The firft and third Examples having Remainders, the Years are common Years of three hundred and fixty-five. Days; but the fecond and fourth, having no Remainders, are Leap-Years of three hundred and fixty-fix Days.

With Regard to any other Years, the whole Date is to be divided by 4; and, if there's no Remainder, it is Leap-Year; but, if 1, 2, or 3 remains, it is the firft, fecond, or third after Leap-Year; according to the Distich published by Mr. Street, in his Aftronomia Carolina: Where he has given Diftichs for finding the Cycle of the Moon or Golden Number, Epact, Moon's Age, &c. which being of great Ufe to affift the Memory, I fhall infert fuch as are agreeable to the Gregorian or New Style. That for finding the Leap-Year is,

Divide the Year by 4, what's left shall be
For Leap-Year o, for past 1, 2, or 3.

Exam. For the Year 1754.

4) 1754 (438

16

15

12

34
32

2 fecond after Leap-Year.

To find the Dominical or Sunday Letter for any Year.

The Diftich for this, made to answer to the Gregorian Calendar, is,

Divide the Year and Fourth of it by 7,

What's left fubtract from 7, the Letter's given.

That is, to the Year of the Chriftian Era add the fourth Part, and divide this Sum by 7; then fubtract what remains (even if it be a Cypher) from 7, and the Remainder is the Dominical Letter, accounting as follows:

Here it is to be obferved, that every Leap-Year has two Dominical Letters; that found by this Rule is the Sunday Letter from the twenty-fifth Day of February to the End of the Year; and the next in the Order of the Alphabet ferves from the first of January to the twenty-fourth of February.

Hence C is the Dominical Letter for the Year; but D, the next in the Order of the Alphabet, is the Dominical Letter for January and February. From this Interruption of the Dominical Letter every fourth Year, it is twenty-eight Years before the Dominical Letter returns to the fame Order; which, were it not for the Leap-Years, would return to the fame every seven Years. This Cycle of twenty-eight Years is called the Cycle of the Sun; tho' it has no Relation to the Sun's Motion, but is fo called from its Ufe in finding the Sunday Letter, becaufe Sunday ufed to be called Die Solis, the Sun's Day.

The Diftich for finding the Golden Number, Cycle of the Sun, and Roman Indiction, is this,

When 1, 9, 3, to the Year hath added been,
Divide by 19, 28, 15.

That is, for the Golden Number, add 1 to the Year, then divide by 19, and the Remainder is the Golden Number; if

nothing

nothing remains, 19 is the Golden Number. (The Ule of the Golden Number will be fhewn below.) In the fame Manner, 9 being added to the Year, and the Sum divided by 28, the Remainder, if any, is the Cycle of the Sun; if nothing remains, the Cycle is 28,

The Ufe of this Cycle is for finding the Dominical Letter by the following Table.

A Table of the Dominical Letters for the New
Style, according to the Cycle of the Sun.

Cycle. Letter. || Cycle. | Letter. || Cycle. Letter. || Cycle. | Letter.

This Table, by the prefent Rule, will ferve but to the End of this Century. The Leap-Year being to be omitted in the Year 1800, will make it neceffary to add 25 to the Date of the Year, and then dividing by 28, it will give the Cycle right for the Table during the next Century. And this is a general Rule to be obferved, that, when a Leap-Year has been abated, add 16 to the Number which was before added to the Year, and reject 28 when it exceeds it; then, this Number being added to the Year, and the Sum divided by 28, the Re

mainder

mainder will be the Cycle for finding the Dominical Letter. Thus, in the nineteenth Century it will be 25, and in the twentieth Century 13, which Number will ferve two Centuries, for the Year 2000 is a Leap-Year.

Example. To find the Dominical Letter for the Year 1975, and for the Year 2056.

Of the Golden Number, or Lunar Cycle.

The Golden Number is a Period of nineteen Years, invented by Meton, an Athenian, and from him called the Metonic Cycle. The Use of this Cycle is to find the Change of the Moon; because, after nineteen Years, the Changes of the Moon fall on the fame Days of the Month as in the former nineteen Years; tho' not at the fame Time of the Day, there being an Anticipation of one Hour, twenty-feven Minutes, forty-one Seconds, and thirty-two Thirds; which, in three hundred and twelve Years, amounts to a whole Day: Hence, the Golden Number will not fhew the true Change of the Moon for more than three hundred and twelve Years, without being varied. But the Golden Number is not fo well adapted to the Gregorian as the Julian Calendar, the Epact being more certain in the New Style, to find which the Golden Number is of Ufe. The Way of finding the Golden Number has been already fhewn above.

Thus for the Year 1754.

Add

19) 1755 (92

171

45
38.

7 Golden Number.

The

The Epact is the Excess of the Solar above the Lunar Year, or twelve Synodical or Lunar Months; which being fomewhat more than ten Days and twenty-one Hours, to avoid Fractions, the annual Epact is eleven Days.

By the Golden Number, called alfo the Prime, to find the Epact.

I

For the Gregorian or New Style, take 1 from the Golden Number or Prime; then

Divide by 3, for each one left add 10,

30 reject, the Prime makes Epact then.

That is, after I has been taken from the Golden Number, divide the Remainder by 3; if I remains, add ro to the Dividend, and that will be the Epact; if 2 remains, add 20 to the Dividend; but, if nothing remains, the Dividend is the Epact.

A Table of the nineteen Epacts for the Julian
and Gregorian Accounts, by the Gold. Num.