182 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
the particular characteristics of the molecules. We shall see later that the 
phenomenon is also differential, i.e., it occurs only when the masses or diameters of 
the molecules are not the same for the two kinds. Thus when they are alike in mass 
and dynamical properties /3' 0 (and consequently also D T ) is exactly zero (cf. (8‘ 13)); 
this is true whatever the nature of the molecules. 
( b ) The First Approximation to D T . 
The first approximation to D T is obtained by substituting the value of /3' 0 given, to 
this degree of accuracy, by (9’20), viz. (cf. (9'17), (9‘09)-(9'13)), 
_ 3 (m 1 + m 2 ) RT e ; (^ ] — 1 
2TTv 0 m 1 m 2 K' u (0) 
We shall not go beyond a first approximation in the general case, but (as in § 13 (e) 
with regard to D 12 ) we shall briefly examine the order of magnitude of the corrections 
introduced by further approximations, by a consideration of the special case when 
and <t 2 I<tx are very small (§ 7). 
(c) The Value of D T when rnf n 2 and aj<r 2 are very large. 
In this instance the value of /3' 0 is given by (7'22), and 
(14-04) 
D t = 
3\JtT D' x 
27r^m 2 K / 12 (0) D' 
When the molecules are rigid elastic spheres of radii o-j, o- 2 , this assumes the form 
(14*05) 
D t = 
_3X2_D\ 
\Qv {j (cr 1 +(T 2 Y (JlTrm^^ D' 
or (cf. (7‘26)) the same expression except that Dj/D replaces D\/D'. In each case the 
suffix 1 to D or D' denotes the second minor of the corresponding determinant. 
We have already given the value of D as far as the fourth row and column (§13 ( e )). 
From this we find that the first three approximations to Dj/D are, with their 
successive differences equal to 
_ 5 _ 
12 
0-417 
2280 
4608 
0'494 
556416 
1061681 
0'524. 
77 
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