984 Sir J. J. Thorns 



on on a 



The energy at x possessed by an electron coming from 

 <7f is 



i 



r A(z-fl) e X ^?7, 



which we shall write as e~ kx (f>(£, x) ; <£(f, x) vanishes when 

 # = £. 



The energy Q carried in unit time across unit area at x is 

 therefore given by the equation 



Hence 



since . #M = ^ 



Let E = Jmt0 2 be the mean energy of the electrons at as, 

 where m is the mass of an electron ; then Q = iE/e, and the 

 preceding equation becomes 



g-Kap + X + /3 i >)E = X ( > (5) 



Since a is the coefficient of recombination, upBt is the chance 

 of an electron combining with a positive ion in a time St ; 

 since in the time St it passes over a space Sx—ivSt, the 

 chance of its recombining while traversing a distance Sx is 



—pSx. We have expressed this chance by ftpSx-, hence (3 = — . 



By equations (2) and (3) 



qive 

 1 1 



Hence fip=~. 



Thus ^+(ap+\+^)E = Xe;. ... (6) 



cix \ 1 j 



and therefore 



=W(^4). . (7) 

 \we (3iJ w 



