﻿410 Dr. Norman Campbell on 



freely a distance less than b. Accordingly all these free 

 electrons have been produced between x and x — b. If the 

 number of free electrons produced per second in any layer is 

 q Xi since the probabitity that an electron produced at x—y 

 collides for the first time at x is 1$ e &. where 



</(• 



<■) = i ?,- r Nr s % (20) 



q x is not, as before, equal to f (a?), for the value of f(x) 

 as Ave cross any layer is changed not only by the number of 

 electrons produced there, but also by the number of electrons 

 which disappear there, forming complex ions. In fact, 



/(,.)= <ix _,/(,.) (21) 



To determine q x the considerations which lead to (8) are 

 still valid, and we have 



qx=n p + *f(x-b) (22) 



The functions concerned here are, of course, discontinuous 

 in just the same way as those considered previously. In 

 order to proceed further in this direction it is again necessary 

 to assume that they are continuous, and the conditions 

 necessary to determine the integration constants will again 

 be taken as those at x — b. If we again take 



/0)=Ae^+B, . . . . . (23) 



we get 



N+/3 



(l-«-N+/S.6)l . (24) 



We shall have four integration constants, A, B, and two 

 derived from integrating (20) to find g(x). To determine 

 these we have the four independent conditions at w = b, 



f(b) = f*e-X b + £n pe-*'dy,. . . (25) 

 9 {b)=n 1 + n pb-f{b), (26) 



g f (b)=n l Ne- m +\ b v p^e-~^d I/ , . (27) 



«- o 



q b = n p + an 1 . 



