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Philofophers and learned Men as this. Some have thought the Earth and Sea to be a living Creature, which, by it's Respiration, causeth this ebbing and flowing. Others imagined that it proceeds, and is provoked, from a great Whirl-pool near Norway, which, for fix Hours, abforbs the Water, and afterwards difgorges it in the fame space of Time. Scaliger, and others, fuppofed that it is caused by the oppofite Shores, especially of America, whereby the general Motion of the Sea is obftructed and reverberated. But most Philofophers, who have observed the Harmony that these Tides have with the Moon, have given their Opinion, that they are entirely owing to the Influence of that Luminary. But the Queftion is, what is this Influence? To which they only anfwer, that it is an occult

Hence alfo both the Luminaries, placed in the Equinoctial at the Time of their Conjuntion or Oppofition, which happens near the Equinoxes in March, or September, produce the highest Tides in the whole Year.

Which Experience also confirms, because the Sun is a little nearer the Earth in the Winter than in the Summer; therefore the higheft Spring Tides happen a little before the Vernal Equinox, and a little after the Autumnal, viz. in February and October, rather than precifely upon the EquinoEtial Days.

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5. The librating Motion of the Waters, which are apt to retain the Motion impreffed upon them, and continue to move tho' the Actions of the Luminaries cease, make the greatest menftrual Spring Tides (explain'd

in Artic. 3.) not precisely on the New and Full Moons, but generally they are the third Tides after them.

6. Things would happen conftantly and regularly thus, if the whole Earth were covered with very deep Sea; but by reafon of great and fmall Islands which top the Tide, and the Streights between them, alfo the Shelves and Shallows along which the Tides are to be propagated, the Variety of this Phænomenon is almoft infinite, and scarcely to be explained by this Theory; but when juft Obfervations are diligently made, all these particular Caufes may be found out and known. See Newton's Prin. Math. Phil. Book 3. Prop. 24. Greg. Phyf. and Geometr. Aftron. Bock 4. Prop. 64, 65. alfo Halley's Differtation in Phil. Tranf. No 226.

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Jurin's Appendix.
Quality,

Quality, or Sympathy, whereby the Moon attracts all moist Bodies. But thefe are only Words, and fignify no more than that the Moon does it by fome means or other, but they do not know how': Which is the Thing we want.

DES Cartes explains it by his general Hypothefis thus: In the forementioned Figure of Propofition 9. let ABCD be the Vortex, with the Earth in it's Center, and which, with the Earth and Moon in it, is carried in a larger Vortex about the Sun. Let M be the Center of the first Vortex, EFGH the Earth, 1234 the Superficies of the Sea, which for plainnefs we will fuppofe to cover the whole Earth; and 5678 the Superficies of the Air furrounding the Sea. If therefore there were no Moon in the Vortex, the Point T, the Center of the Earth, would coincide with the Point M, the Center of the Vortex ; but fince the Moon is about B, the Center of the Earth must be between M and D; because, fince the celeftial Matter of this Vortex moves fomething swifter than the Earth or Moon, which is carried only with it, unless the Point T were a little further diftant from B than from D, the Prefence of the Moon would hinder it from moving fo freely between B and T, as between T and D; and feeing the Place of the Earth in the Vortex is not determined, but by the equal Force of the circumambient celeftial Matter, it is plain that it ought therefore to approach fomewhat towards D. And for the fame Reason, when the Moon fhall be in C, the Center of the Earth ought to be between M and A, fo that always the Earth may recede a little from the Moon. Moreover, fince we fuppofed the Moon to be about B, not only the Space between B and T, but also that between T and D, thro' both which the celeftial Matter flows, is made fome thing narrower; hence it follows, that the cele

