Example.—Required the day on which Easter Sunday falls in the year 1840?1st, For this year the golden number is ((1840 + 1) / 19)r= 17, and the epact (Table III. line C) is 26.2nd, After the 7th of March the epact 26 first occurs in Table III. at the 4th of April, which, therefore, is the day of the new moon.3rd, Since the new moon falls on the 4th, the full moon is on the 17th (4 + 13 = 17).4th, The dominical letters of 1840 are E, D (Table I.), of which D must be taken, as E belongs only to January and February. After the 17th of April D first occurs in the calendar (Table IV.) at the 19th. Therefore, in 1840, Easter Sunday falls on the 19th of April. The operation is in all cases much facilitated by means of the table on next page.
Such is the very complicated and artificial, though highly ingenious method, invented by Lilius, for the determination of Easter and the other movable feasts. Its principal, though perhaps least obvious advantage, consists in its being entirely independent of astronomical tables, or indeed of any celestial phenomena whatever; so that all chances of disagreement arising from the inevitable errors of tables, or the uncertainty of observation, are avoided, and Easter determined without thepossibility of mistake. But this advantage is only procured by the sacrifice of some accuracy; for notwithstanding the cumbersome apparatus employed, the conditions of the problem are not always exactly satisfied, nor is it possible that they can be always satisfied by any similar method of proceeding. The equinox is fixed on the 21st of March, though the sun enters Aries generally on the 20th of that month, sometimes even on the 19th. It is accordingly quite possible that a full moon may arrive after the true equinox, and yet precede the 21st of March. This, therefore, would not be the paschal moon of the calendar, though it undoubtedly ought to be so if the intention of the council of Nice were rigidly followed. The new moons indicated by the epacts also differ from the astronomical new moons, and even from the mean new moons, in general by one or two days. In imitation of the Jews, who counted the time of the new moon, not from the moment of the actual phase, but from the time the moon first became visible after the conjunction, the fourteenth day of the moon is regarded as the full moon: but the moon is in opposition generally on the 16th day; therefore, when the new moons of the calendar nearly concur with the true new moons, the full moons are considerably in error. The epacts are also placed so as to indicate the full moons generally one or two days after the true full moons; but this was done purposely, to avoid the chance of concurring with the Jewish passover, which the framers of the calendar seem to have considered a greater evil than that of celebrating Easter a week too late.
TableV.—Perpetual Table, showing Easter.
Epact.
Dominical Letter.For Leap Years use theSECONDLetter.
A
B
C
D
E
F
G
*
Apr. 16
Apr. 17
Apr. 18
Apr. 19
Apr. 20
Apr. 14
Apr. 15
1
" 16
" 17
" 18
" 19
" 13
" 14
" 15
2
" 16
" 17
" 18
" 12
" 13
" 14
" 15
3
" 16
" 17
" 11
" 12
" 13
" 14
" 15
4
" 16
" 10
" 11
" 12
" 13
" 14
" 15
5
" 9
" 10
" 11
" 12
" 13
" 14
" 15
6
" 9
" 10
" 11
" 12
" 13
" 14
" 8
7
" 9
" 10
" 11
" 12
" 13
" 7
" 8
8
" 9
" 10
" 11
" 12
" 6
" 7
" 8
9
" 9
" 10
" 11
" 5
" 6
" 7
" 8
10
" 9
" 10
" 4
" 5
" 6
" 7
" 8
11
" 9
" 3
" 4
" 5
" 6
" 7
" 8
12
" 2
" 3
" 4
" 5
" 6
" 7
" 8
13
" 2
" 3
" 4
" 5
" 6
" 7
" 1
14
" 2
" 3
" 4
" 5
" 6
Mar. 31
" 1
15
" 2
" 3
" 4
" 5
Mar. 30
" 31
" 1
16
" 2
" 3
" 4
Mar. 29
" 30
" 31
" 1
17
" 2
" 3
Mar. 28
" 29
" 30
" 31
" 1
18
" 2
Mar. 27
" 28
" 29
" 30
" 31
" 1
19
Mar. 26
" 27
" 28
" 29
" 30
" 31
" 1
20
" 26
" 27
" 28
" 29
" 30
" 31
Mar. 25
21
" 26
" 27
" 28
" 29
" 30
" 24
" 25
22
" 26
" 27
" 28
" 29
" 23
" 24
" 25
23
" 26
" 27
" 28
" 22
" 23
" 24
" 25
24
Apr. 23
Apr. 24
Apr. 25
Apr. 19
Apr. 20
Apr. 21
Apr. 22
25
" 23
" 24
" 25
" 19
" 20
" 21
" 22
26
" 23
" 24
" 18
" 19
" 20
" 21
" 22
27
" 23
" 17
" 18
" 19
" 20
" 21
" 22
28
" 16
" 17
" 18
" 19
" 20
" 21
" 22
29
" 16
" 17
" 18
" 19
" 20
" 21
" 15
We will now show in what manner this whole apparatus of methods and tables may be dispensed with, and the Gregorian calendar reduced to a few simple formulae of easy computation.
