374 Mr. W. Sutherland on Thermal 



Thermal Transpiration with the beautiful experimental estab- 

 lishment of its simple quantitative laws, simple in the illumi- 

 nation of his theory, but complex enough without it. Unfor- 

 tunately the mathematical form of Reynolds's theory is wearily 

 cumbersome ; one gathers that Maxwell found it distasteful, 

 and Fitzgerald (Phil. Mag. [5] xi.) describes it as inelegant 

 and unnecessarily elaborate. 



A great objection to Reynolds's mathematics is that it does 

 not join on naturally with that developed for the general pur- 

 poses of the kinetic theory of gases ; it has a certain interest 

 of individuality about it, but this fails to compensate for the 

 waste of mental energy to the reader who has to adapt himself 

 to it. But what appears to me to be the fatal objection to 

 Reynolds's mathematical method, is that it takes the mind away 

 from definite physical concepts of the actual operation of the 

 causes of thermal transpiration and radiometer motion ; and 

 the object of the present paper is to construct a theory of 

 these that will fall into line with the current kinetic theory 

 of gases and keep the physics of the phenomena to the fore. 



The most convenient starting-point is the laws discovered 

 by Clausius (Pogg. Ann. cxv. 1862) for the conduction of 

 heat in gases. In a vertical cylinder of gas, bounded by a 

 solid wall impermeable to heat and two conducting plane 

 ends, the lower at temperature 6 X and the upper at a higher 

 temperature 6 2 , when the flow of heat has become steady, the 

 pressure throughout the cylinder is constant, and the tempe- 

 rature 6 at distance x from the lower end of the cylinder 

 whose whole length is / is given by the equation 



#=of+(ef-e?)xii, 



and the distribution of density is determined in accordance 

 with these two results. Now in the establishment of the law 

 of the temperature, it was shown by Clausius that in a mass 

 of gas which is not uniform in temperature there is motion of 

 the gas in the direction of variability ; but it is assumed (as 

 it can easily be proved) that under ordinary circumstances 

 this motion can never produce an appreciable departure from 

 uniformity of pressure, because the rate at which a variation 

 of pressure throughout a mass of gas is effaced is so rapid in 

 comparison with the motion which might produce a variation 

 of pressure, that such a variation can never get itself estab- 

 lished to an appreciable extent. But when in place of an 

 ordinary cylinder we consider a very fine tube, we must take 

 account of the effect of viscosity in reducing the velocity with 

 which an inequality of pressure along the tube can get itself 

 effaced ; and if the tube becomes fine enough, this velocity 



