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in no danger of being confounded or mistaken one for an other; and lastly, I shall demonstrate the Ule of this period in regulating the several Epochas and Computations of Chronology.

The Confideration of Cycles makes properly a Part of Ecclefiaftical Computations, they being chiefly contrived for determining the New and Full Moons, and regulating the Festiyals of the Church depending thereon. In a View of Chronology therefore such as this, designed only for the Uses and Purposes of History, it will not be necessary to confider them any farther than as they go to the Composition of the Julian Period, and consequently make a part of the Civil Measures of Time. Cycles in the general are no more than certain Periods or Series of Years, proceeding in an orderly Succession from first to last, when they are supposed to begin again, and lo preserve the fame Tenour in a constant Train of Revolutions. Thus the continued Series of Sabbatical Years among the Fews, is called the Sabbatical Cycle, which thence consisted of seven Years; as a System of fifty Years continually recurring, made their Jubilean Cycle. In like Manner, if we should suppofe the Sun and Moon to set out together from any Point of the Zodiac, and after a certain Succession of Years to meet again in the fame Point of the Heavens ; as this Event must always happen upon the like Revolution of Years ; this Number of Years would necessarily form a Cycle, by which to determine for ever the Coincidence of these two Luminaries in the Heavens. And accordingly this is the Intent of the Lunar Cycle, or Cycle of the Moon, of so great Note in Chronology. But in order to trace the Origin and Formation of it with the greater Exactness, we must go back to the ancient Form of the Year in use among the yeros and Greeks, which tho' properly Lunar, yet as they were obliged also to regard the Solar Motions, hence arose the Necessity of Intercalations, and of establishing a Cycle to regulate and adjust there Intercalations. The Year at first in ufe among the Jews, was not fettled by Astronomical Rules, but made up of Lunar Months, set out by the Phases or Appearances of the Moon. When they saw the New Moon, then they began their Months, which consisted alternately of 29 and 30 Days, for the Reafons given above. None of them had fewer than 29 Days, and therefore they never looked for the New Moon before the Night following the 29th Day; and if they then saw it, the next Day was the first Day of the following Month. Neither bad any of their Months more than 30 Days; and there

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fore they never looked for the New Moon after the Night
following the 30th Day, but if they saw it not then, con- ,
cluded its Appearance was obstructed by Clouds; and of 12
of these Lunar Months, their common Year confifted. But
as this falls in Days short of a Solar Year, every one of
these comman Years, in respect of the Sun's Course, began
11 Days sooner than the former ; which in 33 Years, would
carry back the Beginning of the Year thro' all the four Sea-
fons. This Inconvenience they were under a Necessity of
preventing for the Sake of their Festivals, The Feast of the
Passover was fixed to the Middle of the Month Nisan, and
ordered to be celebrated by the eating of the Pafchal Lamb,
and the offering up of the Wave Sheaf, as the first Fruits of
their Barley Harvest. The Feast of Pentecost was kept the
goth Day after the 16th of Nifan, the Day on which the
Wave Sheaf was offered ; and celebrated by the offering of
the two Wave Loaves, as the first Fruits of their Wheat
Harvest. And lastly, the Feast of Tabernacles always began
on the 15th of Tifri, being fixed to the Time of gathering
in the Fruits of the Earth. It is evident therefore that
the Parlover could not be observed, till the Lambs were grown
fit to be eaten, and the Barley to be reaped ; nor the Pente-
coft till the Wheat was ripe, nor the Feast of Tabernacles
till the Ingathering of the Vineyard and Oliveyard were
over. And therefore these Festivals being fixed to these set
Seasons of the Year, it was necessary to adjust the Lunar
Reckoning to the Sun's Course, and thereby prevent their
Months from receding too far from the Seasons. For this pur-
pole, fametimes in the third Year, and sometimes in the second,
they cast in another Month, making the Year then consist of
13 Months; whereby they constantly reduced their Lunar
Year, as far as fuch an Intercalation could affect it, to that
of the Sun, and never suffered the one to vary from the other
above a Month. These Intercalations were regulated by the
High-Priest and Sanhedrim, and Notice given of what they
ordained in this Matter over all the Land. But when they
became dispersed over all Nations, so as neither to have pro-
per Opportunities of making the requisite Observations, nor
Means of communicating them when made, it was then found
necessary to establish fixed and stated Rules of Intercalation,
that so they might be every where uniform herein. And up-
on this Occasion it was, that the Cycles and Astronomical
Calculations of the Greeks, were with some little Variation
first introduced among them.
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You see therefore that the Jewish Years, tho' properly and singly considered they were indeed Lunar, yet by these Intercalations, and the keeping of their Months constantly fixed to the same Seasons, they became in their collective Sums truly Solar. The fame Thing happened also among the Greeks, and for a like Reason. Their Years were indeed Lunar, as consisting of Months measured by the Motion of the Moon, but at the same time they took care to adjuft these to the Solar Reckoning, for the Sake of their Festivals, especially for the Sake of the Olympiads. For being directed by an Oracle to observe all their solemn Sacrifices and Festivals Hata teia, i. e, according to Three; and this being interpreted to mean Years, Months and Days, and that the Years were to be reckoned according to the Course of the Sun, and the Months and Days according to that of the Moon, they thought themselves obliged hereby to observe all these Solemnities, at the same Seasons of the Year, and on the same Month, and on the same Day of the Month. And therefore Endeavours were made to bring all these to meet together, that is, to bring the same Months, and all the Days of them, to fall as near as possible within the Time of the Sun's Course. The Difficulty therefore lay in finding out such Intercalations as without disturbing the Lunar Revolutions, would by the additional Months thence arising, keep the regular Months duly fixed to the faine Seasons. For as the Lunar Year fell only 11 Days short of the Solar ; to have added these annually, would have broke in upon the Succession of their Months, and destroyed the whole Scheme of their Year. For with them, in the same Manner as with the Jews, their Months always began with a New Moon, and their Years were always made up of these Lunar Months, so as to end exactly with the last Day of the last Moon, and to begin exactly with the first Day of the next Moon. It was neces: sary therefore for the bringing of all to fall right according to the Directions of the Oracle, that the Intercalation should þe made by Months; and to find out such an Intercalation of Months, as would at length bring the Solar Year and the Lunar Year to an exact Agreement, so that both should begin from the same Point of Time, was that which was to be done for this Purpose. For thus only could the Solemnities be always kept to the same Seasons of the Year, as well as to the same Months, and the same Days of them, and constantly be made to fall within the Compass of one Lunar Month at most sooner or later, within the fame Times of the Solar Year, And therefore in ordeş hereunto Cycles were to be

