he had been in at court gave him the opportunity of amassing great riches; and he thought he could not better expend them than in the service of his country, and by doing all he could to promote the true interest of it both in church and state; and God prospered him in the work, according to the great zeal with which he laboured in it.

About this time flourished "Meto, the famous Athe

An. 432.

Artax. 33.

nian astronomer, who invented the Enneadecæteris, or the cycle of the nineteen years, which we call the cycle of the moon; the numbers whereof being, by reason of the excellency of their use, written in the ancient calenders in golden letters, from hence, 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. For it is still of as great use to the Christians, for the finding out of Easter, and also to the Jews for the fixing of their three great festivals, as it was to the ancient Greeks for the ascertaining of the times of their festivals. And for this last end was it that Meto invented it. For the Greeks, being directed by an oracle to observe all their solemn sacrifices and festivals, Karargia, that is, 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 P 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 same times of the sun's course, that so the same solemnities might always be celebrated within the same seasons of the year, as well as in the same months, and on the same days of them. The difficulty lay in this, that, whereas the year, according

n Diod. Sic. lib. 12, p. 305. Ptolemæi Magna Syntaxis, lib. 3, c. 2. o Gemin. in Isagogo, c. 6.

p Vide Scaligerum de Emendatione Temporum, Petavium de Doctrina Temporum, aliosque chronologos.

to the course of the sun (which is commonly called the solar year) is made by that revolution of it which brings it round to the same point in the ecliptic; and the Greeks reckoned their months by those revolutions of the moon which brought it round to the same conjunction with the sun, that is, from one new moon to another, and twelve of these months made their common year (which is commonly called the lunar year,) this lunar year fell eleven days short of the solar. And therefore their oracle could not be observed in keeping their solemnities to the same seasons of the year without intercalations: for otherwise their solemnities would be anticipated eleven days every year, and, in thirty-three years space, would be carried backward through all the seasons of the year (as is now done in Turkey, where they use this sort of year :) and to intercalate these eleven days every year would make as great a breach upon the other part of the oracle as to the months and days; for then every year would alter the day, and every three years the month: and, besides, it would make a breach upon 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 necessary, therefore, for the bringing of all to fall right according to the directions of the oracle, that the intercalations should be 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 same times of the solar year. And, therefore, in order hereunto, cycles were to be invented; and, to find out such a cycle of years, wherein, by the intercalation or addition of one or more months, this might

And

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 twenty-two days, and a lunar month making twenty-nine days and an half, this intercalation, instead of bringing the lunar year to a reconciliation with the solar, overdid it by seven days and an half; which being a fault that was soon perceived, for the mending of it, the Tetraæteris was introduced, which was a cycle of four years. Wherein it was thought, that an intercalation of one month would bring all that to rights which was overdone by the like intercalation of the Dieteris. this was contrived chiefly with a respect to their Olympic games for they being the chiefest of their solemnities, and celebrated once every four years, care was taken to bring this solemnity every fourth year as near as they could to the same time of the solar year in which it was performed the Olympiad before, which regularly ought always to have been begun, according to the original institution of that solemnity, 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 forty-three days and an half, the adding one lunar month, or twenty-nine days and an half, (of which it consists,) fell short of curing this defect full fourteen days; which fault soon discovering itself, for the amending of it, they intercalated alternatively one four years with one month, and the next four years with two months, which brought it to the Octoeteris, or the cycle 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 eight solar years, that they differed from them only by an excess of one day, fourteen hours, and nine minutes: and therefore this cycle continued much longer in use than any of the rest. But at length the errour, by in

creasing every year, grew great enough to be also discovered; which produced the invention of several other cycles for the remedying of it; of which this invented by Meto, of nineteen years, is the perfectest : for it brings the two luminaries to come to about the same points within two hours, one minute, and twenty seconds; so that, after nineteen years, the same new moons and the same full moons do within that space come about again to the same points of time in every year of this cycle in which they happened in the same year of the former cycle. And to a nearer agreement than this, no other cycle can bring them. This cycle is made up of nineteen lunar years and seven lunar months, by seven intercalations added to them. The years of this cycle in which these intercalations were made, were the third, sixth, eighth, eleventh, fourteenth, seventeenth, and nineteenth, according to Petavius; but, according to Mr. Dodwell, they were the third, fifth, eighth, eleventh, thirteenth, sixteenth, and nineteenth. Each of these seven intercalated years consisted of thirteen months, and the rest of twelve. The chief use of this cycle among the Greeks being to settle the times of celebrating their solemnities, and that of their Olympiads being the chiefest of them, and on the fixing of which the fixing of all the rest did depend, it was in the first place applied to this purpose; and the rule of these Olympiads being, that they were 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; and this Meto observed this year to be on the twenty-first day of the Egyptian month Phamenoth, which reduced to the Julian year, falls on the twenty-seventh of June. And therefore the Greeks having received this cycle, did, from this time forward, celebrate their Olympiads on the first full moon after the twenty-seventh day of our June; and thenceforth also began their year from the new moon preceding; whereas before they began it from the winter solstice: and they calculated both the new moon and the full moon by this cycle; so that from this time the new moon immediately preceding the first full moon after

the summer solstice was the beginning of their year, and that first full moon after the said solstice, in every fifth year, was the time of their Olympiads. For that year, in the beginning of which this solemnity was cel ebrated, was, in their computation of time, called the first year of that Olympiad, reckoning from the new moon preceding; 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,

But this use of the cycle ceasing with the solemnities of the heathen Greeks after that Christianity had gotten the ascendant in the Roman empire, it thenceforth became applied to another use, and that not only by the Christians, but also by the Jews: for by it the Christians, after the council of Nice, settled our Easter; and from them, some few years after, the Jews learned to make the like use of it for the fixing the time of their passover, and the making of their intercalations in order to it. But of the manner how each of them applied it for these purposes, there will be hereafter an occasion fully to treat, in a place more proper for it.

The war between the Athenians and Lacedemoni

An. 431.

Artax. 34.

ans, called the Peloponnesian war (of which Thucydides and Xenophon have written the history,) began about the end of the first year of the 87th Olympiad, which lasted twenty-seven years. As soon as they had entered on it, both parties sent their ambassadors to king Artaxerxes to engage him on their side, and pray his aid in the war.

About the same time, there broke out a most grievous pestilence, which did overrun a great part of the world. It first began in Ethiopia; from thence it came into Lybia and Egypt; and from Egypt it invaded Judea, Phoenicia, and Syria; and from those parts it spread itself through the whole Persian empire; from whence it passed into Greece, and grievously afflicted the Athenian state, destroying a great

q Thucydides, lib. 2.

r Thucydides gives an account of the first twenty-one years of this war, and Xenophon's Hellenics continues the Greek history from thence. s Thucydides, lib. 2. Herodotus, lib. 7.