TIDE, a regular periodic oscillation to which the surface of the sea at any place is subject. The oscillation takes place about twice a day, the periodic time being, on an average, about 12 hours and 26 minutes. Consequently if high tide occurs at noon one day, it will occur next day some 50 minutes later. This is pre cisely the interval of time which elapses between two successive meridian pas sages of the moon; and that there must be some connection between the tides and our satellite was early recognized by astronomers. The explanation, however, was lacking till Newton proved them to be a necessary conseauence of the law of gravitation. The phenomenon of the tide is, indeed, a case of perturbations, of exactly the same nature as the irregu larities which the action of the sun pre duces on the motions of the moon. If we compare the attraction of the moon on a particle of the earth's surface with the attraction exerted on the earth as a whole, we readily see that, accord ing as the particle is on the nearer or further side of the earth, the former at traction is greater or less than the lat ter; and it is to this difference of attrac tion, to which the waters yield, that the whole phenomenon of tide is due. The nearer waters are driven toward the moon, the further waters away from it. If the earth were spherical and uniform ly covered with water, the tendency would be to make the water arrange itself in the form of a spheroid with the longer axis pointing toward the moon; and did the earth always present the same face to the moon, this would be rigorously the case.
Such is the equilibrium theory of tides, as originally given by Newton. It ac counts so far for the phenomena, such as the simultaneous existence of high water at places diametrically opposite, but does not even approximately correspond to the true state of affairs. Newton was fully aware of this, and indeed has given the solution of the problem on other and truer assumptions. If the hypothetical earth covered uniformly with water is rotating, so as to present each point of its surface successively to the moon, each particle of water will be moving with a certain momentum which will be suffer ing retardation or acceleration according to its position relatively to the moon. The longer diameter of the water ellip soid will consequently not point in the direction of the moon; and the result will be the formation of two diametrically opposite waves, flowing round the earth in a direction contrary to its rotation. This is the kinetic theory, which forms the basis of Laplace's theory of tides. It also fails in practical application, since the continuity of the surface waters on the earth is very much broken by the distribution of land.
More recently Young and Airy have approached the question as one of wave motion, basing their theory on the mo tion of waves in canals. Until com paratively recent times we have been regarding the moon as the sole tide producing agent, but it is evident that the sun must have a similar action, though not so marked because of its much greater distance. It was proved by
Newton that the disturbing forces exert ed by two bodies on the same particle are directly as their masses, and inversely as the cubes of their distances; hence the ratio of the disturbing force exerted by the sun to that exerted by the moon 7 : 16. The principal tidal wave is that caused by the moon, but on it must be superposed that due to the sun. When the sun and moon are in syzygy, at times of new and full moon, their tidal waves will be superposed crest on crest, and the effect will be what is called a spring tide.
When they are in quadrature, trough will coincide with crest, the lunar tide will be partially neutralized by the solar tide, and the result will be the so-called neap tide. The average spring tide will be to the average neap tide as 16 + 7 : 16 — 7 == 23 : 9.
Besides this effect in amplitude, an other effect is caused by this combination of tides, namely the priming and lagging of the tides. For when the two vertices do not coincide, the maximum of the re sultant tidal wave will be at a point intermediate to the vertices, so that the time of high water will be now in ad vance now behind the time it would have been had the moon been the sole agent. Not only, then, are the waters of the ocean subject to diurnal and semi-diurnal oscillations, but these are subject to a monthly, semi-monthly, and even annual variation, besides being more or less af fected by prevailing winds and coast configuration. The height of the tidal wave which circulates round the earth is not great—at most some 7 feet, a very small quantity compared to the size of our globe, In estuaries, bays, creeks, straits, etc., however, the difference be tween high and low water is much greater than this—as much as 50 feet in the Bay of Fundy, Nova Scotia. The explanation of such phenomena is to be found in the momentum with which the water is pushed forward by the ad vancing wave. In such a sea as the Mediterranean, which is all but cut off from communication with the great oceans, and which is itself not sufficiently extensive to be very perceptibly acted on by the sun and moon, the tides are very small, not exceeding a few inches.
The attempt to establish a complete theory from abstract principles has proved a failure; and the only true meth od by which to get an insight into the particular laws which govern tidal action at any given place is continued observa tion. By means of Lord Kelvin's tide gauge a graphical representation of the tidal oscillation at any place can be easily obtained; and by harmonic analysis of the curve, the constituent factors may be easily discovered, and the comparative effects of their several causes estimated.
One efficient cause in retarding tides hao not been mentioned, namely, fluid fric tion, which, as first noticed by Kant, must act as a continual brake to the earth in its rotation; and this gradual slackening in the earth's speed of rota tion must go on till the day is of the same length as the lunar month, when matters will be as required in the equilibrium theory given above.