VIII. TIDAL DEFORMATION OF THE SOLID EARTH (cont.)

44. Rigidity of the Earth

Although the computation of oceanic tides is as yet impossible, it cannot be admitted that perfect rigidity in the earth would augment the tides in the proportion of 5 to 2, although they might perhaps be augmented in the proportion 4 to 3. Thus Thomson concludes that the earth’s mass must have an effective rigidity at least as great as that of steel. If it were true, as was held until recently, that the earth is a fluid ball coated with a crust, that crust must be of fabulous rigidity to resist the tidal surgings of subjacent fluid. Hence we are led to the conclusion that far the larger portion of the earth’s mass, if not all of it, is a solid of great rigidity. Up to the present time the argument by which the tides of long period were proved to have approximately their equilibrium height has generally been accepted without much doubt, but we have (§ 17) shown good cause for rejecting Laplace’s argument, at least for a fortnightly tide. It appeared formerly that, from numerical data as to the heights of the tides of long period, we should be able to compute the actual effective rigidity of the earth’s mass. But from § 18 we see that, although these tides remain incalculable, yet with such oceans as ours the tides of long period must conform much more nearly to the equilibrium laws than do the tides of short period. Thus a comparison of the observed heights of the tides of long period with the equilibrium law still remains of interest, although the evaluation of the earth’s rigidity appears with present data unattainable. Acting on the old belief, Mr G. H. Darwin has compared the lunar fortnightly and monthly tides, as observed for thirty-three years at various Indian and European ports, with the equilibrium theory, and has found that the tide-heights were about two-thirds of the equilibrium height. [Footnote 374-1] From this the conclusion was drawn that the effective rigidity of the earth was as great as that of steel. Whilst, then, this precise comparison with the rigidity of steel falls to the ground, the investigation remains as an important confirmation of Thomson's conclusion as to the great effective rigidity of the earth. When extensive and accurate knowledge of the tides has been attained, the attempted evaluation of the rigidity may conceivably be possible, because there is a minute tide with a period of 18·6 years (§ 23, schedule [A, iii.]) of which Laplace’s argument must hold good. Great accuracy will, however, be necessary, because the height of the tide at the equator only amounts to one-third of an inch, and a preliminary inquiry seems to show that there are other relatively considerable variations of sea-level arising from unexplained causes. [Footnote 374-2]

Sir W. Thomson’s solution of the strain of an elastic sphere has been also used to determine what degree of strength the materials of the earth must have in order that the great continental plateaus and mountains may not sink in. [Footnote 374-3] In another investigation it has been shown that local elastic yielding on the coast-lines of continents may produce an augmentation of apparent tide in certain places on account of the flexure of the upper strata, when a great weight of water is added and subtracted from the adjacent oceanic area at high and low tide. [Footnote 374-4] There is reason to believe that such flexure has actually been observed by a delicate form of level on the coast of the Bay of Biscay. [Footnote 374-5]


Footnotes

374-1 Thomson and Tait, Nat. Phil., vol. i. pt. ii., 1883, § 847 sq.

374-2 Darwin, "On 19-yearly Tide at Karachi," in Brit. Assoc. Report, 1886.

374-3 G. H. Darwin, Phil. Trans., pt. i,, 1882. p. 187, with correction, Proc. Roy. Soc., 1885.

374-4 Id., Brit. Assoc. Rep., 1882, or Phil. Mag., 1882.

374-5 D’Abbadie, Annales Soc. Sc. de Bruxelles, 1881, or quotation by Darwin, loc. cit.








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