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

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 fhifts 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 exhibit the fame 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 fucceeding Revolutions of the fame. For what is the Dominical Letter for any one Year of this Cycle, is alfo the Dominical Letter of the fame Year of the next Round thereof, and fo on for ever. Hence it is easy with the Help of fuch a Table, to find the Dominical Letter for any Year, if you once know to what Year of the Solar Cycle, the given Year correfponds. Now to find the Year of the Solar Cycle anfwering 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 Chriftian Era, you add 9, and divide the Sum by 28, the Quotient expreffes the Number of Revolutions of the Cycle from the 9th Year before Chrift, and the Remainder gives the Year of the Solar Cycle; but if nothing remains, then does the given Year anfwer to the 28th or laft of this Cycle. As the Operation here is of the fame Nature with that for finding the Golden Number, I hold it needless to illuftrate it by a particular Example, and therefore fhall 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 Syftem of 15 Julian Years continually recurring, about whofe Original Chronologers and Hiftorians are greatly divided. The most general Opinion supposes it to have been inftituted for the Sake of certain Tributes and Taxes, the Time of whofe Payment was thereby made known to the Roman Subjects. What these Taxes were, on what Occafion they began, and why they were confined to a Cycle of 15 Years, is ftill Matter of Difpute among the Learned. We only know that they were in ufe after the Time of Conftantine the Great, and that Juftinian the Emperor commanded them to be inferted in all publick Inftruments. Though the Taxes and Tributes that firft gave Occafion to thefe IR

dictions,

dictions, have long fince ceased, yet they ftill continue to have a diftinguished Place in the Calendar, because the Popes make use of them in their Bulls. For ever fince Charlemaign invefted the See of Rome with fovereign Power, the Pontiffs, who before made ufe of the Years of the Emperors, have chofen 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 eafily find, that the first Year of this Cycle is connected with the 3d before Chrift, so that by adding 3 to the given Year of Chrift's Nativity, and dividing the Sum by 15, you will find the Year of the Indiction in the fame Manner as you did before that of the Lunar and Solar Cycles. I have only one Obfervation 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 Syftem of Years of which the Cycle confifts, but also to every Year of the faid System. Thus the 14th Year, for Inftance, of the Solar Period, is denominated 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 5th Year of the Lunar Cycle, or the 5th Lunar Cycle; and fo for the Indiction. This Remark was neceffary here, in order to prevent any Confufion or Perplexity that might afterwards arife, from the promifcuous Use of these Terms in the Sequel of this Difcourfe.

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

G. That is what I am now to go upon; and in Order to proceed with the greater Clearnefs, in a Matter of fuch Nicety and Importance, I must begin with obferving, 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 Compofitions of Cycles in this Science, fo are there of course various and manifold Periods. But I fhall here confine myself wholly to the Confideration 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 eafy and familiar to you. This Period,

as

as I have before hinted, is compounded of the three Cycles already explained; but to enable you the better to understand the Origin, Frame, and Usefulness of it, take the following Obfervations.

If we fuppofe the three Cycles of the Sun, Moon, and Indiction to begin together, in fuch manner, that the first Year of the Solar Cycle, be alfo the firft Year of the Lunar Cycle, and the first of the Indiction; then as the Cycle of Indiction terminates in 15 Years, and muft begin a-new, it is evident, that the 16th Year of this Series, will be the 16th Year of the Solar and Lunar Cycles, and the firft Year of the fecond Indiction. Again, as the Lunar Cycle revolves into itself after 19 Years, if you advance to the 20th Year of the Series, you will have 20 for the Character of the Solar Cycle, 1 for that of the Lunar, and 5 for the Indiction. Proceeding on in this Manner, you will find every Year to exhibit different Cycles, and if you continue the Progreffion till fuch Time as Cycles return again in the fame Order as when you first set out, that is, till the first Year of these three feveral Cycles coincide and fall together, you will find that this cannot happen till after an Interval of 7980 Years; for then and not fooner will the fame Order of Cycles return, and begin a fecond Period of the like Kind with the former.

This Syftem of Years, comprehending all the poffible Changes of thefe Cycles, may alfo more readily be found by multiplying the three Cycles continually into one another, viz. 28, 19, and 15: For the Product thence arifing muft neceffarily be the fame with the aforefaid Period, as is well known to all who are acquainted with the Powers and Combinations of Numbers. What is particularly happy in the Conftitution of this Period, and arifes evidently from the Manner of generating it above defcribed, is, that all the Years of it are diftinguished by their peculiar Cycles; infomuch that no one Year of the whole Period has the fame Cycles with any other Year thereof. For we have feen that the fame Order of Cycles does not return till the Period is elapfed, and a new one of the fame Kind begins. By this Means all the Years of this Period are accurately diftinguished, so that if the Cycles are duly marked, it is impoffible to mistake one for another. This Jofeph Scaliger obferving, and how ufeful fuch a Measure of Time might be, if applied to the Purposes of Chronology, thought of adapting the Years of it to the Julian Form, making them begin from the first Day of January, and thence gave it the Name of the Julian Period. The Cycles of which it was compofed, were also taken accord

