Transpiration and Radiometer Motion. 375 



may be reduced till it is merely comparable with, or even 

 much smaller than, the velocity with which motion caused by 

 varying temperature may be tending to establish inequality 

 of pressure. Thus, then, in discussing the conductivity of 

 gas in a nonconducting tube of capillary dimensions, we 

 could no longer enjoy the convenient simplification which 

 comes into the problem of Clausius when he writes the pres- 

 sure constant as one of his fundamental equations, but from 

 purely kinetic considerations we should have to determine the 

 laws both of the variation of pressure and of temperature 

 associated with the steady flow of heat. But in the actual 

 problem of thermal transpiration if we lose one simplification 

 we gain another, because we have to do, not with noncon- 

 ducting walls, but with walls conducting so well and with so 

 large a thermal capacity compared to that of the gas, that the 

 law of variation of temperature is fixed entirely by the pro- 

 perties of the solid ; so that the gas, if subject to varying 

 pressure, is also subject to a fixed law of temperature which 

 we are freed from having to find. 



In the kinetic theory the molecules which are considered 

 characteristic of an element are those that have experienced a 

 collision in it ; those passing through without collision are 

 taken account of in the elements where they do collide. If 

 the element is a short length of our tube, we do not consider 

 the molecules rebounding from the solid wall as characteristic 

 unless they also encounter other molecules in the element, 

 and thus we might appear to be neglecting the most charac- 

 teristic molecules of the element. But this is not really so, 

 because those reflected from the side of the tube and moving 

 to a cooler element, as a rule collide with those coming from 

 a still cooler element and including an equal number that 

 have come from its walls, so that the colliding pairs on the 

 average possess the qualities that are to characterize the ele- 

 ment in which they collide. Thus, then, if we do not have 

 to take account of reflexion from the walls of the tube, we 

 can consider the gas in it as part of an indefinite mass such 

 that the temperature throughout a plane perpendicular to the 

 axis is the same as that in the section of the tube made by the 

 plane. We wish to find the number of molecules crossing 

 any section of the tube. This is done by Clausius in his 

 theory of conduction in gases, and with greater refinements 

 of accuracy by Tait (Trans. Roy. Soc. Edinb. xxxiii.) ; but 

 for the sake of clearness we will make the calculation here to 

 a degree of accuracy suitable for present requirements. 



If there are n molecules per unit of volume in a small 

 element dB, and each has v encounters per second, then the 



2 E2 



