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from that which the solid spheroid would give? What if it ap- 
peared that the precession and nutation thus calculated for a fluid 
interior agreed better with observation than the result hitherto ob- 
tained by supposing the earth solid? If this were so, we should 
have evidence of the earth’s interior fluidity, evidence, too, of a per- 
fectly novel and most striking nature. But to answer these ques- 
tions is far from an easy task ; the precession of the solid earth is a 
problem in which Newton erred, and in which the greatest mathe- 
maticians of modern times have not found their greatest strength 
superfluous. Yet how incomparably more difficult in all cases is the 
mechanics of fluid tlfan of solid bodies! It may, therefore, require 
more than one trial before any satisfactory solution of the problem 
can be obtained. Mr. Hopkins has attacked it by the aid of cer- 
tain hypotheses, and the result is, so far, not favourable to the de- 
cisiveness of this test of the interior condition of the earth; but not- 
withstanding this state of things, I venture to say on your behalf, 
Gentlemen, that an idea so full of promise of that which we so 
much desire, and which seems to be so utterly out of our reach, 
the knowledge of the condition of the centre of the earth,—that 
such an idea is not to be lightly abandoned*. 
* The following are the results at which Mr. Hopkins has arrived, sup- 
posing the earth to consist of a homogeneous spheroidal shell filled with 
a fluid mass of the same density as the shell :— 
1. The precession will be the same, whatever be the thickness of the 
shell, as if the whole earth were solid. 
2. The lunar nutation will be the same as for the solid spheroid, to such 
a degree of approximation, that the difference would be inappreciable to ob- 
servation. 
3. The solar nutation will be sensibly the same as for the solid spheroid; 
unless the thickness of the shell be very nearly of a certain value, some- 
thing less than one fourth the earth’s radius, in which case this nutation 
might become much greater than for the solid spheroid. 
4. In addition to the above motions of precession and nutation, the pole 
of the earth would have a small circular motion, depending entirely on the 
internal fluidity. The radius of the circle thus described would be the 
greatest when the thickness of the shell should be least ; but the inequality 
thus produced would not, for the smallest thickness of the shell, ex- 
ceed a quantity of the same order as the solar nutation; and for any but 
the most inconsiderable thickness of the shell, would be entirely inappre- 
ciable to observation. 
Mr. Hopkins intends hereafter to consider the case of variable density. 
