distribution of the two fluids is called the natural state; when this state is disturbed in any body, the body is said to be electrified, and the various phenomena of electricity begin to take place.
"Material bodies do not all behave in the same way with respect to the electric fluid: some, such as the metals, do not appear to exert any influence on it, but permit it to move about freely in their substance: for this reason they are called conductors. Others, on the contrary—very dry air, for example—oppose the passage of the electric fluid in their interior, so that they can prevent the fluid accumulated in conductors from being dissipated throughout space."
When an excess of one of the electric fluids is communicated to a metallic body, this charge distributes itself over the surface of the body, forming a layer whose thickness at any point depends on the shape of the surface. The resultant force due to the repulsion of all the particles of this surface-layer must vanish at any point in the interior of the conductor, since otherwise the natural state existing there would be disturbed; and Poisson showed that by aid of this principle it is possible in certain cases to determine the distribution of electricity in the surface-layer. For example, a well-known proposition of the theory of Attractions asserts that a hollow shell whose bounding surfaces are two similar and similarly situated ellipsoids exercises no attractive force at any point within the interior hollow; and it may thence be inferred that, if an electrified metallic conductor has the form of an ellipsoid, the charge will be distributed on it proportionally to the normal distance from the surface to an adjacent similar and similarly situated ellipsoid.
Poisson went on to show that this result was by no means all that might with advantage be borrowed from the theory of + Attractions. Lagrange, in a memoir on the motion of gravitating bodies, had shown[1] that the components of the attractive force
- ↑ Mém. de Berlin, 1777. The theorem was afterwards published, and ascribed to Laplace, in a memoir by Legendre on the Attractions of Spheroids, which will be found in the Mém, par divers Savans, published in 1785.
