MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 181 
pressures, are necessary in order to obtain evidence from diffusion as to the best 
molecular model. It is, therefore, of some importance to consider the variation of 
D 12 with pressure (or density) and temperature. 
n+3 
The first approximation to D ]2 (13‘06) varies as T 2 (»-u +1 in the case of molecules 
which are n th power centres of force, the case n =co , T 3/l , corresponding to rigid 
elastic spheres (cf. ‘ Phil. Trans.,’ A, vol. 211, p. 479). It may readily be seen that 
the correction factor V'/V in (l3'0l) is independent of h or T for these particular 
molecular models (cf. ‘ Phil. Trans.,’ A, vol. 216, § 9 (B), p. 321). 
Another molecular model, considered in my two previous memoirs, is the rigid 
elastic sphere surrounded by a field of attractive force (the Sutherland molecule). 
The first approximation to I) I2 in this varies as T' ?/ ' 2 /(l + S'/T), where S' is known as 
Sutherland’s constant of diffusion.* It may be proved without difficulty, as in the 
case of the coefficient of viscosity for a simple gas (cf my second memoir, §§ 9-11) that 
the correction V'/V is usually intermediate between unity and the value corresponding 
to rigid elastic spheres without attraction. The correction factor in the case of 
Sutherland’s molecules also depends upon the temperature, but the variation is so 
very slight as to be negligible. 
As regards variation with density, the first approximation to D 13 varies inversely 
as the total density of the gas mixture, and is independent of the relative proportions 
of the two gases. The correction factor V'/V in (l3‘0l) has been seen to vary with 
the relative proportions (vfv^), but if : v 2 is fixed, the factor may readily be shown 
not to vary with the total density v 1 + v 2 . 
§ 14. The Coefficient of Thermal Diffusion. 
(a) The General Formula for D T . 
The coefficient of thermal diffusion D T was defined in § 10 (a) by the equation 
(14’01) 
w 
T) 19T = _r) d log T 
T T T 0x ’ 
and was found to be given by (cf (10T0), (5’36)) 
(1U02) 
D t = —iB 0j 8' 0 T = lAAJfiT 
i v'o (<LA>J 
V ($mJ>mn) 
In the case of Maxwellian molecules it was found that (3' 0 vanishes (cf. (6"05)), so 
that for a gas composed of such molecules D T is zero, and the phenomenon of thermal 
diffusion is non-existent. This, together with the absence of variation of D 12 with 
vjv 2 (cf. § 13 (g)), is one of the few properties of a gas which depends essentially on 
* Cf . Sutherland, ‘ Phil. Mag.’ (5), 38, p. 1, 1894, and my first memoir, p. 479. 
2 c 2 
