186 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
§ 15. The Coefficient of Pressure Diffusion. 
Iii § 10 we saw that, among other causes, a pressure gradient is an agent in 
producing diffusion, according to the law (cf (10‘08)), 
(15'01) 
where (cf (10‘09) ), 
(15’02) 
if 
(15-03) 
The phenomenon depends essentially on the difference of mass of the molecules, and 
we may note also that, like thermal diffusion, it tends to zero with \ or X 2 . If wii/ms 
is very large, k p clearly has the value X 2 , except when X 2 is very nearly equal to 1. 
It is interesting to compare the degree of diffusion produced by equal gradients of 
log p 0 and log T. This is equivalent to comparing k p and k T . When m l jm 2 is very 
large, k p /k T = 1 /0'51 or approximately 2, if <xj/cr 2 is also large (cf (14"06)), or 
(39+X 2 )/l5X! if <r l = <t 2 (cf (14"07)), save when Xi is small. The factor k p , unlike k T , 
is not dependent on the relative size of the molecules. 
In Table VI. are given the values of k p corresponding to the three typical pairs 
of gases considered in § 14 (c). It appears that D p is of thrice or four times the 
magnitude of D T for such gases. 
u' = D„ - ^ = D t a lo - g -^ 
’ p 0 dx p dx 
D, 
_ m o TV _ XiX 2 (wi\ Tn 2 ) -p, _ 7 r\ 
— U 12 — —- — E ; 12 — K 'p U 
m n \m 1 + X 2 m, 
'p^ 12 > 
_ X t X 2 (m 1 m. 2 ) 
p — X 1 m 1 + X 2 m 2 
§ 16. The Steady State Without Diffusion. 
We will now briefly consider the steady state, without diffusion, of a gas subject 
to the influence of (a) external forces or (b) boundary conditions which maintain a 
constant non-uniform distribution of temperature. If we write zero in place of u' u in 
(10'11), and divide by D 12 , we have 
(16-01) ^ - 2 h(X' 0 + - ^) + k T 8 - = 0 
OX \ v 0 ox) ox 
as the equation of state. It is more convenient to express the middle term as in the 
following equations (substituting for — ^ from 2"04 — ~ being zero, since the state 
v 0 OX ot 
