S97 



PERIODS OP REVOLUTION. 



PERIODS OF REVOLUTION. 



393 



year of astronomers in our day, may be considered as more than sum 

 ciently exact for any time. In fact the year is made to consist, in the 

 long run. of 365'2425 d;iys, and a cycle of 400 years is necessary to the 

 complete explanation of this fraction. Supposing the years from 

 A.D. 2001 to A.D. 2400, both inclusive, each fourth year is leap-year 

 beginning with 2004, except only 2100, 2200, and 2300, which gives ir 

 the 400 years 365 days to each year, and 97 intercalated days ; while 

 adding 97 days to 400 years, adds on the average 97-400ths or '2425 

 of a day, to each year. As it is of considerable importance distinctly 

 to comprehend an intercalated cycle, that is one in which fractions are 

 disregarded until they amount to a unit, when they are corrected, to 

 use a common phrase, in the lump, we put down the effect of the 

 correction which is made in the year 1840, being leap-year. In 1836, 

 immediately after the last intercalation was made, the sun was in the 

 vernal equinox at about 39 minutes after 1 P.M. on the 20th of March, 

 and the equinoxes then took place as follows : 



1836 Sun in equinox at l h 39" r x. March 20 



1837 at 7b 23" P.M. March 20 



1838 at 1> 18= A.M. March 21 



1839 st<k 1A.M. March 21 



1840 at 0' 41 P.M. March 20 



The intercalation of 1840 (but for which the sun would have come 

 on the equinox at 41 minutes past noon on the Iwenty-jirtt) has over- 

 done the correction, bringing the equinox nearer to noon than in 1836 

 by 58 minutes. Now this over-correction of nearly an hour in four 

 years is set nearly right by leaving out the correction three times in 

 400 years; a {'revision the necessity of which may be imagined, 

 though ita exactness cannot be appreciated from the preceding rough 

 calcuUtion. 



The Gregorian year, therefore (or the year in the Gregorian refor- 

 mation of the kalendar), is a portion of a cycle of 400 years of 365 

 days, 97 of which have an additional day. [KALEMDAB.] The Julian 

 year, in use before the Gregorian reformation, is a portion of a cycle 

 of 4 years of 365 days, one of which has an additional day. With- 

 out a perfect comprehension of the manner in which the incom- 

 mensurability of the year and day is remedied, no progress can be 

 made in the understanding of the nature and use of chronological 

 periods. 



An ..Era means either the commencement of an indefinite reckoning, 

 or of a succession of periods. In the article JE*.\ will be found the 

 complete description of the most important tcras; but as it often 

 happens that for reference the mere time of an obscure or uncommon 

 sera is wanted without explanation, we subjoin an extensive list, 

 merely giving the leading words, and the date A.D. or B.C. of the vulgar 

 Christian fflra. It is to be remembered that the birth of Jesus Christ 

 is supposed to have taken place in the fourth year B c. of this common 

 sera. The figures following the years refer to months and days : thus 

 A.D. 729 . 6 . 13 would stand for the 13th day of June, A.D. 729. We 

 do not mean to say that the events in the following list did take place 

 in the years, far less in the months, or on the days, which are set down : 

 but only that th.e who used them as ecru, took them as having 

 happened in those years, months, and days. Thus the death of 

 Alexander, according to Clinton, took place in B.C. 823, which is most 

 likely to be right ; but if those who afterwards made an sera of this 

 death, reckoned from the 12th of November B.C. 324, that day is the 

 sera, whether the event happened then or not. 



Mundane era of Constantinople 



Civil a-ra of Constantinople . . 

 Mundane sera of Alexandria . 



Mundane fer of Antioch . . . 



Commencement of Julian period . 

 Common mundane tera (Abp. Usher) 



Mundane ara of the Jews . . . 

 Civil Jewinh aera . . 



Caliyug (Hindu) . . . . . 



jEra of Abraham (Easebius) . 



Olympiads 



Building of Rome (Varro) . 



BuiMing of Rome (Cato) . . . 



JEra of Nabonassar (Babylonian) . 



Metonic cycle . . . . . 



Calippic period . . . . 



Julian reformation . . . . 

 Death of Alexander . 



.ra of ihc KeleuciddD . . . . 

 ^ra of Tyre ..... 



.Zra of Vicramiditya (Hindu) . . 



Csaarean ra of Antioch { J? re f k " 

 I Syrians . 



Spanish Bra 



Xi* of Acilum 



First leap-year of the Augustan re. 



formation 



^Era of the Ascension (as usud in the 



Chronicle of Alexandria) . . . 



BC 508.3.21 (or 4.1) 



B.C 5508.0. 1 



B.C 5502.8 .29 



n.c 5492.9.1 



B.C 4713. 1 . 1 



B.c 4004 



B.C. 3761 (vernal equinox) 



BC. 3761 .10.1 



B.C. 3101 



B.C. 2015. 10. 1 



B.C. 7T6.7 . 1 



21 



21 



26 



15 



B.C. 753.4 

 ll.c. 752 .4 

 B.C. 747 .2 

 B.C. 432.7 

 B.C. 830 

 B.C. 45 

 B.C. 324 

 B.C. S12 

 B.C. 125 

 B.C. 67 

 B.C. 49 

 B.C. 48 

 B.C. 38 . 



