# Page:A Dynamical Theory of the Electromagnetic Field.pdf/36

494
PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD.

Specific Capacity of Electric Induction (D).

(84) If the dielectric of the condenser be air, then its capacity in electrostatic measure is ${\displaystyle {\tfrac {S}{4\pi a}}}$ (neglecting corrections arising from the conditions to be fulfilled at the edges). If the dielectric have a capacity whose ratio to that of air is D, then the capacity of the condenser will be ${\displaystyle {\tfrac {DS}{4\pi a}}}$.

Hence

 ${\displaystyle D={\frac {k_{0}}{k}}}$ (49)

where ${\displaystyle k_{0}}$ is the value of ${\displaystyle k}$ in air, which is taken for unity.

Electric Absorption.

(85) When the dielectric of which the condenser is formed is not a perfect insulator, the phenomena of conduction are combined with those of electric displacement. The condenser, when left charged, gradually loses its charge, and in some cases, after being discharged completely, it gradually acquires a new charge of the same sign as the original charge, and this finally disappears. These phenomena have been described by Professor Faraday (Experimental Researches, Series XI.) and by Mr. F. Jenkin (Report of Committee of Board of Trade on Submarine Cables), and may be classed under the name of "Electric Absorption."

(86) We shall take the case of a condenser composed of any number of parallel layers of different materials. If a constant difference of potentials between its extreme surfaces is kept up for a sufficient time till a condition of permanent steady flow of electricity is established, then each bounding surface will have a charge of electricity depending on the nature of the substances on each side of it. If the extreme surfaces be now discharged, these internal charges will gradually be dissipated, and a certain charge may reappear on the extreme surfaces if they are insulated, or, if they are connected by a conductor, a certain quantity of electricity may be urged through the conductor during the reestablishment of equilibrium.

Let the thickness of the several layers of the condenser be ${\displaystyle a_{1},a_{2}}$, &c.

Let the values of ${\displaystyle k}$ for these layers be respectively ${\displaystyle k_{1},k_{2},k_{3}}$, and let

 ${\displaystyle a_{1}k_{2}+a_{2}k_{2}+etc.=ak\,}$ (50)

where ${\displaystyle k}$ is the "electric elasticity" of air, and ${\displaystyle a}$ is the thickness of an equivalent condenser of air.

Let the resistances of the layers be respectively ${\displaystyle r_{1},r_{2}}$, &c, and let ${\displaystyle r_{1}+r_{2}+etc.=r}$ be the resistance of the whole condenser, to a steady current through it per unit of surface.

Let the electric displacement in each layer be ${\displaystyle f_{1},f_{2}}$, &c.

Let the electric current in each layer be ${\displaystyle p_{1},p_{2}}$, &c.

Let the potential on the first surface be ${\displaystyle \Psi _{1}}$ and the electricity per unit of surface ${\displaystyle e_{1}}$.

Let the corresponding quantities at the boundary of the first and second surface be ${\displaystyle \Psi _{2}}$ and ${\displaystyle e_{2}}$, and so on. Then by equations (G) and (H),