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the New and Full Moons in the Heavens, and adjust them to the Solar Course. And as a better Cycle for this Purpose than the 19 Years Cycle was not to be found, because none other can bring the Course of the Sun and Moon to a nearer Agreement, the Christian Church accordingly pitched upon it, as the best Rule they could follow for the fixing of their Easter. And so great a Value did they set upon it by reason of its great Usefulness in Ecclesiastical Computations, that the Numbers of it were written in the ancient Calendars in golden Letters; from whence in our present Almanacks, that Number of this Cycle, which accords with the Year for which the Almanack is made, is called the Golden Number. Now the Golden Number for any Year whatsoever of the Chriftian Æra, may be easily found by the following plain Rule. The first Year of Christ according to the Computation in Old Stile, fell in with the 2d Year of the Lunar Cycle, and therefore if to the given Year of the Christian Æra you add one, and divide the Sum by 19, the Quotient shews the Number of Revolutions of the Cycle from the Beginning of the said Æra, and the Remainder after Division is the Golden Number required; but if nothing remains, the Golden Number is 19. Suppose for Example the Golden Number of the Year 1746 were required: Then 1746 added to i makes 1747, and that divided by 19, gives 91 for the Quotient, with a Remainder of 18. And therefore 18 is the Golden Number for that Year; and 91 the Quotient expresses the Number of Revolutions of this Cycle from the Beginning of the Year preceding the Birth of Chrift.

P. But does this Cycle of 19 Years bring the Solar and Lunar Revolutions to so exact an Agreement, as to be always an invariable Rule in this Cafe ?

û. Altho’ the Metonic Cycle comes indeed very near the Truth, so as to fhew the Lunations for the space of three Centuries without the Error of a fingle Day; yet the Diffe. rence continually increasing, grows in Time to be considerable. For 19 Lunar Years, and 7 intercalated Months, of which this Cycle consists, falling short of 19 Julian Years almost an Hour and an half, hence it hath followed, that in every one of the Years of this Lunar Cycle, the New Moons and Full Moons have happened just so much sooner each Month, than in the fame Years of the Cycle immediately preceding. And hereby it hath come to pass, that after the elapsing of so many Rounds of this Cycle, as have revolved from the Times of the Nicene Council to the Year 1746, the New Moons and Full Moons in the Heavens, have anticipated the New


and Full Moons in the Calendar of the Common Prayer Book, four Days and an half; because the New Moons and Full Moons are there stated, not according to the present Times, but according to the Times of that Council. These last are called Ecclesiastical New Moons, to distinguish them from the true ones in the Heavens; and the general Table or Rule for finding Easter for ever may still be applied, if we make the proper Allowance above described. That is, in calculating the New Moons we must reckon four Days and an half before the Time assigned by the Calendar ; or, which amounts to the same, call the Day of the New Moon as you find it by the Calendar, the fifth Day of the Moon's Age. In the Gregorian Reformation of the Calendar, the Golden Number is thrown out, and the Epact introduced in the Place of it. But as it is not my Intention here to meddle with Ecclesiastical Computations any farther than is necessary to give a clear Idea of the Cycles that constitute the Julian Period, I fall here conclude my Observations upon the Lunar Cycle, which I have endeavoured to explain in the most full and distinct Manner, not only becaufe of its great Note in ancient Computation, but also for the distinguished Place it still retains in our Civil Calendar.

P. What other Cycles besides this of the Moon, are made use of in the Composition of the Julian Period ?

G. The Julian Period, besides the Lunar Cycle, takes in also two others: That of the Sun as it is commonly called, and the Cycle of Indiction. The Solar Cycle is lo called, not from expressing any Number or Series of Solar Revolutions, but because by its Heip we know the Dominical Letter, or the Character of Sunday. But to enable you the better to comprehend this, I must observe, that as we divide Time into Weeks, and describe the Day of the Week by seven several Names; so are those Days distinguished in the Calendar by seven Letters set in alphabetical Order before them, and repeated to them in a constant Round throughout the whole Year. These Letters are the first seven of the Alphabet, A, B, C, D, E, F, G; and the Custom is, to assign the Letter A to the first Day of the Year; which if it happens to be a Sunday, then A is the Letter for Sunday, or the Dominical Letter; and the rest are applied in Order to the other Days of the Week. Now as the Number of Days in a Week are seven, and the Number of Letters applied to them also seven, it is evident, that whatever Letter answers to the first Sunday of the Year, will stand for Sunday all the Year round, the Revolution of Days and Letters being in

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this Respect the same, and perfectly coinciding. It is manifeft likewise, that if the Year was made up of an exact Number of Weeks, the Dominical Letter would continue constantly and invariably the same, because the first Day of the Year would always fall upon the same Day of the Week, and of Consequence create no Interruption or Disturbance in the Order and Succession of Letters. But as this is not the Case, the odd Day or Days must unavoidably break in apon the Series, and to take Account of these Alterations, is the Design of the Solar Cycle. As the common Julian Year confifts of 52 Weeks and one Day; if the first Day of the Year falls upon a Sunday making A the Dominical Letter, then will the last Day of the Year also fall upon a Sunday, and the first Day of the next succeeding Year will be Monday. But as the Letter A is always appropriated to the first Day of the Year, it now of course becomes the Characteristick of Mon. day, and the Letter that in due Order of Succession falls to Sunday, is G, which therefore becomes the Dominical Let. ter of the Year. A like Train of Things will also shift the Dominical Letter of the ensuing Year back by one Letter, and throw it upon F. And this Revolution, were it allowed to run on without Interruption, would be determined in seven Years.

