Tides in oceans bounded by meridians III. Ocean bounded by complete meridian semidiurnal tides

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Abstract
The first two parts of this series of memoirs have dealt with the general equations for the motion in an ocean bounded by a complete meridian (Proudman 1936) and with their application to the diurnal tide (Doodson 1936 a ). This present memoir is concerned with the semidiurnal tide ( K2 ). The investigation, as in Part II, is dependent upon the formulation and numerical solution of the equations resulting from the use of sixty-three co-ordinates or variables, and the solution has been effected and is illustrated for twenty values of the depth of the ocean, from very large to medium depths. Though a part of the work of solution is common to all cases, in effect twenty sets of equations, each set having sixty-three equations, have been solved. The results are of exceedingly great interest in connexion with tidal theory. The genesis and development of amphidromic systems, as the depth is changed, can be fully traced. The possible systems of cotidal lines are of great variety. The type of amphidromic system changes so rapidly with the depth that a single illustration of the tides for a particular depth is of doubtful value for comparison with an actual ocean. It is hoped that the complete series of illustrations will provide material for the derivation of principles which can be applied to terrestrial oceans.

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