144 Mr. 0. Reynolds on Thermal Transpiration 



result of a somewhat common and, certainly, historical error 

 in mechanical analysis. 



In order to make this clear I will recur somewhat to the 

 history of the kinetic theory of gases from 1860. In that year 

 the Phil. Mag. contained a paper by Maxwell in two parts, the 

 first containing his law of distribution, the law of logarithmic- 

 decrement of inequalities in distribution for rigid particles, 

 and the theory of viscosity, and the second part containing 

 the theories of diffusion and the conduction of heat. 



After this there appeared (Pogg. Ann. 1862) a paper by 

 Clausius " On the Conduction of Heat by Gases." This was 

 avowedly in answer to a challenge by M. Jochmann, but in 

 reality for the purpose of correcting Maxwell's somewhat 

 ill- considered theory of conduction and replacing it by 

 another on a sound foundation. 



In the first paragraph of the second part of his paper 

 Maxwell says : — 



" We have shown, 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, w r ill be reestablished 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." 



According to the assumption in the second sentence quoted, 

 if the gas were in steady condition and at rest, no matter 

 what were the space variations of condition, the molecules 

 would leave a spherical element, taken about a point P, 

 after having undergone collision within it, with the same 

 mean characteristics in all directions as if the gas about P 

 had been uniform. And in this case the molecules would 

 reach a plane with mean characteristics as from uniform 

 gas with the mean characteristics of the gas at the points 

 at which they last underwent collision. Maxwell seems to 

 have made an error in his analysis which somewhat obscured 

 the results which should follow from this assumption, other- 

 wise it would have appeared to him (in equation 28) that 

 according to the assumption gas could not be at rest and at 

 the same time conducting heat. 



Clausius carefully points out these facts both in a note to 

 art. (6) in his paper and in a note to art. (24). 



