It is also observ'd, that cæteris paribus, the Æquinoctial Spring Tides in March and September, or near them, are the Highest, and the Neap Tides the lowest; which proceeds from the greater Agitations of the Waters, when the fluid Spheroid revolves about a great Circle of the Earth, than when it turns about in a lesser Circle; it being plain that if the Moon were constituted in the Pole, and there stood, that the Spheroid would have a fix'd Position, and that it would be always high Water under the Poles, and low Water every where under the Æquinoctial: And therefore the nearer the Moon approaches the Poles, the less is the agitation of the Ocean, which is of all the greatest, when the Moon is in the Æquinoctial, or farthest distant from the Poles. Whence the Sun and Moon, being either conjoined or opposite in the Æquinoctial, produce the greatest Spring Tides; and the subsequent Neap Tides, being produc'd by the Tropical Moon in the Quarters, are always the least Tides; whereas in June and December, the Spring Tides are made by the Tropical Sun and Moon, and therefore less vigorous; and the Neap Tides by the Æquinoctial Moon, which therefore are the stronger: Hence it happens, that the difference between the Spring and Neap Tides in these Months, is much less considerable than in March and September. And the reason why the very highest Spring Tides are found to be rather before the Vernal and after the Autumnal Equinox, viz. in February and October, than precisely upon them, is, because the Sun is nearer the Earth in the Winter Months, and so comes to have a greater effect in producing the Tides.
Hitherto we have consider'd such Affections of the Tides as are Universal, without relation to particular Cases; what follows from the differing Latitudes of places, will be easily understood by the following Fig. (Vide Fig. 2. Plate 1.)
Let ApEP be the Earth cover'd over with very deep Waters, C its Center, P, p, its Poles, AE the Æquinoctial, F, f, the parallel of Latitude of a Place, D, d, another Parallel at equal distance on the other side of the Æquinoctial, H, h, the two Points where the Moon is vertical, and let K, k, be the great Circle, wherein the Moon appears Horizontal. It is evident, that a Spheroid describ'd upon Hh, and Kk, shall nearly represent the Figure of the Sea, and Cf, CD, CF, Cd, shall be the heighths of the Sea in the places f, D, F, d, in all which it is High-water: And seeing that in twelve Hours time, by the diurnal Rotation of the Earth, the Point F is transferr'd to f, and d to D: The height of the Sea CF will be that of the High-water when the Moon is present, and Cf that of the other High-water, when the Moon is under the Earth: Which in the case of this Figure is less than the former CF. And in the opposite Parallel Dd, the contrary happens. The Rising of the Water being always alternately greater and less in each place, when it is produc'd by the Moon declining sensibly from the Æquinoctial; that being the greatest of the two High-waters in each diurnal Revolution of the Moon, wherein she approaches nearest either to the Zenith or Nadir of the place: Whence it is, that the Moon in the Northern Signs, in this part of the World, makes the greatest Tides when above the Earth, and in Southern Signs, when under the Earth; the Effect being always the greatest where the Moon is farthest from the Horizon, either above or below it. And this alternate Increase and Decrease of the Tides has been observ'd to hold true on the Coast of England, at Bristol by Captain Sturmy, and at Plymouth by Mr. Colepresse.
But the Motions hitherto mentioned are somewhat alter'd by the Libration of the Water, whereby, though the Action of the Luminaries should cease, the Flux and Reflux of the Sea would for some time continue: This Conservation of the impress'd Motion diminishes the differences that otherwise would be between two consequent Tides, and is the reason why the highest Spring-Tides are not precisely on the New and Full Moons, nor the Neaps on the Quarters; but generally they are the third Tides after them, and sometimes later.
