tude of Places. Vertices of its longer Axis defcribing nearly, the Parallel on the Earth's on the Lati Surface, which the Moon, because of the diurnal Motion, feems to defcribe, and the other a Parallel as far on the other Side of the Equator. The whole Sea is divided into two oppofite hemifpheroidal Floods, one on the North Side of the Equator, the other on the South Side of it, which come by Turns to the Meridian of each Place after an Interval of 12 Hours. Now the Vertex of the hemifpheroidal Flood which moves on the fame Side of the Equator with any Place, will come nearer to it than the Vertex of the oppofite hemifpheroidal Flood which moves in a Parallel on the other Side of the Equator; and therefore the Tides in all Places without the Equator, will be alternately greater and lefs; the greatest Tide when the Declination of the Moon is on the fame Side of the Equator with the Place, will happen about three Hours after the Appulfe of the Moon to the Meridian above the Horizon, and the leaft Tide about three Hours after the Appulfe of the Moon to the Meridian below the Horizon, the Height of the Tide in the first Case, being expreffed by a Semidiameter of the elliptic Section of the Spheroid nearer the tranfverse Axe than in the latter Cafe, and confequently is greater; and the Tide, when the Moon changes her Declination, which was the greatest will be changed into the leaft, for then the hemifpheroidal Flood which is oppofite to the Moon, moves on the fame Side of the Equator with the Place, and therefore its Vertex comes nearer to it than the Vertex of the hemifpheroidal Flood under it. And the greatest Difference of thofe Tides will be in the Solftices, because the Vertices of the two hemifpheroidal Floods in that Cafe defcribe the oppofite Tropics, which are the fartheft from each other of any two parallel Circles they can defcribe. Thus it is found by Observation, that the Evening Tides in the Summer exceed the Morning Tides, and the Morning Tides in Winter exceed the Evening Tides; and we learn (Pro. 24. B. 3.) that at Plymouth, according to the Obfervations of Coleprefs this Difference amounts to one Foot, and at Briftol, according to thofe of Sturmy to 15 Inches. Newton (de Mundi Syftemate, page 58.) found, that the Height of the Tides de- The Height creases in each Place, in the duplicate Ratio of the Cofine of the La- decreases in titude of this Place. Now we have feen, that at the Equator, they the duplidecrease in the duplicate Ratio of the Cofine of the Declination of cate Ratio each Luminary; therefore in all Places without the Equator, half the of the Sum of the Heights of the Tides Morning and Evening, that is, their Latitude. mean Height decreafes nearly in the fame Ratio. Hence the Diminution of the Tides arifing from the Latitude of Places, and the Declination of the Luminaries may be determined. XXV. of the Tides of the cofine of the Tides The Height of the Tides depend likewife upon the Extent of the The Height Sea in which they are produced, whether the Seas be entirely fepa- depend on the Exten rated from the Ocean, or communicate with it by a narrow Channel; for of the Seas. if the Seas be extended from Eaft to Weft 90 Degrees, the Tides will be the fame as if they came from the Ocean, becaufe this Extent is fufficient that the Sun and Moon may thereby produce on the Waters of the Sea their greatest and leaft Effect; but if thofe Seas be fo narrow, that each of their Parts are raised and depreffed with the fame Force, there can be no fenfible Effect, for the Water cannot rife in any one Place without finking in another; hence it is, that in the Baltick-Sea, the Black Sea, the Cafpian-Sea, and other Seas or Lakes of lefs Extent, there is neither Flood nor Ebb. The Tides diterranean are scarce fenfible. XXVI. In the Mediterranean-Sea, which is extended from Eaft to Weft only in the Me- 60 Degrees, the Flood and Ebb are scarce ferfible, and Euler has given a Method for determining their Quantity. Those fmall Tides are ftill rendered lefs by the Winds and Currents which are very great in this Sea; hence it is, that in most of thofe Ports, there are scarce any regular Tides, except in thofe of the Adriatick Sea, which having a greater Depth, the Elevation of the Waters are rendered more sensible; hence it is, that the Venetians were the firft who made Obfervations on the Tides of the Mediterranean. Caufes which influence the Tides that are indeter minable. XXVII. Besides the affignable Causes which serve to account for the Phenomena of the Tides, there are feveral others which produce Irregularities in thofe Motions which cannot be reduced to any Law, because they depend on Circumstances which are peculiar to each Place; fuch are the Shores on which the Waters flow, the Straits, the different Depths of the Sea, their