11.12 



9.1 



10.19 



1. 1 



B.C. 30 . 1 . 1 

 A.D. 8 

 A.D. 38 



* There is some incorrectness, but great conreniencc In this. Astronomers 

 Bow sometimes use such a notation as 1850-61, not to denote 1859 years and 

 61-100ths of a year, but the moment at which 61-lOOths of the 1859th year 

 hare elapsed. 



-Era of Salivahan (Hindu) . . A .D. 77 

 .Era of Diocletian, or of Martyrs . . A.D. 284 . 9 . 17 

 Indiction of Constantinople . .A.D. 312.9.1 

 jEra of the Armenians . ... A.D. Ml . 7 * 1 



Hegira A.D. 622.7. 16 



.Era of Yezdegird . . . . A.D. 632 . 6 . 16 

 Gregorian reformation, or new style . A.D. 1582 

 English adoption of the Gregorian 

 reformation A. D . 1752 



Among the various sources of confusion may be noticed 1, an old 

 practice of astronomers, who call the year immediately preceding and 

 following the vulgar sera, not 1 but 0, as calculation requires ; 2, the 

 discrepancies arising from different times of beginning the year. 'The 

 most important of these to the English reader is the following : 

 Before the change of style in 1752, and from the 14th century to that 

 time, the legal and ecclesiastical year began on the 25th of March, 

 though it was very common in writings, &c., to begin it on the 1st of 

 January. Hence January, February, and twenty-four days of March, 

 were in one year, according to lawyers, c. ; and in another according 

 to others. Thus the Revolution, so called, of 1688, took place in the 

 February of that legal year, or, as we should now say, February, 1689. 

 It is frequently written thus : February, 168|, or February, 1688-9. 

 Thus, King Charles was beheaded January 30, 1645, or January 30. 

 1648-9. 



We now come to the artificial periods which are of most use in 

 chronological researches : these are 



1. The cycle of the sun, or more properly the cycle of Sundays. 



2. The cycle of the moon, or of nineteen years, or of the Golden 

 number, or of the Primes, or the Metonic cycle with its sera altered. 

 [METOK, in Bioo. Dry.] 



3. The cycle of indictions. 



4. The Paschal cycle. 



5. The Julian period. 



1. The cycle of the sun is a period of 28 years, compounded of 

 7 and 4, the number of days in a week, and the number of years in 

 the interval of two leap-years. This, in the old style, makes the 

 Sundays return to the same clays of the year ; every year of the cycle 

 being in this respect exactly the same as the same year of the pre- 

 ceding cycle. Thus, the year A.D. 1 being the tenth in its solar cycle, 

 and the DOMINICAL LETTER being for that year B, or the 2nd of 

 January being Sunday, the 2nd of January was also Sunday in the 

 year A.D. (1 + 28), or A.D. 29, also in A.D. (29 + 28), or A.D. 57, &o. 



The series of dominical letters for the complete solar cycle is as 

 follows : attached to each dominical letter is what is called the 

 concurrent of the year, meaning the number of days elapsed over and 

 above a complete number of weeks, from the beginning of the cycle 

 (not including the first day) to that of the year in question, the con- 

 current being written 7 where would perhaps have been better. 



1 GF 1 



2 K 2 



3 I) 3 



4 C 4 

 t BA 6 

 8 G 7 

 7 1? 1 



8 E 2 



9 DC 4 



10 B 5 



11 A 6 



12 Q 7 



13 FE 2 



14 D * 



15 C 4 



16 B 5 



17 AG 7 



18 F 1 



19 E 2 



20 D 3 



21 CD 5 



22 



23 G 



24 F 



A 6 

 7 

 1 



25 ED S 



26 C 4 



27 B 5 



28 A 6 



Connected with this table is one of what were called solar regulars 

 (regulators would have been the modem term), one for each mouth, as 

 follows : 



Jan. 2 

 Feb. 6 



March 5 



April 

 May 



June 



July 

 Aug. 

 Sept. 



Oct. 2 

 Nov. 5 

 Dee. 7 



The Wble given in DOMINICAL LETTER would save some of the 

 following process, which however it is better to give. 



Old Style. To find the part of the solar cycle in which any given 

 year is round. If the year be A.D., add 9 and divide by 28 ; the 

 remainder (or 28 if the remainder be 0) is the year of the solar cycle 

 required. But for a year B.C., deduct 10 from the date, and divide by 

 28 ; the remainder deducted from 28 gives the year. The dominical 

 letter and concurrent are then taken from the preceding table. And 

 M find on what day of the week the first day of any month full, to the 

 concurrent of the year add the regular of the month, the sum (dimi- 

 nished by 7, if it can be done) shows the day, 1 being Sunday, 

 2 Monday, 4c. (But in leap-year one day later must be taken for 

 every month after February.) Thus to find the day on which the tcra 

 of the Hegira fell, or July 16, 622 A.D., 622 + 9 or 631 divided by 28 

 jives the remainder 15, which is the year of the cycle. The concurrent 

 s 4, which added to the regular of July 1, gives 6, or Thursday for 

 ;he 1st July, and Friday for the 16th; whence Friday is the day 

 equired. 



The perpetuity of the solar cycle, in the connection of its numbers 

 with the dominical letters, &c., is destroyed by the new style, in which 

 L similar cycle of no legs than 2800 years exists. Up to the end of 

 ;his century, however, the cycle of 28 years, as it now exists, will 

 remain undisturbed,* and it may therefore be worth while to give the 



Sine* A.D. 1900 Is not leap-year, the whole cycle will then be overthrown, 

 but since *,. 2000 is leap-year, it may be reconstructed so as to last till 2100. 



