AS AFFECTING P K FJ C E S S 1 N AND N U T A C ION 9 



Tho observed precession of the earth's axis corresponds very closely (Thomson 

 and Tait, § 828) with tiiat due to a splieroid of its external ellipticity and probable 

 law of internal density ; but the fact docs not afford, therefore, the suppos(-d argu- 

 ment for rigidity. I have, in the memoir cited at the head of this paper, illustrated 

 by the case of the steel rod how very great must be the rigidity of a solid earth 

 which should exhibit no sensible tidal distortion ; and it follows that a mere ihin 

 crusf. must be of almost infiniteli/ unyielding nniterial to effectually suppress such 

 distortion. And, conceding the (implied) infinite rigidity to a shell or crust, I 

 have furthermore demonstrated (Addendum to paper cited) the fallacy of Mr. 

 Hopkins' conclusion that a minimum thickness of 800 or 1000 miles must be 

 assigned to it. There can be, therefore, no propriety in attributing (with Sir Wm. 

 Tliomson) to Mr. Hopkins "the discovery of the earth's solidity." Masterly as is 

 much of his investigation, the vague formula he presents as his final result will 

 bear no such ponderous weight of conclusion as he lays upon it, even if the 

 specific errors I have elsewhere pointed out did not vitiate it; while the ])reter- 

 natural rigidity required for his shell abstracts from its merits as a genuine " Re- 

 search in Physical Geology.'" Moreover, Mr. Hopkins' argument loseS' whatever 

 claims to decide the point which accuracy conceded to his theorem would give, 

 when, instead of the considerable discrepancy (8 to 7, he supposes it to be) in the 

 calculated and of observed precessions (on which he fc'.mds his conclusions) there 

 is, as we now know, none; or, at least, none assignable. 



My conclusion concerning Mr. Hopkins' celebrated problem (see "Addendum"), 

 and my criticism of his results, are fully sustained by the language of Sir Wm. 

 Thomson when he says " a very slight deviation of the inner surface of the 

 shell" (supposed perfectly rigid) "from perfect sphericity would suffice, in virtue 

 of the quasi-rigidity due to vortex-motion, to hold back the slu41 from taking 

 sensibly more precession than it would give to the liquid, and to cause the liquid 

 (homogeneous or heterogeneous) and the shell to have sensibly the same preces- 

 sional motion as if the whole constituted one rigid body." (That there is vot 

 "sensiblv the same precessional motion" for the cise of lieteroyeneousness, forms the 

 main burden of Mr. Hopkins' results.) 



Allusion has already been made (note 1, p. 4) to Mr. Hoi)kiris' "case of rotary 

 motion not before investigated." It is that of the small reciprocal oscillation of 

 shell (considered ii^ perfectly rigid) and the internal fluid. By direct action on the 

 shell itself, and by induced pressure of the fluid on the shell, the whole precessional 

 effect of the foreign attraction takes effect primarUi) on the shell alone; from which 

 ensues a divergence of axes of shell and fluid (as represented in Fig. 2), and a 

 development of reactive force in the fluid (through the displacement of its planes 

 of rotation), by which, "precisely as if it were solid," the fluid reacts upon the 

 shell and adds its moment of inertia to that of the shell, reducing the mean rate 

 of precession to that corresponding to the entire mass. This common mean 



' It is true that physicists had not thoupht of the exigencies of rigidity in this connection until 

 Sir Wm. Thomson pointed them out; nevertheless a "Research into tlie physical geology" of the 

 case, viewed as to its matlicinaticul roqniroments, ought to have suggested such e.xigcncies. 

 2 August, 1877. 



