304 Prof. J. C. Maxwell on Stresses in Rarefied Gases [Apr. 11, 



the body must experience during Alpine ascensions. Professor Planta- 

 mour, of Geneva,* from observations made at Geneva and the Great 

 St. Bernard, concludes that there is no marked difference between the 

 hygrometric states at various altitudes. According, however, to Dr. 

 Lombard, who has considerable knowledge and experience of climate, 

 the air appears to be, as a rule, much drier above 1,500 metres than 

 below that altitude. 



III. " On Stresses in Rarefied Gases arising from Inequalities of 

 Temperature." By J. Clerk Maxwell, F.R.S., Professor 

 of Experimental Physics in the University of Cambridge. 

 Received March 19, 1878. 



(Abstract.) 



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 pres- 

 sure 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 jbe 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 the given point, measured in a given direction, be denoted by 

 h, and the absolute temperature by 9 ; then the space- variation of the 

 temperature for a point moving along this line will be denoted by 

 d9 



— , and the space- variation of this quantity along the same line by 

 d 2 9 . ... 



— There is in general a particular direction of the line h, for which 



dh 2 



d 2 1 



is a maximum, another for which it is a minimum, and a third for 



dh 9 



which it is a maximum-minimum. These three directions are at right 

 angles to each other, and are the axes of principal stress at the given 

 point ; and the part of the stress arising from inequalities of tempera- 

 ture is in each of these principal axes a pressure equal to — 



6 P 6 dh 2 ' 



where /u is the coefficient of viscosity, p the density, and 9 the absolute 

 temperature. 



3. Now, for dry air at 15° C, j*=l'9 X 10" 4 in centimetre-gramme- 

 * Lombard. " Climat des Montagnes," 1873. 



