MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 183 
These indicate the magnitude of D,/D sufficiently for our purpose, though for an 
accuracy of (say) \ per cent, it might perhaps be necessary to carry the calculation 
two or three steps further. If we take the limit of these approximations as 0‘58, 
we have (cf. (13' 13)) 
(14'06) 
D t = 0‘58 
3A a 
16i/ 0 (cTj + (X 2 ) 2 (A/7rTO 2 ) I' 
0*51A 2 D 12 . 
In this case, therefore, D T is comparable with D 12 , though it may be remarked that 
if A 2 is too nearly equal to unity, our assumption (§7) that the effect of collisions 
among the lighter molecules is negligible may require revision. It may, indeed, 
be readily seen from the general expression for D T that this always vanishes if either 
A x or A 2 becomes zero. 
We may briefly examine the case also of n th power centres of force by means 
of (13*19). Considering only a first approximation, the following results are obtained 
for various values of n :— 
First Approximations to D\/D'. 
n — 5 
(m = 
1) 
D'j/D' = 0, exactly. 
n — 7 
(m = 
f) 
0*156, approximately. 
n — 9 
(to = 
1) 
0*227 
?5 
n = 13 
(to = 
i) 
0*294 
n = 17 
(to = 
i) 
0*326 
5 5 
n - 33 
(to = 
1) 
0*372 
5 9 
n = co 
(to = 
o) 
0*417 
5? 
The general formula for the first approximation to D\/D r is readily seen to be 
r , 1— m k n— 5 / 4 \ 
6— m n—% \ n—U 
The last table shows that a very slight excess of n over its value for Maxwellian 
molecules (n — 5) suffices to raise D r to a considerable proportion of its magnitude 
corresponding to n = co (rigid elastic spheres). The phenomenon of thermal diffusion 
clearly disappears only under conditions which must be fulfilled with great nicety. 
As an instance of the correction introduced by a second approximation in the case 
of a finite value of n, it may be noticed that the result of a second approximation 
for n = 9 is 0‘246. 
