CYCLE

, a certain period or series of numbers proceeding orderly from first to last, then returning again to the first, and so circulating perpetually.

Cycles have chiefly arisen from the incommensurability of the revolutions of the earth and celestial bodies to one another. The apparent revolution of the sun about the earth, has been arbitrarily divided into 24 hours, which is the basis or foundation of all our mensuration of time, whether days, years, &c. But neither the annual motion of the sun, nor that of the other heavenly bodies, can be measured exactly, and without any remainder, by hours, or their multiples. That of the sun, for example, is 365 days 5 hours 49 minutes nearly; that of the moon, 29 days 12 hours 44 minutes nearly.

Hence, to swallow up these fractions in whole numbers, and yet in numbers which only express days and years, cycles have been invented; which, comprehending several revolutions of the same body, replace it, after a certain number of years, in the same points of the heaven whence it first departed; or, which is the same thing, in the same place of the civil calendar.

There are various cycles; as, the cycle of Indiction, the cycle of the moon, the cycle of the sun, &c.

Cycle of Indiction, is a series of 15 years, returning constantly around like the other cycles; and commenced from the third year before Christ; whence it happens that if 3 be added to any given year of Christ, and the sum be divided by 15, what remains is the year of the indiction. See Indiction.

Cycle of the Moon, or the Lunar Cycle, is a period of 19 years; in which time the new and full moons return to the same day of the Julian year. See CALIPPIC.

This cycle is also called the Metonic period or cycle, from its inventor Meton, the Athenian; and also the Golden Number, from its excellent use in the calendar: though, properly speaking, the golden number is rather the particular number which shews the year of the lunar cycle, which any given year is in. This cycle of the moon only holds true for 310 7/10 years: for, though the new moons do return to the same day after 19 years; yet not to the same time of the day, but near an hour and a half sooner; an error which in 310 7/10 years amounts to an entire day. Yet those employed in reforming the calendar went on a supposition that the lunations return precisely from 19 years to 19 years, for ever.

The use of this cycle, in the ancient calendar, is to shew the new moon of each year, and the time of Easter. In the new one, it only serves to find the Epacts; which shew, in either calendar, that the new moon falls 11 days too late.

As the Crientals began the use of this cycle at the time of the Council of Nice in 325, they assumed, that the first year of the cycle the paschal new moon fell on the 13th of March: on which account the lunan cycle 3 fell on the 1st of January in the third year.

The Occidentals, on the contrary, placed the number 1 to the 1st of January, which occasioned a considerable difference in the time of Easter. Hence, Dionysius Exiguus, on framing a new calendar, persuaded the Christians of the west to salve the difference, and come into the practice of the church of Alexandria.

To find the Year of the Lunar Cycle, is to find the golden number. See Golden-Number.

Cycle of the Sun, or Solar Cycle, is a period or revolution of 28 years; beginning with 1, and ending with 28; which elapsed, the Dominical or Sundayletters, and those that express the other feasts, &c, return into their former place, and proceed in the same order as before. The days of the month return again to the same days of the week; the sun's place to the same signs and degrees of the ecliptic on the same months and days, so as not to differ one degree in a hundred years; and the leap years begin the same course with respect to the days of the week on which the days of the month fall.

This is called the cycle of the sun, or the solar cycle, not from any regard to the sun's course, which has no concern in it; but from Sunday, anciently called dies solis, the sun's day; as the dominical or sunday letter is chiefly sought for from this revolution.

The reformation of the calendar under pope Gregory the 13th, occasioned a considerable alteration of this cycle: In the Gregorian calendar, the solar cycle is not constant and perpetual; because every 4th secular year is common; whereas, in the Julian, it is bissextile. The epoch, or beginning of the solar cycle, both Julian and Gregorian, is the 9th year before Christ. And therefore,

To find the Cycle of the Sun for any given year: add 9 to the number given, and divide the sum by 28; the remainder will be the number of the cycle, and the quotient the number of revolutions since Christ. If there be no remainder, it will be the 28th or last year of the cycle.

Great Pascal Cycle, is another name for the Victorian or Dionysian Period. Which see.