"We propose... to enter at some length into the mathematical theories, and the experimental observations, applying to the two subjects of Tides and Waves of water. But we do not intend to treat them with the same extension. We shall give the various theories of Tides in detail sufficient to enable the reader to understand the present state of the science... and we shall advert to the principal observations which throw light either on the ordinary phænomena of tides, or on the extraordinary deviations that occur in peculiar circumstances. In thus treating the Tides, it will be necessary for us to enter largely into the theory of Waves. We shall take advantage of this circumstance for the introduction several propositions, not applying to the theory Tides, but elucidating some of the ordinary observations upon small Waves. But these investigations will be limited to that class which is most closely connected with tides, namely, that in which similar waves follow each other in a continuous series, or in which the same mathematical process may be used as when similar waves follow each other. In this class will be included nearly all the phænomena of waves produced by natural causes, and therefore possessing general interest. But it will not include the waves of discontinuous nature produced by the sudden action of arbitrary causes, which have been the subject of several remarkable mathematical memoirs, but which possess no interest for the general reader."