508 Notices of Memoirs — M. Delaunay 



change of direction in the rotary axis of the globe as a whole. The 

 moon in its turn also produces an analogous effect by its action on 

 this same pad, and it is the joint action of the sun and moon which 

 ultimately produces the slow and complicated motion of the earth's 

 axis, of which the precession and nutation are constituent parts. 



In determining the effect due to these actions of the sun and moon 

 upon the equatorial swelling of the terrestrial globe, the earth is 

 regarded as a solid body, in which all parts are so intimately con- 

 nected with one another that its entire mass is subject to the effects 

 of these disturbing influences. 



If, on the contrary, the earth consists of a liquid mass covered by 

 a solid crust, this is no longer the case ; the action of the sun and 

 moon would be communicated to the entire solid crust of the globe ; 

 but the liquid interior, in consequence of its fluidity, could not par- 

 ticipate in the effects of these actions. The disturbing forces in 

 question, by only influencing the solid external crust of the globe, 

 affect its total mass in a much less degree than if they influenced the 

 entire terrestrial globe itself; wherefore the changes which take 

 place in the rotary motion of the solid crust would be much greater 

 than those which would occur if the globe is regarded as an entirely 

 solid body ; and these changes would be the more intense in pro- 

 portion as the solid crust of the globe is supposed to be less thick. 



This, then, is the basis of Mr. Hopkins' reasoning, from which he 

 draws the conclusion, that in order to make the effect of the actions 

 of the sun and moon upon the equatorial swelling of the earth agree 

 with the magnitude arrived at by astronomical observations of the 

 phenomena of precession and nutation, it becomes necessary to assign 

 to the solid external crust of the globe a thickness of at least from 

 800 to 1000 English miles, or in other words of from one-fifth to one- 

 fourth of the earth's radius ; a result very different from the feeble 

 thickness which geologists are wont to attribute to the solid external 

 shell of our sphere. 



This grave objection brought by Mr. Hopkins against previously 

 accepted views has been followed up by Professor Thomson, of Glas- 

 gow, in his memoir on the Eigidity of the Earth (Phil. Trans. 1863, 

 p. 573), where he introduces it as follows : 



''1. That the earth cannot, as many geologists suppose, be a liquid 

 mass enclosed in only a thin shell of solidified matter is demon- 

 strated by the phenomena of precession and nutation. Mr. Hopkins, 

 to whom is due the grand idea of thus learning the physical con- 

 dition of the interior from phenomena of rotatory motion presented 

 by the surface, applied mathematical analysis to investigate the 

 rotation of rigid ellipsoidal shells enclosing liquids, and arrived at 

 the conclusion that the solid crust of the earth must be not less than 

 800 to 1000 miles thick. Although the mathematical part of the 

 investigation might be objected to, I have not been able to perceive 

 any force in the arguments by which this conclusion has been con- 

 troverted, and I am happy to find my opinion in this respect con- 

 firmed by so eminent an authority as Archdeacon Pratt (Figure of 

 the Earth, 1860, § 85.) 2. It has always appeared to me, indeed, 



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