III. DYNAMICAL THEORY OF TIDES
10. Historical Explanation
The problem of tidal oscillation is essentially a dynamical one. Even when the ocean is taken as covering the whole earth, it presents formidable difficulties, and this is the only case in which it has been hitherto solved.[Footnote 358-4] Laplace gives the solution in bks. i. and iv. of the Mécanique Céleste; but his work is unnecessarily complicated by the inappropriate introduction of spherical harmonic analysis, and it is generally admitted that his investigation is difficult. Airy, in his "Tides and Waves" (in Ency. Metrop.) presents the solution free from that complication, but he has made a criticism of Laplaces method which we believe to be wrong. Sir W. Thomson has written some interesting papers (in Phil. Mag., 1875) in justification of Laplace, and on these we base the following paragraphs. This portion of the article is given more fully than others, because there exists no complete presentment of the theory free from objections of some kind.
358-4 Sir W. Thomson's paper "On the Gravitational Oscillations of Rotating Water," in Phil. Mag., August 1880, bears on the same subject. It is the only attempt which has hitherto been made to consider the effects of the earth's rotation on the oscillations of land-locked seas.
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