24- Mr. H. Hennessy on the Attraction of Spheroids. 



Both in these and in the previous series of experiments, I 

 have detailed, in the last column, those values which would 

 be equal to a constant quantity, if the radii were really in 

 inverse proportion to the thickness of the deposited films. 

 Each of the tables shows how little this law is confirmed by 

 rcry experiments; the progress of one value to another is in 

 fact so considerable, that e.g. in Table VII. the numbers vary 

 from 17*4' to 129*75. To decide what circumstances could 

 have exerted so remarkable an influence upon the experiments 

 of M. E. Becquerel, that when taken into consideration his 

 experiments might be made to accord with those just detailed, 

 is a problem for the solution of which I do not feel myself 

 adequate. 



Dr. W. Beetz. 



III. On the Attraction of Spheroids. 

 By Henry Hennessy, Esq.* 



1. TN the mathematical theory of the attractions of sphe- 

 Jl roids, a well-known theorem occurs, which was first 

 pointed out by Laplace, and of which he has given demon- 

 strations in .the third book of the Mecanique Ce'leste, and in 

 the Connaissance des Temps for 1820. The remarkable cha- 

 racter, as well as the fundamental importance of this theorem, 

 excited several eminent geometers to thoroughly examine the. 

 demonstrations given by its discoverer. The result was, that 

 not only were these demonstrations considered defective, but 

 also, according to Lagrange and Ivory, the generality of the 

 theorem was thought incapable of being established. 



Notwithstanding these objections, the truth of the theorem 

 in question seems never to have been doubted by its illustrious 

 discoverer; and similar views appear to be entertained by 

 some of his successors. Among the rest, M. de Pontecoulant 

 presents, in the twentieth article of the fifth book of his The'orie 

 Analytique du Systeme du Monde, a demonstration of this 

 theorem, which he considers free from any serious objection. 

 On closely examining his investigation I perceived two errors, 

 which in the end compensate each other ; and it also appeared 

 that some points in it were capable of being more rigorously 

 established. I hope, therefore, that the following demonstra- 

 tion, which is free from the defects alluded to, will not be 

 considered useless. 



To render this improved form of M. De Pontecoulant's 



* Communicated by the Author. 



