Mr. J. C. Maxwell on the Dynamical Theory of Gases. 391 



of viscosity hi this form has heen 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 de- 

 duced, from experiments on the viscosity of gases, to be that of the 

 inverse fifth power of the distance, any other law of force being at 

 variance with the observed fact that the viscosity is proportional to 

 the absolute temperature. In the mathematical 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 functions of the velocity of molecules of the first sys- 

 tem : — 



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 velo- 

 city. 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 

 considered ; 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 demonstra- 

 tion 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 neg- 

 lected. In the quiet diffusion of two gases, the volume of either 

 gas diffused through unit of area in unit of time is equal to the 

 rate of diminution of pressure of that gas as we pass in the direction 

 of the normal to the plane, multiplied by a certain coefficient, called 

 the coefficient of interdiffusion of these two gases. This coefficient 

 must be determined experimentally for each pair of gases. It varies 

 directly as the square of the absolute temperature, and inversely as 

 the total pressure of the mixture. Its value for carbonic acid and 

 air, as deduced from experiments given by Mr. Graham in his paper 



