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Plate fore the distance between the Earth's centre and
the waters on its surface under and opposite to the Moon will be increased. For, let there be three bodies at H, O, and D: if they be all equally attracted by the body M, they will all move equally fast toward it, their mutual distances from each other continuing the same.
If the attraction of M be unequal, then that body which is most strongly attracted will move fastest, and this will increase its distance from the other body. Therefore, by the law of gravitation, M will attract H more strongly than it does O, by which the distance between H and O will be increased: and a spectator on will perceive H rising higher toward Z. In like manner, O being more strongly attracted than D, it will move farther toward M than D does : consequently, the distance between 0 and D will be increased; and a spectator on 0, not perceiving his own motion, will see D receding farther from him toward n : all effects and appearances being the same, whether D recedes from O, or O from D.
297. Suppose now there is a number of bodies, as A, B, C, D, E, F, G, H, placed round O, so as to form a flexible or fluid ring: then, as the whole is attracted towards M, the parts at H and D will have their distance from O increased; while the parts at B and F, being nearly at the same distance from Mas O is, these parts will not recede from one another; but rather, by the oblique attraction of M, they will approach nearer to 0. Hence, the fluid ring will form itself into an ellipse ZI B Ln K F N Z, whose longer axis n o 2 produced will pass through M, and its shorter axis BOF will terminate in B and F. Let the ring be filled with fluid particles, so as to form a sphere round 0; then, as the whole moves toward M, the fluid sphere being lengthened at Z and n, will assume an oblong or oval form. If M be the Moon, the Earth's centre, ABCDEFGH the sea covering the
Earth's surface, it is evident, by the above reason. Plate ing, that while the Earth by its gravity falls toward the Moon, the water directly below her at B will swell and rise gradually toward her: also the water at D will recede from the centre (strictly speaking, the centre recedes from D), and rise on the opposite side of the Earth : while the water at B and is depressed, and falls below the former level. Hence, as the Earth turns round its axis from the Moon to the Moon again, in 24 hours, there will be two tides of food and two of ebb in that time, as we find by experience.
298. As this explanation of the ebbing and lowing of the sea, is deduced from the Earth's constantly falling toward the Moon by the power of gravity, some may find a difficulty in conceiving how this is possible, when the Moon is full, or in opposition to the Sun; since the Earth revolves about the Sun, and must continually fall toward it, and therefore cannot fall contrary ways at the same time: or, if the Earth beconstantly falling toward the Moon, they must come together at last. To remove this difficulty, let it be considered, that it is not the centre of the Earth that describes the annual orbit round the Sun, but the* common centre of gravity of the Earth and Moon together: and that while the Earth is moving round the Sun, it also describes a circle round that centre of gravity; going as many times round it in one revolution about the Sun as there are lunations or courses of the Moon round the Earth in a year: and therefore, the Earth is constantly falling toward the Moon from a tangent to the circle it describes round the said common centre of gravity. Let M be the Moon, TW part of
* This centre is as much nearer the Earth's centre than the Moon's, as the Earth is heavier, or contains a greater quantity of matter than the Moon, namely, about 40 times. If both bodies were suspended on it, they would hang in equilibrio. So that dividing 240,000 miles, the Moon's distance from the Earth's centre, by 40, the excess of the Earth's weight above the Moon's, the quotient will be 6000 miles, which is the distance of the common centre of gravity of the Earth and Moon from the Earth's centre.
Plate the Moon's orbit, and C the centre of gravity of
the Earth and Moon; while the Moon goes round Fig. 11. her orbit, the centre of the Earth describes the cir.
cle dg e round C, to which circle ga k is a tangent: and therefore, when the Moon has gone from M to a little past W, the Earth has moved from g to c; and in that time has fallen toward the Moon, from the tangent at a to e; and so on, round the whole circle.
