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Correspondence between the Tides and Phases of the Moon shown by Kepler.-Erroneous popular Notion of the Moon's Influence.-Actual Manner in which the Moon operates.-Influence of the Sun. -Combined Action of the Sun and Moon.-Spring Tides.-Counter-action of the Sun and Moon.-Neap Tides.-Priming and Lagging of the Tides.-Discussions at the British Association.-Whewell's Researches.-Effect of Continents and Islands on the Tides.-General Progress of the Great Tidal Wave.-Velocity of the Tidal Wave.-Range of the Tide.



THE phenomena of the tides of the ocean are too remarkable and important to the social and commercial interests of mankind, not to have attracted notice at an early period in the progress of knowledge. The intervals between the epochs of high and low water everywhere corresponding with the intervals between the passage of the moon over the meridian above and below the horizon, suggested naturally the physical connexion between these two effects, and indicated the probability of the cause of the tides being found in the motion of the moon.

KEPLER developed this idea, and demonstrated the close connexion of these phenomena; but it was not until the theory of GRAVITATION was established by Newton, and its laws fully developed, that all the circumstances of the tides were clearly explained, and shown incontestably to depend on the influence of the sun and moon.

There are few subjects in physical science about which there prevail more erroneous notions among those who are but a little informed, than with respect to the tides. A common idea is, that the attraction of the moon draws the waters of the earth toward that side of the globe on which the moon happens to be placed, and that consequently they are heaped up on that side, so that the oceans and seas acquire there a greater depth than elsewhere; and thus it is attempted to be established that high water will take place under, or nearly under, the moon. But this neither corresponds with the fact, nor, if it did, would it explain it. High water is not produced merely under the moon, but is equally produced upon those parts most removed from the moon. Suppose a meridian of the earth so selected, that, if it were continued beyond the earth, its plane would pass through the moon; then we find that, subject to certain modifications, a great tidal wave, or what is called high water, will be formed on both sides of this meridian; that is to say, on the side next the moon, on the side remote from the moon. As the moon moves in her monthly course { round the earth, these two great tidal waves follow her. They are, of


course, separated from each other by half the circumference of the globe. As the globe revolves with its diurnal motion upon its axis, every part of its surface passes successively under these tidal waves; and at all such parts as they pass under them, there is the phenomenon of high water. Hence it is that in all places there are two tides daily, having an interval of about twelve hours between them. Now if the common notion of the cause of the tides were well founded, there would be only one tide daily; viz., that which would take place when the moon is at or near the meridian.

That the moon's attraction upon the earth simply considered would not explain the tides, is easily shown. Let us suppose that the whole mass of matter on the earth, including the waters which partially cover it, were attracted equally by the moon; they would then be equally drawn toward that body, and no reason would exist why they should be heaped up under the moon; for if they were drawn with the same force as that with which the solid globe of the earth under them is drawn, there would be no reason for supposing that the waters would have a greater tendency to collect toward the moon than the solid bottom of the ocean on which they rest. In short, the whole mass of the earth, solid and fluid, being drawn with the same force, would equally tend toward the moon; and its parts, whether solid or fluid, would preserve among themselves the same relative position as if they were not attracted at all.

When we observe, however, in a mass composed of various particles of matter, that the relative arrangement of these particles is disturbed, some being driven in certain directions more than others, the inference is, that the component parts of such a mass must be placed under the operation of different forces; those which tend more than others in a certain direction being driven with a proportionally greater force. Such is, in fact, the case with the earth, placed under the attraction of the moon. NEWTON showed that the law of gravitation is such, that its attraction increases as the distance of the attracted object diminishes, and diminishes as the distance of the attracted object increases. The exact proportion of this change of energy of the attractive force, is technically expressed by stating that it is the inverse proportion of the square of the distance; the meaning of which is, that the attraction which any body like the moon would exercise at any proposed distance, is four times that which it would exercise at twice the distance; nine times that which it would exert at three times the distance; one fourth of that which it would exercise at half the distance, and one ninth of that which it would exercise at one third the distance, and so on. Thus we have an arithmetical rule, by which we can with certainty and precision say how the attraction of the moon will vary with any change of its distance from the attracted object. Let us see how this will be brought to bear upon the explanation of the effect of the moon's attraction upon the earth.

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Let A, B, C, D, E, F, G, H, represent the globe of the earth, and, to simplify the explanation, let us first suppose the entire surface of the globe to be covered with water. Let M, the moon, be placed at the distance K L from the nearest point of the surface of the earth. Now it will be very apparent that the various points of the earth's surface are at different distances from the moon, M. A and G are more remote than H; B F still more remote; C and E more distant again, and D more remote than all. The attraction which the moon exercises at H is, therefore, greater than that which it exercises at A and G, and still greater than that which it produces at B and F; and the attraction which it exercises at D is least of all. Now this attraction equally affects matter in every state and condition. It affects the particles of fluid as well as solid matter, but there is this difference between these effects; that where it acts upon solid matter, the component parts of which are at different distances from it, and therefore

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