PERIODS OF REVOLUTION. 



PERIODS OF REVOLUTION. 



jears of the solar cycle answering to the decad* of the century, and 

 the UUle o dominical letter*, concurrent*, and regular* : 



To find the 1st of April, 1838 : the year is 25 of the cycle, and leap- 

 year, and the concurrent 3 added to 2, the regular of April, with 1 

 allowed lor leap-year, give* 6, or Friday. 



There are many perpetual almanac*, as they are called, by which 

 uch questions as the preceding can be solved by reference, without 

 calculation. But when the almanac of a particular year is wanted in 

 totality, there must be thirty-five distinct almanacs set out, to meet 

 every possible location of Easter-day, with an index by which the year 

 is to show which almanac to turn up. Several of the monastic orders 

 constructed almanac* for themselves on this principle, with their own 

 peculiar days of ceremony duly entered : and M. Franoccur published 

 a general one at Paris in 1842. On this hint Mr. De Morgan con- 

 structed hi* ' Book of Almanacs,' 1851, in which the *koU at manor of 

 any year, the moon * ezcepted, is turned up at once, whether in old or 

 new style. 



2. The cycle of the moon is that of 19 years, which is very nearly 

 235 complete lunations, as follows : the 235 mean lunations of 

 29-53059 days each make 6939 '69 days, while 19 years of 365 days 

 each give 6935 days, and, allowing 4] days for leap-years, 693975 days. 

 Hence 235 lunations fall short of 19 Julian years by '06 of a day, or 

 one day in about 317 years. During a period of 800 years, and as for 

 as the mean place of the moon is concerned [EASTER], the new and 

 full moons of the cycle of nineteen years would fall on the some days. 

 On the assumption of 235 lunations exactly corresponding to 19 years, 

 all the rules for finding Easter are founded; and in the steadiness 

 with which this false assumption was held to, lies the. value of Easter 

 in chronology. If the astronomers hod been allowed to vary Easter 

 according to the latest improvements in determining the moon's place, 

 the chronology of the details of the different years of the middle ages, 

 confused as it sometimes is, would rarely have been anything but 

 confusion ; in chronological reckoning nothing is of any importance 

 compared with keeping to one unvaried rule ; and the reformation 

 (so called) of the calendar was, in our opinion, anything but an 

 improvement. 



Chronologists have two cycles of nineteen yean each, the first of 

 which is the cycle of nineteen years (so called), cr of the golden 

 number, and the second, which begins three years later, they call the 

 lunar cycle. These of course only differ in their time of commence- 

 ment, the year 4 of the first cycle being always 1 of the second. To 

 show the manner in which accuracy was attempted, it is worth while 

 to quote the date of one charter, from the ' Art de verifier lea Dates,' 

 particularly as all the dates are quite exact : " Acts sunt haw, anno ab 

 incanutione Domini MCIX., indictione u., epacta XVIL, concurrent* iv., 

 cyclus lunaris v., cyclus decemnovennolia VHL, regularis paschai iv., 

 terminus paachalis XIIH. kal Maii, dies paschalis vn. kol. Mali, lunto 

 ipsius (diei paschic) xxi." 



After what ha* been said on EASTER, there is no occasion, to enter 

 on that subject here. A 



The epact of the year is usually stated as being the moon's age at 

 the beginning of the year : this i* a correct definition as to the epact of 

 the Gregorian calendar, but not so as to that which preceded. The 

 epact of the old calendar U a number depending on the year in such 

 manner that the epact of the year, increased by what was called the 

 lunar regular of any month, gives (with deduction of 29, if necessary) 

 the age of the moon on the first day of that month ; so that the age of 

 the moon at the beginning of the year is the epact, together with the 

 regular of January. Thus the epact of every year may be increased or 

 diminished at plearore, provided all the numbers in the table of 

 regular* be as much diminished or increased ; and different tables of 

 epacU will be found in diflerent works, the difference being of course 

 compensated in the regulars, or else in the rule for applying them. 

 The epact of each year of the cycle of 19 years must be 1 1 more than 

 r the preceding, abating 30 as fast as it arises ; this must be the 

 case in every table, and the most common table of epact* gives 29 as 

 the epact of the first year of the cycle, 10 as that of the second, 21 as 

 that of the third, Ac. Corresponding to thi, 9 is the regular of 

 January, 10 of February, 4c. It is not worth while to give the table, 

 not only because it i* now useless, even for old chronology, but because 



Vnnt ire sddcd of finding the new or full mooni of ny j-er, within a 

 day, without anjr calculation : and aUo mean* of calculation to Hod them within 

 two hour*. 



it fails for those year* of the decemnovennal cycle in which two full 

 moon* come in the same month. 



Again, the annual regular, or the regular cited in charter* (as in our 

 previous quotation, where it U called the paschal regular), is neither 

 the solar regular described in the former part of this article, nor the 

 lunar regular just mentioned, but a third regular belonging to the 

 whole year, and which, added to the concurrent previously described, 

 gave (7 being abated, if necessary) the last day of the moon preceding 

 the paschal moon. Thus, A.D. 874, the concurrent being 4 and the 

 annual regular 5, their sum 9 diminished by 7, or 2, gives Monday as 

 the last day of the ante-paschal moon. 



