S22 Prof. 0. W. Richardson : 



o -hd0 o . Let n x denote the normal to d$ 1 and r the radius 

 from d$ to d^ x . 



Then it follows from the equation on p. 820, that the 

 number of ions received per second by dS, whose resultant 

 velocity lies between ty and ifr + dyjr is 



n-tyZ cos # F(^ cos O ) Fity sin O ) dty sin O d0 o d(p d& . 



d$ 1 cos nfr — r 2 sin O d& d(f> . 



The number received by unit area of the surface at d$ l 

 from dS , and for which yjr lies between ty and yjr + dty 

 is therefore 



nf* cos O F(^ cos 6> ) Fi(^ sin O ) df™*™ 1 r rfS . 



The total number received by the surface B from A and for 

 which ^ lies between the assigned limits is thus 



A B 



dn^ = n^ d^jr f fdS ffd^ F(^ cos O ) F x (^ sin O ) 



cos n A r cos wi'V 



where the integral with respect to <^S X is only to be extended 

 over those portions of the surface B which are directly 

 visible from ^S . 



The pressure normal to dSx = momentum communicated 

 per second 



oo A 



= d$ 1 nm(yjrhty ffF(^cos0 o ) F^ sin O ) ^^±l^Jh^ d $ Qm 



The kinetic energy received by the whole surface B per 

 second is 



B oo A 



T=n(lpS 1 (V^tf(F(^ cos O ) FiOfr sin O ) C0Sn ° y 08 " 1 *' ^ 



The value of F(-^ cos O ) F^^ sin O ) given by Maxwell's 

 law is 2 e~ m . The current to B is therefore 



7T 



oc A B 



