FOUNDATIONS OF THE KINETIC THEORY OF GASES. 91 



But, if the above argument be, even in part, admitted, we are not led to 

 any such conclusion, and we can obtain ns 3 (as above) as a quantity of the 

 second rank. We have already seen that ns 2 is inversely proportional to the 

 mean free path, and is thus also of the second rank. From these data Ave may 

 considerably improve our approximations to the values of n and of s. 



Taking Maxwell's estimate of the mean free path in hydrogen, we have (to 

 an inch as unit of length) 



5^ = 880.10- 8 . • 



From these values of ns 2 and ns 3 we have, approximately, for 0° C, and 1 

 atmosphere, 



n = 16.10 20 , s = 6.10-\ 



The values usually given are 



n = 3.10 w , s = 2-3.1(T s . 



It must be recollected that the above estimate rests on two assumptions, 

 neither of which is more than an approximation, (a) that the particles of 

 hydrogen behave like hard spheres, (b) that they exert no mutual molecular 

 forces. If there were molecular attraction the value of ns 3 would be greater 

 than that assumed above, while ns 2 would be unaltered. Thus the particles 

 would be larger and less numerous than the estimate shows. 



[Of course, after what has been said, it is easy to see that V should be 

 diminished further by a quantity proportional to the surface of the containing 

 vessel and to the radius of a sphere. But though this correction will become 

 of constantly greater importance as the bulk occupied by a given quantity of 

 gas is made smaller, it is probably too minute to be detected by experiment.] 



IX. Effect of External Potential. (Added June 15, 1886.) 



31. Another of Maxwell's most remarkable contributions to the Kinetic 

 Theory consists in the Theorem that a vertical column of gas, when it is in 

 equilibrium under gravity, has the same temperature throughout. He states, 

 however, that an erroneous argument on the subject, when it occurred to him in 

 1866, " nearly upset [his] belief in calculation."" 15 ' He has given various investiga- 

 tions of the action of external forces on the distribution of colliding spheres, but 



* Nature, viii., May 29, 1873. Maxwell's name does not occur in the Index to this volume, though 

 he has made at least five contributions to it, most of which hear on the present subject : — viz. at pp. 85, 

 298, 361, 527, 537. 



