[From the Philosophical Transactions of the Royal Society, Part I. 1879.] 



XCIII. On Stresses in Rarified Gases arising from Inequalities of Temperature. 



1. IN this paper I have followed the method given in my paper " On 

 the Dynamical Theory of Gases" (Phil. Trans., 1867, p. 49). I have shewn 

 that when inequalities of temperature exist in a gas, the pressure at a given 

 point is not the same in all directions, and that the difference between the 

 maximum and the minimum pressure at a point may be of considerable magnitude 

 when the density of the gas is small enough, and when the inequalities of 

 temperature are produced by small* solid bodies at a higher or lower temperature 

 than the vessel containing the gas. 



2. The nature of this stress may be thus defined : Let the distance from 

 a given point, measured in a given direction, be denoted by h ; then the space- 



* The dimensions of the bodies must be of the same order of magnitude as a certain length 

 X, which may be defined as the distance travelled by a molecule with its mean velocity during 

 the time of relaxation of the medium. 



The time of relaxation is the time in which inequalities of stress would disappear if the rate 

 at which they diminish were to continue constant. Hence 



\*7>/ P 



On the hypothesis that the encounters between the molecules resemble those between " rigid 

 elastic" spheres, the free path of a molecule between two successive encounters has a definite 

 meaning, and if I is its mean value, 



; 3 /7r\i Sir , ft 



f =oMo ) = -Q-A=lll8A. 



2 r \2ppJ 



So that the mean path of a molecule may be taken as representing what we mean by "small". 



If the force between the molecules is supposed to be a continuous function of the distance, 



the free path of a molecule has no longer a definite meaning, and we must fall back on the 

 quantity X, as defined above. 



VOL. II. 86 



