180 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
values here theoretically deduced. The values of n, calculated from the variation of 
viscosity with temperature, on the hypothesis that the molecules are the n th power 
centres of force, are given alongside. The formula of interpolation used to obtain D n 
from D 12 is based on the theory of rigid elastic spherical molecules, and this, together 
with the rather early date of the diffusion constants used (they were determined by 
Loschmidt), may prevent us from expecting a very close agreement with theory. I 
have not calculated the theoretical values of k for values of n between 5 and oo, 
since they depend on certain integrals which must be evaluated by quadratures; but 
it would be interesting to have these quantities determined.] 
n. 
D n pi 
Theory. 
00 
1-200 
Hydrogen. 
12 
1-36 
Carbon-monoxide. 
' 9-3 
1-34 
Oxygen. 
7-9 
1-43 
Carbon-dioxide. 
5-2 
1-50 
Theory. 
5-0 
1-504 
Perhaps the most satisfactory comparison between theory and experiment is 
provided by calculating <n both from the coefficient of diffusion, as above, and also 
in some other way as, e.g., from the coefficient of viscosity k x . Assuming that the 
experimental data and the molecular representation underlying the theory are 
satisfactory, the accordance of the two values of cr affords a complete check on the 
theory of D 13 and k jointly. Such a comparison was made in my first memoir (‘ Phil. 
Trans.,’ A, vol. 211, p. 480), using the approximate formulae for D 12 and k there 
given ; the confirmation of the theory thus provided was perhaps as good as the 
accuracy of the data might allow one to expect. The table in that paper requires 
revision, because of the corrections to my original formulae which have been deduced 
in the present and my second memoir. Until more modern and accurate data for 
the coefficient of diffusion are available, however (and of such there is need), this 
revision is hardly worth while in view of the smallness of the corrections mentioned. 
In connection with this matter, finally, it may be pointed out that in tables giving 
values of D 12 intended for accurate theoretical purposes it is necessary to specify the 
ratio by volumes of the diffusing gases, since the theoretical expression for D 12 , in 
general, involves this ratio (^ : vd). This practice has not usually been adopted 
hitherto. 
(k) The Variation of D 12 with Pressure and Temperature. 
Since the theoretical expression for D 12 , on whatever molecular hypothesis, contains 
at least one quantity (molecular diameter or force constant) which is not directly 
measurable, two or more values of D 12 , corresponding to different temperatures or 
