62 Electric and Magnetic Science 



be reversed in direction. Since the resultant force at the latter 

 point vanishes, we must have S=s ; so the resultant force at the 

 exterior point is 2s. But s is proportional to the charge per 

 unit area of the surface, as is seen by considering the case of 

 an infinite plate ; which establishes the theorem. 



When several conductors are in presence of each other, the 

 distribution of electricity on their surfaces may be determined 

 by the principle, which Poisson took as the basis of his work, 

 that at any point in the interior of any one of the conductors, 

 the resultant force due to all the surf ace -layers must be zero. 

 He discussed, in particular, one of the classical problems of 

 electrostatics namely, that of determining the surface-density 

 on two charged conducting spheres placed at any distance from 

 each other. The solution depends on Double Gamma Functions 

 in the general case ; when the two spheres are in contact, it 

 depends on ordinary Gamma Functions. Poisson gave a solution 

 in terms of definite integrals, which is equivalent to that in 

 terms of Gamma Functions ; and after reducing his results to 

 numbers, compared them with Coulomb's experiments. 

 f The rapidity with which in a single memoir Poisson passed 

 from the barest elements of the subject to such recondite 

 problems as those just mentioned may well excite admiration. 

 His success is, no doubt, partly explained by the high state of 

 development to which analysis had been advanced by the great 

 mathematicians of the eighteenth century ; but even after 

 allowance has been made for what is due to his predecessors, 

 Poisson' s investigation must be accounted a splendid memorial 

 u of his genius. 



Some years later Poisson turned his attention to magnetism ; 

 and, in a masterly paper* presented to the French Academy in 

 1824, gave a remarkably complete theory of the subject. 



His starting-point is Coulomb's doctrine of two imponderable 

 magnetic fluids, arising from the decomposition of a neutral 

 fluid, and confined in their movements to the individual elements 



* Mem. <le 1'Acad., v, p. 247. 



