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; whilst the parts at B and F, being nearly at the same distance from M as O is, these parts will not recede from one another; but rather, by the oblique attraction of M, they will approach nearer to O. Hence, the fluid ring will form itself into an ellipse ZIBLnKFNZ, whose longer Axis nOZ produced will pass through M, and it’s shorter Axis BOF will terminate in B and F. Let the ring be filled with bodies, so as to form a flexible or fluid sphere round O; then, as the whole moves toward M, the fluid sphere being lengthned at Z and n, will assume an oblong or oval form. If M is the Moon, O the Earth’s center, ABCDEFGH the Sea covering the Earth’s surface, ’tis evident by the above reasoning, that whilst the Earth by it’s gravity falls toward the Moon, the Water directly below her at B will swell and rise gradually towards her: also, the Water at D will recede from the center [strictly speaking, the center recedes from D] and rise on the opposite side of the Earth: whilst the Water at B and F is depressed, and falls below the former level. Hence, as the Earth turns round it’s Axis from the Moon to the Moon again in 243⁄4 hours, there will be two tides of flood and two of ebb in that time, as we find by experience.
Fig. II.
298. As this explanation of the ebbing and flowing 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 towards it, and therefore cannot fall contrary ways at the same time: or if the Earth is constantly falling towards the Moon, they must come together at last. To remove this difficulty, let it be considered, that it is not the center of the Earth that describes the annual orbit round the Sun; but the [[63]]common center of gravity of the Earth and Moon together: and that whilst 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 towards the Moon from a tangent to the Circle it describes round the said common center of gravity. Let M be the Moon, TW part of the Moon’s Orbit, and C the center of gravity of the Earth and Moon: whilst the Moon goes round her Orbit, the center of the Earth describes the Circle ged round C, to which Circle gak is a tangent: and therefore, when the Moon has gone from M to a little past W, the Earth has moved from g to e; and in that time has fallen towards the Moon, from the tangent at a to e; and so 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 it’s distance from the Moon, it is next to nothing when compared with the distance of 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 Tides are not highest when the Moon is on the Meridian.
Fig. I.
300. On this Theory so far as we have explained it, the Tides ought to be highest directly under and opposite to the Moon; that is, when the Moon is due north and south. But we find, that in open Seas, where the water flows freely, the Moon M is generally past the north and south Meridian as at p when it is high water at Z and at n. The reason is obvious; for though the Moon’s attraction was 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 move farther than otherwise it could have done. And as experience shews, that the day is hotter about three in the afternoon, than when the Sun is on the Meridian, because of the increment made to the heat already imparted.
Nor always answer to her being at the same distance from it.
301. The Tides answer not always to the same distance of the Moon from the Meridian at the same places; but are variously affected by the action of the Sun, which brings them on sooner when the Moon is in her first and third Quarters, and keeps 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.