234 
PROFESSOR CLERK MAXWELL OK STRESSES IK RARIFIEI) 
the temperature, if we superpose one system of temperatures on another, we also 
superpose the corresponding 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 direction 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, so as to form a body of any shape, heated in any manner, 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 rarified gases, and this, apparently, as long as inequalities of 
temperature are maintained % 
I think we must look for an explanation in the phenomenon discovered in the case 
of liquids by Helmholtz and Piotrowski,* and for gases by Kundt and Warburg,! 
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 condensation. 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. 
g 
The coefficient of sliding for air on glass was found to be G=- centimetres, where p 
is the pressure in millionths of an atmosphere. Hence at ordinary pressures G 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 h parallel to that surface, there null 
also be a sliding of the gas in contact with the solid over its surface in the direction h 
with a finite velocity = —. 
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 instantaneous effect of permission being given to the gas to slide must be 
to diminish the action of all tangential stresses on the surface, without affecting the 
normal stresses, and in course of time to set up currents sweeping over the surfaces 
of solid bodies, thus completely destroying the simplicity of our first solution of the 
problem. 
14. When external forces, such as gravity, act on the gas, and when the thermal 
phenomena produce differences of density in different parts of the vessel, then the well' 
* Wiener Sitzb., xl., 1860, p. 607. 
t Pogg. Ann., civ., 1875, p. 337. 
