THE 



PHILOSOPHICAL MAGAZINE 

 AND JOURNAL. 



30^" APRIL 1825. 



XXXIX. On the Tlieory of the Figure of the Earth. By 



J. Ivory, Esq. M.A. F.R.S. 



" /^E cas est jiisqu'ji present le seul pour lequel on ait 



^^ trouve line solution rigoreuse, qu'on doit a Maclaurin ; 

 de sorte que le problenie de la figure de la terre, envisage phy- 

 siquemeut, n'est resoluexactementqu'en supposantle spheroide 

 fluid et homogene." — Lagrange, Mec. Anal. torn. i. p. 204'. 



These are the words of the correct and elegant Lagrange, 

 after having demonstrated that a homogeneous" elliptical sphe- 

 roid fulfills the conditions of equilibrium when it revolves upon 

 an axis and its particles attract one another in the inverse pro- 

 portion, of die square of the distance. They must not be un- 

 derstood in the utmost extent of their meaning ; for what is 

 proved, falls short of a physical solution of the problem of the 

 figure of the earth, even on the supposition of a homogeneous 

 fluid. Two things are necessary to a comj/lete theory : — in the 

 first place, we must know the laws of the equilibrium of a ho- 

 mogeneous mass of fluid, the particles of which attract one 

 another and are subjected to a centrifugal force; in the se- 

 cond place, we must investigate all the figures that possess 

 the properties which these laws require. Maclaurin merely 

 proved that a homogeneous fluid, which has the figure of an 

 oblate spheroid, will be in equilibria when its particles are 

 acted upon by the supposed forces. 



After iiuich discussion and many attempts, the conditions of 

 the equilibrium of a fluid mass, such as we find them in all 

 the books at the present day, were given by Clairaut in his 

 work on the figure of the earth. 



" Clairaut publia en 174..'5 son ouvrage sur laTheorie de la 

 Figure de la Terre. II y donne les equations generales jusqii' 

 alors inconnues, de re(juilibrc des fluidessoit homogcnes, soit 

 heterogenes, ou com|K)ses d'un nombre quelcontjue de fluides, 

 cjuelles que soient les forces qui animent chacune de leurs 

 molecules, et en supposant entre ces molecules une attraction 

 inutuelle suivant ime loi quelconciue." — Mec. Celeste, liv. ll""* 

 p. a. 1823. 



^'ul. fl.5. So. '.'/2i: April 182.7. II h The 



