Let M, (fig. 4.) represent the moon as before ; 0, the centre of the earth ; and Z and N, those parts of the surface which are the nearest to the moon, and the farthest from her. Then, because the point Z is nearer to the moon than any other part of the hemisphere H Z R, it is evident that the waters will be more strongly attracted by her, about that point, than at others which are more re mote ; and since this attraction acts in a contrary direction to that of the earth, the waters in all parts, from H R to Z, must have their gravity or tendency to wards the centre 0 diminished : and as this tendency is the least at the point Z, they will consequently stand higher there than in any other part of the hemisphere. Agkin, in the opposite hemisphere H N R, al hough the attraction of the moon con spires with that of the earth, yet, as it is known to decrease in proportion as the squares of the distances increase, it is plain that the joint influence of the two forces, taken together, will be less at the point N, on the side opposite to the moon, than at those parts which lie nearer to H It; and consequently, as the gravity of the waters, or their tendency towards .he centre, is also the least at that point, they will be more elevated there than in any other part of the hemisphere ; so that the attractive force of the moon will evident ly raise the waters, both at that point of the surface which is nearest to her, and at that which is farthest from her, at the same time, as was to be shown.
Following this system, then, it is to be observed, that at any port or harbour which lies open to the ocean, the action of the moon will tend to elevate the waters there, when she is on the meridi an of that place, whether it be above the horizon or below it. But the water can not he raised at one place, without flow ing from and being depressed at another; and these elevations and depressions will obviously be the greatest at opposite points of the earth's surface. When the moon raises the waters at Z and N, they will be depressed at H and It; and when they are raised by her at H and R, they will be depressed at Z and N. And as the moon passes over the meridian, and is in the horizon twice every day, there will therefore be two tides of flood, and two of ebb, in that time, at the interval of about six hours and eleven minutes each; which is exactly conformable to theory and experience.
From what has been hitherto said, it may be supposed, that the moon is the sole agent concerned in producing the tides. But it will be necessary to observe, before we quit the subject, that the influ ence of the sun would also produce a similar effect, though in a much less de gree, than from his superior magnitude we should naturally be led to imagine. For it is not the entire actions of those bodies upon the whole globe of the earth that is here to he considered, but only the inequalities of those actions upon dif ferent parts of it. The whole attractive
force of the sun is far superior to that of the moon ; but as his distance from the earth is nearly 400 times greater, the forces, with which he acts upon different parts of it, will be much nearer to equali ty than those of the moon ; and conse quently will have a less effect in produc ing any change of its figure. For it is to be observed, that, if all parts of the earth were equally attracted, they would sutler but little change in their mutual si tuations. That this doctrine may be still more clearly understood, let it be consi dered, that though the earth's diameter hears a considerable proportion to the dis tance of the earth from the moon, yet this diameter is almost nothing, when com pared to the distance of the earth from the sun. The difference of the sun's at traction, 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. Newton calculated the effect of the sun's influence in this case, and found that it is about three times less titan that of the moon. The action of the sun alone would therefore be sufficient to produce a flux and reflux of the sea ; but the ele vations and depressions occasioned by this means would be about three times less than those produced by the moon. The tides, then, are not the sole produc tion of the moon, but of the joint forces of the sun and moon together : or, pro perly speaking, there are two tides, a solar one and a lunar one ; which have a joint or opposite effect, according to the situa tion of the bodies which produce them. When the actions of the sun and moon conspire together, as at the time of new and full moon, the flux and reflux become more considerable ; and in this case they are called the spring tides. But when one tends to elevate the waters, whilst the other depresses them, as at themoon's first and third quarters, the effect will be exactly the contrary ; the flux and reflux, instead of being augmented, as before, will now be diminished ; and they are then called the neap tides. But as this is a matter of some importance, it may be Worth while to enter into a more minute explanation of it.
For this purpose, let S (fig. 5) repre sent the sun, MINH the earth, and F C the moon, at her full and change. Then, because the sun, S, and the moon, C, are nearly in the same right line with the centre of the earth, 0, their actions will conspire together, and raise the water about the zenith, Z, or the point immediately under them, to a greater height than if only one of these forces acted alone. But it has VOL. If.