Recreations in Astronomy / With Directions for Practical Experiments and Telescopic Work

by Henry White Warren

The figure of the earth, even on the ocean, is irregular, in consequence of the greater preponderance of land—and hence greater density—in the northern hemisphere. These irregularities are often very perplexing in making exact geodetic measurements. The tendency of matter to fly from the centre by reason of revolution causes the equatorial diameter to be twenty-six, miles longer than the polar one. By this force the Mississippi River is enabled to run up a hill nearly three miles high at a very rapid rate. Its mouth is that distance farther from the centre of the earth than its source, when but for this rotation both points would be equally distant.

If the water became more dense, or if the world were to revolve faster, the oceans would rush to the equator, burying the tallest mountains and leaving polar regions bare. If the water should become lighter in an infinitesimal degree, or the world rotate more slowly, the poles would be submerged and the equator become an arid waste. No balance, turning to 1/1000 of a grain, is more delicate than the poise of forces on the world. Laplace has given us proof that the period of the earth's axial rotation has not changed 1/100 of a second of time in two thousand years.

Tides.

But there is an outside influence that is constantly acting upon the earth, and to which it constantly responds. Two hundred and forty thousand miles from the earth is the moon, having 1/81 the mass of the world. Its attractive influence on the earth causes the movable and nearer portions to hurry away from the more stable and distant, and heap themselves up on that part of the earth nearest the moon. Gravitation is inversely as the square of the distance; hence the water on the surface of the earth is attracted more than the body of the earth, some parts of which are eight thousand miles farther off; hence the water rises on the side next the moon. But the earth, as a whole, is nearer the moon than the water on the opposite side, and being drawn more strongly, is taken away from the water, leaving it heaped up also on the side opposite to the moon.

A subsidiary cause of tides is found in the revolution of the earth and moon about their common centre of gravity. Revolution about an axis through the centre of a sphere enlarges the equator by centrifugal force. Revolution about an axis touching the surface of a flexible globe converts it into an egg-shaped body, with the longer axis perpendicular to the axis of revolution. In Fig. 56 the point of revolution is seen at the centre of gravity at G; hence, in the revolution of earth and moon as one, a strong centrifugal force is caused at D, and a less one at C. This gives greater height to the tides than the attraction of the moon alone could produce.

Fig. 56.

If the earth had no axial revolution, the attractive point where the tide rises would be carried around the earth once in twenty-seven days by the moon's revolution about the earth. But since the earth revolves on its axis, it presents a new section to the moon's attraction every hour. If the moon were stationary, that would bring two high tides in exactly twenty-four hours; but as the moon goes forward, we need nearly twenty-five hours for two tides.

The attractive influence of the sun also gives us a tide four-tenths as great as that of the moon. When these two influences of the sun and moon combine, as they do, in conjunction—when both bodies are on one side of the earth; or in opposition, sun and moon being on opposite sides of the earth—we have spring or increased tides. When the moon is in its first or third quarter, i. e., when a line from the moon to the earth makes a right angle with one from the sun to the earth, these influences antagonize one another, and we have the neap or low tides.