The theory, of which a brief outline has just been stated, applies to what are called negative waves by a mere change in the sign of the coefficients of the trigonometrical factors. These waves are depressions below the general surface of the water, and, like the others, they have a progressive motion. Such waves, for example, are those which are formed by the paddles of a steam-boat.
All the theories concur in showing that the difference between the diurnal and semidiurnal tides is great in middle latitudes, and small at the equator and poles ; and in this respect they are at variance with the actual phenomena. From observations it is found that this differ ence is as great at certain places near the equator as near the latitude of either tropic : it has also been found to be great at Petropaulowski and in Norfolk Sound, while in Europe it is small. It has been attempted to account for the latter circumstance by assuming that each title-wave in this part of the world is composed of two, which flow towards the same place in opposite directions at intervals of about twelve hours. It is supposed that the semidiurnal waves of these tides, being in the same state or phase, produce together a like effect, but that the diurnal waves are iu opposite states ; so that the superior high tide of one wave coinciding with the inferior high tide of the other, they together produce a mean height of water differing but little from that of the united semidiurnal tides.
We cannot here enter into the details of the investigations relating to the theories of the oscillations of water, or the discussion of the experiments which have been made on waves in arthicial canals, the methods of making observations ou tides, and accounts of the par ticular tides in rivers and seas ; but the experimental researches of Mr. Scott Russell have made so important an accession to our know ledge of waves, in its relation to practical as well as theoretical science, that this article would be defective without a summary of their results. The details of his experiments will be found chiefly in the Trans actions of the Royal Society of Edinburgh,' vol. xiv., and in the Report of the Seventh Meeting of the British Association for the Advancement of Science.' At the time when Mr. Russell's hydrodynamical researches were commenced, the celestial mechanics of the tides, as we have seen in the preceding portion of this article, had been analysed aud explained in a manner satisfactory both to astronomers and mathematical physicists, but a great variety of considerations relating to the pro pagation of the tides along the surface of the globe—constituting their terrestrial mechanism—remained without explanation. The solar
and lunar attraction having generated the tides, exercise little or no influence over the subsequent propagation of them. It is not until 50 or 60 hours after their creation that the tides reach our shores, having moved in the interval in every possible direction, and with every velocity from 100 down to 10 miles an hour. " This moving elevation of fluid," in the words of the committee on waves, appointed by the British Association in 1836, " may be conveniently designated a ware, aud its history will be the history of the tidal rave ; but to confer upon it the name of wave does not imply that its laws are those which belong to any other similar elevation with which we are acquainted. It was necessary to investigate the nature of this tido wave—to examine the hydrodynamical mechanism by which it is transferred from one place to another—to determine the laws which regulate its form and its velocity—to ascertain if any relations exist between the form and dimensions of its bed, and its own form and rate of transference. These and many similar points," including also the effect of the wind upon the tide-save, "were still unknown." Laplace, Lubbock, and Whewell had severally pointed out how much was required to be known, and the last had shown that a great number of curious facts in fluid motion had been established by the tide researches, some of which had been discussed and others instituted and pursued by himself, of which he expressed a hope that the theory of hydrodynamics would one day be able to render a reason.
Such having been the condition of science on the subject when Mr. Russell began his inquiries, the following is a condensed statement, but nearly in the words of the Committee, of the " General Results" he obtained, and which have eventually been found to possess much more than the value which had been anticipated.