Extent, the Bays, the Winds, &c. fo many Causes which alter the Motion of the Waters, and confequently retard, increafe, or diminish the Tides, and are not reducible to Calculation. Hence it is, that in fome Places, the Flood falls out the third Hour after the Culmination of the Moon, and in other Places the 12th Hour; and in general, the greater the Tides are, the later they happen, because the Causes which retard them act fo much longer. If the Tides were very fmall, they would immediately follow the Culmination of the Moon, because the Action of the Obftacles which retard them would be rendered almost infenfible; this is partly the Reason why the great Tides which happen about the new and full Moon, follow later the Appulfe of the Moon to the Meridian, than those which happen about the Quadratures; the latter being less than the former. XXVIII. Velocity of Euler relates that at St. Malos, at the Time of the Syfigies, it is the Waters of the Sea. High-Water the fixth Hour after the Appulfe of the Moon to the Meridian, and the Retardation increases more and more until at Dun kerk and Offend, it happens at Midnight. From this Retardation the Velocity of the Waters may be determined, and Euler concludes from thofe, and other Obfervations, that they move at the Rate of eight Miles an Hour; but it is eafy to perceive, that this Determination cannot be general. XXIX. The Tides are always greater towards the Coafts than in the open The Tides Sea, and that for several Reasons; first the Waters beat against the are greater towards the Shores, and by the Re-action, are raised to a greater Height. Secondly, Coafts, and they come with the Velocity they had in the Ocean where their Depth why. was very confiderable, and they come in great Quantity, confequently meet with great Resistance whilft they flow on the Shores; from which Circumftance, their Height is still encreased. Finally, when they pass over Shoals, and run through Straights, their Height is greatly encreafed, because being beat back by the Shores, they return with the Force they had acquired from the Effort they had made to overflow them. Hence it is, that at Bristol, the Waters are raised to fo great a Height at the Time of the Syfigies, for the Shores on this Coaft, are full of Windings and Sand-Banks, against which the Waters beat with great Violence, and are much impeded in their Motion. XXX. of feveral Thofe Principles ferve to account for the extraordinary great Tides Explication which are observed in fome Places, as at Plymouth, Mount St. Michael, Phenomena the Town of Avranches in Normandy, &c. where Newton fays, the Wa- of the ters rife to 40 or 50. Feet, and fome Times higher. It may happen, that the Tide propagated from the Ocean, arrives at the fame Port by different Ways, and that it paffes quicker through fome of thofe Ways than through the others; in this Cafe, the Tide will appear to be divided into feveral Tides, fucceeding one another, having very different Motions, and no ways refembling the ordinary Tides. Let us fuppofe, for Example, that the Tides propagated from the Ocean, arrive at the fame Port by two different Ways, one of which is a readier and easier Paffage, fo that a Tide arrives at this Port through one of those Inlets at the third Hour after the Appulfe of the Moon to the Meridian, and another through the other Inlet, fix Hours after, at the 9th Hour of the Moon. When the Moon is in the Equator, the Morning and Evening Tides in the Ocean being equal, in the Space of 24 Hours, there will arrive four equal Tides to this Port, but one flowing in as the other ebbs out, the Water must stagnate. When the Moon declines from the Equator, the 'l'ides in the Ocean are alternately greater and lefs, confequently two greater and two leffer Tides would arrive at this Port by Turns, in the Space of 24 Hours. The two greatest Tides would make the Water acquire its greatcft Height at a mean Time Tides. At the En- Rivers the betwixt them, and the two leffer would make it fall lowest, at a mean Time between those two leaft Tides, and the Water would acquire at a mean Time betwixt its greatest and leaft Height, a mean Height; thus in the Space of 24 Hours, the Waters would rife, not twice, as usual, but once only to their greatest Height, and fall lowest only once. If the Moon declines towards the Pole elevated above the Horizon, its greatett Height would happen the third, the fixth, or the 9th Hour after the Appulse of the Moon to the Meridian; and if the Moon declines towards the oppofite Pole, the Flood would be changed into Ebb. XXXI. All which happens at Batham in the Kingdom of Tonquin, in the Latitude of 20d. 50m. North. The Day in which the Moon paffes the Equator, the Waters have no Motion of flux and reflux: as the Moon removes from the Equator, the Waters rife and fall once