628 Mr. K. D. Kleeman on the Secondary Cathode 

 equations (3) and (6) we have 



^ = aR-N = (A 2 -A 1 ) v /a^F 



at that surface, that is 



a(A 1 + A 2 + ^)-N = (A 3 -A 1 ) v /a 3 ^P ) . (8) 



by equation (7). At the surface for which x = n we have 

 R = 0, and thus 



N 



= Ai e~* V^-62 + A 2 e n ^-& 2 + . — - . . . (9) 



a — o v • 



The values o£ A 1 and A 2 for a layer of thickness n are 

 given by equations (8) and (9). In the case of a layer of 

 thickness giving the maximum amount of radiation, we 

 require the values of A l and A 2 obtained when n is made 

 infinite. 



It will be seen by inspection that if \xe substitute for A 2 

 in equation (8), and n is made infinite, the equation becomes 



and therefore 



- &N 



1 = (a + \/a 2 ^¥) (a - b) * 



From equation (9) it appears that when n becomes infinite, 

 A 2 becomes infinitely small, but the product A 2 «» V« 2 -i^ i s 

 always finite. 



Substituting the above value for A 1 in equation (7) and 

 putting A 2 = 0, we obtain 



R N ~ a-b+ \/a 2 -b* 

 l ~ a-b a + \/d 2 -b 2 ' 



that is 



•d _ Ki 1 — #+ ^1 — k 



1 ">(!--/<;) >2- K +2 sJX^k 



substituting for a, b, and N. 



Since Kj denotes the number of electrons ejected per c.c. 



we may put K x = — ^- in this equation, where p is the 



density of the substance, w the atomic weight, and M 2 the 