All these things would regularly come to pass, if the whole Earth were cover'd with Sea very deep; but by reason of the shoalness of some places, and the narrowness of the Streights, by which the Tides are in many cases propagated, there arises a great diversity in the Effect, and not to be accounted for, without an exact Knowledge of all the Circumstances of the Places, as of the Position of the Land, and the Breadth and Depth of the Channels by which the Tide flows; for a very slow and imperceptible Motion of the whole Body of the Water, where it is (for Example) 2 Miles deep, will suffice to raise its Surface 10 or 12 Feet in a Tides time; whereas, if the same quantity of Water were to be convey'd up a Channel of 40 Fathoms deep, it would require a very great Stream to effect it, in so large Inlets as are the Channel of England, and the German Ocean; whence the Tide is found to set strongest in those places where the Sea grows narrowest; the same quantity of Water being to pass through a smaller Passage: This is most evident in the Streights, between Portland and Cape de Hague in Normandy, where the Tide runs like a Sluce; and would be yet more between Dover and Calais, if the Tide coming about the Island from the North did not check it. And this force being once impress'd upon the Water, continues to carry it above the level of the ordinary height in the Ocean, particularly where the Water meets a direct Obstacle, as it is at St. Malo's; and where it enters into a long Channel, which running far into the Land, grows very streight at its Extremity; as it is in the Severn-Sea at Chepstow and Bristol.
This shoalness of the Sea, and the intercurrent Continents are the reason, that in the open Ocean the time of High water is not at the Moons appulse to the Meridian, but always some Hours after it; as it is observ'd upon all the West Coast of Europe and Africa, from Ireland to the Cape of Good Hope: In all which a S. W. Moon makes High-water, and the same is reported to be on the West side of America. But it would be endless to account all the particular Solutions, which are easie Corollaries of this Hypothesis; as why the Lakes, such as the Caspian Sea, and Mediterranean Seas, such as the Black Sea, the Streights and Baltick, have no sensible Tides: For Lakes having no Communication with the Ocean, can neither increase nor diminish their Water, whereby to rise and fall; and Seas that communicate by such narrow Inlets, and are of so immense an Extent, cannot in a few Hours time receive or empty Water enough to raise or sink their Surface any thing sensibly.
Lastly, to demonstrate the Excellency of this Doctrine, the Example of the Tides in the Port of Tunking in China, which are so extraordinary, and differing from all others we have yet heard of, may suffice. In this Port there is but one Flood and Ebb in 24 Hours; and twice in each Month, viz. when the Moon is near the Æquinoctial there is no Tide at all, but the Water is stagnant; but with the Moons Declination there begins a Tide, which is greatest when she is in the Tropical Signs: Only with this difference, that when the Moon is to the Northward of the Æquinoctial, it Flows when she is above the Earth, and Ebbs when she is under, so as to make High-water at Moons-setting, and Low-water at Moons-rising: But on the contrary, the Moon being to the Southward, makes High-water at rising, and Low-water at setting; it Ebbing all the time she is above the Horizon. As may be seen more at large in the Philosophical Transactions, Numb. 162.
The Cause of this odd Appearance is propos'd by Mr. Newton, to be from the concurrence of two Tides; the one propagated in six Hours out of the great South-Sea along the Coast of China; the other out of the Indian-Sea, from between the Islands in twelve Hours, along the Coast of Malacca and Cambodia. The one of these Tides, being produc'd in North Latitude, is, as has been said, greater, when the Moon being to the North of the Equator is above the Earth, and less when she is under the Earth. The other of them, which is propagated from the Indian Sea, being raised in South-Latitude, is greater when the Moon declining to the South, is above the Earth, and less when she is under the Earth: So that of these Tides alternately greater and lesser, there comes always successively two of the greater and two of the lesser together every Day; and the High-water falls always between the times of the arrival of the two greater Floods; and the Low-water between the arrival of the two lesser Floods. And the Moon coming to the Æquinoctial, and the alternate Floods becoming equal, the Tide ceases, and the Water stagnates: But when she has pass'd to the other side of the Equator, those Floods which in the former Order were the least, now becoming the greatest, that That before was the time of High-water, now becomes the Low-water, and the Converse. So that the whole appearance of these strange Tides, is without any forcing naturally deduc'd from these Principles, and is a great Argument of the Certainty of the whole Theory.