MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 157 
also have suffixes 11, 12, or 22, and the formulae (9"37)-(9'39) will need to be modified 
in a manner sufficiently obvious. 
When n = 5, i.e., when the molecules are Maxwellian, it is clear that 
(9'40) 
(9-41) 
K' u (0) =^-I 1 (5)[K u (m I +mJ 1 ‘, 
Air 
k, = 1 = ahhi 
Ii(5) 
§ 10. The Equation op Diffusion. 
(a) Definitions of the Various Coefficients of Diffusion. 
In our analysis of molecular motions (§1) the rate of inter-diffusion was expressed 
in terms of u' 0 , which is defined by the equations 
(10-01) (vi + Va)u'o = i'i(h-Mo) = -r 2 {u 2 -U 0 ) = 
D + v 2 
Further, by (3’15) and (2'06), we have, as the equation of diffusion, 
( 10 - 02 ) 
u, 
— It A 0 a 0 f _, 
i sxh 
2 h dx 
-X'- 
v 0 m 0 ox) ox 
Hence it appears that the agents effective in causing diffusion are (taking the 
terms of this equation in order) a concentration-gradient or variation in the relative 
proportions of the two component gases, external forces of unequal amounts per unit 
mass of the two gases, and variations in the total pressure or the temperature of the 
composite gas. 
When the pressure and temperature are uniform, and the external forces are such 
as to make X' 0 , Y' 0 , Z ' 0 zero, diffusion can take place only if there is a variation in the 
relative concentration of the component gases. In this case we may compare (10"02) 
which now has the special form 
(10-03) 
— 1 A ' J_ SYo =_L A CL — 
0 9 0 °2 h dx 9i/ 0 0 °2 hdx 9v a u °2hdx’ 
with the ordinary equation of diffusion 
(10-04) 
v 0 U o — (U\ uf — D 12 V‘2 (u 2 Uq) — Dj 2 
ax’ 
where D 12 is the coefficient of diffusion. By comparison we have 
(10 05) D 12 = -iA 0 RTa' 0 . 
z 2 
