264: Prof. J. J. Thomson on the Theory of Conduction of 



the differential equations and the boundary conditions »!=<) 

 when # = 0, and ?i 2 = when x—l. From the equation 



— =±7r(? h -n 2 )e, 

 we have 



or 



where C is the constant of integration. When X has its 

 minimum value we see from equation (1) that n^^ — ^; hence 

 from (9) and (10) at such a point we have 



k x x 



irtt ( 12 > 



hence if we determine the point Q where X is a minimum, this 

 equation will give us the ratio of the velocities of the positive 

 and negative ions. 



We see that a positive ion starting from the positive 

 plate, and a negative ion starting from the negative plate, 

 reach this point simultaneously. 



If X is the minimum value of X, and f the distance of a 

 point between the plates from Q, we may write equation (11) 

 in the form 



if I is the maximum current, this may be written 



x-x^+w^I+i-). . . . {13) 



We see from this equation that if we measure the values of 

 X at two points and I, the maximum current, we can deduce 

 the value of 



and since from (12) we know the value of k v >k 2 , we can 

 deduce the values of k ± and k 2 . 



If the positive ion moves more slowly under a given 

 potential gradient than the negative ion, then we see *from 

 (12) that Q is nearer to the positive than to the negative 



