THE 



PHILOSOPHICAL MAGAZINE 



AND 



ANNALS OF PHILOSOPHY. 



[NEW SERIES.] 



NOVEMBER 1827. 



LIII. On the Figure of Equilibrium of a Homogeneous Planet 

 in a Fluid State ; in reply to the Observations of M.. Poisson, 

 published in this Journal for July last. By J. Ivory, Esq. 

 M.A. F.R.S. 



[Concluded from p. 247.] 

 TT follows from what has already been proved, that a homo- 

 -^ geneous planet entirely fluid cannot have a permanent 

 figure unless all the level surfaces, or surfaces of equal pres- 

 sure, be similar to one another and similarly posited about 

 the centre of gravity. But there is no figui'e possessed of 

 this property except the elliptical spheroid oblate at the poles 

 and protuberant at the equator. Such, therefore, and no 

 other, would be the figure of every planet, could we suppose 

 it entirely fluid and homogeneous. But the consequences we 

 have mentioned cannot be deduced from the single principle, 

 that gravity is every where perpendicular to the surface of the 

 planet. Another condition, no less essential to insure the equi- 

 librium of the fluid mass, is expressed by the algebraic for- 

 mula already employed, viz. 



A . V = C. 



This formula contains two very remarkable properties of a 

 homogeneous planet in equilibrio : First, the attraction of all 

 the matter of a stratum contained between two level surfaces, 

 upon all the interior particles, has no other effect than to 

 cause an etjuable pressure over all the surface of the fluid upon 

 which the stratum lies : Secondly, the attraction of the stratum 

 uj)on any particle in the inside, is equal in all opposite direc- 

 tions. These two properties are necessarily connected, so 

 that one cannot take place without the other. According to 

 this theory, it is the loregoing formula, or the properties of 



New Series. Vol. 2. No. II. Nov. 1827. 2 T which 



