Page:Philosophical magazine 23 series 4.djvu/31

applied to Statical Electricity. 16

These relations are independent of any theory about the internal mechanism of dielectrics; but when we find electromotive force producing electric displacement in a dielectric, and when we find the dielectric recovering from its state of electric displacement with an equal electromotive force, we cannot help regarding the phenomena as those of an elastic body, yielding to a pressure, and recovering its form when the pressure is removed.

According to our hypothesis, the magnetic medium is divided into cells, separated by partitions formed of a stratum of particles which play the part of electricity. When the electric particles are urged in any direction, they will, by their tangential action on the elastic substance of the cells, distort each cell, and call into play an equal and opposite force arising from the elasticity of the cells. When the force is removed, the cells will recover their form, and the electricity will return to its former position.

In the following investigation I have considered the relation between the displacement and the force producing it, on the supposition that the cells are spherical. The actual form of the cells probably does not differ from that of a sphere sufficiently to make much difference in the numerical result.

I have deduced from this result the relation between the statical and dynamical measures of electricity, and have shown, by a comparison of the electro-magnetic experiments of MM. Kohlrausch and Weber with the velocity of light as found by M. Fizeau, that the elasticity of the magnetic medium in air is the same as that of the luminiferous medium, if these two coexistent, coextensive, and equally elastic media are not rather one medium.

It appears also from Prop. XV. that the attraction between two electrified bodies depends on the value of $E^{2}$, and that there- fore it would be less in turpentine than in air, if the quantity of electricity in each body remains the same. If, however, the potentials of the two bodies were given, the attraction between them would vary inversely as $E^{2}$, and would be greater in turpentine than in air.

Prop. XII. — To find the conditions of equilibrium of an elastic sphere whose surface is exposed to normal and tangential forces, the tangential forces being proportional to the sine of the distance from a given point on the sphere.

Let the axis of z${\displaystyle }$ be the axis of spherical coordinates.

Let $\xi ,\eta ,\zeta$ be the displacements of any particle of the sphere in the directions of x, y, and $z$.

Let $p_{xx},p_{yy},p_{zz}$ be the stresses normal to planes perpendicular to the three axes, and let $p_{yz},p_{zx},p_{xy}$ be the stresses of distortion in the planes yz, zx, and $xy$.