176 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
The sign of equality corresponds to the limiting case k = 1 , ^ = /jl 2 , i.e., to the case 
of self-diffusion, in which instance, therefore, b i /d 1 = & 2 /cZ 2 = b l2 /d 12 , e 0 being indepen¬ 
dent of : v 2 , as we have already seen (§13 {/))■ 
We cannot unconditionally make the further statement that b x ld x f>b l2 jd l2 , since 
the necessary condition for this, viz., M 1 /M 2 i>/(p), is not always fulfilled; but it is 
easy to prove that 
(13'36) 
if 
b\ ^ b 12 
di d^ 
(13-37) 
k > i — 3 (1 + 80 m 2 - 1 00 w*). 
Mi 
When yuj = ju. 2 = the last condition becomes kf> 1, so that if k = 1 we have, as 
before, b l fd l = b 12 /d 12 ; if ^ = /x 2 = ^ and k < 1, then bjd 1 < b V2 /d 12 . The condition 
(13'37) may be roughly expressed by saying that the more equal the molecular 
masses, the more equal, also, must be the molecular radii in order that b 1 /d 1 shall 
exceed b 12 /d 12 ; or, conversely, the more unequal the masses, the more unequal, also, 
may be the radii, consistently with the truth of (13’37). 
Clearly, if (13*37) is satisfied, and 
b\ \ b 12 6, 
d,^ d l2 ^ d 2 
e 0 steadily increases as the proportion of the heavier gas varies from 0 to 1, and 
consequently, also, I) ]2 steadily increases (cf. (13'07)). If, however, (13'37) is not 
satisfied, e 0 and D 12 will first increase to a maximum and then diminish slightly, as 
the ratio v l : increases from 0 to 1. 
As regards the actual value of e U5 the range (corresponding to all possible ratios of 
molecular mass or radius) is from the minimum value of (&j — l) 2 c/f, which is clearly 
zero (when fx 2 = 0 and v 2 = 0, i.e., when the heavier molecules are infinitesimal in 
number and the lighter molecules are infinitesimal in mass) to the maximum value of 
(k 1 — l) 2 b/e, which is T x g- (when n 2 = 0 and v } ^ 0). The maximum value of (Z^—1 )“ajd 
is ir<T 9 > which lies between the above limits. The corresponding range of (l—e,,) -1 , the 
correction factor to the first approximation (13’06) to I) 12 , which is introduced on 
making a second approximation, is consequently from 1 to 1'083. Hence, in con¬ 
junction with § 13 (e), we may conclude that for rigid elastic spherical molecules the 
total possible range in the complete correction factor V'/V to the first approximation 
to D 12 (cf. (I3'0l)) is from 1 to — or 1'132 (cf. (13’14)). 
9 7T 
It would not be difficult to construct a table showing the values of (l— e 0 ) -1 for 
various typical pairs of gases, but owing to the fact that there are three variables 
concerned (i.e., m 1 /m 2 , crjo--,, and vjv 2 ) it would need to be somewhat complicated, and 
