THE

OF TIDE S.

HE Tides, or the Flux and Reflux of the Sea, is that regular Motion of the Waters by which they rise and fall at certain equal Intervals of Time.

The Doctrine of Tides remained in Obfcurity, till the immortal Sir Ifaac Newton explained it by his great Principle of Gravity and Attraction. For having demonftrated that there is a Principle in all Bodies within the Solar Syftem, by which they mutually attract each other, in Proportion to the Squares of their Distances, it follows, that those Parts of the Sea which are immediately under the Moon must be drawn towards it, and confequently whenever the Moon is nearly vertical, the Sea will be raised, which occafions the flowing of the Tide there.

By the Earth's diurnal Rotation from Weft to Eaft in 24 Hours, the Sun apparently revolves from East to West in the fame Time; fo by the fame Rotation, the Moon apparently revolves from Eaft to Weft in the Space of 24 Hours 49 Minutes, commonly called a Lunar Day, so as in that Time to return to the Meridian she set out at; and as the Sun apparently moves round the Earth in a Year, fo the Moon really moves round it in about 29 Days; confequently, if the Sun and the Moon are both upon the Meridian at any Time, it will be 29 Days and an Half before they are upon the fame Meridian again, or in Conjunction, and about Half that Time, viz. 14 Days 18 Hours before they are upon oppofite Meridians, or in Oppofition. Now, as the Sun attracts the Earth, though much less than the Moon, being at so vaft a Distance from it, yet when they are both upon the Meridian, either in Oppofition or Conjunction, that is, at Full and Change, their joint Attraction confpires to raise the Tides higher than when they act cross-ways. Hence the Tides are higher than ordinary twice every Month, and are called Spring Tides; but this does not happen till two or three Days after, when the Attractions of the Sun and Moon have been united some Time. But when the Sun and the Moon act cross-ways, or are 90° afunder, the Tides are leffened in Proportion to the Difference of their Powers of Attraction, and produce what we call Neap Tides, which happen foon after the first and laft Quarter of the Moon, when the Sun has leffened the Attraction of the Moon for fome Time.

The Moon being the principal Caufe of raifing the Tides, they are always found to follow her, and confequently muft always be fhifting from Weft to Eaft as the Moon does, fo that it is High, Water at any Place when the Moon is upon the Meridian of that Place at Full or Change, it will be about 49 Minutes later on the following Day, 1 Hour 38 Minutes later on the fecond Day, falling back 49 Minutes every 24 Hours, until the Moon comes to the oppofite Meridian; and then it will be High Water again. Thefe Tides regularly rife and fall twice in the 24 Hours, wherefore by knowing

the Time of the Moon's Southing at any Place, and the Time of High Water at Full or Change at that Place, we can find the Time of High Water on any other Day at the fame Place, by allowing 49 Minutes later for every Day fince the Full or Change, or 24 Minutes later for every Tide.

Thefe Tides would be regular from West to Eaft were the whole Earth covered with deep Water, but seeing their Course is obstructed by Land lying in their Way, furrounding Iflands, running up winding Rivers, and otherwife affected by Shoals, ftriking against Capes and Head-Lands, they are often forced to take long Circuits and various Directions to come to the Levels; that the Setting of the Tides and Times of High Water are different at different Places.

The Tides rifing higher in Bays and Rivers than in the open Sea, is occafioned by its ftriking against the contracting Banks of Bays and Rivers, accumulate the Water, and cause it to rise higher than in the open Seas.

The Tides are higher than ordinary twice every Year, viz. about the Vernal and Autumnal Equinoxes, and the Neap Tides lefs, which are occafioned by the Sun's being nearer to the Earth at thefe Times than at any other Time of the Year, and confequently the Power of Attraction is ftronger; for by drawing up the Water when the Sun and Moon are upon the Meridian, to a greater Height than ordinary, the Water 90° diftant from the Meridian, muft fubfide in the fame Proportion.

The Method generally prefcribed for finding the Time of High Water at any Place; is contained in the following Particulars:

To find the Leap Year.

Divide the given Year by 4, if nothing remains it is Leap Year, but if 1, 2, or 3 remains, they fhew that is fo many Years after Biffextile, or Leap Year, as the Remainder is: thus the Year 1796 divided by 4, gives 449, and the Remainder is (0) fhews it is Leap Year:

To find the Golden Number for any Year.

RULE. Add one to the given Year, and divide the Sum by 19 the Remainder will be the Golden Number.

EXAMPLE.

Required the Golden Number of 1796.

By adding one to that Year, it gives 1797, this divided by 19, gives 94 for the Quotient, and the Remainder is 11, the Golden Number for 1796.