And, first, to find the dominical letter. Let L denote the number of the dominical letter of any given year of the era. Then, since every year which is not a leap year ends with the same day as that with which it began, the dominical letter of the following year must be L - 1, retrograding one letter every common year. Afterxyears, therefore, the number of the letter will be L -x. But as L can never exceed 7, the numberxwill always exceed L after the first seven years of the era. In order, therefore, to render the subtraction possible, L must be increased by some multiple of 7, as 7m, and the formula then becomes 7m+ L -x. In the year preceding the first of the era, the dominical letter was C; for that year, therefore, we have L = 3; consequently for any succeeding yearx, L = 7m+ 3 -x, the years being all supposed to consist of 365 days. But every fourth year is a leap year, and the effect of the intercalation is to throw the dominical letter one place farther back. The above expression must therefore be diminished by the number of units inx/4, or by (x/4)w(this notation being used to denote the quotient,in a whole number, that arises from dividingxby 4). Hence in the Julian calendar the dominical letter is given by the equation
This equation gives the dominical letter of any year from the commencement of the era to the Reformation. In order to adapt it to the Gregorian calendar, we must first add the 10 days that were left out of the year 1582; in the second place we must add one day for every century that has elapsed since 1600, in consequence of the secular suppression of the intercalary day; and lastly we must deduct the units contained in a fourth of the same number, because every fourth centesimal year is still a leap year. Denoting, therefore, the number of the century (or the date after the two right-hand digits have been struck out) byc, the value of L must be increased by 10 + (c- 16) - ((c- 16) / 4)w. We have then
that is, since 3 + 10 = 13 or 6 (the 7 days being rejected, as they do not affect the value of L),
This formula is perfectly general, and easily calculated.
As an example, let us take the year 1839. In this case,
Hence
L = 7m+ 6 - 1839 - 459 + 2 - 0L = 7m- 2290 = 7 × 328 - 2290.L = 6 = letter F.
L = 7m+ 6 - 1839 - 459 + 2 - 0L = 7m- 2290 = 7 × 328 - 2290.L = 6 = letter F.
L = 7m+ 6 - 1839 - 459 + 2 - 0
L = 7m- 2290 = 7 × 328 - 2290.
L = 6 = letter F.
The year therefore begins with Tuesday. It will be remembered that in a leap year there are always two dominical letters, one of which is employed till the 29th of February, and the other till the end of the year. In this case, as the formula supposes the intercalation already made, the resulting letter is that which applies after the 29th of February. Before the intercalation the dominical letter had retrograded one place less. Thus for 1840 the formula gives D; during the first two months, therefore, the dominical letter is E.
In order to investigate a formula for the epact, let us make
E = the true epact of the given year;J = the Julian epact, that is to say, the number the epact would have been if the Julian year had been still in use and the lunar cycle had been exact;S = the correction depending on the solar year;M = the correction depending on the lunar cycle;
E = the true epact of the given year;
J = the Julian epact, that is to say, the number the epact would have been if the Julian year had been still in use and the lunar cycle had been exact;
S = the correction depending on the solar year;
M = the correction depending on the lunar cycle;
then the equation of the epact will be
E = J + S + M;
E = J + S + M;
E = J + S + M;
so that E will be known when the numbers J, S, and M are determined.
