122 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
where R is the “ universal gas constant.” These equations define li and T ; we shall 
call T x , T 2 the absolute temperatures of the component gases. According to the 
theorem of equipartition of energy, in the uniform steady state of a gas they are 
equal. In the slightly disturbed states which we shall consider, the differences 
h 1 —h 2 , Tj— T 2 will be small.* 
We further define p u p 2 , p 0 , the mean hydrostatic pressures of the separate 
components of the gas, and of the total gas, by the equations 
(1'17) 
Pi = - J'O'i. Pi = sT 2 m 2 C/ = 
2 h 0 
Rr 0 T 
v 2*-2> 
(118) 
p ,= Pl+Ps = ^ + ^^J 
The last equation also defines h 0 and T 0 ; the latter will be called the absolute 
temperature of the composite gas. Clearly 
(IT 81) T 0 = \T 1 + \ 2 T 2 , 
We shall define T' 0 ,£/ 0 , h' 0 by the equations 
— = -f- ^2. 
K A A 
(1T82) 
(1T83) 
(1H84) 
n = A (Tj—T 0 ) = -A 2 (T 2 -T 0 ) = X 1 A 2 (T 1 -T 2 ), 
*>'°=wr = R ‘° r ° 
The following equations are inverse to the above : 
(1-185) T, = T,+ D, x 2 = 
A 1 
0 X, ' 
(1T86) 
Pi = X 2 (po + A?4) 5 p 2 = A (po-Ap'o). 
* [In the paper as originally communicated, no account was taken of these differences, a preliminary 
examination having indicated that they do not materially affect the theory of diffusion. The distinction 
between Tj and T 2 has been re-introduced at the suggestion of a referee, in order that its influence, if any, 
on the phenomenon of thermal diffusion might be made clear. It will appear that Tx - T 2 is a small 
multiple of the rate of change of A' 0 (or A) with time, so that in steady states of the gas it is a small 
quantity of the second order only ; in particular, the phenomenon dealt with in § 16 is unaffected. 
Throughout the paper, wherever a distinction is made between h\ and K, Tj and To, or wherever T' 0 
(equation l - 182) appears, this has been introduced on revision (June, 1916). The original form of the 
equations may be found by making the difference zero. An appendix has also been added on account of 
this extension .—June 2, 1916.] 
