LEMM A.

The Place of the Moon in the Zodiac being known, from an Ephemeris, or by Calculation, or Aftronomical Obfervation, and also it's Latitude, and the Hour of the Day; to find, on the Terreftrial Globe, what Place the Moon will be vertical to at the given Hour, and to fhew all the Places that the Moon will pass over, one after another, that Day.

THIS Problem is of great Use for obferving the Flux and Reflux of the Sea. You will find the Method of folving it in Chapter xxx. Propofition 14. where it is more commodiously explained. However the more knowing Reader may anticipate it here, or learn it aforehand from the Rules there delivered.

PROPOSITION XVI.

The Tides are highest in thofe Places over which the Moon is vertical, unless fome of the Obftacles abovementioned in Propofition 14 hinder; but the further any Place is from that, the lefs (cæteris paribus) is the Flux and Reflux.

BECAUSE thofe Places are more preffed, and the fwelling of the Sea is greater, over which the Moon fqueezeth the celeftial Matter, whereby greater Tides are produced: but, where the incumbent Matter is lefs fqueezed, and other Caufes confpire, the Alteration will be lefs.

PRO

PROPOSITION XVII.

The Altitude of the Tides are divers in the fame Place at different Times, and they are high and low, according as the Moon is further from or nearer to the Zenith of the Place.

SINCE the Moon every Day changes her Place in the Ecliptic, fhe will be vertical now to one Place, and then to another, and confequently varies her Distance from the Zenith of any particular Place. Which being granted, it follows, as a Corollary of the laft Propofition, that the Tides in any one Place are conftantly altering, whether their Variation be fenfible, or infenfible.

PROPOSITION XVIII.

The greatest fwelling of the Ocean, or High-Water, ought to be in that Place when the Moon is in the Meridian Circle (above or below); but in divers Places it is High-Water when the Moon is otherwise pofited.

SINCE the Moon, in the Meridian, is nearer any Place than when he is in the Horizon, (because the Hypotenuife of any right-angled Triangle is longer than the Perpendicular) it follows (by Propofition 16, of this Chapter) that then it ought to be High-Water in that Place (where she is full South). And when she is full North, or in the lower Part of the Meridian Circle, it ought to be alfo High-Water in the fame Place, because, tho' fhe be not there, yet the oppofite Part of the Vortex of the Earth is straitned, and hath the fame Effect, as if the Body of the Moon itself were prefent.

BUT

BUT there are many Places and Shores where it is not High-Water precifely at the Time of the Moon's fouthing or northing in the Meridian Circle, (as the Philofophers of the former Age thought) but perhaps a little before, or after, she makes her appulfe to the Meridian, viz. when she approacheth a Vortex fomething distant from it, East or West. Neither doth a full Tide always happen when the Moon is in the fame Azimuth; but it is very often High-Water, efpecially at the New and Full Moon, a little before the conftant Time, or before the Moon approaches that Azimuth. At London it is High-Tide when the Moon is three Hours from the Meridian, or South-Weft, and North-Eaft (k). On the Shore of China, in the Harbour of Maccao, a Portuguese Sailor thus ftated the Time of High-Water. The Elevation of the Pole, or the Latitude of the Place, is 22 degr. 20 min. In the Year 1584 on the nineteenth Day of September it was Full Moon, and the fame Day, it was High-Water half an Hour, or three quarters, paft Eight in the Morning; fo that the Moon was then three Hours and a quarter diftant from the Meridian; hence the Azimuth, or Point fhe was then in, may be found by a Problem in Chapter xxx.

IN the Year 1585, February the third, which was alfo the third from the New Moon, it was obferved to be High-Tide a little after twelve; and therefore at the New Moon, which was February the first, it was full Sea about forty Minutes after Ten.

HENCE the Azimuth the Moon was then in may be found.

(k) See the Note (m) below. VOL. I.

S

IN

IN the Year 1585, February the fixteenth, it was obferved to be High-Water, at Full Moon, almost at Noon, viz. at half an Hour paft Eleven,

IN the Year 1585, June the fecond, which was the fourth Day after the New Moon, it was High-Tide exactly at twelve, therefore at the Conjunction it was High-Tide at nine in the Fore

noon.

THE fame Sailor adds, that the Time of High and Low-Water doth not agree with the Time that is computed from the Motion of the Moon, except for five Days before and after the New Moon. But there is fome Ambiguity in thefe Words, and others following, which we have therefore omitted. But the Caufe of this Variation is, that the Sea rifes nine Hours in the Port of Maccao, and ebbs only three, as is obferved in the next Propofition.

HERE follow fome Obfervations made by a Dutch Sailor of the Time of High-Water, on the Days of the New and Full Moon, at different Places.

AT twelve o'Clock (on the New and Full Moon Days) it is High-Water along the Shore of Flanders, at Enckhuysen in Holland, at Hoorn, at Emden in Eaft Friefland, at the Mouth of the River Elbe, at the Mouth of the Eyder, at the Islands of Jutland, at Dover in England, &c.

AT forty five Minutes paft twelve, at Flushing in Zealand.

AT half an Hour paft one, at the weftern Shore of the Isle of Wight, at Calais, at the Mouth the River Thames in England, along the Shores of Zealand, at the Mouth of the River Schelde, in the Meufe, at [Gorcum].

AT three o'Clock, at Amfterdam, Rotterdam, Dort, and Newcastle in England, before the Flemish Sand-Banks, at Armentier in Flanders, at the

I

Mouth

Mouth of the River Garonne, along the South Shore of England, on the Coaft of France, Gascoigne, Bifcay, Gallicia, Portugal, and Spain; on the western Shore of Ireland, all the way to Shetland.

AT a quarter before four in the Afternoon, at Roban in France, in the Maefe, at Rochelle in France, in the River Garonne, in the Bays upon the Shore of Spain, Portugal, Gallicia, in the Bays on the Southern Shore of Bretagne in France, on the Shore of Gascoigne, on the western Shore of Ireland.

AT half an Hour past four, from the Texel to the fouthern Shore of Ireland.

AT a quarter past five, in all the Ports on the South of Ireland, at Plymouth in England, and at other fouthern Places between that and Wales.

AT fix o'clock in the Morning and Evening, at Hamburgh in the Elbe, at Bremen, on the Eaft fide of the Texel, at Antwerp, in the English Chanel as far as the Scilly Islands.

AT a quarter before feven in the Evening, at Falmouth, and in Bristol Chanel, at St Nicolas and Podeffamke, as far as Weymouth and Hartpool.

AT half an Hour past seven at the Road in the Texel, at Kilduyna, in the middle of the Chanel, befide Plymouth, and as far as the Foreland of Lizard-Point.

AT a quarter paft eight in the Evening, about the Isle of Wight, at the Weft fide of the Flie Island.

AT nine o'clock, at the Mouth of the River Eems in Friefland, on the Eaft fide of the Flie Ifland, along the Shores of Friefland, and on the eastern Shore of the Isle of Wight.

AT half an Hour past ten, at the Mouth of the River Thames, on the Shore of Normandy and Picardy.