CHRONOLOGY.'

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at the equinoctial point. During Csssar’s reign the vernal equinoxliad been observed by Sosigenes on the 25th of March ; but bythe time of the Nicene council it had gone backward to the21st. The cause of the error was not then known •/‘but in 1582,when the equinox happened on the 11th of March, it was thoughtproper to give the calendar its last correction. Pope GregoryXIII. having invited to Rome a considerable number of mathe-maticians and astronomers, employed ten years in the examinationof their several formula;, and at last gave the preference to thatof Aioisius and Antoninus Lelius, who were brothers. Ten dayswere now' cut off in the month of October, and the 5th of thatmonth was reckoned the 15th. To prevent the seasons from re-ceding in time to come, lie ordained that one day should bedddeil every fourth or bissextile year as before; and that the 1600thyear of the Christian era, and every fourth century thereafter,should he a bissextile or leap-year. One day therefore is to lieintercalated in the years 2000, 2400, 2800, See. but in the othercenturies, as 1700, 1S00, 1900, 2100, &c. it is to be suppressed,mid these are to be reckoned as common years. Even this cor-rection, however, is not absolutely exact; but the error must bevery inconsiderable, and scarcely amounting to a day and an ballin 5000 years. The commencement of the vear has been deter-mined by the date of some memorable event, such as the creationof the world, the universal deluge, a conjunction of planets, theincarnation of our Saviour, &c. and of course has been referred todifferent points in the ecliptic. The Chaldxan and the Egyptianyears were dated from the autumnal equinox- The ecclesiasticalyear of the Jews began in the spring ; but, in civil affairs, theyretained the epocli of the Egyptian year. The ancient Chinesereckoned from the new moon nearest to the middle of Aquarius;but, according to some recent accounts, the beginning of theiryear was transferred, (B. C. 1740,) to the new moon nearest tothe winter solstice. This likewise is the date of the Japaneseyear. Diemschid, or Gemschid, king of Persia, observed, on theday of his public entry into Persepolis, that the sun entered intoAries, in commemoration of this event, he ordained the be-ginning of the year to lie removed from the autumnal to thevernal equinox. This epoch was denominated Neuruz, viz. newday; and is still celebrated with great pomp and festivity. SeeEpochs. The ancient Swedish year commenced at the wintersolstice, or rather at the time of the sun’s appearance in the hori-zon, after an absence of about 40 days, borne of the Grecianstates computed from the vernal, some from the autumnal equinox,and others from the summer tropic. The year of Romulus com-menced in March, whence the four last months, September,October, November, and December, were really what theirnames import, the 7th, 8th, 9th, and 10th months. Numa,without altering these names, began the year in January, whichCaesar continued. The Greeks distributed their years into systemsof four, calling them Olympiads, from the return of the Olympicgames every four years. ‘ And the Romans sometimes reckonedby lustra, or periods of five years. The lurks and Arabs datethe year from the 16 th of July ; and the American Indians reckonfrom the first appearance of the new moon of the vernal equinox.The church of Rome lias fixed new-year’s-day on the Sundaythat corresponds with the full moon of the same season. TheVenetians, Florentines, and l’isans in Italy, and inhabitants ofTreves in Germany, begin the year at the vernal equinox. Theancient clergy reckoned from the 25lh of March ; and this methodwas observed in Britain, until the introduction of the new styleA. D. 1752, after which our year commenced on the 1st day ofJanuary, and consists- of 363 days in common years and 366in leap-years, and thus our civil year is made nearly to correspondwith the astronomical year. It belongs to astronomers to ascertainthe exact length of the astronomical year, which they find-todiffer when the admeasurement is made by the revolution of thesun from certain remarkable points in the heavens to the sameagain. To these they gave different denominations. The firstis called the solar year, and is the time in which the sun performsa revolution from the equinoctial point to the same again, or fromany point of the ecliptic to tire same point again. It consists of365 (t. 4 h. 48'. 48". The second is the sidereal, which is mea-sured by the sun’s return to any star or fixl point in the heavensfrom which he set out, its length is 365 d. 6h. 9'. 24". Thethird is called the anomalistic year, and reckoned by the sun’smotion from the apogee to the apogee again, and contains 365 d.

