperature and the molecular densities, but is independent of the other 
characteristics of the gas. We shall term this process the thermal flux of diffusion; 