The epact J depends on the golden number N, and must be determined from the fact that in 1582, the first year of the reformed calendar, N was 6, and J 26. For the following years, then, the golden numbers and epacts are as follows:
1583, N = 7, J = 26 + 11 - 30 = 7;1584, N = 8, J = 7 + 11 = 18;1585, N = 9, J = 18 + 11 = 29;1586, N = 10, J = 29 + 11 - 30 = 10;
1583, N = 7, J = 26 + 11 - 30 = 7;1584, N = 8, J = 7 + 11 = 18;1585, N = 9, J = 18 + 11 = 29;1586, N = 10, J = 29 + 11 - 30 = 10;
1583, N = 7, J = 26 + 11 - 30 = 7;
1584, N = 8, J = 7 + 11 = 18;
1585, N = 9, J = 18 + 11 = 29;
1586, N = 10, J = 29 + 11 - 30 = 10;
and, therefore, in general J = ((26 + 11(N - 6)) / 30)r. But the numerator of this fraction becomes by reduction 11 N - 40 or 11 N - 10 (the 30 being rejected, as the remainder only is sought) = N + 10(N - 1); therefore, ultimately,
On account of the solar equation S, the epact J must be diminished by unity every centesimal year, excepting always the fourth. Afterxcenturies, therefore, it must be diminished byx- (x/4)w. Now, as 1600 was a leap year, the first correction of the Julian intercalation took place in 1700; hence, takingcto denote the number of the century as before, the correction becomes (c- 16) - ((c- 16) / 4)w, whichmust be deducted from J. We have therefore
With regard to the lunar equation M, we have already stated that in the Gregorian calendar the epacts are increased by unity at the end of every period of 300 years seven times successively, and then the increase takes place once at the end of 400 years. This gives eight to be added in a period of twenty-five centuries, andx/25 inxcenturies. But 8x/25 = 1/3 (x-x/25). Now, from the manner in which the intercalation is directed to be made (namely, seven times successively at the end of 300 years, and once at the end of 400), it is evident that the fractionx/25 must amount to unity when the number of centuries amounts to twenty-four. In like manner, when the number of centuries is 24 + 25 = 49, we must havex/25 = 2; when the number of centuries is 24 + 2 × 25 = 74, thenx/25 = 3; and, generally, when the number of centuries is 24 +n× 25, thenx/25 =n+ 1. Now this is a condition which will evidently be expressed in general by the formulan- ((n+ 1) / 25)w. Hence the correction of the epact, or the number of days to be intercalated afterxcenturies reckoned from the commencement of one of the periods of twenty-five centuries, is {(x- ((x+1) / 25)w) / 3}w. The last period of twenty-five centuries terminated with 1800; therefore, in any succeeding year, if c be the number of the century, we shall havex=c- 18 andx+ 1 =c- 17. Let ((c- 17) / 25)w=a, then for all years after 1800 the value of M will be given by the formula ((c- 18 -a) / 3)w; therefore, counting from the beginning of the calendar in 1582,
By the substitution of these values of J, S and M, the equation of the epact becomes
It may be remarked, that asa= ((c- 17) / 25)w, the value ofawill be 0 tillc- 17 = 25 orc= 42; therefore, till the year 4200,amay be neglected in the computation. Had the anticipation of the new moons been taken, as it ought to have been, at one day in 308 years instead of 312½, the lunar equation would have occurred only twelve times in 3700 years, or eleven times successively at the end of 300 years, and then at the end of 400. In strict accuracy, therefore,aought to have no value tillc- 17 = 37, orc= 54, that is to say, till the year 5400. The above formula for the epact is given by Delambre (Hist. de l'astronomie moderne,t. i. p. 9); it may be exhibited under a variety of forms, but the above is perhaps the best adapted for calculation. Another had previously been given by Gauss, but inaccurately, inasmuch as the correction depending on ''a'' was omitted.
