MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
527 
for example, tend to assume the form of which cgdh is the profile. The thick- 
ness of the stratum of imperfect fluid would then be greatest at A, and least at E. 
On solidifying, the new stratum thus added to the shell would have the same 
proportional thickness, and its interior surface would in this particular case be more 
elliptical than its exterior surface. If, as seems extremely probable, the imperfectly 
fluid stratum be thin, and if it strongly adhere to the shell, it will exercise no sensible 
pressure on the perfect fluid, and must consequently take the form impressed on it 
without any sensible resistance. 
12. It can be easily shown that in general the pressure of the perfect fluid will not 
be constant. Let a spheroidal mass of fluid be conceived, consisting of nearly 
similar spheroidal strata, these strata increasing in density as their radii decrease. 
The ellipticities of the bounding surfaces of any stratum will depend on the con- 
stitution and thickness of the strata outside it. If possible let the mass outside the 
stratum be removed, without altering the law of density of the remaining fluid : it is 
manifest that equilibrium will be obtained only where the surface of the stratum at 
any point becomes perpendicular to the resultant of all the forces acting on that 
point. With the same law of density as the entire mass, and urged by the same 
forces, the ellipticity of its surface must be the same as that of the surface of the 
primitive mass. If, however, the law of density changed in such a way as to render 
the remaining fluid more homogeneous, the ellipticity of its surface would be greater 
than that of the primitive fluid spheroid*. Hence we may conclude — (1.) that if the 
angular velocity and law of density of the nucleus remained unchanged after the 
formation of the first stratum of the shell, the outer and inner surfaces of that stratum 
would be similar, and its attraction on the interior mass would consequently, by a 
well-known theorem, be evanescent. The next formed stratum would thus also have 
similar surfaces, and so on with every stratum, until the mass should have completely 
solidified. In this case, therefore, the surfaces of all the strata would have the same 
ellipticity as the outer surface. (2.) If the forces acting on the nucleus after the 
solidification of the first stratum of the primitive fluid were such as to give the surface 
of the nucleus a tendency to become less oblate, the ellipticity of the interior surface 
of the imperfectly fluid stratum would be less than that of its exterior surface, and 
the resulting attraction of the shell after the solidification would manifestly tend to 
increase in the same direction the effect of the forces previously in action. (3.) If, 
on the contrary, the resultant of all these forces were such as to increase the oblate- 
ness of the perfect fluid, it is evident, from the preceding considerations, that the 
inner surface of the shell so produced would always be more elliptical than its outer 
surface. 
These conclusions will be necessarily modified when the influence of the isothermal 
surfaces in the interior of the spheroid is considered. It seems that no complete and 
general solution of the problem of finding the forms of these surfaces has been yet 
* See Poisson, Mecanique, ii. p. 546, 2n(i edition. 
3 Y 2 
