456 MATHEMATICAL APPENDICES 61 1 



APPENDIX V 

 DIFFUSION 



51*. General Theory of Diffusion 



IT is not my intention to investigate the theory of diffusion of 

 gases with the same mathematical rigour as the simpler theory of 

 viscosity. I limit myself here to supplying the mathematical 

 explanations desirable for those going more deeply into the theory 

 of diffusion developed in the text, and these I shall found upon 

 Maxwell's law. 



As to the distribution of the two gases, I make only the 

 assumption that the whole pressure of the mixture 



P=Pl + P2=P 



possesses everywhere the same constant value P, and therefore 

 keeps this same value always ; and also that, corresponding to it, 

 there are always at every point the same number 



N t +N, 

 of molecules of the two kinds in unit volume. 



As in the investigation given in the text, we determine for one 

 of the two kinds of gas the number of molecules which in unit 

 time pass in the direction of increasing x through a surface- 

 element dS of a section of the diffusion tube at a distance x from 

 the beginning of the tube. We form this sum with the assumption 

 of the validity of Maxwell's law of distribution of speeds. This 

 assumption is not strictly admissible, since the deduction of this 

 law presupposes the state of motion of the whole gas to be every- 

 where the same. But the application of this law to our problem 

 is allowable as a good approximation, if we can look upon the 

 ratio of mixture of the two gases in the space filled by them, not 

 simply as a continuous function of the position, but also as one 

 that varies very slowly. For, with this hypothesis, that ratio and 

 the whole state of the mixture can be assumed to be constant 