Having determined the epact of the year, it only remains to find Easter Sunday from the conditions already laid down. Let
P = the number of days from the 21st of March to the 15th of the paschal moon, which is the first day on which Easter Sunday can fall;p= the number of days from the 21st of March to Easter Sunday;L = the number of the dominical letter of the year;l= letter belonging to the day on which the 15th of the moon falls:
P = the number of days from the 21st of March to the 15th of the paschal moon, which is the first day on which Easter Sunday can fall;
p= the number of days from the 21st of March to Easter Sunday;
L = the number of the dominical letter of the year;
l= letter belonging to the day on which the 15th of the moon falls:
then, since Easter is the Sunday following the 14th of the moon, we have
p= P + (L -l),
p= P + (L -l),
p= P + (L -l),
which is commonly called thenumber of direction.
The value of L is always given by the formula for the dominical letter, and P andlare 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 8th (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 consequently 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,l= D = 4; for D is the dominical letter of the calendar belonging to the 22nd of March. But it is evident that whenlis increased by unity, that is to say, when the full moon falls a day later, the epact of the year is diminished by unity; therefore, in general, whenl= 4 +x, E = 23 -x, whence,l+ E = 27 andl= 27 - E. But P can never be less than 1 norlless than 4, and in both cases E = 23. When, therefore, E is greater than 23, we must add 30 in order that P andlmay have positive values in the formula P = 24 - E andl= 27 - E. Hence there are two cases.
By substituting one or other of these values of P andl, according as the case may be, in the formulap= P + (L -l), we shall havep, or the number of days from the 21st of March to Easter Sunday. It will be remarked, that as L -lcannot either be 0 or negative, we must add 7 to L as often as may be necessary, in order that L -lmay be a positive whole number.
By means of the formulae which we have now given for the dominical letter, the golden number and the epact, Easter Sunday may be computed for any year after the Reformation, without the assistance 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 havex= 1840,c- 16 = 2, ((c- 16) / 4)w= 0, therefore
L = 7m+ 6 - 1840 - 460 + 2= 7m- 2292= 7 × 328 - 2292 = 2296 - 2292 = 4L = 4 = letter D . . . (1).
L = 7m+ 6 - 1840 - 460 + 2= 7m- 2292= 7 × 328 - 2292 = 2296 - 2292 = 4L = 4 = letter D . . . (1).
L = 7m+ 6 - 1840 - 460 + 2
= 7m- 2292
= 7 × 328 - 2292 = 2296 - 2292 = 4
L = 4 = letter D . . . (1).
For the golden number we have N = ((1840 + 1) / 19)r; therefore N = 17 . . . (2).
For the epact we have
E = 27 - 2 + 1 = 26 . . . (3).
E = 27 - 2 + 1 = 26 . . . (3).
E = 27 - 2 + 1 = 26 . . . (3).
Now since E > 23, we have for P andl,
P = 54 - E = 54 - 26 = 28,
P = 54 - E = 54 - 26 = 28,
P = 54 - E = 54 - 26 = 28,
consequently, sincep= P + (L -l),
p = 28 + (4 - 3) = 29;
p = 28 + (4 - 3) = 29;
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
right braceisleft brace
9 weeks
right bracebefore Easter.
First Sunday in Lent
6 weeks
Ash Wednesday
46 days
Rogation Sunday
right braceisleft brace
5 weeks
right braceafter Easter.
Ascension day or Holy Thursday
39 days
Pentecost or Whitsunday
7 weeks
Trinity Sunday
8 weeks
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 Regensburg that the new style and the Gregorian correction of the intercalation should be adopted. Instead, however, of employing the golden numbers and epacts for the determination of Easter and the movable feasts, it was resolved that the equinox and the paschal moon should be found by astronomical computation from the Rudolphine 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 of history and chronology began to be generally felt; and at length the Calendar (NewStyle) Act 1750 was passed for the adoption of the new style in all public and legal transactions. The difference of the two styles, which then amounted to eleven days, was removed by ordering the day following the 2nd of September of the year 1752 to be accounted the 14th of that month; and in order to preserve uniformity in future, the Gregorian rule of intercalation respecting the secular years was adopted. At the same time, the commencement of the legal year was changed from the 25th of March to the 1st of January. In Scotland, January 1st was adopted for New Year's Day from 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 thefullmoons. 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 whenever 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.
