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any distinction of the sexes. “The pious votary,” says he, “ will by this method, more entirely acquaint himself with the writer of these tracts, than he could by the most punctual account of HIS name,” &c.

It is strange that Mr. Ballard, who had read this preface, by the quotations he makes from it, did not perceive this; or, if he did, would take no notice of it.

Yours, &c.

OBED. REPERET.

1754, Jan.

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XVI. Sir Isaac Newton on the Ancient Year.

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HAVE perused the paper, which his Lordship the Bishop of Worcester sent to Dr. Prideaux, and find it filled with excellent observations concerning the ancient year; but do not find it proved, that any ancient nation used a year of twelve months, and 360 days, without correcting it from time to time by the luminaries, to make the months keep to the course of the moon, and the years to the course of the sun, and returns of the seasons and fruits of the earth,

The first nations, before they began to use artificial cycles, kept a reckoning of time by the courses of the sun and moon, Gen. i. 15; and, for knowing what days of every month in the year they were to celebrate as festivals or fasts, and to what Gods, it was requisite to have a calendar, in which calendar it was obvious to set down thirty days to a lunar month, and twelve lunar months to a solar year, these being the nearest round numbers, answering to the courses of the sun and moon: and hence it came to pass that the ancients reckoned the luni-solar year to consist of twelve months, and 360 days, in which they supposed the sun moved round the heavens. But I do not find that in civil affairs any na. tion adhered to this luni-solar calendar, where they found it differ froin the courses of the sun and moon; but rather corrected it from time to time, taking a day or two from the month, as often as they found this month too long for the course of the moon, and adding a month to the year as often as they found twelve lunar months too short for the return of the four seasons, and fruits, of the earth. And thus to correct the calendar of the luni-solar business of the priests: and from the reformation of this primitive calendar to make it agree better and better with the courses of the sun and inpon, and need to be corrected

year was the

seldomer by them, came all the forms and cycles of years which have been ever since invented.

For after they found that twelve lunar months were too short for the return of the sun and seasons, they added a month every other year, and thereby formed the Trieteris, more properly called Dieteriș. And when they found this biennial cycle too long, so as to need a correction once in eight years, they thereby formed the Octoeteris of the ancients, the half of which was their Tetraeteris : and these cycles were as ancient among the Greeks as the days of Cadmus and Minos, and Hercules Ideus, and the great Bacchus, or Osiris : and therefore seem to have been brought into Greece, by the ancient colonies of the Egyptians and Phænicians, and army of Bacchus. Afterwards some Greeks altered the manner of inserting the three intercalary months; and, at length, when they found that the Octoeteris was too short for the seasons and coůrse of the sun, and wanted to be corrected sometimes by the course of the sun, to make it keep to the seasons, Meton found out the Cyclus decemnovalis, in which seven months were added in nineteen years, and this cycle is still in use. And as for the length of the months, some of the Greeks made them to consist of twenty-nine days, and thirty, alternately; and by this cycle were enabled to keep a reckoning without correcting it by the course of the moon above once in a year or two.

The Chaldeans reduced the luni-solar year to a cycle of twelve

years, and therefore seem to have added a month to the end of every third year, and at the end of

and at the end of every twelve years to have rectified their cycle by the courses of the sun and moon: for all cycles of years were for regulating the intercalation of months.

The luni-solar year being of an uncertain length, and for that reason unfit for astronomical uses; the Egpytians, when for the sake of navigation, they applied themselves to the observation of the stars, measured the just length of the solar year hy the heliacal risings and setting of the stars, and laying aside the calendar year, making the solar year to consist of 365 days; and this year was received by the astronomers at Babylon, and by the Persian magi; and by the Greeks in their Æra Philippæa, and being corrected by Julius Cæsar, by the addition of a day in four years, be came the year of the Romans, and has been farther corrected by Pope Gregory XIII.

On the contrary, the people of Arabia Felix using the old year of twelve lunar months, without correcting it by the sun, have propagated down to the Mahometan nations a

year purely lunar, keeping their months to the courses of the moon.

Thus you see all 'nations have endeavoured to make their years keep to the courses of the sun and moon, or one of them; and therefore that any nation should use a year of 360 days, without regarding the course of either luminary, is not to be believed without good proof. Simplicius, in his commentary on the 5th of Aristotle's Physical Acroasis, (apud Theodor. Gazam de Mensibus) tells us,

“We seat the beginning of the year either upon the summer solstice, as the people of Attica, or upon the autumnal equinox, as the inhabitants of Asia, or upon the winter solstice as the Romans do, or upon the vernal equinox, as do the Arabians and people about Damascus; and the beginning of the month, either upon the full moon with some, or upon the new." He tells us, that the ancient

year

of the Romans, Greeks, Asiatics, Syrians, and Arabians, was lunisolar, and agreed with the courses of the sun and moon: so the year which the Israelites brought out of Egypt was luni-solar, and began in autumn, and Moses removed the beginning to the spring, and the first month thereof was called Abib, from the earing of the corn in that month. And accordingly Diodorus tells us, that Uranus, an ancient king of Egypt and Lybia, used the luni-solar year: so also the vear which the Samaritans brought from the provinces of the Assyrian empire, and that which the Jews brought from Babylon was luni-solar, and began in the spring. The Chaldees were an Arabic nation, and Arabian years were lunisolar, and began in the spring as above. And Scaliger and others inform us, that the ancient years of Persia, India, China, and the adjacent isles were also luni-solar. And the nature of a luni-solar year is to consist of lunar months, and solar periods.

