60 Electric and Magnetic Science 



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 communi- 

 cated 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 110 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 



I Attractions. Lagrange, in a memoir on the motion of gravitating 



bodies, had shown* that the components of the attractive force 



* Mem. 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 Mem. par divers Snvanx, published in 178o. 



