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VII. On Stresses in Ravijied Gases arising from Inequalities of Temperature. 
By I. Clerk Maxwell, F.R.S., Professor of Experimental Physics in the 
University of Cambridge. 
Received March. 19,—Read April 11, 1878. 
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 shown 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-variation of the 
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temperature for a point moving along this line will be denoted by —, and the space- 
CCIb 
d?9 
variation of this quantity along the same line by —. 
do 9 
There will, in general, be a particular direction of the line h for which — is a 
maximum, another for which it is a minimum, and a third for which it is a maximum” 
minimum. These three directions are at right angles to each other, and are the 
* The dimensions of the bodies must he 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 
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 l is 
its mean value, 
1 = 
^\=1T78X 
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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. 