Hebrew 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 commencement of the Christian era. The year is luni-solar, and, according as it is ordinary or embolismic, 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 distribution 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 year is embolismic when R < 7.
The calendar is constructed on the assumptions that the mean lunation is 29 days 12 hours 44 min. 3⅓ sec., and that the year commences on, or immediately after, the new moon following the autumnal equinox. The mean solar year is also assumed to be 365 days 5 hours 55 min. 25-25/57 sec., so that a cycle of nineteen of such years, containing 6939 days 16 hours 33 min. 3⅓ sec., is the exact measure of 235 of the assumed lunations. The year 5606 was the first of a cycle, and the mean new moon, appertaining to the 1st of Tisri for that year, was 1845, October 1, 15 hours 42 min. 43⅓ sec., as computed by Lindo, and adopting the civil mode of reckoning from the previous midnight. The times of all future new moons may consequently be deduced by successively adding 29 days 12 hours 44 min. 3⅓ sec. to this date.
To compute the times of the new moons which determine the commencement of successive years, it must be observed that in passing from an ordinary year the new moon of the following year is deduced by subtracting the interval that twelve lunations fall short of the corresponding Gregorian year of 365 or 366 days; and that, in passing from an embolismic year, it is to be found by adding the excess of thirteen lunations over the Gregorian year. Thus to deduce the new moon of Tisri, for the year immediately following any given year (Y), when Y is
the second-mentioned number of days being used, in each case, whenever the following or new Gregorian year is bissextile.
Hence, knowing which of the years are embolismic, from their ordinal position in the cycle, according to the rule before stated, the times of the commencement of successive years may be thus carried on indefinitely without any difficulty. But some slight adjustments will occasionally be needed for the reasons before assigned, viz. to avoid certain festivals falling on incompatible days of the week. Whenever the computed conjunction falls on a Sunday, Wednesday or Friday, the new year is in such case to be fixed on the day after. It will also be requisite to attend to the following conditions:—
If the computed new moon be after 18 hours, the following day is to be taken, and if that happen to be Sunday, Wednesday or Friday, it must be further postponed one day. If, for an ordinary year, the new moon falls on a Tuesday, as late as 9 hours 11 min. 20 sec., it is not to be observed thereon; and as it may not be held on a Wednesday, it is in such case to be postponed to Thursday. If, for a year immediately following an embolismic year, the computed new moon is on Monday, as late as 15 hours 30 min. 52 sec., the new year is to be fixed on Tuesday.
After the dates of commencement of the successive Hebrew years are finally adjusted, conformably with the foregoing directions, an estimation of the consecutive intervals, by taking the differences, will show the duration and character of the years that respectively intervene. According to the number of days thus found to be comprised in the different years, the days of the several months are distributed as in Table VI.
The signs + and - are respectively annexed to Hesvan and Kislev to indicate that the former of these months may sometimes require to have one day more, and the latter sometimes one day less, than the number of days shown in the table—the result, in every case, being at once determined by the total number of days that the year may happen to contain. An ordinary year may comprise 353, 354 or 355 days; and an embolismic year 383, 384 or 385 days. In these cases respectively the year is said to be imperfect, common or perfect. The intercalary month, Veadar, is introduced in embolismic years in order that Passover, the 15th day of Nisan, may be kept at its proper season, which is the full moon of the vernal equinox, or that which takes place after the sun has entered the sign Aries. It always precedes the following new year by 163 days, or 23 weeks and 2 days; and Pentecost always precedes the new year by 113 days, or 16 weeks and 1 day.
TableVI.—Hebrew Months.
Hebrew Month.
OrdinaryYear.
EmbolismicYear.
Tisri
30
30
Hesvan
29+
29+
Kislev
30-
30-
Tebet
29
29
Sebat
30
30
Adar
29
30
(Veadar)
(...)
