Transpiration and Radiometer Motion. kll 



force F on the solid from hot to cold. If then a porous plate 

 had one face heated and was hung on to a string with this 

 face and the opposite cool one vertical, the tangential force 

 F acting along all the passages would deflect the string from 

 the vertical, a case of radiometer motion ; if two such plates 

 were mounted in a vertical plane and free to revolve round a 

 vertical axis lying between them, and one face of one was 

 warmed by irradiation, it would move away from the source, 

 and thus a continuous rotation could be kept up as in an 

 ordinary radiometer. 



In discussing thermal transpiration we confined our atten- 

 tion to fine tubes, such as might represent the passages in 

 porous plates ; but as we saw that the phenomena depended 

 for the most part on the ratio of the radius of a passage to the 

 mean free path of the gas, it follows that our deductions for 

 fine tubes will hold for tubes of any size with rare enough 

 gas to give a free path as large as may be necessary ; thus 

 with the means of getting high enough vacua and with 

 delicate manometers it should be possible to demonstrate 

 thermal transpiration along an ordinary gas-pipe or the 

 largest gas main ; in the radiometer we have generally to do 

 with thermal transpiration going on in spaces of ordinary 

 size. 



We have already obtained in (5) an expression for the 

 traction exercised on the gas in the tube by the whole surface 

 of a tube along which the temperature varies ; thus 



F = nrowVR a ; 



a curious result that the traction on the surface should be 

 proportional to the square of the radius, but it is to be 

 remembered that the tube is supposed to be long enough in 

 comparison with its diameter, and of sufficient thermal 

 capacity, to dominate the temperature of the gas so thoroughly 

 that the temperature throughout any section of the tube is the 

 same as that of the wall. This traction has been found for 

 the case when the motion duo to thermal transpiration along 

 the tube has become steady ; but in connexion with radiometer 

 motion it is necessary to consider the traction before the 

 steady state is established. Imagine a solid surface over 

 which the temperature varies to be suddenly introduced into 

 a mass of gas at rest and uniform in temperature, and let us 

 determine the traction which the solid immediately exerts on 

 the gas. The first effect is to make the layer of gas in contact 

 with the solid take the temperature of the solid at every point 

 of the surface, and therefore each molecule that encounters 

 the surface acquires on the average the velocity u given by 



