ECCLESIASTICAL.] CALENDAR 677 The value of L is always given by the formula for the dominical letter, and P and I arc easily deduced from the epact, as will appear from the following considerations. When P = 1, the full moon is on the 21st of March, and the new moon on the eighth (21 - 13 = 8), therefore the moon s age on the 1st of March (which is the same as on the 1st of January) is twenty- three days ; the epact of the year is consequently twenty-three. When P 2 the new moon falls on the ninth, and the epact is con sequently twenty-two ; and, in general, when P becomes 1 + x, E becomes 23 - x, therefore P + E - 1 + x + 23 - x 24, and P = 24 - E. In like manner, when P ^ 1, I -1) = 4 ; for D is the dominical L-lter of the calendar belonging to the 22nd of March. But it is evident that when I is increased by unity, that is to say, when the fuij moon falls a day later, the cpact of the year is dimin ished by unity ; therefore, in general, when I 4 + x, E 23 - x, whence I + E = 27 and I = 27 - E. I>ut P can never be less than 1 nor I less than 4, and in both cases E = 23. When, therefore, E is greater than 23, we must add 30 in order that P and I may have positive values in the formula P = 24 - E and I 27 - E. Hence there are two cases. P = 24 - E AYhen < 24, When E> 23, 15 v substituting one or other of these values of P and I, according as the case ma} be, in the formula p = P + (L - 1), we, shall have j), or the number of days from the 21st of March to Easter Sunday. It will be remarked, that as L-Z cannot either be or negative, we must add 7 to L as often as may be necessary, in order that L-l may be a positive whole number. By means of the formula? which we have now given for the domin ical letter, the golden number, and the epact, Easter Sunday may be computed for any year after the reformation, without the assist ance of any tables whatever. As an example, suppose it were required to compute Easter for the year 1840. By substituting this number in the formula for the dominical letter, we have a = 1840, (1). I = 27 - E, or ( -- P = 54 - E c - 16 = 2, ^-) w = therefore L = 7m + 6 - 1840 -460 + 2 = 7m - 2292
7 x 328 - 2292 = 2296 - 2292
L = 4 = letter!) /1840 + 1 For the golden number we have N -- ( -. ..,. - I , ; therefore N = 17 .....* (2). ^N + 10<N-lh /17 + 100 /177 1 or the epact we have ! = 27 ; likewise c- 16 = IS - 16 = 2, -g~ = l, = ; therefore E = 27-2 + 1 = 26... ....................... (3). Xow since E > 23, we have for F and I, P = 54-E = 54-26 = 28, consequently, since p = P + (L - I), p- 28 + (4-3)- 29; that is to say, Easter happens twenty-nine days after the 21st of March, or on the 19th April, the same result as was before found from the tables. The principal church feasts depending on Easter, and the times of their celebration, are as follows : - Septuagesima Sunday ............. First Sunday in Lent ............... is Ash Wednesday ...................... ] legation Sunday .................... Ascension day or Holy Thursday Pentecost or Whitsunday ......... Trinity Sunday ..................... The Gregorian calendar was introduced into Spain, Portugal, and part of Italy, the same day as at Rome. In France it was received in the same year in the month of December, and by the Catholic states of Germany the year following. In the Protestant states of Germany the Julian calendar was adhered to till the year 1700, when it was decreed by the diet of Ratisbon that the new style and the Gregorian correction of the intercalation should be adopted. Instead, however, of employing the golden numbers and epaots for the determination of Easter and 9 weeks 6 weeks 46 days 5 weeks before j Easter. 39 days after 7 weeks Easter. 8 weeks the movable feasts, it was resolved that the equinox and the paschal moon should be found by astronomical com putation from the Iludolphine tables. But this method, though at first view it may appear more accurate, was soon found to be attended with numerous inconveniences, and was at length, in 1774, abandoned at the instance of Frederick II. king of Prussia. In Denmark and Sweden the reformed calendar was received about the same time as in the Protestant states of Germany. It is remarkable that Russia still adheres to the Julian reckoning. In Great Britain the alteration of the style was for a long time successfully opposed by popular prejudice. The inconvenience, however, of using a different date from that employed by the greater part of Europe, in matters <.f history and chronology, began to be generally felt ; and at length, in 1751, an Act of Parliament was passed for the adoption of the new style in all public and legal transac tions. The difference of the two styles, which then amounted to eleven days, was removed by ordering the day following the 2d of September of the year 1752 to be accounted the 14th of that month ; and in order to pre serve uniformity in future, the Gregorian rule of intercala tion respecting the secular years was adopted. At the same time, the commencement of the legal year was changed from the 25th of April to the 1st of January. In Scotland, the new style was adopted from the begin ning of 1600, according to an Act of the privy council in December 1599. This fact is of importance with reference to the date of legal deeds executed in Scotland between that period and 1751, when the change was effected in England. With respect to the movable feasts, Easter is determined by the rule laid down by the Council of Nice ; but instead of employing the new moons and epacts, the golden numbers are prefixed to the days of the full moons. In those years in which the line of epacts is changed in the Gregorian calendar, the golden numbers are removed to different days, and of course a new table is required when ever the solar or lunar equation occurs. The golden numbers have been placed so that Easter may fall on the same day as in the Gregorian calendar. The calendar of the church of England is therefore from century to century the same in form as the old Roman calendar, excepting that the golden numbers indicate the full moons instead of the new moons. HEBKEW CALENDAR. In the construction of the Jewish calendar numerous details require attention. The calendar is dated from the Creation, which is considered to have taken place 3760 years and 3 months before the commence ment of the Christian era. The year is luni-solar, and, according as it is ordinary or cmbolismic, consists of twelve or thirteen lunar months, each of which has 29 or 30 days. Thus the duration of the ordinary year is 354 days, and that of the embolismic is 384 days. In either case, it is sometimes made a day more, and sometimes a day less, in order that certain festivals may fall on proper days of the week for their due observance. The distiibu- ti-.m of the embolismic years, in each cycle of 19 years, is determined according to the following rule : The number of the Hebrew year (Y) which has its commencement in a Gregorian year (x) is obtained by the addition of 3761 years; that is, Y = x + 3761. Divide the Hebrew year by 19 ; then the quotient is the number of the last completed cycle, and the remainder is the year of the current cycle. If the remainder be 3, 6, 8, 11, 14, 17, or 19 (0), the year is embolismic ; if any other number, it is ordinary. Or, otherwise, if we find the remainder
the yoar is embolismic when R < 7,