10 Mr. Ivory on the Equilibrium of a Fluid 



By proceeding with these data in the same manner as before, 

 I have found, 



M = 0-003333 + 1-720 N 



M = 0-003272 + -947 N. 

 Neglecting the terms containing N, we have two new deter- 

 minations of the earth's ellipticity, which agree very well 

 with the former quantities. The mean of all the seven results 

 is extremely near ^ w coinciding almost exactly with what we 

 obtain from the pendulums in London and Paris. It is cer- 

 tainly remarkable that all the seven results fall between 

 •00326, which is the ellipticity adopted in France, and -00346, 

 which is the like quantity deduced by Captain Sabine from 

 his own experiments. 



July 4, 1826. J. IVORY. 



II. On the Equilibrium of a Fluid attracted to a fxt Centre. 

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



To the Editor of the Philosophical Magazine and Journal. 

 Sir, 

 TPAKING a hint from the Quarterly Journal of Science just 

 ■*■ published, the extreme case of a fluid in equilibrio by a 

 centrifugal force and the attraction of its particles to a fixt 

 centre, will illustrate the investigations I sent you in the be- 

 ginning of the month. This is the view of the figure of the 

 earth adopted by Huygens, and is equivalent to an infinite 

 density at the centre ; whereas Newton supposed an attractive 

 force diffused uniformly from particle to particle through the 

 whole mass. As Clairaut has solved the problem, we may 

 take the solution of it in his book *, viz. 



in which equation, tt is the intensity of the central force; 

 — the measure of the centrifugal force ; n the index of attrac- 



r ° ' 



tion; and x,y t the coordinates of a point in the surface of the 



fluid, x being parallel, and y perpendicular, to the axis of re- 



f t 



volution. Now let ?r = 1 ; n = — 2; 4- = <P = -^ ; x — R 



sin 9, y — R cos $ ; then, 



If the figure of the fluid be nearly spherical, we may sup- 



* Tkeorie de la Figure de la Terre, part. i. § xxix. 



pose 



