Discovery of the Longitude (which at Sea is only practicable this way) may at length be brought to light, to the great Honour of your Majesty, and Advantage of your Subjects.

All the surprising Phænomena of the Flux and Reflux of the Sea, are in like manner shewn to proceed from the same Principle; which I design more largely to insist on, since the Matter of Fact is in this Case much better known to your Majesty than in the foregoing.

If the Earth were alone, that is to say, not affected by the Actions of the Sun and Moon, it is not to be doubted, but the Ocean, being equally press'd by the force of Gravity towards the Center, would continue in a perfect Stagnation, always at the same height, without either Ebbing or Flowing; but it being here demonstrated, that the Sun and Moon have a like Principle of Gravitation towards their Centers, and that the Earth is within the Activity of their Attractions, it will plainly follow, that the Equality of the pressure of Gravity towards the Center will thereby be disturb'd; and though the smallness of these Forces, in respect of the Gravitation towards the Earth's Center, renders them altogether imperceptible by any Experiments we can devise, yet the Ocean being fluid and yielding to the least force, by its rising shews where it is less press'd, and where it is more press'd by its sinking.

Now if we suppose the force of the Moon's Attaction to decrease as the Square of the Distance from its Center increases (as in the Earth and other Cœlestial Bodies) we shall find, that where the Moon is perpendicularly either above or below the Horizon, either in Zenith or Nadir, there the force of Gravity is most of all diminished, and consequently that there the Ocean must necessarily swell by the coming in of the Water from those parts where the Pressure is greatest, viz. in those places where the Moon is near the Horizon: But that this may be the better understood, I thought it needful to add the following Figure, (Vide Fig. 1. Plate 1.) where M is the Moon, E the Earth, C its Center, and Z the place where the Moon is in the Zenith, N where in the Nadir.

Now by the Hypothesis it is evident, that the Water in Z, being nearer, is more drawn by the Moon, than the Center of the Earth C, and that again more than the Water in N; wherefore the Water in Z hath a tendency towards the Moon, contrary to that of Gravity, being equal to the excess of the Gravitation in Z, above that in C: And in the other case, the Water in N, tending less towards the Moon than the Center C, will be less pressed, by as much as is the difference of the Gravitation towards the Moon in C and N. This rightly understood, it follows plainly, that the Sea, which otherwise would be Spherical, upon the Pressure of the Moon, must form it self into a Spheroidal or Oval Figure, whose longest Diameter is where the Moon is vertical, and shortest where she is in the Horizon; and that the Moon shifting her Position as she turns round the Earth once a Day, this Oval of Water shifts with her, occasioning thereby the two Floods and Ebbs observable in each 25 Hours.

And this may suffice, as to the general Cause of the Tides; it remains now to shew how naturally this Motion accounts for all the Particulars that have been observ'd about them; so that there can be no room left to doubt, but that this is the true cause thereof.

The Spring Tides upon the New and Full Moons, and Neap Tides on the Quarters, are occasion'd by the attractive Force of the Sun in the New and Full, conspiring with the Attraction of the Moon, and producing a Tide by their united Forces: Whereas in the Quarters, the Sun raises the Water where the Moon depresses it, and the contrary; so as the Tides are made only by the difference of their Attractions. That the force of the Sun is no greater in this Case, proceeds from the very small Proportion the Semi-diameter of the Earth bears to the vast distance of the Sun.

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