a Day, and come to their greatest Height when the Moon is near the Tropics; with this Difference, that when the Moon declines towards the North-Pole, the Waters flow in whilft the Moon is above the Horizon, and ebb out whilft fhe is under the Horizon, fo that it is High-Water at the setting of the Moon, and Low-Water at her rifing. But when the Moon declines towards the South-Pole, it is High-Water at the rifing, and Low-Water at the fetting of the Moon; the Waters ebbing out during the whole Time the Moon is above the Horizon. The Tide arrives at this Port by two Inlets, one from the Chinese Ocean, by a readier and fhorter Paffage between the Ifland of Leuconia and the Coast of Canton, and the other from the Indian Ocean, between the Coaft of Cochin-China and the Ifland of Borneo, by a longer and lefs. readier Paffage; but the Waters arrive fooner by the readiest and shortest Paffage; hence they arrive from the Chinese Ocean in fix Hours, and from the Indian Ocean in 12 Hours, confequently the Tide arriving the third and ninth Hour after the Appulfe of the Moon to the Meridian, there result the above Phenomena. XXXII. At the Entrance of Rivers, there is a Difference in the Time of the Tides flowing in and ebbing out, arifing from the Current of the River, which running into the Sea, retards its Motion of flux, and accelerates its longer than Motion of reflux, confequently makes the Ebb last longer than the Flood, the Flood, and why. which is confirmed by Experience; for Sturmius relates, that above Bristol, at the Entrance of the River Oundal, the Tide is five Hours flowing in, and feven Hours ebbing out. Hence it is alfo, that all other Circumstances being alike, the greatest Floods arrive later at the Mouths of Rivers than elsewhere. XXXIII. diurnal the Earth. It has been found, as has been already mentioned, that the Tides At the Poles depend on the Declination of the Luminaries, and the Latitude of the there is no Place; hence at the Poles there is no diurnal ebbing and flowing of the Tides but Waters of the Sea; for the Moon being at the fame Height above the fuch as Horizon during 24 Hours, cannot raise the Waters; but in thofe Re- the Revoludepend on gions, the Sea has a Motion of flux and reflux depending on the Revo- tion of the lution of the Moon about the Earth every Month; in confequence of Moon about which the Waters are at the lowest when the Moon is in the Equator, because she is then always in the Horizon with refpect to the Poles; and as the Moon declines either towards the North or South Pole, the Sea begins to ebb and flow, and when her Declination is greatest, the Waters are raised to their greatest Height at the Pole towards which the declines; and as this Elevation, which does not exceed ten Inches, is produced but by a very flow Motion, the Force of Inertia increases it very little, confequently is fcarce fenfible. XXXIV. But it is only at the there is no diurnal Poles that Tides, for in the Fri It is only at the Poles that the Waters have no diurnal Motion; in the Frigid-Zone, there is one Tide every Day instead of two, as in the Torid-Zone, and in our Temperate-Zones; and it is eafy to fhew, that this Paffage of two Tides to one, is not effected fuddenly, but like all other Effects of Nature, is produced gradually. For we have seen, that the Morning and Evening Tides in our Temperate-Zones are unequal, gid-Zone not only as to their Height, but also as to the Time of their Duration; there is one and why that the remoter the Place is from the Equator, the greater is this In- there are equality between the two Tides which immediately fucceed each other, not two as both as to their Height and the Time of their Duration, for the greatest Regions of Tide should last longer than the leaft; and notwithstanding which they the Earth. both cease in 12h. 24m. nearly; therefore, in those Regions where the Moon after her Appulse to the Meridian above or below the Horizon, returns to it in this Interval, the leaft Tide will entirely vanish, and there will remain but the greatest Tide, which alone will fill up the Interval of 12b. 24m. XXXV. in the other Moon pro The Force of the Sun and Moon are fufficient to produce the Tides, Why the but are incapable of producing any other fenfible Effects here below; Sun and for the Force (S) of the Sun in its mean Distance, being to the Force ducing the (G) of Gravity, as I to 12868200, and the Force (S) of the Sun being Tides, proto the Force (L) of the Moon, as 1 to 4,4815, by the Compofition of duce no Ratios LXS is to SXG, or the Force (L) of the Moon in her mean ible Effects Distance, is to the Force (G) of Gravity, as 4,4815 to 12868200, or here below. as 1 to 2871400. And fince S+L is to L as 5,4815 to 4,4815, S+L XL is to LXG or the Sum of the Forces (S+L) of the Sun and Moon other fenf |