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Fourier Analysis of Ocean Tides IIIWith JAVA animation by Bill Casselman2. A conversation in a railway carriageIn 1872 Kelvin was preoccupied with the tidal prediction, and in particular with the problem of summing a large number of harmonic motions with irrationally related frequencies. Here is how the solution came to him, in his own words (Mathematical and Physical Papers, Vol. VI Cambridge 1911, p. 286).
Dramatis Personae. The Author: William Thompson, later (1892) Lord Kelvin. Mr Tower: Beauchamp Tower, an engineer and inventor. His 1883 experiments on lubrication were the basis for the ``Reynolds Equation,'' later treated by Sommerfeld. Mr White: James White of Glascow, ``Philosophical Instrument Maker to the University.'' The model was soon succeeded by the First Tide Predicting Machine, which was completed in 1875, and could sum 10 tidal constituents. It was succeeded in turn by a second (about 1880), a third (about 1883) and a ``Fourth British Tide Predictor'' (1910). The machine illustrated here is the third. Click for larger image
The functioning of this mechanism, and the way in which the various constituents contribute to the tide, are illustrated in a JAVA applet contributed by Bill Casselman of the University of British Columbia.

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