(29)
Nisan
30
30
Yiar
29
29
Sivan
30
30
Tamuz
29
29
Ab
30
30
Elul
29
29
Total
354
384
The Gregorian epact being the age of the moon of Tebet at the beginning of the Gregorian year, it represents the day of Tebet which corresponds to January 1; and thus the approximate date of Tisri 1, the commencement of the Hebrew year, may be otherwise deduced by subtracting the epact from
The result so obtained would in general be more accurate than the Jewish calculation, from which it may differ a day, as fractions of a day do not enter alike in these computations. Such difference may also in part be accounted for by the fact that the assumed duration of the solar year is 6 min. 39-25/57 sec. in excess of the true astronomical value, which will cause the dates of commencement of future Jewish years, so calculated, to advance forward from the equinox a day in error in 216 years. The lunations are estimated with much greater precision.
The following table is extracted from Woolhouse'sMeasures, Weights and Moneys of all Nations:—
TableVII.—Hebrew Years.
296 Cycle.
JewishYear
NumberofDays
Commencement(1st of Tisri).
5606
354
Thur.
2
Oct.
1845
07
355
Mon.
21
Sept.
1846
08
383
Sat.
11
Sept.
1847
09
354
Thur.
28
Sept.
1848
10
355
Mon.
17
Sept.
1849
11
385
Sat.
7
Sept.
1850
12
353
Sat.
27
Sept.
1851
13
384
Tues.
14
Sept.
1852
14
355
Mon.
3
Oct.
1853
15
355
Sat.
23
Sept.
1854
16
383
Thur.
13
Sept.
1855
17
354
Tues.
30
Sept.
1856
18
355
Sat.
19
Sept.
1857
19
385
Thur.
9
Sept.
1858
20
354
Thur.
29
Sept.
1859
21
353
Mon.
17
Sept.
1860
22
385
Thur.
5
Sept.
1861
23
354
Thur.
25
Sept.
1862
24
383
Mon.
14
Sept.
1863
297 Cycle.
5625
355
Sat.
1
Oct.
1864
26
354
Thur.
21
Sept.
1865
27
385
Mon.
10
Sept.
1866
28
353
Mon.
30
Sept.
1867
29
354
Thur.
17
Sept.
1868
30
385
Mon.
6
Sept.
1869
31
355
Mon.
26
Sept.
1870
32
383
Sat.
16
Sept.
1871
33
354
Thur.
3
Oct.
1872
34
355
Mon.
22
Sept.
1873
35
383
Sat.
12
Sept.
1874
36
355
Thur.
30
Sept.
1875
37
354
Tues.
19
Sept.
1876
38
385
Sat.
8
Sept.
1877
39
355
Sat.
28
Sept.
1878
40
354
Thur.
18
Sept.
1879
41
383
Mon.
6
Sept.
1880
42
355
Sat.
24
Sept.
1881
43
383
Thur.
14
Sept.
1882
298 Cycle.
5644
354
Tues.
2
Oct.
1883
45
355
Sat.
20
Sept.
1884
46
385
Thur.
10
Sept.
1885
47
354
Thur.
30
Sept.
1886
48
353
Mon.
19
Sept.
1887
49
385
Thur.
6
Sept.
1888
50
354
Thur.
26
Sept.
1889
51
383
Mon.
15
Sept.
1890
52
355
Sat.
3
Oct.
1891
53
354
Thur.
22
Sept.
1892
54
385
Mon.
11
Sept.
1893
55
353
Mon.
1
Oct.
1894
56
355
Thur.
19
Sept.
1895
57
384
Tues.
8
Sept.
1896
58
355
Mon.
27
Sept.
1897
59
353
Sat.
17
Sept.
1898
60
384
Tues.
5
Sept.
1899
61
355
Mon.
24
Sept.
1900
62
383
Sat
14
Sept.
1901
299 Cycle.
5663
355
Thur.
2
Oct.
1902
64
354
Tues.
22
Sept.
1903
65
385
Sat.
10
Sept.
1904
66
355
Sat.
30
Sept.
1905
67
354
Thur.
20
Sept.
1906
68
383
Mon.
9
Sept.
1907
69
355
Sat.
26
Sept.