To find the Epact for any Year.

NOTE. The Epact is the Moon's Age at the Beginning of the Year, or rather the firft of March. The Epact advances II every Year, to 30, because the Solar Year is 11 Days longer than the Lu

nar Year, and as the Epact increases, it fhews the Moon's Age at the Beginning of the Year; it is here fuppofed, that at the End of 19 Years, the Sun and Moon make all the Variety of Situations. they poffibly can with one another, and thence begin, and go over the fame again. The Golden Number at the Birth of Chrift was 1, which is the Reason that one is added to the given Year, to find the Golden Number,

RULE. Divide the given Year by 19, the Remainder multiply by 11, and the Product will be the Epact; if it does not exceed 29, but if it does, fubtract 30 from it as often as you can, and the Remainder will be the Epact, for it never exceeds 29.

EXAMPLE.

What is the Epact of the Year 1796.

1796, divided by 19, gives 94, and the Remainder 10, multiplied by 11, gives 110; this divided by 30, gives 3, and the Remainder is 20; which is the Epact for 1796.

To find the Moon's Age.

To the Epact, add the Day of the Month, and the Epact, or Number for the Month; the Sum if it does not exceed 30 is her Age; but if it does, fubtract 30 from it, as often as you can, and the Remainder is her Age.

NOTE. The Epact or Number for each Month is found thus: Divide the Number of Days contained between the first of January, and the firft Day of any Month, by 29, the Remainder will be the Number for that Month.

Required the Number or Epact for Sept. 1796?

Anf. 7.5 The Number of Days contained between the firft of January 1796, and firft of Sept. are 244 Days, divided by 29, gives 8 for the Quotient, and 7 for the Remainder, which is the Number fought, and fo for any other Month.

EXAMPLE.

Required the Moon's Age April 29th, 1796.

Day of the Month

Epact for the Year

Number for the Month

29

20

3

30)52(1
30

22 Moon's Age

Number for the Months are nearly as follows:

In com. Years

In Leap Years

Jan. Feb. Mar. Apr. May. June. July. Aug. Sep. O&. Nov. Dec.

3

3

4 4 6 7 8 10 10

5.5

To find the Moon's Southing on any Day of ber Age.

Since the Sun returns to the Meridian he has left in the Space of 24 Hours, and the Moon, in about 24 Hours 49 Minutes, therefore, if the Moon leaves the Meridian at the fame Time that the Sun does, on any Day, the next Day fhe will come to the Meridian 49 Minutes after him, falling back, about 49 Minutes every Day; whence to find the Time of the Moon's Southing, or coming to the Meridian, on any Day, we have this eafy Rule:

Multiply the Day of her Age by 49, and divide the Product by 60, the Quotient is the Hours, and the Remainder the Minutes Afternoon when she fouths. Or, which is rather eafier, and in many Refpects fufficiently exact for the Mariner's Purpofe; Multiply the Moon's Age by 4, and divide the Product by 5, the Quotient is the Hours, and the Remainder multiplied by 12, gives the Minutes Afternoon when she is upon the Meridian; but if this Time exceeds 12, fubtract 12 Hours from it, and the Remainder is the Time of her Southing in the Morning.

N. B. From the Full Moon to the Change the comes to the Meridian, or fouths in the Morning, but from the Change to the Full in the Afternoon.

EXAMPLE.

Required the Moon's Southing April 29, 1796?

Hence it appears that the Moon comes to the South, at 58 Minutes after 5 in the Morning.

To find the Time of High Water on any Day of the Moon's Age at any Place. From the Obfervations of many Perfons, there have been collected the Times when it is High Water on the Days of the New and Full Moon, on moft of the Sea Coafts of Europe, and at several

other Places, and thefe Times are commonly put in a Table against the Names of the Places, in an Alphabetical Order, for which Reafon, it is called the Tide Table; but in this Treatife, the Times of high Water at Full and Change Days, are fet down after the Latitude and Longitude of each Place, in the Table of Latitudes and Longitudes of Places.

RULE. To the Time of the Moon's Southing on the given Day, add the Time of High Water at Full and Change at the given Place, taken from the Table; the Sum is the Hour, paft Noon, on the given Day, when it is High Water at that Place; and if this Hour exceeds 12, fubtract 12 from it, and the Remainder fhews the Time of High Water in the Morning; but if it exceeds 24, fubtract 24 from it, and the Remainder fhews the Time of High Water in the Afternoon.

EXAMPLE I.

EXAMPLE II.

At what Time will it be High Water at Required the Time of High London, April 29th, 1796? Water at Dover, Oct. 12, 1796 ?