"The first person who clearly pointed out the accepted cause of the tides and showed its agreement with the effects, was Sir Isaac Newton. He discovered a relationship between the moon and the tides, and by the application of his new principles of geometry, the attraction was made clear.
"The ocean, it is well known, covers more than one half the globe; and this large body of water is found to be in continual motion, ebbing and flowing alternately, without the least intermission. For instance, if the tide is now at high water mark, in any port or harbour which lies open to the ocean, it will presently subside, and flow regularly back for about six hours, when it will be found at low water mark. After this it will again gradually advance for six hours; and then recede in the same time to its former situation, rising and falling alternately twice a day, or in the space of about twenty-four hours. The interval between its ebb and flow is not precisely six hours, for there is a little difference in each tide; so that the time of high water does not always happen at the same hour, but is about three quarters of an hour later each day, for about thirty days, when it again recurs as before. For example, it is high water to-day at noon, it will be low water at eleven minutes after six in the evening; and, consequently, after two changes more, the time of high water the next day will be at about three quarters of an hour after noon; the day following it will be at about half an hour after one, the day following that at a quarter past two, and so on for thirty days; when it will again be found to be high water at noon, as on the day the observation was first made. This exactly answers to the motion of the moon which rises every day about three quarters of an hour later than upon the preceding one, and by moving in this manner round the earth, completes her revolution in about thirty days, and then begins to rise again at the same time as before.
"To make the matter still plainer; suppose, at a certain place, it is high water at three o'clock in the afternoon, upon the day of the new moon; the following day it will be high water at three quarters of an hour after three; the day after that at half an hour past four; and so on till the next new moon, when it will again be high water exactly at three o'clock, as before. By observing the tides continually at the same place, they will always be found to follow the same rule; the time of high water, upon the day of every new moon, being exactly at the same hour, and three-quarters of an hour later every succeeding day.
"The change of the tides is in such exact conformity with the motion of the moon that, independently of mathematical calculations, a thoughtful person would certainly be induced to look to her as their cause.
Fig. 68. Theory of the tides
"The waters at Z, on the side of the earth, A, B, C, D, E, F, G, H, next the moon M, ([Fig. 68]) are more attracted by the moon than the central parts of the earth, O, and the central parts are more attracted by her than the waters on the opposite side of the earth at n; and therefore the distance between the earth's centre and the waters on its surface under and opposite to the moon will be increased. Let there be three bodies at H, O, and D; if they are all equally attracted by the body M, they will all move equally fast toward it, their mutual distance from each other continuing the same. If the attraction of M is unequal, then that body which is most strongly attracted will move most quickly and will increase its distance from the other body. M will attract H more strongly than does O, by which the distance between H and O will be increased, and a spectator on O 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 O and D will be increased; and a spectator on O, not perceiving his own motion, will see D receding farther from him towards N; all effects and appearances being the same, whether D recedes from O, or O from D.
"Suppose now there is a number of bodies, as A, B, C, E, F, G, H, placed round O, so as to form a flexible or fluid ring; then, as the whole is attracted toward 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 near to O. Hence, the fluid ring will form itself into an ellipse Z, n, L, N, whose longer axis n, O, Z, produced will pass through M, and its shorter axis B, O, F, will terminate in B and F. Let the ring be filled with fluid particles, so as to form a sphere round O; 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 is the moon, O the earth's centre, A, B, C, D, E, F, G, H, the sea covering the earth's surface, it is evident, by the above reasoning, that whilst the earth by its gravity falls toward the moon, the water directly below 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; whilst the water at B and F is depressed, and falls below the former level. Hence as the earth turns round its 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.
"That this doctrine may be still more clearly understood, let it be considered that, although the earth's diameter bears a considerable proportion to the distance of the earth from the moon, yet this diameter is almost nothing when compared to the distance of the earth from the sun. The difference of the sun's attraction, therefore, on the sides of the earth under and opposite to him, will be much less than the difference of the moon's attraction on the sides of the earth under and opposite to her; and, for this reason, the moon must raise the tides much higher than they can be raised by the sun. The effect of the sun's influence, in this case, is nearly three times less than that of the moon. The action of the sun alone would, therefore, be sufficient to produce a flow and ebb of the sea; but the elevations and depressions caused by this means would be about three times less than those produced by the moon.