IN RELATION TO THE EARTH'S INTERNAL STRUCTURE. 35 



and the nutation essentially the same as for a homogeneous spheroid ; but for tlie 



actual case of a heterogeneous fluid contained in a heterogeneous shell he finds 



that the ellipticity of the inner surface of the sliell must be less than that of the 



exterior in the proportion of the observed precession to tlie precession of a homoge- 



7 

 neons spheroid of same external ellipticity, a proportion which he assumes to be , 



in accordance to the then received numbers for ellipticity, and for the mass of the 

 moon. 



Tlie fulfilment of the condition, in the actual constitution of the earth, is improb- 

 able ; for the isotliermal surfaces are in all ])robability (and indeed by liis own 

 mathematical conclusions) of progressively greater ellipticity from the surface in- 

 wards, lie finds, however, tlie requisite decrease of ellipticity in the fluid surfaces 

 of equal densltij, assuming the well-known hypothetical law of density of Laplace 



sin ch 

 n= A — /^^; hut we know not the influence which pressure has upon solidification, 



and it seems probable that the interior surface of the shell would conform nearly to 

 the surfaces of eqiuil temperature. The demand whicli he makes for 800 or lOOO 

 miles thickness of shell is therefore a minimum (for the data used), while the more 

 prohuble result is a much greater thickness or even entire solidity. But however 

 elegant may be Mr. Hopkins' analysis, the basis of the structure is but slender, and 

 those results have not been generally accepted as fully decisive of the question. 



Sir Wm. Thomson, F.Il.S., brings forward (Philosophical Transactions, 1863; 

 also Thomson's and Tait's Treatise on Natural Philosophy, 1867) arguments 

 against the popular theory of a thin crust, which are more forcible. A thin crust 

 would itself undergo tidal distortion, and the height of the apparent tides of the 

 ocean be thereby much reduced, while i\ic-actu(xl precession would be diminished 

 in the same ratio; that is, the differential forces of the sun and moon would expend 

 themselves in producing these solid tides instead of producing precession. 



From a theoretical investigation (given in a separate jiapcr in the same volume)' 

 of the deformation experienced by a homogeneous elastic spheroid under the influ- 

 ence of any external attracting force, he arrives at the result that, if the earth had 

 no greater rigidity than steel or iron, it would yield about | as much to tide-produc- 

 ing influences as if it had no rigidity — more than | as much if its rigidity did not 

 exceed that of glass. Moreover, the apparent ocean tides (or difference of high 

 and low water level) would be (li II is the measure for a perfectly rigid earth) 



0.59 //, if the earth had the rigidity of iron or steel only; -, II if it had that of 



1 4- 



glass. -* 



As to precession, the centrifugal force of the crowns of the tidal elongation would 

 balance \ of the dynamic couple residting from the sun's or moon's attraction 

 if the earth had only the rigidity of glass, and -| if it had only that of steel. 



" That the eflective tidal rigidity, and what we call the precessional effective 



' Sec also " Treatise on Natural Philos.," § 832 el scq. 



