472 Mr. A. P. Chattock on an 



— and 4- electricity respectively. These coatings, which are 

 really due to a slight protruding of all the — particles in one 

 surface and all the + in the other, correspond exactly with 

 the " fictive layers " of electricity, which for mathematical 

 purposes are assumed to appear on the bounding surfaces of a 

 dielectric under similar conditions. 



Arrange that the lines of force of the field enter and leave 

 the mixture normally, and consider a particle in the interior. 

 It is urged with a force of fq dynes in the direction of the 

 field (/ being numerically equal to the slope of potential at 

 the point considered) . If fq be not too great, the particle 

 will be displaced a distance o, which is small compared with 

 the distance d between it and its nearest neighbours. In 

 other words, d has been shortened by 8 on one side and 

 increased by 8 on the other in the direction of /. Let M be 

 Young's Modulus for the mixture. Then, if there are n par- 

 ticles per sq. cm. of a surface at right angles to /, — . - is 



the mechanical force required to produce the displacement 8 

 in the particle considered. Hence 



2M S ,. . 



-■d=te w 



Now if it were possible to continue the process of displace- 

 ment by increasing / until the + particles had moved a 

 distance d relatively to the — particles, the fictive layer at 



n 

 either end would contain - particles per sq. cm., and its 



density would therefore be — = p. Consequently, if the 



displacement is only S, the value of p will be ~- . -v 

 But (K-l) , 



where K is the specific inductive capacity of the mixture. 

 Hence 



qn 8_ (K-1)/ 



2 ' d~ 4tt W 



Combining (1) with (2), and putting —^ for n, 



V 



(K-l)Mtf* 



7T 