1908
70
383
Thur.
16
Sept.
1909
71
354
Tues.
4
Oct.
1910
72
355
Sat.
23
Sept.
1911
73
385
Thur.
12
Sept.
1912
74
354
Thur.
2
Oct.
1913
75
353
Mon.
21
Sept.
1914
76
385
Thur.
9
Sept.
1915
77
354
Thur.
28
Sept.
1916
78
355
Mon.
17
Sept.
1917
79
383
Sat.
7
Sept.
1918
80
354
Thur.
25
Sept.
1919
81
385
Mon.
13
Sept.
1920
300 Cycle.
JewishYear
NumberofDays
Commencement(1st of Tisri).
5682
355
Mon.
3
Oct.
1921
83
353
Sat.
23
Sept.
1922
84
384
Tues.
11
Sept.
1923
85
355
Mon.
29
Sept.
1924
86
355
Sat.
19
Sept.
1925
87
383
Thur.
9
Sept.
1926
88
354
Tues.
27
Sept.
1927
89
385
Sat.
15
Sept.
1928
90
353
Sat.
5
Oct.
1929
91
354
Tues.
23
Sept.
1930
92
385
Sat.
12
Sept.
1931
93
355
Sat.
1
Oct.
1932
94
354
Thur.
21
Sept.
1933
95
383
Mon.
10
Sept.
1934
96
355
Sat.
28
Sept.
1935
97
354
Thur.
17
Sept.
1936
98
385
Mon.
6
Sept.
1937
99
353
Mon.
26
Sept.
1938
5700
385
Thur.
14
Sept.
1939
301 Cycle.
5701
354
Thur.
3
Oct.
1940
02
355
Mon.
22
Sept.
1941
03
383
Sat.
12
Sept.
1942
04
354
Thur.
30
Sept.
1943
05
355
Mon.
18
Sept.
1944
06
383
Sat.
8
Sept.
1945
07
354
Thur.
26
Sept.
1946
08
385
Mon.
15
Sept.
1947
09
355
Mon.
4
Oct.
1948
10
353
Sat.
24
Sept.
1949
11
384
Tues.
12
Sept.
1950
12
355
Mon.
1
Oct.
1951
13
355
Sat.
20
Sept.
1952
14
383
Thur.
10
Sept.
1953
15
354
Tues.
28
Sept.
1954
16
355
Sat.
17
Sept.
1955
17
385
Thur.
6
Sept.
1956
18
354
Thur.
26
Sept.
1957
19
383
Mon.
15
Sept.
1958
302 Cycle.
5720
355
Sat.
3
Oct.
1959
21
354
Thur.
22
Sept.
1960
22
383
Mon.
11
Sept.
1961
23
355
Sat.
29
Sept.
1962
24
354
Thur.
19
Sept.
1963
25
385
Mon.
7
Sept.
1964
26
353
Mon.
27
Sept.
1965
27
385
Thur.
15
Sept.
1966
28
354
Thur.
5
Oct.
1967
29
355
Mon.
23
Sept.
1968
30
383
Sat.
13
Sept.
1969
31
354
Thur.
1
Oct.
1970
32
355
Mon.
20
Sept.
1971
33
383
Sat.
9
Sept.
1972
34
355
Thur.
27
Sept.
1973
35
354
Tues.
17
Sept.
1974
36
385
Sat.
6
Sept.
1975
37
353
Sat.
25
Sept.
1976
38
384
Tues.
13
Sept.
1977
303 Cycle.
5739
355
Mon.
2
Oct.
1978
40
355
Sat.
22
Sept.
1979
41
383
Thur.
11
Sept.
1980
42
354
Tues.
29
Sept.
1981
43
355
Sat.
18
Sept.
1982
44
385
Thur.
8
Sept.
1983
45
354
Thur.
27
Sept.
1984
46
383
Mon.
16
Sept.
1985
47
355
Sat.
4
Oct.
1986
48
354
Thur.
24
Sept.
1987
49
383
Mon.
12
Sept.
1988
50
355
Sat.
30
Sept.
1989
51
354
Thur.
20
Sept.
