MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. ID I 
expression in (18'02) for a composite gas does not, however, agree with the corre¬ 
sponding first approximation in my original memoir (‘ Phil. Trans.,’ A, vol. 211, p. 452, 
cf. 40 and 4l). This is because it was there assumed (§2) that thermal conduction 
was independent of diffusion, whereas we have seen that a temperature gradient 
is inseparable from either diffusion or a concentration gradient; this invalidates the 
equations (24) of that paper. The second term within the square bracket of (18’02) 
especially arises from the terms in the velocity-distribution function which represent 
the diffusion effect, although the first term is also affected. Evidently even the first 
approximation to 3- involves the quotient of a homogeneous quartic in i\, v 2 by the 
product of two homogeneous quadratics, a complexity which makes it hardly worth 
while to compare the result with the scanty experimental data at present available. 
A brief discussion of my earlier formula, which may be expected to differ only slightly 
from (18‘02) in numerical magnitude, is given in § 18 of my first memoir. 
§ 19. The Specific Energy of Diffusion. 
In § 12 (c) we saw that in a gas which is at rest and at a uniform temperature, 
so that no conduction of heat is taking place, there may yet be a continual rise in 
temperature if diffusion is going on. The gas being at rest as a whole, no gain 
of thermal energy accrues through the medium of internal friction, and the thermal 
flux of diffusion may proceed also in the absence of external forces, i.e., solely as 
a result of variations of concentration. However the diffusion is produced, in the 
latter or any of the other ways described in § 10, the equation of energy will contain 
a term equivalent to that on the right of the following equation :—■ 
( 19 -01) = 
This is identical with (12’22), and assumes that only the thermal flux of diffusion 
is operating to increase the heat energy of the gas. 
By (12‘23) we have the following expression for 13, which we have termed the 
specific energy of diffusion :— 
(19'02) 33 = 2r {v,a r + v 2 a_ r ) 
•J a 0 i 
_ _ RT B 0 /T 0 i/ t , 
J A 0 Ra r 0 X 1 X 2 
= _ RT Dr , 
Xi\ 2 J D ia ’ 
by (9‘20) and (10’05), (10T0). Since C„, the specific heat at constant volume for the 
composite gas, is given by 
1 
R 
