1204 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



V'OC = - ^ (RCll) (134) 



and 



V. vac + - OlVC^ + 3C) = 0. (135) 



Now let S(1L) be the inverse function to (R(1l), i.e. the function such that 



S((R(^)) = 01. 

 Then from (134) we have 



01 = s(- -V'ocV (136) 



Substitution of (136) into (135) yields after some computation 



ss'v^(v^ac) - - (ss" + s'')(vv^3c)' 



(137) 



+ SVOC- VV^OC - ^ (S + 7)V'5C = 



where s'(^) = — S(^), etc. 



/ N \ 

 S, S', S" are considered as given functions of I — - V^OC I . 



The simplest meaningful choice of S is 



(138) 



(/, K : prescribed constants) 



corresponding to constant mean lifetime recombination. For this S, (137) 

 specializes to 



J(K - 7V25C)V2(V23C) - 72(vv2ac)2 



(139) 

 ■f JV3C'W5Q, - {y + K - 7V23C)V2aC = 0. 



If any 3C can be found satisfying (139), the associated 11 is given (from 

 (136)) by 