1990
52
385
Mon.
9
Sept.
1991
53
353
Mon.
28
Sept.
1992
54
355
Thur.
16
Sept.
1993
55
384
Tues.
6
Sept.
1994
56
355
Mon.
25
Sept.
1995
57
383
Sat.
14
Sept.
1996
304 Cycle.
JewishYear
NumberofDays
Commencement(1st of Tisri).
5758
354
Thur.
2
Oct.
1997
59
355
Mon.
21
Sept.
1998
60
385
Sat.
11
Sept.
1999
61
353
Sat.
30
Sept.
2000
62
354
Tues.
18
Sept.
2001
63
385
Sat.
7
Sept.
2002
64
355
Sat.
27
Sept.
2003
65
383
Thur.
16
Sept.
2004
66
354
Tues.
4
Oct.
2005
67
355
Sat.
23
Sept.
2006
68
383
Thur.
13
Sept.
2007
69
354
Tues.
30
Sept.
2008
70
355
Sat.
19
Sept.
2009
71
385
Thur.
8
Sept.
2010
72
354
Thur.
29
Sept.
2011
73
353
Mon.
17
Sept.
2012
74
385
Thur.
5
Sept.
2013
75
354
Thur.
25
Sept.
2014
76
385
Mon.
14
Sept.
2015
305 Cycle.
5777
353
Mon.
3
Oct.
2016
78
354
Thur.
21
Sept.
2017
79
385
Mon.
10
Sept.
2018
80
355
Mon.
30
Sept.
2019
81
353
Sat.
19
Sept.
2020
82
384
Tues.
7
Sept.
2021
83
355
Mon.
26
Sept.
2022
84
383
Sat.
16
Sept.
2023
85
355
Thur.
3
Oct.
2024
86
354
Tues.
23
Sept.
2025
87
385
Sat.
12
Sept.
2026
88
355
Sat.
2
Oct.
2027
89
354
Thur.
21
Sept.
2028
90
383
Mon.
10
Sept.
2029
91
355
Sat.
28
Sept.
2030
92
354
Thur.
18
Sept.
2031
93
383
Mon.
6
Sept.
2032
94
355
Sat.
24
Sept.
2033
95
385
Thur.
14
Sept.
2034
306 Cycle.
5796
354
Thur.
4
Oct.
2035
97
353
Mon.
22
Sept.
2036
98
385
Thur.
10
Sept.
2037
99
354
Thur.
30
Sept.
2038
5800
355
Mon.
19
Sept.
2039
01
383
Sat.
8
Sept.
2040
02
354
Thur.
26
Sept.
2041
03
385
Mon.
15
Sept.
2042
04
353
Mon.
5
Oct.
2043
05
355
Thur.
22
Sept.
2044
06
384
Tues.
12
Sept.
2045
07
355
Mon.
1
Oct.
2046
08
353
Sat.
21
Sept.
2047
09
384
Tues.
8
Sept.
2048
10
355
Mon.
27
Sept.
2049
11
355
Sat.
17
Sept.
2050
12
383
Thur.
7
Sept.
2051
13
354
Tues.
24
Sept.
2052
14
385
Sat.
13
Sept.
2053
307 Cycle.
5815
355
Sat.
3
Oct.
2054
16
354
Thur.
23
Sept.
2055
17
383
Mon.
11
Sept.
2056
18
355
Sat.
29
Sept.
2057
19
354
Thur.
19
Sept.
2058
20
383
Mon.
8
Sept.
2059
21
355
Sat.
25
Sept.
2060
22
385
Thur.
15
Sept.
2061
23
354
Thur.
5
Oct.
2062
24
353
Mon.
24
Sept.
2063
25
385
Thur.
11
Sept.
2064
26
354
Thur.
1
Oct.
2065
27
355
Mon.
20
Sept.
2066
28
383
Sat.
10
Sept.
2067
29
354
Thur.
27
Sept.
2068
30
355
Mon.
16
Sept.
2069
31
383
Sat.
6
Sept.
2070
32
355
Thur.
24
Sept.
2071
33
384
Tues.
13
Sept.
2072