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Updated: May 3, 2025


This is one of the remarkable facts which can be deduced from a prolonged study of the tides. The demonstration of the law of the tide-producing force is of a mathematical character, and I do not intend in these lectures to enter into mathematical calculations.

We have here taken an oval to represent the shape into which the water is supposed to be forced or drawn by the tidal action of the tide-producing body. This may possibly be a correct representation of what would occur on an ideal globe entirely covered with a frictionless ocean.

She is the most effective of all Tugs; and now that we understand the convertibility and conservation of force, we may be able to use her Tide-producing powers through the agency of electricity for mechanical purposes. Is the moon inhabited? It seems to me that the entire absence of atmosphere and water forbids the supposition at least of any form of life with which we are acquainted.

For instance, if the two bodies were brought within half their original distance of each other, the relative size of each body, as viewed from the other, will be doubled; and what we have called the leverage of the tide-producing ability will be increased twofold.

There is, however, a simple line of reasoning which, though it falls far short of actual demonstration, may yet suffice to give a plausible reason for the law. The tides really owe their origin to the fact that the tide-producing agent operates more powerfully on those parts of the tide-exhibiting body which are near to it, than on the more distant portions of the same.

Of the previous history of these appulsing suns the theory gives us no account; they are simply supposed to arrive within what may be called an effective tide-producing distance, and then the drama begins. Tides always go in couples; if there is a tide on one side of a globe there will be a corresponding tide on the other side.

On the other hand, the moon's diameter being much less than that of the earth, the efficiency of a tide-producing body in its action on the moon would be less than that of the same body at the same distance in its action on the earth; but the diminution of the tides from this cause would be not so great as their increase from the former cause, and therefore the net result would be to exhibit much greater tides on the moon than on the earth.

This apparent paradox will disappear when we enunciate the law according to which the efficiency of a tide-producing agent is to be estimated. This law is somewhat different from the familiar form in which the law of gravitation is expressed. The gravitation between two distant masses is to be measured by multiplying these masses together, and dividing the product by the square of the distance.

The nearer the two bodies are together, the larger proportionally will be the differences in the distances of its various parts from the tide-producing body; and on this account the leverage, so to speak, of the action by which the tides are produced is increased.

The law for expressing the efficiency of a tide-producing agent varies not according to the inverse square, but according to the inverse cube of the distance. This difference in the expression of the law will suffice to account for the superiority of the moon as a tide-producer over the sun.

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