IN RELATION TO TUE EARTH'S INTERNAL STRUCTURE. 39 



for the earth, may be made evident from the following considerations : A rod of 

 steel extending towards the snn from the centre to the snrface of the earth, would 

 be elongated by the difierential 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 attraction of the elevated particles produces 0".793 of this, and the 

 remaining 0'''.542 is the proper measure of the direct action of the solar force. In 

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

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

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

 sponding to a tensile force of 1.S7 lbs. (taking the coefficient of elasticity at 34 

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

 by Sir W. Thomson is recognized when it is seen how excessively minute would be 

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

 commensurable with fluid tide-waves.^ 



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

 Appendix to " Treatise, &c."), 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. 



' M. Delaunay, President of the French Academ}', after quoting (Comptes rcndus 1808) from the 

 paper of Sir W. Thomson to wliich I have already referred, the results of IIoi)kius and some corro- 

 borating remarks from Sir W. Thomson's paper (referred to above), says: "Ainsi, on Ic voit, I'ob- 

 jeetion raise en avant par AI. Hopkins, contre les idees generalement admises par Ics geologues sur 

 la fluidite interieure du globe terrestre, est regardee par plusieurs savants anglais comme parfaitement 

 foiidee. Je suis d'un avis diametralement oppose: je crois que 1' objection de AE. Hopkins ne repose 

 sur aucun fondement reel." M. Delaunay then refers to an experiment made under liis direction with 

 a glass vase 0" 24 in diameter, as furnishing decisive proof that the "viscosity" of a lifpiid as per- 

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

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

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

 arlniit that the effect of the perturbing forces to which precession and nutation are due extend only 

 to a portion of the mass of the terrestrial globe ; the entire mass ought to be carried along (entraincc) 

 by the 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 

 for estimating 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 

 this (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 as 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. Delaunay possesses the crucial character which he attributes to it. Yiscosity, considered as an 

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

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

 it varies inversely as the diameter of the enveloping shell. The effect of viscosity of tlie fluid con- 

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

 diameter, would be expressed (nearly enoun-li) by the fraction ' -^ . 