2

according to the Manner and Computation in ufe among the Latins; and as by their joint Confent, the first Year of the Chriftian Æra had 10 for the Character of the Solar Cycle, 2 for that of the Lunar, and 4 for the Indiction, which three Cycles correfpond with no other Year of the Julian Period but the 4714th, he connected this very Year with the firft of the vulgar Chriftian Æra, and thereby laid a Foundation for applying the whole Series of Time both before and after this great Event, to the other Years of his celebrated Period.

Having thus explained the Nature, Origin and Properties of this univerfal Meafure of Time, I fhall now proceed to fhew how we are to apply it for the univerfal Purposes of Chronology. And in the firft place let me obferve, that it affords a general and eafy Rule for the finding the Year of any of the three Cycles. For as the first Year of the Period is alfo the first Year of every Cycle in it, by dividing any Year thereof by the Numbers compofing the Cycles, viz. 28, 19, and 15, the refpective Quotients will fhew the Number of the Cycles elapfed from the Beginning, and the Remainders will be the Years of the feveral Cycles, correfponding to the fuppofed Year of the Period. Thus if it was required to find the Characters of the three Cycles for the 6467th Year of this Period, which anfwers to the prefent Year of our Lord 1754Divide 6467, the given Year of the Julian Period, by 28 the Cycle of the Sun, and the Quotient gives the Number of Rounds of the Solar Cycle that have elapfed from the Beginning of the Period, and the Remainder is the prefent Year of the faid Cycle. In like Manner if you divide by 19, the Quotient will exprefs the Rounds of the Lunar Cycle, and the Remainder will be the Golden Number. The fame Method of proceeding, if you divide by 15, will ferve for the Indiction. This Rule you fee is eafy, and faves you the Trouble of retaining particular Numbers in your Mind, as in thofe already given. It is alfo univerfal, and will ferve for the, Years before Chrift as well as after, when once you know how to refer them to the Julian Period, as will be afterwards taught. Nor is this to be looked upon as an inconfiderable Advantage, because by thus knowing how to find at any Time the Years of the Cycles, you can by the Help of the Calendar, and the other ufual Tables, find the Dominical Letter, the New and Full Moons, with all the other Ecclefiaftical Calculations depending thereon.

But I now proceed to what is my chief Defign in this Explication of the Julian Period, viz. the connecting it with

the

the feveral Epochas of Hiftory, that thereby we may be enabled to compare them together, and view the whole Current of Time in a regular, fucceffive Course. We have already seen that the firft Year of the Chriftian Æra coincides with the 4714th of this Period, and that therefore 4713 Years of it were elapfed when the Epocha of Chrift's Nativity began. If therefore to any Year of our Lord's Nativity, we add 4713, that will be the Year of the Julian Period, anfwering to the given Year of the Chriftian Æra. Now as the Year of our Lord's Nativity is univerfally known and in common Ufe, nothing can be easier than this Connection; and fince it is ufual among Chriftians to refer all other Epochas to this, the Manner of reducing them to the univerfal Period is equally obvious. I would know for Inftance in what Year of the Julian Period the Epocha of the Hegira begins. This is a celebrated Æra in ufe among the Mahometans and Arabs, which took its rife on Occafion of Mahomed's Flight from Mecca. The Turks make use of it in all their Computations of Time, and to give it the greater Weight, have affixed to the Word Hegira a peculiar Signification, making it imply an Act of Religion, whereby a Man forfakes his Country, and gives Way to the Violence of Perfecutors, and Enemies of the Truth. Now the firft Year of the Hegira coincides with the 622d of our Lord. Add this to 4713, and you have 5335, the Year of the Julian Period in which the Epocha of the Hegira begins. In like manner, if I would know in what Year of the Julian Period the Norman Conqueft happened, this being an Epocha of great Note in England, to 1066 the Year of Christ answering to the faid Conqueft, I add 4713, and the Sum 5779 gives the Year required.

Thus you fee that the reducing of the Years and Epochas after Chrift's Nativity to the Julian Period, is extremely eafy. Those which precede it coft a little more Time, and require great Accuracy of Calculation; it being neceffary to afcertain the Year before Chrift's Birth in which they begin, which often must be deduced from a long Train of Conclufions. However, the great Advantages of this Connection when once made, abundantly atones for the Trouble of it, as it proves ever after a fure and infallible Guide in these Matters. Befides, the Calculations are already made to our Hands in Books writ on purpose, so that we have only to apply to them. Knowing therefore the Year before Christ in which any Epocha begins, if you substract that from 4714,

the