236 Geological Sodety : — Anniversary of 1839. 



that which the sohd spheroid would give ? What if it appeared 

 that the precession and nutation thus calculated for a fluid interior 

 agreed better with observation than the result hitherto obtained 

 by supposing the earth sohd ? 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 

 mathematicians of modern times have not found their greatest 

 strength superfluous. Yet how incomparably more difficult in 

 all cases is the mechanics of fluid than of solid bodies ! It may, 

 therefore, require more than one trial before any satisfactory solu- 

 tion of the problem can be obtained. Mr. Hopkins has attacked 

 it by the aid of certain hypotheses, and the result is, so far, not 

 favorable to the decisiveness of this test of the interior condition 

 of the earth ; but notwithstanding 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 aban- 

 doned.* 



M. Necker of Geneva, offered an addition to the causes of con- 

 vulsions of the earth, which are contemplated by our Geological 



* The following are the results at which Mr. Hopkins has arrived, supposing 

 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 de- 

 gree of approximation, that the difference would be inappreciable to observation. 



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, something 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 flu- 

 idity. Tlie 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, exceed a quantity of the same order 

 as the solar nutation ; and for any but the most inconsiderable thickness of the 

 shell, would be entirely inappreciable to observation. 



Mr. Hopkins intends hereafter to consider the case of variable density. 

 [See our present volume, p. 364. — Ed. Lon. and Ed. Phil. Mag.] 