Geminus tells us, that all the ancient Greeks, by their laws, and the dietates of their oracles, made their years agree with the sun, and their months and days of the month with the course of the moon, so that the same sacrifices might always fall upon the same seasons of the year, and upon the same days of the lunar month; and that they counted this acceptable and grateful to the Gods, and according to the institutions of their country. And Cicero saith, that the Sicilians and other Greeks, to make their days and months agree

with the courses of the sun and moon, sometimes took away a day or two from the month (that is, from the calendar month of thirty days) and sometimes made the month larger by one or two days. And Censorinus, that the

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several nations of Italy had their several years, but all of them by months variously intercalated, and corrected their civil calendar years by that one true natural year. By this practice therefore, the ancient festivals and solemnities of the nations of Greece, Sicily, and Italy, which were cele. brated on certain days of certain months, (as the Olympiads, and Pythick games, Bacchanalia, Cerealia, &c.) kept to the same seasons of the

year,

and Hesiod's year began in summer, after the rising of the Pleiades, and his month Lenæon was a winter month, as he represents. And by the like practice, the months of the Asiatics kept their seasons.

For Galen tells us, Quod tempus Romæ est September, Pergamanis apud nos, Hyperborelæus, Athenis vero Mysteria, ea namque erant Boedromione. And the same is to be understood of the years and months of the Jews. The Sanhedrim proclaimed the new moons upon the first appearance of the new moon, and if the corn was not ripe enough for offering the first fruits thereof, upon the middle of the 13th month, they added that month to the old year, and began the new year with the 14th. And by some such practice, the months of the Chaldaic years also kept to the same seasons. the Dieteris, Tetraeteris, and Octoeteris of the Greeks, arose from the intercalation of months, so did the Dodecaeteris of the Babylonians; and the end of such intercala- ; tions, was to make the year keep to the sun, and the months to the seasons.

Suidas tells us that 120 sari are 2220 years, according to the reckoning of the Chaldeans, a sarus containing 222 lunar months, which are eighteen years six months : in this reckoning twelve lunar months make the year of the Chaldees, and eighteen such years and six months (I think he means intercalary months) make the sarus. And Athenæus, lib. 14, tells us out of Berosus, that upon the 16th day of the month Lous, (that is on the 16th day of the lunar month, called Lous by the people of Macedonia) the Babylonians celebrated annually the feast of Sacæa. This feast therefore kept to the same season of the year,

and

so did the Babylonian lunar month, in which it was seated.

When therefore Cleobulus, one of the seven wise men, or Hippocrates, or Herodotus, or Aristotle, or Plutarch, or Manetho, describe the ancient year of the Greeks, Románs, or Egyptians to consist of twelve equal months, or 360 days, or Cyrus, in allusion to those days, cut the river Gindus into 360 channels: or the Atheniansín allusion to the same days erected 360 days (statues) to Demetrius, they are to be understood of the calendar year of the ancients, not yet corrected by the courses of the sun and moon. And when they had at

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Athens four Qura, intimating the four seasons of the year, twelve palgía og Teiluç according to the months, every pargice had thirty yern, corrected from time to time by the heavens, so as to make it keep the four seasons. And when Herodotus intercalates a month of 30 days every other year, he is to be understood of the Dieteris of the ancients, continued for seventy years together, without correcting it by the moon. And when Moses reckons the duration of the food, by months of thirty days, he is to be understood of the calendar months, not corrected by the moon, by reason of the rainy weather, which did not suffer her to appear. And when David appointed twelve courses of guards, one for every month in the year, (I. Chron. xxvii.) he had respect only to the calendar months of the Mosaic year, leaving the intercalary months unprovided, because they were uncertain, and might be supplied by the twelve courses alone, the course which should serve upon the first month of the next year, serving upon the intercalary month when it happened, and the next course serving upon the first month of the next year. And when the Babylonians, as Diodorus tells us, say that there are twelve chief gods, and to every one of these assign a month, and a sign in the zodiac, and say that through these twelve signs the sun makes his course every year, and the moon every month, they describe the Chaldaic year to be solar, and to consist of twelve equal lunar months, answering to the twelve signs with their de. grees, and mean the months and days in the calendar year, not yet corrected by the courses of the sun and moon : and by the relation and correspondence which those months have to the twelve signs, they fix them to the seasons of the year, by such corrections as were to be made for that purpose. This year the Jews, during their stay at Babylon, made use of in their contracts and civil affairs, and in their journey from Babylon to Jerusalem, brought it home along with them, calling their own months ever after, by the names of the Babylonian; which they would not have done if their own lunar months had not been the same with those of Babylon.

So then the luni-solar year with its calendar, was very ancient and universal, being used by Noah, and propagated down from him to his posterity, and giving occasion to tlie division of the zodiac into twelve signs, and that of a circle into 360 degrees, and to the invention of the Dieteris, Tetraeteris, and other ancient cycles, for avoiding the trouble of correcting it every month by the moon, and every year by the sun, and continuing to be used in Egypt till

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