Mr. J. C. Maxwell on the Dynamical Theory of Gases. 393 



an excessively small time ; so that the equations are applicable even 

 to the case of the most acute audible sounds, without any modifica- 

 tion on account of the rapid change of motion. 



This relaxation is due to the mutual deflection of the molecules 

 from their paths. It is then shown that if the displacements are 

 instantaneous, so that no time is allowed for the relaxation, the gas 

 would have an elasticity of form, or "rigidity," whose coefficient is 

 equal to the pressure. 



It is also shown that if the molecules were mere points, not having 

 any mutual action, there would be no such relaxation, and that the 

 equations of motion would be those of an elastic solid, in which the 

 coefficient of cubical and linear elasticity have the same ratio as that 

 deduced by Poisson from the theory of molecules at rest acting by 

 central forces on one another. This coincidence of the results of two 

 theories so opposite in their assumptions is remarkable. 



6th. The coefficient of viscosity of a mixture of two gases is then 

 deduced from the viscosity of the pure gases ; and the coefficient of 

 interdiffusion of the two gases, The latter quantity has not as yet 

 been ascertained for any pair of pure gases ; but it is shown that suf- 

 ficiently probable values may be assumed, which being inserted in 

 the formula agree very well with some of the most remarkable of 

 Mr. Graham's experiments on the Transpiration of Mixed Gases*. 

 The remarkable experimental result that the viscosity is independent 

 of the pressure and proportional to the absolute temperature is a 

 necessary consequence of the theory. 



(y) The rate of conduction of heat is next determined, and it is 

 shown, 



1st. That the final state of a quantity of gas in a vessel will be 

 such that the temperature will increase according to a certain law 

 from the bottom to the top. The atmosphere, as we know, is colder 

 above. This state would be produced by winds alone, and is no doubt 

 greatly increased by the effects of radiation. A perfectly calm and 

 sunless atmosphere would be coldest below. 



2nd. The conductivity of a gas for heat is then deduced from its 

 viscosity, and found to be 



5_J p^H_ 



3y-l p o o S' 



where y is the ratio of the two specific heats, p the pressure, and p 

 the density of the standard gas at absolute temperature O , S the 

 specific gravity of the gas in question, and \x its viscosity. The con- 

 ductivity is, like the viscosity, independent of the pressure, and pro- 

 portional to the absolute temperature. Its value for air is about 

 35 1 00 of that of wrought iron as determined by Principal Forbes. 

 Specific gravity '0069. 



For oxygen, nitrogen, and carbonic oxide, the theory gives the 

 conductivity equal to that of air. Hydrogen according to the theory 

 should have a conductivity seven times that of air, and carbonic acid 

 about J of that of air. 



* Philosophical Transactions, 1846. 



