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597. The tides are not uniform, either as to time or amount. They occur about 50 minutes later every day (as we shall explain hereafter), and sometimes rise much higher and sink much lower than the average. These extraordinary high and low tides are called, respectively, spring and neap tides.

598. The cause of the tides is the attraction of the Sun and Moon upon the water of the ocean. But for this foreign influence, as we may call it, the waters having found their proper level, would cease to heave and swell, as they now do, from ocean to ocean, and would remain calm and undisturbed, save by their own inhabitants and the winds of heaven, from age to age.

In this figure, the Earth is represented as surrounded by water, in a state of rest or equilibrium, as it would be were it not acted upon by the Sun and Moon.


599. To most minds, it would seem that the natural effect of the Moon's attraction would be to produce a single tide-wave on the side of the Earth toward the Moon. It is easy, therefore, for students to conceive how the Moon can produce one flood and one ebb tide in twenty four hours.

In this cut, the Moon is shown at a distance above the Earth, and ONE TIDE-WAVE. attracting the waters of the ocean, so as to produce a high tide at A. But as the moon makes her apparent westward revolution around the Earth but once a day, the simple rising of a flood tide on the side of the Earth toward the moon, would give give us but one flood and one ebb tide in twenty-four hours; whereas it is known that we have two of each.

"The tides," says Dr. Herschel, "are a subject on which many persons find a strange difficulty of conception. That the Moon by her attraction, should heap up the waters of the ocean under her, seems to many persons very natural. That the same cause should, at the same time, heap them up on the opposite side of the Earth (viz., at B in the figure), seems to many palpably absurd. Yet nothing is more true."



600. Instead of a single tide-wave upon the waters TWO TIDE-WAVES.


of the globe, directly under the Moon, it is found that on the side of the Earth directly opposite, there is another high tide; and that half-way between these two high tides are two low tides. These four tides, viz., two high and two low, traverse the ocean from east to west every day, which accounts for both a flood and an ebb tide every twelve hours.

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597. Are the tides uniform? What variation of time? As to amount? What are these extraordinary high and low tides called? 598. The cause of tides? How but for this influence? 599. What most obvious effect of the Moon's attraction? Substance of note? Remark of Dr. Herschel? 600. How many tide-waves are there on the globe, and how situated?

In this cut, we have a representation of the tide-waves as they actually exist, except that their height, as compared with the magnitude of the Earth, is vastly too great. It is designedly exaggerated, the better to illustrate the principle under consideration. While the Moon at A attracts the waters of the ocean, and produces a high tide at B, we see another high tide at C on the opposite side of the globe. At the same time it is low tide at D and E.

601. The principal cause of the tide-wave on the side of the Earth opposite the Moon is the difference of the Moon's attraction on different sides of the Earth.


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If the student well understands the subject of gravitation, he will easily perceive how a difference of attraction, as above described, would tend to produce an elongation of the huge drop of water called the Earth. The diameter of the Earth amounts to about 1th of the Moon's distance; so that, by the rule (558), the difference in her attraction on the side of the Earth toward her, and the opposite side, would be aboutth. The attraction being stronger at B (in the last cut) than at the Earth's center, and stronger at her center than at C, would tend to separate these three portions of the globe, giving the waters an elongated form, and producing two opposite tide-waves, as shown in the cut.

602. A secondary cause of the tide-wave on the side of the Earth opposite the Moon, is the revolution of the Earth around the common center of gravity between the Earth and Moon, thereby generating an increased centrifugal force on that side of the Earth.

The center of gravity between the Earth and Moon is the point where they would exactly balance each other, if connected by a rod, and poised upon a fulcrum.




This point which, according to Ferguson, is about 6000 miles from the Earth's center, is represented at A in the above, and also in the next cut.


The point A represents the center of gravity between the Earth and Moon; and as it is this point which traces the regular curve of the Earth's orbit, it is represented in the arc of that orbit, while the Earth's center is 6000 miles one side of it. Now, the law of gravitation requires that while both the Moon and Earth revolve around the Sun, they should also revolve around the common center of gravity between them, or around the point A. This would give the Earth a third revolution, in addition to that around the

601. State the principal cause of the wave opposite the Moon? Demonstrate by diagram. 602. What other cause operates with the one just stated to produce the tidewave opposite the Moon? What is the center of gravity between the Earth and the Moon? Where is it situated? Illustrate the operation of this secondary cause.

Sun and on her axis. The small circles show her path around the center of gravity, and the arrows her direction.

This motion of the Earth would slightly increase the centrifugal tendency at B, and thus help to raise the tide-wave opposite the Moon. But as this motion is slow, corresponding with the revolution of the Moon around the Earth, the centrifugal force could not be greatly augmented by such a cause.

603. As the Moon, which is the principal cause of the tides, is revolving eastward, and comes to the meridian later and later every night, so the tides are about 50 minutes later each successive day. This makes the interval between two successive high tides 12 hours and 25 minutes. Besides

this daily lagging with the Moon, the highest point of the tide-wave is found to be about 46° behind, or east of the Moon, so that high tide does not occur till about three hours after the Moon has crossed the meridian. The waters do not at once yield to the impulse of the Moon's attraction, but continue to rise after she has passed




In the cut, the Moon is on the meridian, but the highest point of the wave is at A, or 45° east of the meridian; and the corresponding wave on the opposite side at B is equally behind.

