The harmonic development of the tide-generating potential

Abstract The harmonic development of the tide-generating potential is the basis of most work on tidal observations, and since 1883 the development given by Sir G. H. Darwin has been universally used and has been of remarkable value. But discrepancies between prediction and observation are serious and have been attributed to faulty “harmonic constants”; it has been assumed that if these were improved better predictions would be obtained, and it has also been tacitly assumed that it is only necessary to consider the harmonic constituents as given by Darwin. Recent work, however, especially at the Tidal Institute, has shown that when all the “Darwinian constituents” are removed from the tidal height there is a residue composed of constituents which are not included in his schedules. These are such that any slight improvements possible in the “constants” usually obtained are comparatively negligible. The obvious course, therefore, was to make a more thorough development of the potential, and in view of the unknown nature of the residues great accuracy was obviously desirable, especially as the possibility of resonance has always to be considered. The development given in this paper, even if it proves to be needlessly thorough for practical tidal work, will cover the needs of research work, since it includes all terms whose coefficients (relatively to the greatest coefficient) are greater than 0·00010.