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XIV. On the Diffusion of Gases ; a Reply to Professor Tait. 

 By 8. H. Burbuky*. 



SUPPOSE a gas at uniform density in a closed vessel, and 

 to the vessel and every molecule in it a small common 

 velocity u be given. Then the gas has mass motion u. 



In the problem of diffusion the gas has density n x inde- 

 pendent of the time but varying from point to point along a 

 tube ; and another gas has density n 3 varying in the opposite 

 way, so that Wi + n 3 is constant. The first gas acquires a 

 steady stream, say from left to right, along the tube. And 

 the question is whether the steady motion of the gas in such 

 circumstances can be " mass motion " as above defined, or not. 



I maintain that it cannot ; and, unless by the weight of his 

 authority, Professor Tait has not shaken my reasoning. 



Take an element of the tube, of length 8x, between the 

 sections A and A'. "Without departing from the statistical 

 method, I say there exists a class v of molecules of the first 

 gas in that element constant in number, namely nyf(v)dv &c, 

 while the particular molecules composing it are continually 

 changing. Without departing from the statistical method, I 

 say there are two, and only two, possible ways in which they 

 can change — (1) by molecules with velocity v passing in or 

 out at A and A', (2) by encounters within the element. As 

 the result of (1), molecules going to the right enter the ele- 

 ment in greater numbers than they leave it. The reverse is 

 the case with those going to the left. From this cause you 

 have an increase of translation-velocity of the class within the. 



element equal to f(v) dv-^- ~r^8x per unit of time. 



(2) By encounters nif(v) dv B Sx molecules leave the class, 

 and as many enter it, per unit of time. The original mole- 

 cules had mean translation- velocity «. The substituted ones 

 have mean translation-velocity a', which is less than a. 



Owing to encounters, you have a loss of translation-velocity 

 to the class within the element equal to Wi/(w) dv B(a — a') hx 

 per unit time. Equating the loss by (2) to the gain by (1), 

 you obtain the condition for steady motion, 



v 2 dn $ -r, , „ 



for each class. 



It cannot be satisfied by " mass motion." I have not 

 " ignored the community of interest which mutual collisions 



* Communicated by the Author. 

 Phil. Mag. S. 5. Vol. 25. No. 153. Feb. 1888. K 



