When Newton had made public his capital discovery, and had shown that the magnitudes or ranges of the tides increase and decrease in accordance with the varying attractions of the moon and sun, the tidal problem was supposed to be nearing a solution. Indeed, Newton thought that he could see in the observed times of tides upon certain shores a justification of his theoretical considerations. His work, however, was only a beginning. Since his time, eminent mathematicians, astronomers and physicists—including Bernoulli, Maclaurin, Euler, Lalande, Laplace, Young, Lubbock, Whewell, Airy, Ferrel, Kelvin, Darwin, Lévy and Hough—have addressed themselves to this subject; while others, like Lagrange, Stokes, Rayleigh, Lamb and Poincaré, have dealt rather with the underlying mathematical and physical problems.
Since it has been universally recognized that the tides result from the attraction of the moon and sun, the popular mind has taken little interest in the manner in which these forces operate in order to produce the tides. The apparent hopelessness of the task has doubtless deterred many investigators from devoting to it a full measure of their attention. In fact, as will be shown below, there is no such thing as "the tidal problem" analogous to the astronomers' "problem of three bodies." The tide involves a number of problems, and to even discover what these problems are requires a good knowledge of the forms, sizes and depths of the oceans, together with a knowledge of the tide-producing forces. The observed tides themselves render great assistance in this matter; for their times and ranges indicate the ways in which the various oceans probably oscillate, and so, in a measure, the underlying tidal problems requiring solution.
General Belief in a Westwardly-progressing Tide Wave
Various theories were instrumental in leading to the belief of a general westward progression of the tide. As before the Copernican system of astronomy became known or generally accepted, the tides were made to accord with the Ptolemaic system then prevailing, so for some time before and after the publication of Newton's "Principia," the tides were made dependent upon the vortices of Descartes's theory.
The Ptolemaic system of astronomy assumed the center of the earth to be the fixed center of the universe around which revolved a series of concentric spheres. The outermost of these was styled the primum mobile; this by its westward motion imparted westward motion to the stars and other heavenly bodies, to the atmosphere, and even to the waters of the oceans. And so before the law of gravitation was established, the notion became prevalent that water had a westward motion (ab oriente in occidentem or ab ortu in occasum) around the globe; and because the flood stream, rather than the ebb, was the one chiefly considered, the flood stream (and so the progression of the tidal wave) was commonly supposed to partake of this westward motion. The