256 Mr Harrison, The distribution of Electric Force hetiueen ttuo 



The numerical solution may be obtained for any particular 

 values of the constants a, b, c, q^, R by approximate methods. In 

 the absence of any definite experimental results with which to 

 compare the calculations, the labour involved in integration is not 

 worth undertaking. 



The case, however, of the saturation current is the most impor- 

 tant, and the integration is simple. It is assumed that recombi- 

 nation of ions does not take place in this case, and therefore the 

 equations reduce to 



= 0, x>R. 



Write Si7eq,{^ + y\=K. 



Then, for x< R, 



for X > R, 



9 log 7. -\-ix- + Bx + G 



(vide Rutherford, Radioactive Substances, etc., p. 67), A, B, G are 

 constants of integration. 

 Now the conditions are 



(1) at ^ = 0, ni = 0, if ^ = be the positive plate, 



(2) at a; = J?, Wg = 0, 



(3) at a; = i^, n^ is continuous, 



(4) Sit x = R, X \B continuous. 



{vide Conduction of Electricity through Gases, chap. iii.). 



dX^ _ _ Sttj 

 ' ' dx kz ' 



(2) and (3) lead to the same condition, which is the same as 

 (1), if 



i = eRqQ. 



Now since there is no recombination 



. [^ R 



1=1 eqolog - dx = eRqo. 

 Jo ^ 