But it so happens in the Julian Computation, that every 4th Year is a Leap-Year, consisting of 366 Days, which make 52 Weeks and 2 Days, and in this case the Dominical Letter will be shifted back by two Letters, and fall the following Year upon the next Letter save one in a retrograde Order, Thus if the Dominical Letter at the Beginning of a LeapYear be A, it will not the following Year fall upon G as in the first Case, but by a double Retrogression, because of the two odd Days, it is shifted back to F. And it is farther to be observed of these Leap-Years, that the same Dominical Letter is not as in common Years, continued to the End of the Year, as might have been done, and the two odd Days suffered then to effect the double Change ; but it has been judged more convenient to change the Dominical Letter in the Month of February, when the intercalary Day is inserted, Whatever therefore is the Sunday Letter at the Beginning of a Leap-Year, so continues till towards the End of February but then, by reason of the Intercalation, the 23d and 24th Days are denoted by the same Letter, in which Case it is evident that the Dominical Letter must for the Remainder of that Year go one Place back. If therefore the Dominical Letter in the Beginning of the Year be A, after the 24th of


a Leap-by reala by the Letter mtherefore after the

February it will be G, and the Year following it is thrown upon F, as we have already said.

*You see therefore that there is a twofold Change happens to the Dominical Letter, according to the Nature of the Year in which it takes place. Every common Year shifts it back by one Letter, and in every Fourth or Leap-Year there is a double Retrogreffion. All these Variations are compleated in 28 Years, after which the Dominical Letters return as before, and exkibit the same Series in a perpetual Train of Revolutions. If therefore a Table is made, representing the Dominical Letters for every Year in Order of this Cycle, it will also serve for all the succeeding Revolutions of the fame. For what is the Dominical Letter for any one Year of this Cycle, is also the Dominical Letter of the same Year of the next Round thereof, and fo on for ever. Hence it is easy with the Help of such a Table, to find the Dominical Letter for any Year, if you once know to what Year of the Solar Cycle, the given Year corresponds. Now to find the Year of the Solar Cycle answering to the given Year, proceed in the following Manner. The Year of our Lord's Nativity fell in with the tenth Year of the Solar Cycle, and therefore if to the given Year of the Christian Æra, you add 9, and divide the Sum by 28, the Quotient expresses the Number of Revolutions of the Cycle from the oth Year before Christ, and the Remainder gives the Year of the Solar Cycle; but if nothing remains, then does the given Year answer to the 28th or last of this Cycle. As the Operation here is of the same Nature with that for finding the Golden Number, I hold it needless to illuftrate it by a particular Example, and therefore shall here conclude my Remarks upon this Cycle, not doubting, but from what has been faid, you will be fufficiently able to comprehend it in all its Varieties and Changes.

It now only remains that I explain to you the Cycle of Indiction, which is a System of 15 Julian Years continually recurring, about whose Original Chronologers and Historians are greatly divided. The most general Opinion supposes it to have been instituted for the Sake of certain Tributes and Taxes, the Time of whose Payment was thereby made known to the Roman Subjects. What these Taxes were, on what Occasion they began, and why they were confined to a Cycle of 15 Years, is still Matter of Dispute among the Learned. We only know that they were in use after the Time of Constantine the Great, and that Juftinian the Emperor commanded them to be inserted in all publick Instruments. Though the 'Taxes and Tributes that first gaye Occasion to these In



bonly know that and that Juftinlöck Inftrur

di&tions, have long since ceased, yet they still continue to have a diftinguished Place in the Calendar, because the Popes make use of them in their Bulls. For ever since Charlemaign invested the See of Rome with sovereign Power, the Pontiffs, who before made use of the Years of the Emperors, have chosen to date their Acts by the Year of the Indiction. At the Time of the Reformation of the Calendar, the Year 1582 was reckoned the tenth Year of the Indiction, whence by numbering back you will easily find, that the first Year of this Cycle is connected with the 3d before Chrif, so that by adding 3 to the given Year of Christ's Nativity, and dividing the Sum by 15, you will find the Year of the Indiction in the same Manner as you did before that of the Lunar and Solar Cycles. I have only one Observation more to make before I quit this Doctrine of Cycles, and it is this: That in the Lan, guage of Chronologers, the general Name of any Cycle is not only applied to the entire System of Years of which the Cycle consists, but also to every Year of the said System. Thus the 14th Year, for Instance, of the Solar Period, is de. nominated indifferently either the 14th Year of the Solar Cycle, or the 14th Solar Cycle. In the like Manner in the Lunar Revolutions; any Year, as the 5th, is called the sth Year of the Lunar Cycle, or the 5th Lunar Cycle; and so for the Indiction. This Remark was necessary here, in order to prevent any Confusion or Perplexity that might afterwards arile, from the promiscuous Use of these Terms in the Sequel of this Discourse.

P. I think I now pretty well understand the Nature and Formation of these Cycles; and therefore 1hould be glad to be informed how they are applied, in the Composition of that general Standard of Epochas, which you some time ago made mention of.

G. That is what I am now to go upon; and in order to proceed with the greater Clearness, in a Matter of such Nicety and Importance, I must begin with observing, that in the Language of Chronologers, as a Round or Revolution of Years makes what they call a Cycle, fo a Round or Revolution of Cycles makes what they call a Period. And as there are various and manifold Compositions of Cycles in this Scio ence, so are there of course various and manifold Periods, But I shall here confine myself wholly to the Consideration of the Julian Period, it being the most important in all Chronology, and what, if well understood, will render every other Part of this Science easy and familiar to you. This Period,

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