TRANSACTIONS OF THE SECTIONS. 7 



Such that the "fi-eatpr semiaxis of the approximately circular ellipse described by the 

 pole is 0"0325. AVere the crust infinitely thin this nutation would be negative, but 

 its amount nineteen times that corresponding to solidity. This would make the 

 greater semiaxis of the approximately circular ellipse described by the pole amomit 

 to 19x0""0885, which is 1""7. It would be negative and of some amount between 

 1"'7 and infinity, if the thickness of the crust were any thing li'om zero to 120 kilo- 

 metres. This conclusion is absolutely decisive against the geological hypothesis of 

 a thin rigid shell full of liquid. 



But interesting in a dynamical point of view as Hopkins's problem is, it can- 

 not afford a decisive argument against the earth's interior liquidity. It assumes 

 the crust to be perfectly stifi' and unj'ielding in its figure. This, of course, it cannot 

 be, because no material is infinitely rigid ; but, composed of rock and possibly of 

 continuous metal in the great depths, may the crust not, as a whole, be stiff enough 

 to practically fulfil the condition of unyieldingness ? No, decidedly it coidd not : 

 on the contrary, were it of continuous steel and 500 kilometres thick, it would 

 yield very nearly as much as if it were india-rubber to the deforming influences of 

 centrifugal force and of the sun's and moon's attractions. Now although the full 

 problem of precession and nutation, and, what is now necessarily included in it, 

 tides, in a continuous revolving liqiud spheroid, whether homogeneous or hetero- 

 geneous, has not yet been coherently worked out, 1 thinli I see far enough towards 

 a complete solution to say that precession and nutations will be practically the 

 same in it as in a solid globe, and that the tides will be practically the same as 

 those of the equilibrium theory. From this it follows that precession and nuta- 

 tions of the solid crust, with the practically perfect flexibilitj^ which it would have 

 even though it were 100 kilometres thick and as stifi' as steel, would be sensibly 

 the same as if the whole earth from surface to centre were solid and perfectly stiff', 

 Hence precession and nutations yield nothing to be said against such hypotheses 

 as that of Uarwiu*, that the earth as a whole takes approximately the figure due to 

 gi-avity and centrifugal force, because of the fluidity of the interior and the flexi- 

 bility of the crust. But, alas for this " attractive sensational idea that a molten 

 interior to the globe underlies a superficial crust, its surface agitated by tidal 

 waves, and flowing freely towards any issue that may here and there be opened for 

 its outward escape " (as Poulett Scrope called it) ! the solid crust would yield so 

 freely to the deforming influence of sun and moon that it would simply carry the 

 waters of the ocean up and down with it, and there would be no sensible tidal 

 rise and fall of water relatively to laud. 



The state of the case is shortly this : — The hypothesis of a perfectly rigid crust 

 containing Hquid violates physics by assrmiing preternaturally rigid matter, and 

 violates dynamical astronomy in the solar semiannual and lunar fortnightly nuta- 

 tions ; but tidal theory has nothing to say against it. On the other hand, the tides 

 decide against any crust flexible enough to perform the nutations correctly with 

 a liquid interior, or as flexible as the crust must be unless of preternaturally rigid 

 matter. 



But now thrice to slay the slain : suppose the earth this moment to be a thin 

 crust of rock or metal resting on liquid matter ; its equilibrium would be unstable ! 

 And what of the upheavals and subsidences ? They would be strikingly analogous 

 to those of a ship which has been rammed — one portion of crust up and another 

 down, and then all down. I maj' say, with almost perfect certainty, that whatever 

 may bo the relative densities of rock, solid and melted, at or about the temperature 

 of liquefaction, it is, I think, quite certain that cold solid rock is denser than hot 

 melted rock ; and no possible degree of rigidity in the crust could prevent it from 

 breaking in pieces and sinking wholly below the liquid lava. Something like this 

 may have gone on, and probably did go on, for thousands of years after solidifica- 

 tion commenced — surface-portions of the melted material losing heat, freezing, 

 sinking immediately, or gTowing to thicknesses of a few metres, when the surface 

 would be cool and the whole solid dense enough to sink. " This process must go 



* " Observations on tho Parallel Heads of Glen Eoj' and other parts of Lochaber in. 

 Scotland, with an attempt to prove that they are of marine origin," Transactions of the 

 Eoyal Society for Feb. 1839, p. 81. 



