2 INTERNAL STRUCTURE OF THE EARTH 



the tides and precession, sensibly tlie same as if the earth were perfectly rio-id), it 

 is enough that the actual rigidity should be several times as great as tlie actual 

 rigidity of iron throughout 2000 or more miles thickness of crust;" I continue as 

 follows: — 



"A theorem fundamental to the establishment of the above propositions is, that 

 a revolving spheroid destitute of rigidity, a homogeneous fluid one, for instance, 

 would have no precession. Sir Wm. Thomson does not matlicmatically demonstrate 

 this theorem, but by use of an hypothesis gives an elegant illustration of its truth, 

 .for which, though to me it- is convincing, I prefer to substitute the following 

 demonstration." 



The demonstration referred to consists in investigating for the diurnal tide 

 of a liomogeneous fluid spheroid, as it is expressed by Laplace, Mec. Cel. Book IV 

 [2316] (Bovvditch), the analytical expression for the "couple" due to the "centri- 

 fugal force" exerted upon the material particles which constitute that tide ; showing 

 the same to be exactly equal and opposite to the precession-producing couple 

 exerted on the oblate spheroid, itself by the foreign attraction (e. ;/. of the sun). 



The method of computing this counteracting couple is identically that used by 

 Laplace in determining the efi"cct of the centrifugal force exerted by the tides in 

 the chapter (Mec. Cel.) on the " Pressure and Attraction of the Sea." I go on to 

 draw the following general conclusion: — 



" By parity of reasoning the truth of Sir Wm. Thomson's propositions concerning 

 a solid but yielding spheroid is made evident ; for exactly in the same ratio to the 

 tides of a fluid spheroid that the solid tidal elevations are produced (the actual 

 ellipticity of the earth being nearly that of equilibrium with the centrifugal forces), 

 will the prccessional couple due to the tide-producing attraction be neutralized by 

 their centrifugal action."^ 



Circumstances, referred to on another page, have caused me to reconsider these 

 opinions ; but as the considerations on which they were founded not only were con- 

 sidered demonstrative by myself, but furnished for ten or fifteen years an unsus- 

 pected basis of belief for the author of " The Kigidity of the Earth" (Phil. Trans., 

 1863); of the "Natural Philosophy" (1867); of the letter to Mr. G. Poulett Scrope 

 (1873),^ it seems pertinent to inquire how far those considerations were in harmony 



' This reasoning maybe put in a little different form to illustrate not only the weight of the argu- 

 ment but what I shall have to set forth in subsequent pages. Two different effects, each complete 

 in itself, are separately attributed to the "couple" exerted by the foreign attraction; one is preces- 

 sion (('. e. angular motion of the earth's mass considered as a rigid solid) ; the other, that distortion 

 of the mass-figure denoted by the diurnal tide. The "cause" is adequate to either effect, separately. 

 Will it produce both? The argument and the mathematical "demonstration" was that the latter 

 effect mnst neutralize the former. Subsequent pages will show that I now regard the former to 

 neutralize, in great degree, the latter ; or, more accurately speaking, the latter to be partially 

 Iransformed into the former. 



' "When those passages were written," says the author, "I knew little or nothing of vortex 

 motion ***** j i,ji(j never once thought of this subject in the light thrown on it by the 

 theory of the quasi-rigidity induced in a liquid by vortex motion." (Glasgow Address.) Professor 

 Tait's Translation of Helmholtz, on Vortex Motion (Crelle's Journal, 1858), appeared in Phil. Mag, 

 ISGf, with a postscript by Sir Wm. Thomson, scarcely that of a novice ; and was followed by com- 



