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XXII. A Note on Thermal Diffusion. By S. Chapman, 

 M.A., D.Sc, and F. W. Dootson,M.A, Sc.I).* 



IN a recent memoir by one of us |, a new mathematical 

 treatment of the kinetic theory of simple and composite 

 gases is developed, in which it is shown that a temperature 

 gradient in a mixture of two gases is sufficient to produce 

 diffusion, independently of any non- uniformity of composition 

 or of the action of external forces. This phenomenon, appa- 

 rently there first announced, has been designated u thermal 

 diffusion." In the case of a uniform mixture of two gases, and 

 in the absence of any other agent tending to produce diffusion, 

 the effect of a temperature gradient maintained in the gas will 

 be to make the heavier gas molecules diffuse in the direction 

 of diminishing temperature, and vice versa for the lighter gas 

 molecules. The amount of the effect is greatest when the 

 gases are mixed in nearly equal proportions by volume, and 

 also is greater the more unequal are the masses and diameters 

 of the gas molecules. It depends, moreover, on the nature of 

 the molecules ; it seems greatest for molecules which behave 

 like rigid elastic spheres, while it vanishes altogether in the 

 one special case when they act like fifth-power centres of force 

 (the model used by Maxwell in his later papers on the kinetic 

 theory). The latter curious fact perhaps explains why the 

 phenomenon remained undiscovered so long by theoretical 

 writers, since till recently Maxwellian molecules were the 

 only ones which could be treated with mathematical accuracy. 

 Let us suppose that a temperature gradient is maintained, 

 by outside means, in a mixture of two gases occupying a 

 closed vessel, there being no external forces. Thermal 

 diffusion will act in the manner indicated, but there will be 

 a limit to the inequality of composition thus set up, since 

 such an inequality of composition tends to right itself by the 

 ordinary process of diffusion. The amount of the resultant 

 concentration-gradient, when the state of the gas has 

 become steady, will depend on the ratio of the ordinary co- 

 efficient of diffusion, J) 12 (say), to a certain coefficient of 

 thermal diffusion, D t , which is defined in the memoir cited. 

 This ratio, D*/D 12 , will be denoted by k t . Let us denote the 

 absolute temperature by T, and the proportions by volume of 

 the heavier and lighter gas by Vi and v 2 respectively (so that 

 v 1 + v 2 = l). Then, in the stead}?- state, the concentration and 



* Communicated by the Authors. 



f Chapman, Phil. Trans. A. 1916 (unpublished); an abstract is given in 

 J?roc. Roy. Soc, December 1916. 



