IN RELATION TO THE EARTH'S INTERNAL STRUCTURE. 39 



fer the ertb, may be made evident from the following considerations: A rod of 

 steel extending towards the sun I'roni the centre to tin- surface of the earth, would 

 lie elongated by the differential force of the sun's attraction 0".975, or one foot, 

 nearly. The height of the solar tide of a homogeneous fluid spheroid is 1".355 ; 

 but the mutual attract ion of the elevated particles produces 0". 793 of this, and the 

 remaining ()'..">I'J i. the proper measure of the direct action of the solar force. In 

 the case of the rod the elastic forces of the steel alone are considered; in the 

 spheroid gravitation is the sole binding force. The maximum extension of the 

 rod per unit of length would bo expressed by the decimal .000000055 corre- 

 sponding to a tensile force of 1.87 Ibs. (taking the coefficient of elasticity at 34 

 millions Ibs.) per square inch.'" The necessity of the extreme rigidity demanded 

 by Sir W. Thomson is rerogni/.ed when it is seen how excessively minute would be 

 tin- elastic forces developed in the production of distortion, in a rigid earth spheroid, 

 commensurable with fluid tide-waves. 1 



In a paper "On the Secular Cooling of the Earth" (Trans. Il.S.E., 1862, and 

 Appendix to "Treatise, &(."). Sir W. Thomson applies a solution of Fourier to 

 the determination of the interior temperature and its rate of increase downwards, 



" See Additional Notes, p. 51. 



1 M. lielannay, President of the French Academy, after quoting (Comptes rcndus 1808) from the 

 |>n|icr (if Sir \V. Thomson to which I have already referred, the results of Hopkins and some corro- 

 borating remarks from Sir \V. Thomson's paper (referred to above), says : "Ainsi, on le voit, 1'ob- 

 MI mise en avant par M. Hopkins, contre lea idces gcneralcmcnt admiscs par les geologucs sur 

 In fluidite intcriruri' du globe terrestre, est regardce par plusicurs savants anglais comme parfaitement 

 fomlre. ,]> Mils d'un avis diametralemcnt oppose: je crois quo I' objection de M. Hopkins ne repose 

 sur aueun foiidi-iui'iit reel." M. Delaunay then refers to an experiment made under his direction with 

 a rlass vase 24 in diameter, as furnishing decisive proof that the "viscosity" of a liquid as per- 

 fectly lluid as water even, is sufficient to cause it to take np the rotary motions of its enveloping 

 shell, provided that those motions arc relatively slow, ns are those which constitute the precession 

 and nutation of the earth; and he goea on to say: "Hence it does not appear to me possible to 

 admit that the effect of the perturbing forces to which precession and nutation arc dne extend only 

 to :i portion of the mass of the terrestrial globe; the entire mass ought to be carried along (entrainec) 

 I iy tlie perturbing actions, whatever may be the magnitude attributed to the interior fluid portion, 

 and consequently the consideration of the phenomena of precession and nutation can furnish no datum 

 : minting the greater or less thickness of the solid crust of the globe." 



M. Delaunay seems to be unaware that Sir W. Thomson coincides with Prof. Hopkins only in 

 thix (as the sequel of the very paper quoted shows), that he demands a great thickness of crust, and, 

 moreover, that the interior, to the depth of this crust, shall be not merely "solid," but possessing a 

 rigidity " several times as great ns that of iron." I have endeavored to show that Sir W. Thomson's 

 argument is irrefragable; but, based upon wholly different considerations, it is certain that no degree 

 of " viscosity" assigned to an internal liquid will refute it 



I have remarked, at the outset of this discussion, that Prof. Hopkins' results "have not been gene- 

 rally accepted as decisive;" but I cannot admit that, as a test of their tenability, the experiment of 

 M. Itelaunay possesses the crucial character which he attributes to it. Viscosity, considered as an 

 accelerating force tending to impart to a fluid the rotary motions of an enveloping shell, is directly 

 proportional to the surface of contact, and inversely to the mans of contained liquid ; in other words, 

 it varies inversely ns the dinmeter of the enveloping shell. The effect of viscosity of the fluid con- 

 tents of the earth compared to those contained in a similar spherical envelope of only ten inches 

 diameter, would be expressed (nearly enough) by the fraction 



