Transpiration and Radiometer Motion. 479 



which is independent of the length but proportional to width 

 and distance from neighbouring surface. To bring out the 

 full signification of these we had better introduce the value 

 of u, and let us suppose % to be ; then the initial and final 

 total tractions exerted by a plane of varying temperature at 

 distance D from a plane of constant temperature are 



bnml>v*\*(n'/n + v'/v)*/108. J ' '* ' 



When the conditions are such that the pressure can remain 

 constant between the surfaces, n / /n-\-2v / /v = 0, and then these 

 become Srawi;\i//24 and bnmDX 2 o /Q /10S, both acting from cold 

 to hot, and therefore the equal and opposite reaction of gas 

 on the surface is from hot to cold. 



But when the conditions are not such that the pressure is 

 kept constant, but that a difference of pressure is established 

 by thermal transpiration which goes on till a steady state is 

 established, the effect of the difference of pressure may be 

 much greater than that of the traction, as the following 

 example will show : — A piston is inserted into a cylinder which 

 it does not quite fit, and is fixed immovable so as to leave a 

 clear space of sectional area a between itself and the cylinder, 

 and the cylinder is closed ; when one end is heated a fall of 

 temperature gets established along the cylinder, and the gas 

 at the cold end begins to transpire through the narrow space 

 into the hot end until the difference of pressure p 2 — p ± 

 sufficient to stop the flow is established; then the total traction 

 of gas on the side of the piston is a(p 2 — p\), while on the area 

 A of the hot end of the piston there is a total pressure 

 A(p 2 —pi)m excess of that acting on the cold end, so that the 

 total force urging the piston from hot to cold is (A + a) (p 2 — joj , 

 which may be made as much more important than the total 

 traction as we please by diminishing a. If the piston is freed 

 it will begin to move under the force (A-fa)(^ 2 — p x ), and 

 become an exaggerated instance of radiometer motion. 



This example makes clear the lines on which to formulate 

 a general theory of radiometer motion ; we have only to 

 adapt our transpiration formulas established for circular tubes 

 to the case of any space bounded by solid walls over which the 

 temperature varies. In the general problem of radiometer 

 motion we have to do with a solid surface over which the 

 temperature varies and which therefore is subject to a traction 

 from hot to cold, and also establishes a higher pressure in the 

 gas towards its hot end than at the cool end ; the relative 

 importance of traction and difference of pressure in producing 

 motion of the body to which the surface belongs depends 



