The problem of determining the free and forced tidal oscillations on a rotating globe, first enunciated by Laplace and solved by him in special cases, was completed by Hough. Valuable as these results are, they deal with oceans wholly covering the globe, and so give little information regarding the tides on the earth which are materially affected by continental barriers. A further stage would be effected by the introduction of simple boundaries. When the barriers are along complete circles of latitude, the problem is relatively simple and solutions have been worked out. General processes for the attack on the problem where the boundaries take any form have been described by Poincare and Proudman§; and an approximate method for determining the free periods of oscillation of an ocean bounded by two meridians when the rate of rotation is small has been given by Rayleigh.|| Analogous problems of the tides in flat rotating seas have been solved in certain cases.¶ The case of the tides on a non-rotating globe bounded by two meridians has also received attention.** This list covers most of the results so far achieved.
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George Ridsdale Goldsbrough (1928) studied this question.