214 Prof. Townsend on the Conductivity produced in 



When X is constant, there evidently exists a certain 

 pressure for which a is a maximum : if p is large no new 

 ions will be formed since the original ions never acquire a 

 large velocity, and if p is very small there will be too few 

 collisions to allow of a large \alue of a. 



The value of p for which a is a maximum is obtained by 

 differentiating the equation, 



X^ 



-4f) 



with respect to p. 



We thus obtain the following equation to determine p in 

 terms of X : — 



/(f)-f/'(f)=° w 



X 



Since this equation involves X, and p, in the form — , we 



conclude that for a given value of X the value of p which 

 gives the maximum value of a is proportional to X. 



The value of — which satisfies equation (9) can be obtained 



immediately from the curve in fig. 8. 



Substituting X 2 for-, a t for /(-), and j£- for /(-) 



in equation 9, we obtain 



«! da,\ 



Xj " d&i 



This relation between the coordinates of a point on a curve 

 [ajSs/lXj)] shows that the tangent at the point passes 

 through the origin. v 



Hence in order to find the value of — which satisfies 



equation (9) it is only necessary to draw a tangent to the 



cuive from the origin, and find the abscissa of the point of 



contact. at 



The value of — thus obtained is 380. Hence the value of 



P . X 



p in millimetres for which a is a maximum is — t?>, where X 



is expressed in volts per centimetre. 



The corresponding value of a. is 



7. Having established the general relation obtained in 