V8L. i.— no. 45.

6 h. 14'. The seasons are regulated by the solar year which isshorter than the sidereal on account of the precession of theequinoxes. See Astronomy.

Of Cycles.

Besides these natural divisions of time arising immediately fromthe revolutions of the heavenly bodies, there are others formedfrom some of the iess obvious consequences of these revolutions,which are called cycles, from die Greek xrax©-, a circle. Themost remarkable of these are the following :

I. The cycle of the sun is a revolution of 2S years, in whichtime the days of the months return again to the same days of theweek ; the sun’s place to the same signs and degrees of the eclip-tic on 4he same months and days, so as not to differ one .degree in100 years; and the leap-years begin the same course over againwith respect to the days of the week on which the days of themonths fall.

II. The cycle of the moon, or the golden number, is a revolu-tion of 19 years; in which time, the conjunctions, oppositions,and other aspects of the moon, are within an hour and a half ofbeing the same as they were on the same days of the months 19years before.

From the cycles of the sun and moon multiplied into one ano-ther, arises a third period of 532 years, which is called the Victorianor Dionysian period: and after the completion of this period, notonly the new and full moons return to the same days of the month,but also the days of the months return to the same days of theweek ; and therefore the dominical letters and the moveable feastsreturn again in the same order. Hence, this cycle is called thegreat Paschal cycle. For to find the year of the Dionysian pe-riod for any year of Christ, to the current year add the number457, and divide the sum by 532, the remainder after the quotientis the year of the period.

hxmnplc. If it he required to find in what vear of the Diony-sian period this present vear of Christ, 1810, is, we must work asfollows: 1810-f 457 = 2267 and 2267-j-532 = 4 and 139 over,therefore 139 is the year of the Dionysian period required.

It is a problem of another kind: having the cycles of the suaand moon, to find the year of the Dionysian period. For exam-ple, suppose the yearof'lhe cycle of the moon to be 17, and of thestm 21: to solve this problem it is required to find a number,which, when it is divided by 19 leaves 17, and when it is dividedby 28 leaves 21. To find this, let it be required to find two num-bers, one of which w ill divide exactly by 28, without a remainder,hut when it is divided by 19 leaves 17 ; and another numberwhich will divide exactly without a remainder by 19, but whenit is divided by 28 leaves 21. It is plain, that the sum of thesetwo numbers will answer the question. We will here shew theanalytical investigation of tlie.se two numbers. We will supposethe Urat number to be 28i/, for it is a multiple of 23 ; and because”this number divided by 19 leaves 17, if we take 17 from it, the re-mainder divided by 19 will be a whole number; since then 19divides 28 y — 17, and it also divides 19?/, therefore it will divide

9:/—17

then- difference, which is 9y — 17; consequently _ is a

19

whole number. Call that whole number n, consequently

19rt—j— 17

9y — 17=19?), and % = 19/i-f-17, and y— -, and

9

because y is a whole number, 9 must divide 19/i-f-17, but 9 di»vides ]8»4-9, therefore it will divide the remainder n-f-8, and

7 i —^—8

consequently-is a whole number. Let that number be 1,

9

and % will be = 1, and y= 4 ; consequently 98 y— 112= to thefirst number to be found. Suppose the second number to be

19J-21

19z, for it must be. a multiple of 19, therefore-— is a whole

28

number; suppose it to be n, then 19z— 21 = 28n, and z =:28«+21

--, which must likewise be a whole number, and therefore

19

2Sn + 2l will be divided by 19 without a remainder: hut 19divides 19?)-f 19, wherefore it will divide the remainder 9n -f-2,

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