Hennessy — Fluid State of Bodies of our Planetary System. 581 



earth's spheroidal figure could not be considered as satisfactory as the 

 fluid theory ; and more recently I have shown, in the Comptes rendus 

 of the Paris Academy of Sciences/ that the observed figure of the 

 planet Mars can be accounted for on the latter theory of its original 

 condition, while the theory of superficial abrasion completely fails. 

 So far as it is possible to know the figures of the other planets, it also 

 appears that these figures conform to the theory of fluidity much better 

 than to the theory of superficial abrasion. The objections of Dr, 

 Haughton to the general fluidity of the planets fall to the ground as 

 completely as those of Playfair to the original fluidity of the earth, 

 But while the theory of superficial abrasion fails to account for the 

 figures of the earth and planets, some inquirers have recently main- 

 tained that such bodies, if totally solid, would acquire a spheroidal 

 shape under the action of rotation.^ 



Figure of a Rotating Fluid compared to a Rotating Solid. 



If a mass of fluid, whose density increases from its surface to its 

 centre, rotates with an angular velocity so small as to cause its surface 

 to differ but little from a spherical surface, it has been proved that the 

 fluid would consist of strata of equal density with spheroidal surfaces 

 similar to that of its outer stratum. The outer stratum will be bounded 

 by an ellipsoid of revolution. A cross section of the whole spheroid 

 in the plane of the axis of rotation would thus show the strata of equal 

 density arranged about the centre with elliptic cross sections. It has 

 been, moreover, proved that the ellipticity of these strata decreases 

 from the surface to the centre.^ This result is independent of any hypo- 

 thesis as to the law of density of the strata ; and its application to the 

 eaith is generally admitted. If the earth had arrived at its present state 

 by the solidification of its crust, without any change whatsoever in 

 the position of the particles of matter from which the crust solidified, 

 the strata of the crust, from its outer to its inner surface, would 

 preserve the shapes they had when in a fluid state. If, as I have de- 

 monstrated, the ellipticities of the strata of the shell become greater 

 than the ellipticity of its outer surface, the cross section tbrough the 

 earth's shell and nucleus would be illustrated by fig. 1. This result is 

 independent of any hypothesis as to the law of density of the matter 

 composing the earth, and rests on the admitted assumptions as to the 

 mechanical and physical properties of the materials of the earth by 

 which its figure has been investigated. Ear from having any hypo- 

 thesis in order to find this result, it was obtained by rejecting the 



^ Comptes rendus de I' Academie des Sciences, Paris, June 14, 1880. FMl. Mag., 

 August, 1880. lb., Jan. 31, 1881, p. 225. lb., April, 1881. 



2 See W. B. Taylor, American Journal of Science, October, 1885. 



^ See Airy's Mathematical Tracts, V-s:a.ii ovl Attractions, p. 177; Pontecoulaut, 

 Theorie Analytique du Systeme du Monde, vol. ii. ; Eesal, Traite Elementaire de 

 Mecaniqiie Celeste, p. 221. 



