190 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
polynomial in i/ l5 v 2 by another, reducing, when v 2 = 0, to the second approximation to 
k u the coefficient of viscosity of a simple gas. The present importance of such a 
second approximation to k 12 does not seem to render the complicated calculation worth 
while. In my first memoir ( loc. cit., pp. 469-472) a comparison of (17'02) with 
experimental data is given, which suggests that the formula satisfactorily represents 
the behaviour of actual gases in respect of the variation of x 12 with vjv 2 * 
When the molecules are rigid elastic spheres, (17'02) has the special form 
k 12 — 
5 
ET 
m x m 2 
, 1 + 5M12) H 2 + I { 1 + o l 1 , + ( 1 + 57 * 21 ) v 2 
_ l 2 ) UiM 2 + j _ 
m x -h mi, (1 + | Ml2 ) ar 1 2 v 1 2 + '|i(o-i + o- 2 ) 2 + y G p 7 T 2 i n^ + (l + 5M21) <P>V 
l V cr 1 + °'2/ j 
where we have quoted from § 9 (f). The special forms appropriate to molecules of 
other particular types may likewise easily be written down. 
§18. The Coefficient of Thermal Conduction. 
In § 12 the following expression for the coefficient of thermal conduction 3- was 
found (c/1 (12'21) ):— 
(18-01) 
3- = ^B 0 
ET 
J 
2 (vJlf + VaP-r) — 
0 -V 
a . 
'(^r 
' VoCt 
-) • 
Owing to the complexity of even a first approximation, we shall not go further 
than this in the present paper ; in making the approximation, we use the results 
of § 9, which lead to the equation 
(18'02) 3 
25 (X 1 m 1 + X 2 m 2 ) (m 1 + w 2 ) C„ET 
2irm ] m 2 K' 12 (0) (a x v 2 + 2a y2 v x v 2 + a 2 v 2 ) 
M 2 
K 
CCiV 1 T 2 Ct \ 2 V\V 2 j ^ (X 2 v 2 J 
^22 / 
2 
(^i — T) 
2 2 
V 1*2*1 
d\V\ T 2cL x2 v x v 2 T 
If we put i/j = 0 in this expression it becomes 
(18-03) 
2 5 ETC,, 
27r£ 11 °K / 12 (0) 
1*]C„ 
by (17 *03) ; this agrees with the first approximation to 3 for a simple gas which was 
given in my two previous memoirs (loc. cit., p. 462, p. 337, respectively). The 
* In particular, the theory there given indicates that the viscosity of a gas mixture may rise to a 
maximum (for a certain value of v x /v 2 ) which exceeds the viscosity of either component separately. This 
had already been proved by Maxwell for the particular type of gas dealt with in his second paper. 
Kuenen has recently shown that the ordinary elastic-sphere theory leads to a similar result, when 
allowance is made for the persistence of velocities after collision (‘Amsterdam Acad. Proc./ 16, p. 1162, 
1914). 
