MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 175 
infer the character of the variation of V r /V itself, in view of our knowledge of the 
mode of convergence of the successive approximations as indicated in § 13 (e). 
(h) The Variation of (1— e 0 ) 1 with :v 2 . 
So far as regards our detailed discussion of e 0 , we shall confine ourselves to the case 
of rigid elastic spherical molecules; for Maxwellian molecules e 0 is identically zero, 
while for n th power centres of force (5 < n < co) 6u is intermediate between 0 and the 
value appropriate to rigid elastic spheres {cf. Tables II., III., § 13), the character of 
its variations being similar in the two cases. 
From § 9 (c) we have 
(13'28) 
e 0 — 
,, _ y fvl+fbj 2 v x v 2 +l) 2 v 2 
dyVi + 2d 12 ViV2 + d'2 v 2 
and in the case of rigid elastic spherical molecules {cf. § 9 ( c) and § 9 (/)) we may 
write 
(13-29) 
(£,-l) 2 -^ = --■— 3 - £ 
12 -% 0 -- +78-H&P 
P 
Mi 
(13 30) {k, 1)^ 3 o-i-OOp_ 17 ^ 
where 
(13*31) p = 
so that 
(4.-i) 
2 u 2 
M2 
k = 
d 2 30-i^-p-l 7 m 
4O-jO-2 ^ 2 
2 ? 
{<T l +<T 2 )'‘ t \ 
(13-32) 0 <p<| 0<£<1. 
Since the suffix 1 refers to the heavier molecules, we have ^ /u 2 and 
(13-33) 
^>- 2 . 
d x d 2 
The condition that ~ shall exceed is readily proved to be 
a 1 9 (JLo 
(13-34) 
M2 
Mi 
<f(p) = 
81-342p + 280p z 
4 /j+ 81_p — 180p* ’ 
and it is found that, for the admissible values of p (i.e., O^p^i), f{p) is positive 
and steadily diminishes as p increases; its least value is consequently f{f), which is 
equal to 13/(9 + 4&). Since k never exceeds unity, f{p)i> 1, and hence M 21 ^f{p)> so 
that 
