178 General Analytical Theorems [OH. vn 



as to increase the volume occupied by dielectric, and also a tendency for this 

 boundary to move so that K will be increased by the consequent change of 

 density. These two tendencies are represented by the two terms of ex- 

 pression (121). 



fiK 



If -=- is negative, an expansion of the dielectric will both increase the 



volume occupied by the dielectric, and will also increase the value of K 

 inside the dielectric. In this case, then, both tendencies act towards an 

 expansion of the dielectric, and we accordingly find that both terms in 

 expression (121) are positive. 



r)Jf 



If -TT is positive, the tendency to expansion, represented by the first 



(positive) term of expression (121) is checked by a tendency to contraction 

 (to increase r, and therefore K) represented by the second (now negative) 



dK 



term of expression (121). If -~ is not only positive, but is numerically 



large, expression (121) may be negative and the dielectric will contract. In 

 this case the decrease in energy resulting on the increase of K produced by 

 contraction will more than outweigh the gain resulting from the diminution 

 of the volume occupied by dielectric. 



These considerations enable us to see the physical significance of all the 



X 2 



terms in expression (120), except the first term -^-(^ 1). To interpret 



this term we must examine the conditions near the edge of the dielectric slab, 

 for it is only here that X t has a value different from zero. We see at once 

 that this term represents a pull at and near the edge of the dielectric, 

 tending to suck the dielectric further in between the plates in fact this 

 force alone gives rise to the tendency to motion of the slab as a whole, which 

 was discovered in 139. 



Returning to the general systems of forces of 199, we may say that the 

 first system (which as we have seen always tends to drag the surface of the 

 dielectric into the region in which K has the greater value) represents the 

 tendency for the system to decrease its energy by increasing the volume 

 occupied by dielectrics of large inductive capacity, whilst the second system 

 (which tends to compress or expand the dielectric in such a way as to 

 increase its inductive capacity), represents the tendency of the system to 

 decrease its energy by increasing the inductive capacity of its dielectrics. 

 That any increase in the inductive capacity is invariably accompanied by a 

 decrease of energy has already been proved in 191. 



