.! .i-2 ILLUSTRATIONS OF THE DYNAMICAL THEORY OF OASES. 



PART II. 



* ON THE PROCESS OF DIFFUSION OF TWO OR MORE KINDS OF MOVING PARTICLES 



AMONG ONE ANOTHER. 



We have shewn, in the first part of this paper, that the motions of a 

 system of many small elastic particles are of two kinds : one, a general motion 

 of translation of the whole system, which may be called the motion in mass ; 

 and the other a motion of agitation, or molecular motion, in virtue of which 

 velocities in all directions are distributed among the particles according to a 

 certain law. In the cases we are considering, the collisions are so frequent that 

 the law of distribution of the molecular velocities, if disturbed in any way, 

 will be re-established in an inappreciably short time ; so that the motion will 

 always consist of this definite motion of agitation, combined with the general 

 motion of translation. 



When two gases are in communication, streams of the two gases might 

 run freely in opposite directions, if it were not for the collisions which take 

 place between the particles. The rate at which they actually interpenetrate each 

 other must be investigated. The diffusion is due partly to the spreading of the 

 particles by the molecular agitation, and partly to the actual motion of the 

 two opposite currents in mass, produced by the pressure behind, and resisted 



* [The methods and results of this paper have been criticised by Clausing in a memoir published 

 in Poggendorffs Annalen, VoL cxv., and in the Philosophical Magazine, VoL xxm. His main objec- 

 tion is that the various circumstances of the strata, discussed in the paper, have not been sufficiently 

 represented in the equations. In particular, if there be a series of strata at different temperatures 

 perpendicular to the axis of x, then the proportion of molecules whose directions form with the 

 axis of x angles whose cosines lie between /t and /x + efyx is not l<lp. as has been assumed by Maxwell 

 throughout his work, but './A//t where If is a factor to be determined. In discussing the steady 

 conduction of heat through a gas Clausius assumes that, in addition to the velocity attributed to 

 the molecule according to Maxwell's theory, we must also suppose a velocity normal to the stratum 

 and depending on the temperature of the stratum. On this assumption the factor H is investigated 

 along with other modifications, and an expression for the assumed velocity is determined from the 

 consideration that when the flow of heat is steady there is no movement of the mass. Clausius 

 combining his own results with those of Maxwell points out that the expression contained in (28) 

 of the paper involves as a result the motion of the gas. He also disputes the accuracy of ex- 

 pression (59) for the Conduction of Heat In the introduction to the memoir published in the 

 PhiL Trans., 1866, it will be found that Maxwell expresses dissatisfaction with his former theory 

 of the Diffusion of Gases, and admits the force of the objections made by Clausius to his expression 

 for the Conduction of Heat. Ed.] 