ftial Matter floweth fafter there, and therefore preffeth more, both the Superficies of the Air at 6 and 8, and of the Water at 2 and 4, than if the Moon had not been in the Diameter of the Vortex BD. Now feeing the Air and Water are both Fluids, and eafily give way to the Preffure, they must be more depreffed about F and H, than they would be if the Moon were not in this Diameter BD; and alfo more elevated towards G and E, where both their Superficies bulge or are prominent. And further, because the Part of the Earth at F, under B, where the Sea is now lowest, in fix Hours Time will be at G, under C, where it is now highest, and after other fix Hours in H, under D, and so on: or rather, because the Moon is moving a little in the mean Time from B towards C, fo as to perform the whole Revolution ABCD in a Month, by which the part of the Earth that is now in F under the Moon's Body, will be in fix Hours, twelve Mi nutes Time, or thereabouts, a little further than G, in that Diameter of the Vortex, which is 90 Degr. diftant from the Place into which the Moon in the mean Time hath moved; therefore the Water will in that Time increase and be highest at F, and in other fix Hours, twelve Minutes, when the Moon is got beyond D, will fettle and be lowest there, &c. Hence it is plain, that the Water of the Sea must constantly ebb and flow in the fame Place, every twelve Hours, twenty four Minutes Time,

THIS is des Cartes's Demonftration, which is very ingeniously contrived to account both for the Tides that happen when the Moon is in the Me ridian of the Place, and thofe alfo that occur when fhe is in the oppofite Point of the Meridian Circle under the Horizon.

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SECT. IV. BUT according to what we obferved in the ninth Propofition, there are feveral Imperfections. in this Demonstration. As firit, it is a wonder that des Cartes did not confider, that, according to his Demonftration, the Water ought to ebb at 2 and 4, when the Moon approaches the Meridian B: and, on the contrary, to flow, when the Earth or Moon (viz. either of them) is removed fix Hours from each other; but this is contrary to Experience, for when the Moon approaches the Meridian of any Place, the Waters flow in that Place, and ebb, back again, at it's departure. But both des Cartes's Words and Figure fhow the contrary; fo that to take away the Abfurdity (and in des Cartes's Method) let us fuppofe the Vortex of the Earth ABCD, and the Waters 1234, to be interfperfed equally about the Center T without any Protuberance, and to revolve with the Earth and the celestial Matter between A B CD and 5678. Let us fuppofe again the Moon to happen into this Vortex at B, and therefore the Space TB to become narrower, and the Water at 2 to be preffed towards E by the celeftial Matter fqueezing thro' it.

THEN while the Water is expelled from 2 to E, I ask where the greateft fwelling will be, whether in the Place E, which is diftant a Quadrant from F (where the Moon is vertical), or in the Place next to F towards E? If you anfwer, the fwelling is greatest about the former Place E, I deny it, because it is contrary to Experience; but Experience fhews the latter to be true, and even Reason convinces us, that when the Moon is over the Place F, the Water will be forced from 2 towards 1, which happens because the greatest fwelling is about 2, not about 1, for here it will be leaft; hence the Places to the weftward have their Tides later, as we know by Experience. And Reafon and the Laws of Hydroftatics require this.""

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For if Water be poured in at 2, that it may flow towards E, there will be the greatest quantity of Water at 2, and a little lefs in the next Place, but least of all at E; and the fame Thing will happen if it be expelled or driven towards E But by the Circumrotation of the Earth, E comes into the Place of F, where at length there will be the greatest Protuberance at E, and the Water will be repelled towards H.

THEREFORE des Cartes's Figure and Demonftration is to be changed, that the fwelling may arife fomewhere about 2, viz. where the Moon is vertical. What more might be faid here we refer to our Treatife upon des Cartes's Phyfics,

PROPOSITION XII.

The general Motion of the Sea from East to West is Stronger, and the Tides are higher at New and Full Moon, than at the Quadratures.

THE Truth of this Propofition appears from Experience. For People that use the Sea testify, that at New and Full Moon, the Face of the Ocean is conftantly rough and troubled, but calm and quiet at the Quadratures. This is easily accounted for by the aforefaid Hypothefis; for when the Moon is at the New or Full, fhe is nearer the Earth than at any other Time of her Age, and is furtheft diftant in her Quadratures, as is fhewn by Aftronomers (g). But when the Moon is nearer the Earth, that is, when the Space BT is lefs, the celeftial Matter being hindered, or obftructed, preffes with greater force the Water from 2 towards 1. But happens o therwife in the Quadratures.

(g) This is falfe. See the Note (e) above.

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