On the Mathematical Theory of Electricity in Equilibrium, 43 



investigated it experimentally for bodies of various forms, could 

 only compare his measurements with the results of his theory 

 by very rude processes of approximation. Without however 

 giving rigorous solutions in particular cases, he examined the 

 general problem with great care, and left nothing indefinite in 

 the conditions to be satisfied, so that it was entirely by analytical 

 difficulties that he was stopped. As an example of the success 

 of his theoretical investigations, we may refer to the well-known 

 demonstration of the theorem (usually attributed to Laplace) 

 relative to the repulsion exercised by a charged conductor on a 

 point near its surface*. 



The memoirs of Poisson, on the mathematical theory, contain 

 the analytical determination of the distribution of electricity on 

 two conducting spheres placed near one another, the solution 

 being worked out in numbers in the case of two equal spheres 

 in contact, which had been investigated experimentally by 

 Coulomb (as well as in another case, not examined by Coulomb, 

 which is given as a specimen of the numerical results that may 

 be deduced from the formulae). The calculated ratios of the in- 

 tensities at different points of the surface he is therefore enabled 

 to compare with Coulomb^s measurements, and he finds an 

 agreement which is quite as close as could be expected, when we 

 consider the excessively difficult and precarious nature of quan- 

 titative experiments in electricity. But the most remarkable 

 confirmation of the theory from these researches is the entire 

 agreement of the principal features, even in some very singular 

 phsenomena, of the experimental results with the theoretical 

 deductions. For a complete account of the experiments, we 

 must refer to Coulomb^s fifth memoir {Histoire de V Academic, 

 1787), and for the mathematical investigations to the first and 

 second memoirs of Poisson [Memoires de VInstitut, 1811), or to 

 the treatise on Electricity lu the "Encyclopaedia Metropolitana," 

 where the substance of Poisson^s first memoir is given. 



The mathematical theory received by far the most complete 

 development which it has hitherto obtained in Greenes '^^ Essay 

 on the Application of Mathematical Analysis to the Theories 

 of Electricity and Magnetism f/^ in which a series of general 

 theorems were demonstrated, and many interesting applications 

 made to actual problemsj. 



Of late years some distinguished experimentalists have begun 

 to doubt the truth of the laws established by Coulomb, and have 

 made extensive researches with a view to discover the laws of 

 certain phsenomena which they considered incompatible with his 

 theory. The most remarkable works of this kind have been 



* See Note II. f Nottingham, 1828. % See Note III. 



