168 Mr. Maxwell on the Dynamical Theory of Gases, [May 31 ^ 



tion of this form of the theory to the phenomena of viscosity, diffusion, and 

 conduction of heat in the Philosophical Magazine for 1860. M. Clausius 

 has since pointed out several errors in the part relating to conduction of 

 heat, and the part relating to diffusion also contains errors. The dynami- 

 cal theory of viscosity in this form has been reinvestigated by M. O. E. 

 Meyer, whose experimental researches on the viscosity of fluids have been 

 very extensive. 



In the present paper the action between the molecules is supposed to be 

 that of bodies repelling each other at a distance, rather than of hard elastic 

 bodies acting by impact ; and the law of force is deduced from experiments 

 on the viscosity of gases to be that of the inverse fifth power of the dis- 

 tance, any other law of force being at variance with the observed fact that 

 the viscosity is proportional to the absolute temperature. In the mathe- 

 matical application of the theory, it appears that the assumption of this 

 law of force leads to a great simplification of the results, so that the whole 

 subject can be treated in a more general way than has hitherto been done. 



I have therefore begun by considering, first, the mutual action of two 

 molecules ; next that of two systems of molecules, the motion of all the 

 molecules in each system being originally the same. In this way I have 

 determined the rate of variation of the mean values of the following func- 

 tions of the velocity of molecules of the first system : — 



a, the resolved part of the velocity in a given direction. 



/3, the square of this resolved velocity. 



y, the resolved velocity multiplied by the square of the whole velocity. 

 It is afterwards shown that the velocity of translation of the gas depends 

 on a, the pressure on /3, and the conduction of heat on y. 



The final distribution of velocities among the molecules is then con- 

 sidered, and it is shown that they are distributed according to the same 

 law as the errors are distributed among the observations in the theory of 



Least Squares and that if several systems of molecules act on one 

 another, the average vis viva of each molecule is the same, whatever be the 

 mass of the molecule. The demonstration is of a more strict kind than 

 that which I formerly gave, and this is the more necessary, as the Law 

 of Equivalent Volumes," so important in the chemistry of gases, is deduced 

 from it. 



The rate of variation of the quantities a, /3, y in an element of the gas 

 is then considered, and the following conclusions are arrived at. 



(a) 1st. In a mixture of gases left to itself for a sufficient time under the 

 action of gravity, the density of each gas at any point will be the same as 

 if the other gases had not been present. 



2nd. When this condition is not fulfilled, the gases will pass through 

 each other by diffusion. When the composition of the mixed gases varies 

 slowly from one point to another, the velocity of each gas will be so small 

 that the effects due to inertia may be neglected. In the quiet diffusion of 

 two gases, the volume of either gas diffused througli unit of area in unit 



