96 ON DIELECTRICS. 



each volume-element is changed by induction into a small magnet, 

 which may, indeed, be considered as an experimental fact. In this 

 way all the mathematical consequences of Poisson's hypothesis may 

 be deduced. 



111. DEFINITION OF DIELECTRIC. A dielectric placed in a field 

 becomes polarized, and the algebraical sum of the masses which 

 form the charge is always null. We know further (59) that, what- 

 ever be the condition of an electrified body, the action which it 

 exerts upon an external point is equal to that of a layer of the same 

 total mass as its own, distributed on the surface according to a certain 

 law ; in the present case the equivalent layer is formed of two sheets 

 having equal masses and opposite signs. 



According to the theory of magnetic induction, which we shall 

 afterwards explain, the action of this layer replaces the effect of 

 polarization, not only for external, but also for internal points. The 

 distribution is determined by the condition, that at two adjacent 

 points, one in air or rather in vacuum, and the other inside the 

 dielectric, the components of the force, perpendicular to the 

 bounding surface, shall be in a constant ratio />&, so that, if Y n 

 and F n are the perpendicular components in air and in the dielectric, 

 taken in the same direction, we have 



^ = /,, or F^FV 



Without attempting, for the moment, to examine thoroughly the 

 intimate nature of the phenomenon, we may regard this equation 

 (i) as defining the function of a certain class of bodies, to which 

 experiment shows that the dielectrics, such as we know them, must 

 belong. 



We have seen (39) that on both sides of an electrified surface 

 the components of the forces parallel to the surface are equal, and 

 that the difference between the perpendicular components is pro- 

 portional to the density of the layer, 



From which, agreeing to count as positive the perpendicular com- 

 ponents on the side of the dielectric, is deduced 



