148 Dr. S. Chapman on the Partial Separation by 



their mutual encounters. If both sets of molecules obey the 

 Maxwellian law, whether or not their force constants are 

 the same, or if they obey any other law during encounter, 

 provided their force constants or diameters are identical, 

 thermal diffusion is not produced. But if their laws of 

 inter-action (not being Maxwellian), or diameters, are dif- 

 ferent, a temperature gradient will cause interdiffusion. 

 When the molecular masses are unequal, and the diameters 

 equal, the heavier gas diffuses towards the cooler regions. 

 When the masses are equal, but the diameters unequal, the 

 larger molecules diffuse in that direction. 



In order to gain some idea of the numerical magnitude of 

 the separating action of thermal diffusion, we shall consider 

 a mixture of v x molecules of radius cri with v 2 molecules of 

 radius er 2 , per unit volume, the masses of each being m. Both 

 will be supposed monatomic, in order that the mathematical 

 theory may apply strictly, though the non-fulfilment of the 

 condition is not likely to affect our estimate seriously. We 

 shall consider only the first approximation to the coefficient 

 of thermal diffusion D*, as given in the memoir and abstract 

 already mentioned. Second and third approximations to D* 

 increase its value only very slightly. If D 12 is the ordinary 

 coefficient of diffusion, the relation between the approxi- 

 mations to D* and D 12 is as follows : — 



J) t =ktD 12 , 



where, in the notation there explained, 



ei(l-e ) 



*i= 



^oA] 



2O 1 2 -0- 2 2 ) + (Xi-XjXoi-ct,) 3 



lir J 4o- 1 2 - + 4o- 2 2 -^ r +— ( —j—\ +- r (<r 1 -to- s y 



in the present case of equal molecular masses. In the last 

 equation \ x and A 2 are defined as follows : — ■ 



so that 



Xi + A 2 = l, \\i — A, 2 1 < 1. 



Clearly &£ is always positive if o"i>0" 2 , whatever be the values 

 of Xj and X 2 . Since the equation of thermal diffusion is (I. c.) 



(where u ' is the velocity of diffusion of the molecules (1), 

 and T is the absolute temperature), and since D t is positive 



