MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 155 
where and a 2 are given by (9'161), (9'162) and a\ 2 by 
(9'22) a\ 2 = MiZ^lf" - ki+ J s Jc 2 —f^kf + ( — + — Vr. 
\ fa Mi / / 
Consequently, by (5'39), to this order of approximation we have 
{9'23) 
(e) The First Approximation to 2 (^y r + r 2 y_ r ). 
The two central terms of the two central equations of type (5'll) are 
(9'24) y 0 \ 1 + + ~ " ^°11 f" — 7-0 (1—t\y^i 2 °) — —— r 1 "U' /n\» 
^2MiM 2 J bxi/ii/ 2 /X]/x 2 U 0 JA 12 f0; 
675^ 
(9'2 5) — yo(l — T 3 o^i2 0 ) + y-o < i 1 + fonvfiz + to 
3 J, 2 _1 
D MlM2 
k 22 r = 
67 5ia 
87r^v 2/ a 1 /x 2 C 0 K / 12 (0)’ 
which lead to the result (equivalent to that obtained as a first approximation 
from 5'40), 
1125 C 1 i' 1 ‘ + 2c 12 y 1 y 2 -j-C 2 v 2 2 
(9'26) 
where 
(9'27), (9'28) 
(9'29) 
(9*30) 
C 0 2 (v 1 y r + v 2 y_ r ) — 
2tK' 12 (0) kfcM 2 -f- 2k 12 c\ 2 v l v 2 + f(jk 22 c 2 v 2 
2’ 
C 1 — 1 4‘TVm 1 2^12°> C 2 — 1 +TaJM21^12 j 
C 12 — l~T(y^l2° + ¥U (^li n + ^22°)) 
MlM2 
C 7 12 — 1 + 
1 Z- °7 0 
1 /C n A/ 22 
TO 
MlM2 
7. 0 
^12 
A second approximation would replace the right-hand factor in (9'26), by the 
quotient of one quartic homogeneous polynomial in v u v 2 by another, and similarly each 
further approximation would increase the degree of both numerator and denominator 
by 2. 
(f) Values of K / i 2 (0) for Particular Molecular Models. 
In connection with the above approximate formuke, and their subsequent 
applications, it is convenient here to write down the values taken by K' 12 (0) and the 
other constants k, when certain particular characteristics are attributed to the 
molecules. 
VOL. ccxvii.— a. z 
