On Thermionics. 823 



and the kinetic energy received per second is 



A B 



T= £JW*»«-*-*> ^ffff C ° Sn ° A ;r SniA ^ S iSj. 



The limits of integration over the surface B being restricted 

 in the same way as before. 



If one surface is the boundary of a small body of negli- 

 gible dimensions then r is constant for any fixed point on 

 the other and 



jjJ Wrcos^ ^ = jp s <WV jJ cos ^ rfg . 

 In particular if A is a small sphere of radius a, 



$-' 



cos n A r d$ = 7ra 2 , 



and if co is the solid angle subtended by B at A 



A B 



Mcos VV cos VV Q Q 



§ 6. Parallel Planes. 



Suppose we have two parallel planes, A and B, whose 

 equations are z—z = and z — a = 0, with a uniform electric 

 field of intensity Z between them. Let an ion with velocity 

 components u v w start from a'oy z in the plane A, #andy 

 being measured along two mutually perpendicular axes 

 parallel to the planes. The equations to the trajectories are 



2 



-r-v) + ^-*»>- 



•° m 



and 



x — Xq __ y — y o 



Solving for w and v we have (see p. 816) 





(11) 



It is clear that the positive signs correspond to the quickest 

 times of transit to a given point, so that by taking the 



3K2 



