480 Mr. W. Sutherland on Thermal 



entirely on the relative position of the movable surface and 

 the fixed surfaces surrounding it. We have seen that for a 

 tube the total traction is nmu^iTW 1 , and for a passage bounded 

 by two parallel planes of width b and distance D apart with 

 the same variation of temperature along both, it is nmifibD/Z 

 along each plane, and as ttR corresponds to b and R to I)/2 

 we see that the traction exerted between the walls of a cylinder 

 of any section and the contained gas may be written in the 

 form nmu 2 sD/ 6 2, where s is the perimeter of a right section of 

 the cylinder, and D is a mean value of the distance between 

 opposite parts of the perimeter. For the difference of pressure 

 established by thermal transpiration along a tube of any 

 section we may use the equations (14) and (17) if in them we 

 interpret 2R as a mean value of the distance between opposite 

 parts of the perimeter ; and in the case where there is a 

 variation of pressure across only a fraction of the perimeter, 

 as for instance in the case where one plane wall has a varying 

 temperature and the opposite one a uniform temperature, we 

 must multiply by a fraction not greatly different from that 

 fraction [1/3 instead of 1/2 in our example). We can there- 

 fore state the fundamental equations of radiometer motion as 

 follows : — If across a length b of the perimeter s of any 

 cylinder a variation of temperature is suddenly established 

 whose average rate is v' over a length I, then the initial total 

 traction between solid and gas is approximately 



blnmXvv'jU. ...... (22) 



When the steady state is reached the total traction is 

 approximately 



&Dnm\ 2 v 2 (w7n + i>7«)Y108, or bD nm\ 2 v^ /p - v'/v) 2 / 108 ,(2Z) 

 and the difference of pressure between the two ends of I is 



_b v 2 —v 1 1 , 24 x 



P2 ^-^ 2 + l , 1 A / (p 2 +p 1 )/4-fB72 + l/(p 2 +p) 1 J ' [ J 



where the values of A' and B' are those given in (19), with 

 H 2 = R 1 = E,. No proof has been furnished here that the 

 introduction of the fraction b/s rigorously adapts our expres- 

 sion (19) to the case where only a fraction b/s of the boundary 

 is operative in producing thermal transpiration, but it is a 

 reasonable enough approximation for experimental results at 

 present available, closer approximation could easily be calcu- 

 lated if required. If in (23) we write (j> 2 —Pi)/l an d (» s — v{)jl 

 for p' and vf we can express the total traction in the steady 

 state entirely in terms of v 2 and v u which completes the 

 solution. 