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invented; and to find out such a Cycle of Years, wherein by the Intercalation or Addition of one or more Months this might be effected, was the great Study and Endeavour of the Astronomers of those Times. The first Attempt that was made for this purpose was that of the Dieteris, a Cycle of two Years, wherein an Intercalation was made of one Month ; but in two Years Time, the Excess of the Solar Year above the Lunar being only 22 Days, and a Lunar Month making 29 Days and an half, this Intercalation, instead of bringing the Lunar Year to a Reconciliation with the Solar, overdid it by 7 Days and an half. This Fault being soon perceived, for the mending of it the Tetraeteris was introduced, which was a Cycle of 4 Years, wherein it was thought that an Intercalation of one Month would bring all that to rights, which was over-done by the like Intercalation of the Dieteris. And this was contrived chiefly with a Respect to the Olympic Games. For they being the chief of their Solemnities, and celebrated once every four Years, Care was taken to bring them every fourth Year as near as possible to the fame Time of the Solar Year, in which they had been performed the Olympiad before. Now this Solemnity, according to the original Institution, was always to begin on the first Full Moon after the Summer Solstice; and it was thought that an Intercalation of one Month in four Years would always bring it to this Time. But four Solar Years exceeding four Lunar Years 44 Days, the adding one Lunar Month, or 29 Days and an half, fell short of curing this Defect, upwards of 14 Days. This Fault likewise foon discovering itself, they intercalated alternatively, one four Years with one Month, and the next four Years with two Months, which brought it to the Octoeteris, or Cycie of eight Years, wherein by intercalating three Months, they thought they brought all to rights, and indeed it came much nearer to it, than any of the former Cycles. For by this Intercalation the eight Lunar Years were brought so near to the eight Solar Years, that they differed from them only by an Excess of one Day and 14 Hours. And therefore this Cycle continued much longer in use than any of the rest. But at length the Error, by increasing every Year, grew great enough to be also discovered, which produced the Invention of several other Cycles, till at length the Metonic Cycle of 19 Years took place, so called from Meto an Athenian, the Inventor of it. This great Astronomer found by Calculation, that if the Sun and Moon were supposed to set out together from any Point of the Zodiac, after 19 Solar Revolutions, they would meet again in the self-fame Point, and Аа 4

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begin a new Period exactly agreeing with the former. These 19 Solar Revolutions he found to contain 235 Lunations, which make 19 Lunar Years, and 7 Lunar Months, to be added to them by 7 Intercalations. So that the whole Cycle confitted of 12 Lunar Years of 12 Months each, and seven intercalated Years of thirteen Months, which corresponding to 19 Solar or Julian Years, the New and Full Moons after that Space, not only return to the same Days of the Yulian Year, but nearly to the fame Hours of the Day. A Course of Observations therefore determining the Days on which the New and Full Moons happo.. during one Revolution of this Cycle, will also serve for the next Revolution of the same, and so on in Succession. The chief Use of this Cycle among the Greeks being to settle the Times of celebrating their Solemnities, and that of the Olympiads being the chief of them, on the fixing of which the fixing of all the rest did depend, it was in the first place applied to this Purpose. And as the Olympic Games were always to be celebrated on the first Full Moon after the Summer Solstice, in order to settle the Time of their Celebration, it was necessary in the first Place to settle the Time of the Summer Solstice. This Mets, the Year he introduced his Cycle, observed to be on the hist Day of the Egyptian Month Phamenoth, which reduced to the Julian Year falls on the 27th of June. And therefore the Grecks having received this Cycle, did from this Time forward celebrate their Olympiads on the first Full Moon after the 27th Day of our June ; and henceforth also began their Year from the New Moon preceding. The Year in the Beginning of which the Olympic Games were celebrated, was in their Computation of Time, called the first Year of that Olympiad ; and in the Beginning of the fifth Year after they celebrated the next Olympiad, which made the Time from one Olympiad to another to be just four Years, according to the Measure of the Years then used.

I have thus given you a full and I hope intelligible Account of the Metonic Cycle, so famous in ancient Chronology; and still known among us under the Name of the Cycle of the Moon or Golden Number. Upon the ceasing of the Greek Solemnities, the Use of this Cycle also ceased, and so continued for several Centuries, till at length after the Council of Nice, the Chriftians introduced it into their Calendar, and made use of it in settling Easter, and the other moveable Feasts. For by a Decree of that Council, Easter-day was fixed to the Sunday after the first Full Moon that followed next after the vernal Equinox: Thus it became necessary in the Chriftian Church as well as among the Greeks, to calculate

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