24 THE TIDAL PROBLEM. 



Darwin relative to their present magnitude, remarking by way of pre- 

 caution that the quotations given, separated as they are from their context 

 and the qualifications it carries, are liable to convey misconception of the 

 author's views on points other than that for which alone they are quoted 

 here, viz, the magnitude of the tides of the lithosphere. He says: 



The chief result of this paper [on Bodily tides of viscous and semi-elastic spheroids, 

 and on the Ocean tides upon a yielding nucleus] may be summed up by saying that it is 

 strongly confirmatory of the view that the earth has a very effective rigidity. But its 

 chief value is that it forms a necessary first chapter to the investigation of the precession 

 of imperfectly elastic spheroids, which will be considered in a future paper. I shall then, 

 as I believe, be able to show, by an entirely different argument, that the bodily tides in the 

 earth are probably exceedingly small at the present time.* 



And again, at the end of the later paper referred to: 



The conclusion to be drawn from all these calculations is that at the present time 

 the bodily tides in the earth, except perhaps the fortnightly tide, must be exceedingly 

 small in amount; that it is utterly uncertain how much of the observed 4" of acceleration 

 of the moon's motion must be referred to the moon itself, and how much to the tidal fric- 

 tion, and accordingly that it is equally uncertain at what rate the day is at present being 

 lengthened.^ 



It has already been made clear that Darwin's inquiry involved the 

 assumption that in an earlier state, when the earth was more largely 

 molten or viscous, the body tides were much greater and more effective 

 than now. But if we substitute the view that the rigidity of the litho- 

 sphere has been nearly what it is at present through the whole history of 

 the earth, as is permitted by the planetesimal hypothesis, the conclusions 

 quoted will apply to the whole period, with such modifications as may be 

 required for differences of distance between the earth and moon. 



The substitution of an elastico-rigid earth for a viscous one affects the 

 rotational influences of the tides qualitatively also. If tidal deformation 

 causes a movement of the molecules of the lithosphere over one another 

 in fluidal fashion, friction is the result, and the tide, under present condi- 

 tions, must have a retardational influence. If, on the other hand, the mole- 

 cules are merely strained elastically in their relations to one another, but 

 do not shift these relations as they do in fluidal motion, the strain and 

 the resilience from it act almost coincidently with the straining force, the 

 original form and relations are almost perfectly restored on relaxation, 

 the friction is slight, and the rotational effect will be essentially negligible. 



Now, when it is considered that a tidal protuberance, at the very most, can 

 warp a line of molecules only in some such measure as g q^q q^q to 15,00^0.000 / 

 it seems clear that the deformation lies far within the strain-limits of crys- 

 talline rock, and probably within the strain limits of all rigid substances 

 in the lithosphere. The only known substances within the outer half of 

 the lithosphere that probably move as fluids under tidal stress, are the 

 relatively trivial threads, tongues, ' or pools of lava within it, and the iso- 

 lated molecules or groups of molecules here and there in the free form in 

 the rigid rock. If we postulate an earth of such a degree of elastic rigidity 



» Phil. Trans. Roy. Soc. Lond., 1879, p. 31. 



' On the precession of a viscous spheroid, etc. <Phil. Trans. Roy. Soc. Lond., Pt. II, 

 1879 (1880), pp. 483-484, 



