THE 



LONDON AND EDINBURGH 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[THIRD SERIES.] 



SEPTEMBER 1836. 



XXXIV. On such Functions as can he expressed by Serieses 

 ofpeiiodic Terms. By James Ivory, Esq., M.A., F.E.S.* 



"l^EVER was any speculation ushered into the mathematical 

 ■^^ world with more unmeasured praise than the analytical 

 theory of Laplace for the attraction of spheroids approaching 

 nearly to spheres. The very general nature of the processes, 

 and the arriving at results by differentiations merely, without 

 tedious and difficult integrations, called forth the admiration 

 of every geometer. It is not the present intention to inquire 

 whether the expectations raised by so novel a method of in- 

 vestigation, have been fulfilled : but it cannot be denied that 

 the grounds of it are obscure, and have never been demon- 

 strated so as to remove every doubt. The subject having been 

 again brought forward, it is very desirable that it should not 

 now be dismissed without a full elucidation. 



The method of Laplace was first published in the Memoirs 

 of the Academy of Sciences in 1782, and afterwards in the 

 third book of the Mecanique Celeste. Objections haviqg been 

 made impugning the generality of the investigation, the author 

 returned to the subject in the eleventh book of the same work, 

 which appeared in 1823. He now greatly restricts the de- 

 monstration before given in the third book : insomuch that 

 according to the new proofs the method is less general than 



* ('ommiinicated by the Author. 



Tliird Series. Vol. 9. No. 53. Sept. 1836. S 



