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III. Researches in Physical Geology. — Third Series. By W. Hopkins, Esq., M.A. , 
F.R.S., Fellow of the Royal Astronomical Society, of the Geological Society, and 
of the Cambridge Philosophical Society. 
Received November 25, 1841, — Read January 13, 1842. 
On the Thickness and Constitution of the Earth's Crust. 
i. The result at which I arrived in my preceding memoir, respecting the preces- 
sional motion of the pole, on the hypothesis of the earth’s interior fluidity, is the 
following : 
where P x denotes the precession of a solid homogeneous spheroid of which the ellip- 
ticity = s 1} that of the earth’s exterior surface, and P' the precession of the earth, sup- 
posing it to consist of an interior heterogeneous fluid, contained in a heterogeneous 
spheroidal shell, of which the interior and exterior ellipticities are respectively s and 
s v the transition being immediate from the entire solidity of the shell to the perfect 
fluidity of the interior mass. 
2. In the application of this result to the actual case of the earth, we must observe, 
in the first place, that, supposing the interior mass to be fluid, its fluidity cannot be 
quite perfect, as explained in the introductory observations to my first memoir. 
Consequently the assumption, made in our investigations, of the absence of all tan- 
gential action between the shell and fluid will not be accurately true. Moreover, it 
would seem extremely probable that the transition from the solidity of the shell to 
the fluidity of the interior mass, instead of being immediate, must be gradual. If, 
however, the thickness of the shell be not considerable with reference to the earth’s 
radius, the fluidity of the portion not remote from the centre will be nearly perfect, 
and the whole of the interior mass, with the exception of that part near the actual 
solid portion, may, as a near approximation, be considered as perfectly fluid with re- 
ference to any mechanical action upon it. Again, supposing the change from the 
solidity of the exterior to the fluidity of the interior mass to be continuous, let us 
conceive a surface passing through all the lowest points of that portion of the mass 
which may be regarded as perfectly solid, and another surface through all the highest 
points of that portion which may be regarded as perfectly fluid. The first of these 
surfaces will be one of equal solidity and the second one of equal fluidity ; the fluidity 
of the mass contained between them being imperfect. Now if we were to consider 
g 2 
