384 ELECTROSTATICS AND MAGNETISM. [PT. II. CH. IX. 



Since this is to be equal to 



for arbitrary values of &x, Sy, $z we must have everywhere 



a 



The first term is the force exerted by the field on the real charge 

 at each point. It is of course in the direction of the field. The 

 second term is due to the polarization, and is proportional to the 

 square of the field strength, and in the direction of fastest decrease 

 of /*. That is, any point of a polarized body tends to move toward 

 the side on which the inductivity is less, or to bring more inductive 

 matter into the field, as stated above. The form of deduction 

 here given is due to Helmholtz*. 



200. Stresses in the Medium. The modern theory of 

 electricity and magnetism, due to Faraday and Maxwell, assumes 

 that bodies do not act directly on other bodies at a distance, but 

 by means of actions transmitted through the intervening medium 

 from particle to particle. The influence of the medium has been 

 made apparent in this chapter, as we in fact started from the 

 expression of the energy as being distributed in all space. It 

 remains to find a system of stresses that shall account for the 

 electrical or magnetic forces which have been here investigated. 



If forces H, H, Z per unit volume act on all portions of a body, 

 for example gravity, these forces will throw the body into a state 

 of strain, and in order to produce equilibrium the applied forces 

 H, H, Z must be balanced by a set of elastic stresses developed in 

 the body. These are forces acting from point to point in the body, 

 and may be specified as follows. Suppose at any point P the 

 body divided into two portions, 1 and 2, by a plane whose normal 

 is n. If we consider a small area dS of this plane containing the 

 point P the portions of the body on the two sides of the plane 



* Wits. Abh. Bd. i., p. 811. See note in Appendix. 



