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from the return of the same seasons, for procuring or gathering the fruits of the earth. This they have subdivided into months, and these again into weeks of seven days each. Observing that the moon appeared to pass through all her phases about 12 times in the return of the same seasons, they divided the year into twelve months, of about 30 days each; so that the year of the ancients consisted of 360 days. But in process of time, they found that this method of estimating the length of the year did not agree with the revolution of the sun; which put them upon various ways of correcting it, either by adding a few days every year, or a whole month after a certain number of years.

At length, Julius Cæsar, about forty years before the commencement of the christian æra, took this troublesome affair in hand. Having obtained from Sysogenes, an eminent mathematician of Alexandria, information that the length of the solar year was about 365 days and a quarter; hence he ordered that the year should consist of 365 days for three years together, and that every fourth year should contain 366. This intercalary day, every fourth year, was inserted after the 23d of February; which, in their way of reckoning the days of the month, was called the sixth of the calends of March, sextilis calendarum. This sixth of the calends was reckoned twice that year, or the 23d and 24th of February were both called the sixth of the calends of March, and hence the year obtained the name of bissextile. In our almanacks, this day is added after the 28th of February.

The above is called the Julian account, or old style, from this rectification of Julius Cæsar, who thought he had thereby made the civil year to keep pace with the solar year; so that the equinoxes and solstices would

constantly return on the same days of the month, in all succeeding years. But this mean length of the civil year, viz. 365 days and six hours, exceeds the tropical year of 365d 5h 48′ 57′′, by 11' 3", which amounts to a whole day in 130 years; so that in that space of time, the equinoxes will anticipate a whole day, or happen one day of the month sooner. In 400 years by the Julian account, there would be contained 400 years, three days, one hour, fifty-three minutes and twenty seconds; hence if three days were left out of the civil account in every 400 years, the civil and solar years would pretty nearly agree together; as the 1 53′ 20′′ would not amount to a whole day in less than 5082 years, and therefore might be neglected as inconsiderable.

In the year 325 of the christian era, when the council of Nice settled the canon for the celebration of Easter, the equinox fell on the 21st of March; but in the year 1582 it fell on the 11th of March, 10 days sooner. Pope Gregory therefore determined to restore the vernal equinox again to the 21st of March, and accordingly ordered the 5th of October 1582 to be called the 15th, and thereby struck out 10 days from the calendar in that year. And to prevent the like anticipation of the equinoxes for the future, by the use of the Julian account, he ordered three days to be left out of it, in every 400 years; by making the centurial years, not divisible by 4, such as 1700, 1800, 1900, 2100, &c. to be common years of 365 days, whereas they would have been bissextile, by the Julian account. Thus while the years 1600, 2000, 2400, are allowed to continue bissextile, the three days of anticipation in 400 years are left out of the calendar. This rectification is called the new stile, or Gregorian ac

count. It was immediately adopted in the countries. where the Pope's authority was acknowledged, but was not admitted in the British dominions, till the year 1752, when they were obliged to strike out 11 days, which they did by calling the 3d of September the 14th, to bring the vernal equinox back to the 21st of March, as it was at the time of the council of Nice.

ERAS AND CYCLES.

IN computations of time, we find it necessary to fix upon some remarkable transaction, as the beginning of our reckoning, which is called an era or epocha. Thus some compute from the creation of the world, 4004 years before Christ; the ancient Greeks from the institution of the Olympiads of 4 years each, 776 years before Christ; the Romans from the building of Rome, 753 years before Christ; the Chaldeans and Egyptians from Nabonassar, king of Babylon, 747 years before Christ; the Mahometans from the flight of Mahomet, called the Hegira, 622 years after Christ; and Christians from the vulgar account of his birth, which is now generally accounted to be 4 years erroneous, or too late.

Astronomers have found that their computations are much facilitated by the invention of certain cycles, of which the following are the most remarkable.

The Cycle of the Sun, is a period of 28 years, after which the same day of the month returns on the same day of the week, and the dominical letters return in the same order. If 365 be divided by 7, it will quote 52, and leave a remainder of one, which shows that there are 52 weeks and one day in a common year; that the first and last days of the year are on the same day of the week, and consequently that the next day

of the week will be the first day of the succeeding year. Now it has been customary to place the first seven letters of the alphabet opposite to the days of the month, and as there are but seven days in the week, the same letter that stands opposite to the Sunday of any week, will stand opposite to all the Sundays of that year, and is therefore called the dominical letter. Now the first of January having the letter A placed opposite to it, in every year, should this day be Monday, the letter G will be the dominical letter for that year, and Monday will be the last day of the year; so that the next year beginning on Tuesday, and having the letter A placed opposite to it, F will be opposite to all the Sundays of that year. For the same reason, E will be the dominical letter for the third year. Thus in seven years all the seven letters would be dominical letters in their turn, beginning at the last and going on in a retrograde order to the first, if they were all common years of 365 days. But as this order is interrupted every fourth year, which contains 366 days, or 52 weeks and two days, the next year must begin two days further in the week than the last, thereby leaping over one, for which reason the fourth is called leap-year. This series cannot return until it be as often interrupted as there are days in the week, that is, seven times. Now as this interruption happens every fourth year, and thereby one day in the week is passed over, it will require 28 years to pass over all the day's of the week, after which time the same days of the month will happen on the same days of the week, and the dominical letter be the same that it was 28 years before. As the 28th and 29th of February are supposed to have the same letter affixed to each of them, as was formerly the case with the 23d and 24th, when

count. It was immediately adopted in the countries where the Pope's authority was acknowledged, but was not admitted in the British dominions, till the year 1752, when they were obliged to strike out 11 days, which they did by calling the 3d of September the 14th, to bring the vernal equinox back to the 21st of March, as it was at the time of the council of Nice.

ERAS AND CYCLES.

IN computations of time, we find it necessary to fix upon some remarkable transaction, as the beginning of our reckoning, which is called an era or epocha. Thus some compute from the creation of the world, 4004 years before Christ; the ancient Greeks from the institution of the Olympiads of 4 years each, 776 years before Christ; the Romans from the building of Rome, 753 years before Christ; the Chaldeans and Egyptians from Nabonassar, king of Babylon, 747 years before Christ; the Mahometans from the flight of Mahomet, called the Hegira, 622 years after Christ; and Christians from the vulgar account of his birth, which is now generally accounted to be 4 years erroneous, or too late.

Astronomers have found that their computations are much facilitated by the invention of certain cycles, of which the following are the most remarkable.

The Cycle of the Sun, is a period of 28 years, after which the same day of the month returns on the same day of the week, and the dominical letters return in the same order. If 365 be divided by 7, it will quote 52, and leave a remainder of one, which shows that there are 52 weeks and one day in a common year; that the first and last days of the year are on the same day of the week, and consequently that the next day

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