or 



Diffusion of Gases. 475 



t ^ hxf{v) dv = Wl B (« - «') &r/M <fo, 



Jg =niB ( a - a ') (1) 



This equation must in steady motion be satisfied for every 

 class of molecules. And it cannot be satisfied without making 

 a a function of v. Were a made constant, molecules with 

 high values of v would begin to gain more translation-velocity 

 than they lose. The arrangement could not be permanent. 



1 0. It is of course true that the effect of encounters between 

 the different classes of molecules of the same gas is to equalize 

 the translation-velocity. A levelling-process is always going 

 on. It is also true, as Professor Tait shows (page 83), that 

 this process goes on very fast ; because B, the number of 

 encounters per second, is a very large quantity. The larger 

 you make B, the smaller you make a and u f . But the equa- 

 tion (1) remains none the less true, and none the less must a 

 be a function of v. 



Nor is it a matter of indifference whether we treat a as 

 constant or not. The greater the absolute speed the greater 

 the number of encounters per unit time. Therefore, for given 

 stream-velocity of the whole gas, the resistance will be greater 

 if that stream-velocity be all attributed to the higher classes 

 than if it be the same for all classes. Therefore, in order to 

 get the same resistance with a constant, we must increase the 

 stream. Any result obtained with a constant can be no more 

 than a superior limit of the stream-velocity ; and the value of 

 such a solution depends on the limits of error being ascertained. 



I think the same error vitiates Professor Tait's treatment of 

 Viscosity and Thermal Conductivity. 



11. As a step towards the true solution, I will endeavour to 

 obtain inferior and superior limits for the stream-velocity in 

 this imaginary case, the molecules of one gas having equal 

 mass and diameter with those of the other. I will further 

 suppose that there exists a point C in the tube at which n x = n 2 . 

 This must be the case if n-^ > n 2 in one reservoir, and n^ < n 2 

 in the other. If we can find the stream-velocity at C, we 

 know it at every point in the tube. 



12. The number of encounters per unit of time for each 

 molecule of the class v is B. I shall assume that at the point 

 C, where n t =^n^ there are for each molecule of the class |B 

 encounters with molecules of gas II., and -JB with other 

 molecules of gas I. 



13. A molecule of gas I. coming out of encounter with 



