818 Prof. 0. W. Richardson : 



To save space let us denote the fraction by 

 X 0»i Vi ~i ®o Vo ~o w ) ; 



then if n is the total number of ions emitted in unit time by 

 unit area of the surface A the total number received by the 

 surface ^r will be the real part of 



nil dS \dw ll/^o)/i(^3)/2(^ 4 )%^ S ' • 



(9) 



Where d$ denotes an element of the surface A and the 

 integral with respect to dw is taken over all the values of 

 w which occur. 



If we multiply the expression (9) by the charge e on an 

 ion we obtain the current to the surface yjr. We can obtain 

 the three components of the resultant pressure on this sur- 

 face due to the impact of the ions if we multiply the integrand 



with respect to d$ by w-tt 1 m ~jr and m-^- 1 respectively. 



The values of the velocities are obtained from equations (2) 

 and should be expressed as functions of x x y l z x .r y z and w 

 by means of the equations previously given. In a similar 

 way we shall obtain the kinetic energy received by the 

 surface if we multiply the integrand by 



im 



m-&Hm 



This must be identical with ne(Y — Y) -\- the value of the 

 integral when 



is substituted for 



^m(u 2 + v 2 + w 2 ) 



mh&nm 



where V is the potential of the surface A and V that of i/r. 

 Since % c/S is equal to du dv we have 



jJ/Oo) fi(h) mOxdS=$f(™«)M«o)Mvo) du dv . 



If the surface B forms the whole of the analytical surface 

 yjr (x y z) = the limits of integration for u and v will be 

 determined, for any value of w , by the values of u and v 

 which correspond to the curve which is the locus of the 

 points at which the trajectories having the given value of 

 w are tangential to the surface ^r(xyz) = 0. They will 

 thus be certain functions of w which are determined by the 

 equation to the surface. If the surface B consists of the 



