Notes concerning tidal oscillations upon a rotating globe

Abstract

Speculations on tidal questions are much hampered by our ignorance of the peculiar influence of the earth’s rotation in any but the simplest cases. The importance of this element was first appreciated by Laplace, and he succeeded in obtaining solutions of various problems relating to a globe completely covered with water to a depth either uniform throughout, or at any rate variable only with latitude. His work has been extended by Kelvin, G. Darwin, and Hough. For an excellent summary, reference may be made to Lamb’s ‘Hydrodynamics,’ which includes also important original additions to the theory. But it must not be overlooked that a theory which supposes the globe to be completely covered with water has very little relation to our actual tides. Indeed, in practice, tidal prediction borrows nothing from Laplace’s theory, unless it be to look for tidal periods corresponding with those of the generating forces. And this correspondence, although perhaps first brought into prominence in connection with Laplace’s theory, is a general mechanical principle, not limited to hydrodynamics. If the theory of terrestrial tides is to advance, it can only be by discarding the imaginary globe completely covered with water and considering examples more nearly related to the facts, as was done in some degree by Young and Airy in their treatment of tides in canals. It is true that we are unlikely to obtain in this way more than very rough indications, but even such are at present lacking. I am told that opinions differ on so fundamental a question as whether the Atlantic tides are generated in the Atlantic or are derived from the Southern Ocean. Probably both sources contribute; but a better judgment, based on some sort of discussion on a priori principles, does not appear hopeless. In this connection, it is interesting to observe that a comparison of spring and neap tides shows that the moon is more effective relatively to the sun than would be expected from the ratio of the generating forces. This indicates some approach to synchronism with a natural free oscillation. That the approach is closest in the case of the moon indicates that free period is longer than those of the actual lunar and solar tides.