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



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 dif- 

 ferent 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 conceiving 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 5 ^ q q q q q q second, an exces- 

 sively small time, so that the equations are applicable, even to the case of 

 the most acute audible sounds, without any modification 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 elasti- 

 city 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 assump- 

 tions 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 inter- 

 diffusion of the two gases. The latter quantity has not as yet been ascer- 

 tained for any pair of pure gases, but it is shown that sufficiently 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 bot- 

 tom 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 visco- 

 sity, and found to be 



3 y-1 p,e, 

 * Philosophical Transactions, 1846. 



