392 Royal Society : — 



on the Mobility of Gases *, is 



D=00235, 

 the inch, the grain, and the second being units. Since, however, 

 air is itself a mixture, this result cannot be considered final, and we 

 have no experiments from which the coefficient of interdiffusion of 

 two pure gases can be found. 



3rd. "When two gases are separated by a thin plate containing a 

 small hole, the rate at which the composition of the mixture varies 

 in and near the hole will depend on the thickness of the plate and 

 the size of the hole. As the thickness of the plate and the diameter 

 of the hole are diminished, the rate of variation will increase, and the 

 effect of the mutual action of the molecules of the gases in impeding 

 each other's motion will diminish relatively to the moving force due 

 to the variation of pressure. In the limit, when the dimensions of 

 the hole are indefinitely small, the velocity of either gas will be the 

 same as if the other gas were absent. Hence the volumes diffused 

 under equal pressures will be inversely as the square roots of the 

 specific gravities of the gases, as was first established by Graham f; 

 and the quantity of a gas which passes through a thin plug into an- 

 other gas will be nearly the same as that which passes into a vacuum 

 in the same time. 



(/3) By considering the variation of the total energy of motion of 

 the molecules, it is shown that, 



1st. In a mixture of two gases the mean energy of translation will 

 become the same for a molecule of either gas. From this follows the 

 law of Equivalent Volumes, discovered by Gay-Lussac from chemical 

 considerations — namely, that equal volumes of two gases at equal 

 pressures and temperatures contain equal numbers of molecules. 



2nd. The law of cooling by expansion is determined. 



3rd. The specific heats at constant volume and at constant pressure 

 are determined and compared. This is done merely to determine 

 the value of a constant in the dynamical theory for the agreement 

 between theory and experiment with respect to the values of the two 

 specific heats ; and their ratio is a consequence of the general theory 

 of thermodynamics, and does not depend on the mechanical theory 

 which we adopt. 



4th. In quiet diffusion the heat produced by the interpenetration 

 of the gases is exactly neutralized by the cooling of each gas as it 

 passes from a dense to a rare state in its progress through the mixture. 



5th. By considering the variation of the difference of pressures in 

 different directions, the coefficient of viscosity or internal friction is 

 determined, and the equations of motion of the gas are formed. 

 These are of the same form as those obtained by Poisson by con- 

 ceiving an elastic solid the strain on which is continually relaxed at 

 a rate proportional to the strain itself. 



As an illustration of this view of the theory, it is shown that any 

 strain existing in air at rest would diminish according to the values 

 of an exponential term the modulus of which is ,i 00) q 00 , 000 second, 



* Philosophical Transactions, 1863. 



t " On the Law of the Diffusion of Gases," Transactions of the Royal Society 

 of Edinburgh, vol. xii. (1831). 



