MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 195 
Hence, if we assign to D 0 (which has so far been arbitrary) the value given by 
9 1/,-, 
(20U4) 
D n = 
8'7TMlM2l'l«'2K / 12 (0) ’ 
we may write the equations (20’09), (20’10) as follows :— 
\ J-° 
A 12 A/i 
(20-15) 
(20-16) 
1 + 
<h —<Li = 1, 
S i+ [l + hiK) = _1. 
We have here introduced the notation 
(20-17) 
7 0 = KMO) 1 0 _ K ' 22 (o) 
1 -K' 12 (0)’ 2 -K' 13 (0) 
From (3"122) we deduce the following equation for <f 0 
(20’18) 
d' 0 = — 2 XjX 2 2 r (S r —S_ T ). 
The first approximation to this is found, from (20"15), (20'16), to be given by 
(20-19) 
<y 0 = — 2 XjX 2 
Xj^i -4- X 2 1^2 
b °Tr 0 
x 1 A°+x 21 4°+ 
Hence, by (3*151) and (20*14) we have 
(20-20) T' 0 = IDoT^'o ^2 
3T a 
1 + 
b °Tr 0 
/Cq tv o 
__ 
^.lTV^fJ.Y^X-2^^- 12 ^ (^12^1 ^“21^2 )j 
= _ w , j0 m 1 +mj{ 1 + 
3 12 2H 
ex'o 
k 1 °k 2 ° _ 1 1 3 x' 
4^i// 2 (Xi2^i F X 21 ^ 2 ) j d>t 
ot 
where D 12 ° is the first approximation to the coefficient of diffusion (cf. (l3"08)), while 
I A is a new quantity, defined by the last equation, which we may term the 
anisothermal diffusion constant. 
We may easily gain some idea of the order of magnitude of I A if we consider two 
gases of similar dynamical properties, he., such that m l = m 2 , and k t ° = & 2 ° = 1. The 
VOL. ccxvn.— a. 2 E 
