Tides in oceans bounded by meridians

Abstract

This is the first part of a series of papers by A. T. Doodson and myself, in which we intend to publish certain investigations which we have been carrying out intermittently for some years. In 1916 I published an account* of a general method of treating the dynamical equations of the tides in which the ordinary differential equations were transformed into an infinite sequence of algebraic equations. One of the chief features of the treatment is that an attempt was made to deal rigorously with questions of convergence. At that time the determination of the tides in a flat rectangular sea, a flat sectorial sea, and an ocean bounded by two meridians constituted mathematical problems which were completely unsolved, and I pointed out that for basins of these shapes and of uniform depth the coefficients in my algebraic equations could easily be evaluated. It is a disadvantage of the method, however, as applied to these systems, that the algebraic equations are naturally arranged in a double sequence and not in a single sequence.