266 PROFESSOR TAIT ON THE 



of bard spherical particles, we have not reckoned the part of the conducted 

 energy which, in real gases, is due to rotation or to vibration of individual 

 particles. 



XIV. Diffusion. 



45. The complete treatment of this subject presents difficulties of a very 

 formidable kind, several of which will be apparent even in the comparatively 

 simple case which is treated below. We take the case of a uniform vertical 

 tube, of unit area in section, connecting two vessels originally filled with different 

 gases, or (better) mixtures of the same two gases in different proportions, both, 

 however, maintained at the same temperature ; and we confine ourselves to the 

 investigation of the motion when it can be treated as approximately steady. 

 We neglect the effect of gravity (the denser gas or mixture being the lower), 

 and we suppose the speeds of the group-motions to be very small in compari- 

 son with the speed of mean square in either gas. [In some of the investigations 

 which follow, there are (small) parts of the diffusion-tube in which one of the 

 gases is in a hopeless minority as regards the other. Though one of the initial 

 postulates (d of § 1) is violated, I have not thought it necessary to suppress the 

 calculations which are liable to this objection; for it is obvious that the condi- 

 tions, under which alone it could arise, are unattainable in practice.] 



Clerk-Maxwell's Theorem (§ 15), taken in connection with our preliminary 

 assumption, shows that at every part of the tube the number of spheres per 

 cubic unit, and their average energy, are the same. Hence, if n v n 2 , be the 

 numbers of the two kind of spheres, per cubic unit, at a section x of the tube 



oi 1 + n 2 = n = constant, (1.) 



Also, if P 1? P 2 , be the masses of the spheres in the two systems respectively, 

 h x and h 2 the measures (§ 3) of their mean square speeds, we have 



PA = P 2 /fi 2 = KPA + n 2 TJh 2 )jn = 2 P /n, . . . (2.) 



where p is the constant pressure. 



Strictly speaking, the fact that there is a translational speed of each layer 

 of particles must affect this expression, but only by terms of the first order of 

 small quantities. 



46. The number of particles of the P x kind which pass, on the whole, 

 towards positive x through the section of the tube is (as in § 39) 



/* CO 



where a, is the (common) translational speed of the P : s, and l/e 1 the mean 



