152 Proceedings of Philosophical Societies, 



[Feb. 



elegantly resolved. It is only necessary, then, to explain that 

 solution in order to complete entirely the theory of the attraction 

 of homogeneous elipsoids. Here M. Legendre leaves Mr. Ivory, 

 who has only resolved this case by means of series, and adopts 

 the method of M. Lagrange, which reduces the problem to the 

 quadratures, and permits the use of the known method of ap- 

 proximation. 



If the elipsoid differ very little from a sphere, then the series 

 which expresses the attractions becomes very convergent ; the 

 law by wliich the coeflicients are regulated is easily perceived, 

 and M. Legendre gives the expressions of it. 



if we do not choose to have recourse to series, or if the eccen- ' 

 tricities of the principal sections are too considerable to allow the 

 series to converge with sufficient rapidity, then M. Legendre has 

 recourse to transcendental eliptics, of which he has given the 

 theory in his Exercises on the Integral Calculus. 



The formulas become much more simple if the elipsoid has 

 two equal axes, or when it becomes a spheroid of revolution ; 

 but the formulas are not quite the same for the flat spheroid and 

 the elongated spheroid. 



Finally, as notwithstanding the unexpected simplicity which 

 results from the process of Mr. Ivory, the solution is still long, 

 and sufficiently intricate, M. Legendre has collected into a 

 synoptical table all the formulas which must be valued in succes- 

 sion, a table which must be very agreeable to young mathema- 

 ticians, who will find nowhere a problem so complete, so various, 

 and so accommodated for practice, as this difficult problem. 



GENERAL PHYSICS. 



Memoir on the Distribution of Electricity on the Surface of 

 Conductors. By M. Poisson. 



The hypothesis most generally received at present to explain 

 the phenomena of electricity is that which ascribes them to two 

 fluids; the particles of each of which mutally repel, while the 

 particles of one fluid attract those of the other. 



It was according to this hypothesis that Coulomb calculated 

 the phenomena which he had observed, and he succeeded in 

 demonstrating that these attractions and repulsions followed the 

 law of the inverse of the square of the distances. Though this 

 hypothesis has not yet acquired all the requisite certainty, yet it 

 offers such a connection between all its parts as inspires us with 

 confidence, till a complete demonstration be obtained, which 

 can only be the result of the constant coincidence of calculation 

 with the phenomena, 



M. Poisson, in the memoir of which we are going to give an 

 account, adopts this hypothesis. His object is to determine 

 analytically the manner in which ejectricity distributes itself on 



