MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 165 
in the absence of thermal conduction and of external forces we shall have as the 
equation of energy 
(12-22) a,C„!?= 2i(K), 
where IB is defined by the equation 
l 00 
(12-23) © = T7 2r( w + ¥ 4 
and is termed the specific energy of diffusion. 
We now proceed to consider in detail the various coefficients of diffusion, conduction, 
viscosity, and specific energy of diffusion for which we have obtained general formulae. 
13. The Coefficient of Diffusion D 12 . 
(a) The General Formula. 
The general formula for the coefficient of diffusion D 12 is obtainable in terms of the 
molecular data by substitution in (10’05) of the value of a' 0 given by (5'35), thus 
(13*01) 
D 12 — ‘?rA 0 ItTX 1 X 3 
v/ (<WO . 
So far as § 9 (6) A 0 had remained quite arbitrary, only the product of A 0 into the 
coefficients a being definite. We there defined A^ as having such a value as to make 
a 00 equal to unity. We now substitute that value (cf. (9*022)), viz., 
(13-02) 
in (13 *01), with the result that 
(13-03) 
A — 27 (m 1 + m 2 ) 
2Tr\ 1 X 2 v 0 m l m 2 K\ 2 ( 0 ) 
D 3 K+ffla) RT V' (S mn a mn ) ^ 
27rj/ u w 1 m 2 K , 12 (0) V (S mn a mn ) ’ 
where V' is the principal minor of V. 
(h) The Case of Maxwellian Molecules. 
In the case of Maxwellian molecules it is readily evident from (6"03) that all the 
elements of the first row and column of V (S mn a mn ), save the initial element a 00 , are 
zero. Hence in this case V is equal to a 00 V', i.e., 
