442 Prof. A. Anderson and Mr. T. Keane on the 



When V is indefinitely increased q/Q tends to the value *05 

 or one twentieth, Since 



»i— Wn *05V 



n L -V + 10' 



n . 19 



the value of — for high pressures is ^- . 



The following is a mathematical discussion of the problem 

 which arises in this experiment. 



Fig, 3. 



Consider a dielectric between two parallel plates A and B 

 at potentials Y and respectively, and let d be the density 

 of the free electrons in the natural state, that is the quantity 

 of negative electricity possessed by unit volume owing to 

 the free electrons which it contains. Then when the field is 

 put on, the density in the neighbourhood of A will be greater 

 than the density in the neighbourhood of B. Let p denote 

 the density at any point. In the natural state the force 

 due to the free electrons will be 



— kirdii 



?> 



where a is the distance between the plates, the specific in- 

 ductive capacity of the dielectric being taken as unity, But, 

 since the whole force is zero in the natural state, it is clear 

 that the force due to the positive atoms and bound 

 electrons will be 



M\x— |Y 



Hence*, if X be the impressed force, the force at any point 

 will be 



lL + 2Trd(2iV — a) -f Force due to the free electrons, 

 as rearranged by the total field. 



Denoting the latter force by P, we have the force at any 

 point per unit quantity of positive electricity equal to 



X-f27rd(2^a) + P, 