299. The Sun's influence in raising the tides is but small in comparison of the Moon's; for though the Earth's diameter bears a considerable proportion to its distance from the Moon, it is next to nothing when compared to its distance from the Sun. And therefore, the difference of the Sun's attraction on the sides of the Earth under and opposite to him, is much less than the difference of the Moon's attraction on the sides of the Earth under and opposite to her: and therefore the Moon must raise the tides much higher than they can be raised
by the Sun. Why the 300. On this theory, so far as we have explained tides are not high
it, the tides ought to be highest directly under and est when opposite to the Moon; that is, when the Moon is the Moon due north and south. But we find, that in open is on the meridian. seas, where the water flow sfreely, the Moon M is
generally past the north and south meridian, as at p, Fig. I.
when it is high water at Z and at n. The reason is obvious; for though the Moon's attraction were to cease altogether when she was past the meridian, yet the motion of ascent communicated to the water before that time would make it continue to rise for some time after; much more must it do so when the attraction is only diminished: as a little impulse given to a moving ball will cause it still to move farther than otherwise it could have done. And as ex. perience shews, that the day is hotter about three in
ways an. swer to
the afternoon than when the Sun is on the meridian, Plet TE because of the increase inade to the heat already imparted.
301. The tides answer not always to the same Nor al. distance of the Moon from the meridian at the same places; but are variously affected by the action of her being the Sun, which brings them on sooner when the at the
same dis. Moon is in her first and third quarters, and keeps tance from them back later when she is in her second and fourth: because, in the former case, the tide raised by the Sun alone would be earlier than the tide raised by the Moon; and in the latter case later.
302. The Moon goes round the Earth in an elliptic orbit, and therefore, in every lunar month, she approaches nearer to the Earth than her mean distance, and recedes farther from it. When she is near- Spring est, she attracts strongest, and so raises the tides and neap most; the contrary happens when she is farthest, because of her weaker attraction. When both luminaries are in the equator, and the Moon in perigeo, or at her least distance from the Earth, she raises the tides highest of all, especially at her conjunction and opposition ; both because the equatorial parts have the greatest centrifugal force from their describing the largest circle, and from the concurring actions of the Sun and Moon. At the change, the attractive forces of the Sun and Moon being united, they diminish the gravity of the waters under the Moon, and their gravity on the opposite side is diminished by means of a greater centrifugal force. At the full, Fig. VI while the Moon raises the tide under and opposite to her, the Sun, acting in the same line, raises the tide under and opposite to him; whence their conjoint effect is the same as at the change; and in both cases, occasion what we call the spring tides. But at the quarters the Sun's action on the waters at O and H diminishes the effect of the Moon's action on the waters at Z and N; so that they rise a little under and opposite to the Sun at () and H, and fall as
much under and opposite to the Moon at Z and N; making what we call the neap tides, because the Sun and Moon then act cross-wise to each other. But, strictly speaking, these tides happen not till some time after; because in this, as in other cases, $ 300, the actions do not produce the greastet effect when
they are at the strongest, but some time afterward. Not great
303. The Sun being nearer the Earth in winter est at the than in summer, $ 205, is of course nearer to it in es, and February and October, than in March and Septemwhy. ber; and therefore the greatest tides happen not till
some time after the autumnal equinox, and return a little before the vernal.
The sea being thus put in motion, would contiwould not nue to ebb and flow for several times, even though immedi. atelycease
the Sun and Moon were annihilated, or their influupon the ence should cease : as if a bason of water were agi. tion of the tated, the water would continue to move for some Sun and time after the bason was left to stand still. Or like
a pendulum, which, having been put in motion by the hand, continues to make several vibrations without any new impulse.
The lunar 304. When the Moon is in the equator, the tides day, what are equally high in both parts of the lunar day, or The tides
time of the Moon's revolving from the meridian to unequal the meridian again, which is 24 hours 50 minutes. heights in the same
But as the Moon declines from the equator toward day, and either pole, the tides are alternately higher and lower why.
at places having north or south latitude. For one of the highest elevations, which is that under the Moon, follows her toward the pole to which sheis nearest, and the other declines toward the opposite pole; each elevation describing parallels as far distant from the equator, on opposite sides, as the Moon declines from it to either side; and consequently, the parallels described by these elevations of the water are twice as many degrees from one another, as the Moon is from the equator; increasing their distance as the Moon