1878.] arising from Inequalities of Temperature. 



307 



this case the equations of motion show that every particle of the gas 

 is in equilibrium under the stresses acting on it. 



Hence any finite portion of the gas is also in equilibrium ; also, since 

 the stresses are linear functions of the temperature, if we superpose 

 one system of temperatures on another, we also superpose the corre- 

 sponding systems of forces. Now the system of temperatures due to 

 a solid sphere of uniform temperature, immersed in the gas, cannot of 

 itself give rise to any force tending to move the sphere in one direc- 

 tion rather than in another. Let the sphere be placed within the finite 

 portion of gas which, as we have said, is already in equilibrium.' The 

 equilibrium will not be disturbed. We may introduce any number of 

 spheres at different temperatures into the portion of gas, and when 

 the flow of heat has become steady the whole system will be in 

 equilibrium. 



12. How, then, are we to account for the observed fact that forces 

 act between solid bodies immersed in rarefied gases, and this, appa- 

 rently, as long as inequalities of temperature are maintained ? 



I think we must look for an explanation in the fact discovered 

 in the case of liquids by Helmholtz and Piotrowski,* and for gases 

 by Kundt and Warburg,f that the fluid in contact with the surface 

 of a solid must slide over it with a finite velocity in order to produce 

 a finite tangential stress. 



The theoretical treatment of the boundary conditions between a gas 

 and a solid is difficult, and it becomes more difficult if we consider that 

 the gas close to the surface is probably in an unknown state of con- 

 densation. We shall, therefore, accept the results obtained by Kundt 

 and Warburg on their experimental evidence. 



They have found that the velocity of sliding of the gas over the 

 surface due to a given tangential stress varies inversely as the pressure 



The coefficient of sliding for air on glass was found to be \=— 



P 



centimetres, where p is the pressure in millionths of an atmosphere. 

 Hence at ordinary pressures X is insensible, but in the vessels exhausted 

 by Mr. Crookes it may be considerable. 



Hence if close to the surface of a solid there is a tangential stress, S, 

 acting on a surface parallel to that of the body, in a direction, k, parallel 

 to that surface, there will also be a sliding of the gas in contact with 



the solid over its surface in the direction h, with a finite velocity =S-" 



13. I have not attempted to enter on the calculation of the effect of 

 this sliding motion, but it is easy to see that if we begin with the case 

 in which there is no sliding, the effect of permission being given to 

 the gas to slide must be in the first place to diminish the action of 



* Wiener Sitzb., xl (1860), p. 607. 

 f Pogg. Ami., civ (1875\ p. 337. 



