Transpiration and Radiometer Motion. 377 



we can write n = n Q + xdn/d;v = n -\-n ! x and v — v Q -\-v'x and 

 \ = \ + X'X /2 ; substituting these values, integrating, neg- 

 lecting products and squares of n'v' and \' f and dropping the 

 suffix as of no more use we get 



Am?{l/4 + X(t//w-X7\)/12} ... (2) 



The number crossing in unit time from the negative side of 

 the tube is obtained from this by changing the sign of n! and 

 v' so that the total gain in unit time from the positive to the 

 negative side of the plane is (since A 7^— —n'jn) 



M? + ?> 8 (3) 



which amounts to the same thing as if the gas had a velocity 



along the tube ; but the result holds not only for a tube, but 

 for any space filled with gas and for any direction in it in 

 which n' and v f are the rates of variation of n and v. The 

 law connecting n and v with position in the general case 

 must be complicated, but for a gas in contact with a solid the 

 thermal capacity of the latter is so great as to make xf and v 

 for the gas at the surface the same as for the solid there, so 

 that the problem simplifies to that of getting the law of n. 

 At a distance z from the solid surface the conditions of n and 

 v are still such as to tend to produce a velocity like u, so that 

 in the general case we have to consider the effect of viscosity 

 in causing these velocities to influence one another. The 

 friction per unit area parallel to the surface at z is rjdu/dz, and 

 the state of the gas cannot be steady till this is constant. 

 Returning to the case of a tube, we see that the steady state 

 will be reached when the velocity d and n are constant 

 throughout a section, and the velocity u is therefore also 

 constant throughout the section. Now under ordinary 

 circumstances there would be friction between the gas and 

 the tube over the whole surface, and therefore iu this case 

 there must be an action between the solid and the gas equal 

 and opposite to the friction, that is to say, that the solid wall 

 of a tube along which heat is being conducted in constraining 

 the gas to take its temperature and share in the conduction 

 of heat exercises a traction on it. The total friction does not 

 exactly neutralize the total traction, but leaves a small 

 resultant part of it which we can determine thus : suppose 

 the tube connects two infinite spaces at the same temperature 



