Thus the tides in our ports are owing to an impulse from the waters of the Antarctic seas raised by the action of the sun and moon. No doubt a similar action raised that tide in the North Polar Ocean which Dr. Kane saw rolling on the northern coast of Greenland in 82° N. latitude, but which, in the present state of the globe, is imprisoned by bars of ice and ice-bound lands.
The tidal wave extends to the bottom of the ocean, and moves uniformly and with great speed in very deep water, variably and slow in shallow water; the time of propagation depends upon the depth of the sea, as well as on the nature and form of the coasts. It varies inversely as the square of the depth—a law which theoretically affords the means of ascertaining the proportionate depth of the sea in different parts. It is one of the great constants of nature, and is to fluids what the pendulum is to solids—a connecting link between time and force.
For example: the tidal wave moves across the Southern Ocean with the velocity of 1000 miles an hour, and in the Atlantic it is scarcely less on account of the deep trough which runs through the centre of that ocean; but the sea is so shallow on the British coast that it takes more time to come from Aberdeen to London than to travel over an arc of 120°, between 60° S. lat. and 60° N. lat.
In deep water the tidal wave is merely a rise and fall of the surface; the water does not advance, though the wave does. Indeed, if so heavy a body as water were to move at the rate of 1000 miles an hour, it would cause universal destruction, since in the most violent hurricanes the velocity of the wind is little more than 100 miles an hour. Besides, it is evident that no ship could either sail or steam against it. When the water is shallow, however, there is a motion of translation in the water along with the tide.
In the deep ocean the undulating motion consists of two distinct things—an advancing form and a molecular movement. The motion of each particle of water is in an ellipse lying wholly in the vertical plane; so that, after the momentary displacement during the passage of the wave, they return to their places again. The resistance of the sea-bed is insensible in deep water; but when the tidal wave, which extends to the very bottom of the ocean, comes into shallow water with diminished velocity, the particles of water moving in vertical ellipses strike the bottom, and by reaction the wave rises higher; and that being continually repeated, as the form moves on the wave rises higher and higher, bends more and more forward, till at last it loses its equilibrium, and then both form and water roll to the shore, and the elliptical trajectories of the particles, which in deep water were vertical, incline more and more, till at length they become horizontal. The distance from the shore at which the water begins to be translated depends upon the depth, the nature of the coast, and the form of the shore. Mr. Scott Russell has demonstrated that in shallow water the velocity of the wave is equal to that which a heavy body falling freely by its gravity would acquire in descending through half the depth of the fluid.