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 a similar cycle of no less than 2800 years exists. Up to the end of this century, however, the cycle of 28 years, as it now exists, will remain undisturbed,* and it may therefore be worth while to give the 3 ears of the solar cycle answering to the decade of the century, and the table o dominical letters, concurrents, and regulars :— To find the 1st of April, 1S36: the year is 25 of the cycle, and leap year, and the concurrent 3 added to 2, the regular of April, with 1 allowed for leap-year, gives 6, or Friday.
There are many perptraal almanacs, as they are called, by which such questions as the preceding can be solved by reference, wlt.hout 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 almanacs for themselves on this principle, with their own peculiar days of ceremony duly entered : and M. Franeceur published a general one at Paris in 1842. On this hint Mr. De Morgan con structed his ` Book of Almanacs,' 1851, in which the ulnae almanac of any year, the moon • excepted, 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 lunatious, as follows : the 235 mean lunatious of 29.53059 days each make 6939'69 days, while 19 years of 365 days each give 6935 days, and, allowing 4f days for leap-years, 6939.75 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 300 years, and as far 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 same 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 Faster in chronology. If the astronomers had been allowed to vary Esster 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 uuvaried rule ; and the reformation (so called) of the calendar was, in our opinion, anything but an improvement Chronologists have two cycles of nineteen years 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 v6rifier lea Dates,' particularly as all the dates are quite exact : " Acta aunt anno ab incarnations Domini max., indictione u., epacta concurrente Iv., cyclus lunaris v., cyclus decemnovennalis regularis peaches iv., terminus paechalis rum kaL Mall, dies paschal; vu. kal. Mail, Inure ipeina (diei paschre) an." After what has been said on EASTER, there is no enter on that subject here.
The epact of the year is usually stated as being tho moon's age at the beginning of the year : this is a correct definition as to the epact of the Gregorian calendar, but not ao as to that which preceded. The epaet of the old calendar Is 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 pleasure, provided all the numbers in the table of regulars be as much diminished or increased; and different tables of erects will be found in different works, tho 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 11 more than that of the preceding, abating 30 as feet as it arises; this must be the case in every table, and the moat common table of epacta gives 29 as the epact of the first year of the cycle, 10 as that of the second, 21 as that of the third, fie. Corresponding to this, 9 is the regular of January, 10 of February, fie. It is not worth while to give the table, not only because it is now useless, even for old chronology, but because it fails for those years of the decemnovenual cycle in which two full moons come in the same month.