260 PHENOMENA DEPENDENT ON MOLECULAR PATHS 97 



If there are N l particles of the first kind and N 2 particles 

 of the second in unit volume, we see at once from the 

 formulae we have established that the whole number of 

 collisions which a particle of the first gas undergoes in unit 

 time is given by the sum 



r, = Ti-^WAv^ + 



while 



r 2 = ,r* a w a n 2 V2 + 



represents the whole number of collisions which a molecule 

 of the second gas experiences in unit time in the mixture. 



Hence for the mean free path of a particle of the first 

 kind we obtain the value 



and similarly for a particle of the second gas, 



Both values are dependent on the numbers N l and N 2 , 

 and are therefore variable with the ratio of the amounts of 

 the two gaseous components in the mixture. 



98. Coefficient of Diffusion 



If we insert these values of the two free paths fci and 2 

 in the formula of 95, viz. 



D = X^&A + N&nj/N, 



we obtain the value of the coefficient of diffusion _D, of 

 which we said in the introductory explanations of 93 that 

 it possesses the same meaning for the process of diffusion 

 as the conductivity does for the propagation of heat. If this 

 analogy were allowed to 4 be perfect we should expect that, 

 just as the conductivity is a constant magnitude, so too is 

 the coefficient of diffusion, which will always keep the same 

 value in all experiments made with the same pair of gases. 

 But this expectation is not justified by our formula. 1 



1 See also Tait, Trans. Boy. Soc. Edin. 1887, xxxiii. p. 266; Phil Mag. 

 [5] xxiii. p. 141. 



