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MR. HENNESSY’S RESEARCHES IN TERRESTRIAL PHYSICS. 
of the earth. Thus an expression for finding has been obtained in which is 
absent, the elimination having been effected between the expressions depending on 
the variation of gravity at the earth’s surface and the precessional phenomena. 
2 
As C — A=C— B=|M% it follows that the difference of the principal moments of 
inertia of the earth is proportional to But from the general expression for and 
from Section IV., it is evident that ^ increases as diminishes, hence we may in 
general conclude that the difference between the greatest and least moment of inertia 
of the earth increases as the thickness of the shell increases. This conclusion being 
independent of any knowledge of the absolute laws of density of the earth’s interior, 
deserves particular attention. 
VI. ON THE EXISTENCE OF A SOLID NUCLEUS WITHIN THE EARTH. 
15. In the preceding investigations the earth has been supposed to solidify solely 
from its surface towards its centre, but it is possible to conceive how from the enor- 
mous pressure on its central strata solidification could also proceed from the centre 
towards the surface. If the influence of pressure in promoting solidification were 
sufficiently great, the earth might have solidified entirely from its centre towards its 
surface, according to the theory proposed by Poisson. It becomes important there- 
fore to examine how far we are justified in adopting the theory of solidification first 
mentioned. 
If solidification took place from the centre towards the surface alone, we should 
believe the earth to be now entirely solid. The forms of the solid strata, composing 
the spheroid in this case, would not be in general the same as if the original fluid mass 
had solidified from its surface towards its centre. Before the solidification of any 
part of the mass, it would consist, in virtue of hydrostatical laws, of a series of sphe- 
roidal strata of equal pressure. Refrigeration at the centre would proceed at an 
almost insensible rate from the impediments to convection adduced in article 6, Part I., 
and from the necessarily slow conducting power of the fluid ; and the theory of solidi- 
fication examined requiring the predominance of pressure over refrigeration as an 
agent in solidifying the mass, it must follow that the forms of the isothermal surfaces 
would have little influence on those of the solidified strata. For greater simplicity, 
I abstract, in the first instance, the effects of refrigeration in contracting the solid 
nucleus and the surrounding fluid. 
The first small nucleus solidified would evidently be bounded by the surface of 
equal pressure due to its radius. No change can take place therefore in the direc- 
tion of the resultant of the forces acting on any molecule of the stratum in contact 
with the solid nucleus, and hence on solidifying it will retain its form. The next 
stratum must become solid, similarly, without changing its form, and so on towards 
the surface. Hence the ellipticities of the strata of the solid spheroid would be the 
same as when it existed in a fluid state. 
