Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/127

 Rh

The surface-density $$\sigma'$$ is that of the apparent electrification produced at the surface of the solid dielectric by induction. It disappears entirely when the inducing force is removed, but if  during the action of the inducing force the apparent electrification  of the surface is discharged by passing a flame over the surface,  then, when the inducing force is taken away, there will appear an  electrification opposite to $$\sigma'$$.

In a heterogeneous dielectric in which $$K$$ varies continuously, if $$\rho'$$ be the apparent volume-density,

Comparing this with the equation above, we find

The true electrification, indicated by $$\rho$$, in the dielectric whose variable inductive capacity is denoted by $$K$$, will produce the same  potential at every point as the apparent electrification, indicated by  $$\rho'$$, would produce in a dielectric whose inductive capacity is every  where equal to unity.