V. The principal constituent of the tides of the North Sea

Abstract

This paper is concerned exclusively with the principal lunar semi-diurnal harmonic constituent of the tides which is denoted by M ₂ . The primary object is to show how the fundamental dynamical equations of the tides may be used to obtain a knowledge of the distribution of the surface-elevation from such observational data as are available. The dynamical equations, as formulated in 4, connect the elevation-gradients with the currents and the external forces, including those of friction. Prom a knowledge of the currents and a hypothesis for the frictional forces the elevation-gradients can be calculated. When the elevation is also known the directions of the co-tidal and co-range lines, and also the distance apart of neighbouring members of these lines, can be calculated. Such conditions are fulfilled for coastal stations, and it is remarkable that, in spite of the great attention that has been paid to co-tidal charts, these simple calculations do not appear to have been previously made. But if the elevation-gradients can be calculated along a line which passes through one or more points at which the elevation is known, it is clear that methods can be devised by which the elevation can be calculated all along the line. Again, such calculations do not appear to have been previously made.