604. The time and character of the tides are also affected by winds, and by the situation of different places. Strong winds may either retard or hasten the tides, or may increase or diminish their height; and if a place is situated on a large bay, with but a narrow opening into the sea, the tide will be longer in rising, as the bay has to fill up through a narrow gate. Hence it is not usually high tide at New York till eight or nine hours after the Moon has passed the meridian.

605. As both the Sun and Moon are concerned in the production of tides, and yet are constantly changing their positions with respect to the earth and to each other, it follows that they sometimes act against each other, and measurably neutralize each other's influence; while at other times they combine their forces, and mutually assist each other. In the latter case, an unusually high tide occurs, called the Spring Tide. This happens both at new and full Moon.

603. What daily lagging of the tides? Interval between two successive high tides? What other lagging? Cause of this last? 604. What modification of the time and character of the tides? 605. Do the Sun and Moon always act together in attracting the waters? Why not? How affect each other's influence? Effect on the tides? What are Spring Tides? When do they occur? Illustrate by diagram the cause of spring tides, when the Sun and Moon are in conjunction.

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Here the Sun and Moon, being in conjunction, unite their forces to produce an extraordinary tide. The same effect follows when they are in opposition; so that we have two spring tides every month-namely, at new and full Moon.

If the tide-waves at A and B are one-third higher at the Moon's quadrature than usual, those of C and D will be one-third lower than usual.

606. When the Moon is in quadrature, and her influence is partly neutralized by the Sun, which now acts against her, the result is a very low tide, called Neap Tide.

The whole philosophy of spring and neap tides may be illustrated by the annexed diagram.

On the right side of the cut, the Sun and Moon are in conjunction, and unite to produce a spring tide.

At the first quarter, their attraction acts at right angles, and the Sun, instead of contributing to the lunar tide-waves, detracts from it to the amount of his own attractive force. The tendency to form a tide of his own, as represented in the figure, reduces the Moon's wave to the amount of one-third.

At the full Moon, she is in opposition to the Sun, and their joint attraction acting again in the same line, tends to elongate the fluid portion of the Earth, and a second spring tide is produced.

Finally, at the third quarter, the Sun and Moon act against each other again, and the second neap tide is the result. Thus we have two spring and two neap tides during every lunation-the former

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at the Moon's cyzygies, and the latter at her quadratures.










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607. Although the Sun attracts the Earth much more powerfully, as a whole, than the Moon does, still the Moon contributes more than the Sun to the production of tides. Their relative influence is as one to three. The nearness of the Moon makes

606. What are Neap Tides? Their cause? Illustrate entire philosophy by diagram. 607. Comparative influence of Sun and Moon in the production of tides? Why Moon's influence the greatest? Substance of note ? Demonstration?

the difference of her attraction on different sides of the Earth much greater than the difference of the Sun's attraction on different sides.

It must not be forgotten that the tides are the result not so much of the attraction of the Sun and Moon, as a whole, as of the difference in their attraction on different sides of the Earth, caused by a difference in the distances of the several parts. The attraction being inversely as the square of the distance (558), the influence of the Sun and Moon, respectively, must be in the ratio of the Earth's diameter to their distances. Now the difference in the distance of two sides of the Earth from the Moon is th of the Moon's distance; as 240,000+8,000=30; while the difference, as compared with the distance of the Sun, is only 7th, as 95,000,000+8,000=11,875.


608. The tides are subject to another periodic variation, caused by the declination of the Sun and Moon north and south of the equator. As the tendency of the tide-wave is to rise directly under the Sun and Moon, when they are in the south, as in winter, or in the north, as in summer, every alternate tide is higher than the intermediate one.

At the time of the equinoxes, the Sun being over the equator, and the Moon within 52° of it, the crest of the great tide-wave will be on the equator; but as the Sun and Moon decline south to A, one tide-wave forms in the south, as at B, and the opposite one in the north, as at

C. If the declination was north, as shown at D, the order of the tides would be reversed. The following diagram, if carefully studied, will more fully illustrate the subject of the alternate high and low tides, in high latitudes, in winter and summer:

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Let the line A A represent the plane of the ecliptic, and B B the equinoctial. On the 21st of June, the day tide-wave is north, and the evening wave south, so that the tide following about three hours after the Sun and Moon, will be higher than the intermediate one at 3 o'clock in the morning.

On the 23d of December, the Sun and Moon being over the southern tropic, the highest wave in the southern hemisphere will be about 8 o'clock P. M., and the lowest about 8 o'clock A.M.; while at the north, this order will be reversed. It is on this account that in high latitudes every alternate tide is higher than the intermediate ones; the evening tides in summer exceeding the morning tides, and the morning tides in winter exceeding those of evening.

609. All spring and neap tides are not alike as to their elevation and depression. As the distances of the Sun and Moon are

608. What other periodic variations mentioned? Explain cause, and illustrate. 609. Are all spring and neap tides alike? By what are they modified? Illustrate by diagram.

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