The paschal term (terminus paacbalia) mentioned in the quotation, 

 meant simply the fourteenth day of the paschal moon. 



8. The Indiction was an edict of the Roman emperors, fixing the 

 tribute ; and as one such edict was supposed to have appeared every 

 fifteen years, year* were naturally reckoned according to their distance 

 from the year of iudiction. There is doubt about the first origin of 

 indiction*, about their meaning and their earliest date : all we have 

 here to do with is the fact, that from Athanasius downwards, they 

 were more or less employed by ecclesiastical writer* in describing 

 epochs. The popes afterwards adopted this mode of dating, and the 

 common indiction * found in chronological tables begins so that A.D. 813 

 is the first year of the firxt cycle of indiction, each cycle containing 15 

 yean. At this rate, A.U. 1 was the fourth year of an imaginary pre- 

 ceding indiction, and the remainder of three more than the date of any 

 year divided by 15 will give it petition in its cycle of indiction. Thus 

 1239, increased by 3 and divided by 15, gives the remainder 1'J, or 

 A.D. 1239 is the twelfth year of a cycle of indiction. 



4. The paschal cycle is one composed of 28 and 19 yean, or 532 

 years, during which time the cycles of the sun and of 19 years run 

 through all their combinations, and recommence them again. Accord- 

 ing to the old system, then, this is the cycle of Easter Days, which 

 begin again in the same order when it is finished: A.D. 1 was the second 

 year of the first paschal cycle, being also 2 of the cycle of 19 years, and 

 10 of its solar cycle. The paschal cycle of the Gregorian calendar 

 would be 53,200 years. 



5. The Julian t period was imagined by Joseph Scoliger, and is a 

 combination- of the solar cycle, the cycle of 19 years, and that of 

 indictions. Now 28 x 19 x 15 gives 7980 years, which is the length of 

 the period in question. It was made to begin at a year B.C., which 

 was the first year of each cycle namely, B.C. 4718 years. Hence, sub- 

 tract any year B.C. from 4714, or add any year A.D. to 4713, and you 

 have the year of the Julian period answering to the date used. The 

 advantage (if it be one) of this period is, that by dividing the year in 

 it by 28, 19, and 15, the remainders show the years of the different 

 cycles belonging to the Julian date used, remembering when the 

 remainder is nothing to substitute the divisor instead. 



For the history of periods not absolutely used in chronology, see 

 their several names, such asMetouic Cycle, under METON, in Bioo. Div., 

 SARDS, SOTBIAC PERIOD, 4c., &c. 



Astronomical periods, actually existing in nature, may be divided 

 into days, connected with the rotations of planets round their axes ; 

 immtla, connected with the rotation of satellites round their primaries; 

 yean, connected with the rotations of primary planets round the sun ; 

 and ttcular periods, connected with slow changes of the elements of 

 orbits. The most convenient period of measurement is the civil or 

 mean solar day at the earth, being the average interval between noon 

 and noon. [SYNODIC REVOLUTION.] 



This period being divided into hours, &c., the octuol rotation of the 

 earth is 23 k 56" 4--09, and is called the sidereal day. The average 

 interval between two transits of the moon over the meridian is 24 k 60" 

 28"32, which might be called the mean tide-day. The rotation of the 

 moon is the time of her revolution round the earth [Moon] ; and the 

 rotations of the planets are as follows (in sidereal time) so as to make 

 24 k the rotation of the earth : 



Hun 



Mercury 

 Venus 

 Earth 

 Mars . 



d. h. in. 

 25 8 

 24 6) 



23 21 

 14 



24 38 



Jupiter . . , 

 Saturn . . , 

 I i.itms unknown. 

 Neptune unknown. 



h. in. 



9 56 



10 29} 



Various months are described in the article MOON, the only ones 

 here necessary to cite being the one already used, of 29 d 12 h 44' 2-9, 

 or 29 -- 53059, the average interval from new moon to new moon, and 



The first indiction of ConsUntine U variously stated to have been A.D. 312, 

 31J, 314, ami 315. 



< f Son> lay that the name was in honour of his father, Julius Scaliger ; some 

 that it waa called from the Julian year. The discrepancy need never have 

 arlacn, for Joseph Scaliger aayn, " Juliinam vocavimus qula ad annum Jalianum 

 acoommodau." ('De emend, temp.,' cd. 1659, Geneve, p. 361.) The false 

 account waa probably fostered by the great honour in which Joseph Scaliger held 

 hi. father, whoae son he frequently called him.elf in his title-page*. But this 

 name referred to a very different person. Tnc Ircati.c just quoted first appeared 

 In 1583, just after the reformation of the calendar: and Scaliger waa a warm 

 opponent of Clavius in this matter. He stood np for the old Julian year. In 

 the very first mention of the period which occurs (Preface, p. ii.),'hc Mya, 

 "Qui anno Jallano, qua) omnium formurum tcmporlbus cut convenientiuima, 

 uti Tolet, U . . , . componct eleganUwimam pcriodum aooorum 7980, . , ." 



