MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 153 
ifc — l) 2 
ZPlP2Pl2-PuP2 2 -P22Pl 2 = - L + 2b 12 V lV2 + b 2 V 2 a ), 
Zb ViV 2 
Also 
(9'12) 
where 
(9 13) bi = , b 2 = 2/* 2 M2i^22 > 2h ]2 — 30 (l 4 /xi/x 2 ) + 
Consequently, if we write 
12 
(9'14) 
J> L 1 i , :'VC _ / j, _, \2 ^i |; i s + 2ft 1B i')2 , a + ^,i. a 2 
— ~ 2 „ .. V^l 1 ' ,1 2 1 o 1 J 2 ’ 
i ^!2 P\\P22 
we have, as our second approximation to a r 0 by (5-35), 
1 
cW+ 2 ^ r 2 + d 2 v 2 
l-( 
(9‘15) a ' 0 - -X,\ a 
We may note that 
(9 16) Ai = — {c? 1 i ' 1 2 + 2 cZ 12 r 1 i '2 + d 2 v 2 ) — (&i — l ) 2 {b\V\ + 2b 12 v 1 v 2 + b 2 v 2 3 )} 
V \ V 2 
= {^lD + 2G/i 2 i>ii i 2 + Ct 2 r 2 }, 
where 
(9161) 
(9162) 
(9163) 
«1 — — &n° (fyW 2 2 — Ml 2 (^1 2 — X^) +^'Ml/ u 2^12°}) 
42 
a 2 — — ^ 22 ° (ImF — M2 2 (^l" - ^ 2 ) + ^5MiM2&12°}> 
Mi 
^12 = d 12 — (k l l) 6 j 2 . 
The determinant V 0 (^ m „a mn ) of (5’37) is, to the same order of approximation as for 
v (<L,«mn) in (9*08), 
(9164) - 
— v l{P‘2P\2 P\P22) + v 2 {P\P\2 P2Pll) — TTIT (^1 l) e l 
P12 Pi p u 
V 2 0 V l 
P22 P2 P\2 
where 
(9 17) e i = 30 (r^a + r 2 Mi) (/Xj /x 2 ) 8 miM 2& 0 12 (u ^ 2 ) + 2 {viH\ 2 k° n v 2 n 2x k 23 ). 
Hence we have, as a first approximation, 
(918) 2r(i,a r + V . r ) - 
-V-l 
Ax C1 
ei. 
