Golden Numbers.
Years. Index.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
1700 1800 8700 C * 11 22 3 14 25 6 17 28 9 20 1 12 23 4 15 26 7 18
1900 2000 2100 B 29 10 21 2 13 24 5 16 27 8 19 * 11 22 3 14 25' 6 17
2200 2400 A 28 9 20 1 12 23 4 15 26 7 18 29 10 21 2 13 24 5 16
2300 2500 u 27 8 19 * 11 22 3 14 25 6 17 28 9 20 1 12 23 4 15
2600 2700 2800 t 26 7 18 29 10 21 2 13 24 5 16 27 8 19 * 11 22 3 14
2900 3000 s 25 6 17 28 9 20 1 12 23 4 15 26 7 18 29 10 21 2 13
3100 3200 3300 r 24 5 16 27 8 19 * 11 22 3 14 25' 6 17 28 9 20 1 12
3400 3600 q 23 4 15 26 7 18 29 10 21 2 13 24 5 16 27 8 19 * 11
3500 3700 p 22 3 14 25 6 17 28 9 20 1 12 23 4 15 26 7 18 29 10
3800 3900 4000 n 21 2 13 24 5 16 27 8 19 * 11 22 3 14 25' 6 17 28 9
4100 m 20 1 12 23 4 15 26 7 18 29 10 21 2 13 24 5 16 27 8
4200 4300 4400 l 19 * 11 22 3 14 25 6 17 28 9 20 1 12 23 4 15 26 7
4500 4600 k 18 29 10 21 2 13 24 5 16 27 8 19 * 11 22 3 14 25' 6
4700 4800 4900 i 17 28 9 20 1 12 23 4 15 26 7 18 29 10 21 2 13 24 5
5000 5200 h 16 27 8 19 * 11 22 3 14 25 6 17 28 9 20 1 12 23 4
5100 5300 g 15 26 7 18 29 10 21 2 13 24 5 16 27 8 19 * 11 22 3
5400 5500 5600 f 14 25 6 17 28 9 20 1 12 23 4 15 26 7 18 29 10 21 2
5700 5800 e 13 24 5 16 27 8 19 * 11 22 3 14 25' 6 17 28 9 20 1
5900 6000 6100 d 12 23 4 15 26 7 18 29 10 21 2 13 24 5 16 27 8 19 *
6200 6400 c 11 22 3 14 25 6 17 28 9 20 1 12 23 4 15 26 7 18 29
6300 6500 b 10 21 2 13 24 5 16 27 8 19 * 11 22 3 14 25' 6 17 28
6600 6800 a 9 20 1 12 23 4 15 26 7 18 29 10 21 2 13 24 5 16 27
6700 6900 P 8 19 * 11 22 3 14 25 6 17 28 9 20 1 12 23 4 15 26
7000 7100 7200 N 7 18 29 10 21 2 13 24 5 16 27 8 19 * 11 22 3 14 25'
7300 7400 M 6 17 28 9 20 1 12 23 4 15 26 7 18 29 10 21 2 13 24
7500 7600 7700 H 5 16 27 8 19 * 11 22 3 14 25 6 17 28 9 20 1 12 23
7800 8000 G 4 15 26 7 18 29 10 21 2 13 24 5 16 27 8 19 * 11 22
7900 8100 F 3 14 25 6 17 28 9 20 1 12 23 4 15 26 7 18 29 10 21
8200 8300 8400 E 2 13 24 5 16 27 8 19 * 11 22 3 14 25' 6 17 28 9 20
1500 1600 8500 D 1 12 23 4 15 26 7 18 29 10 21 2 13 24 5 16 27 8 19
As an example of the use of the preceding tables, suppose it were required
to determine the moon's age on the 10th of April 1832. In 1832 the golden
number is ((1832 + 1) / 19)_r = 9 and the line of epacts belonging to the
century is C. In Table III, under 9, and in the line C, we find the epact
28. In the calendar, Table IV., look for April, and the epact 28 is found
opposite the second day. The 2nd of April is therefore the first day of the
moon, [v.04 p.0997] and the 10th is consequently the ninth day of the moon.
Again, suppose it were required to find the moon's age on the 2nd of
December in the year 1916. In this case the golden number is ((1916 + 1) /
19)_r = 17, and in Table III., opposite to 1900, the line of epacts is B.
Under 17, in line B, the epact is 25'. In the calendar this epact first
occurs before the 2nd of December at the 26th of November. The 26th of
November is consequently the first day of the moon, and the 2nd of December
is therefore the seventh day.
_Easter._--The next, and indeed the principal use of the calendar, is to
find Easter, which, according to the traditional regulation of the council
of Nice, must be determined from the following conditions:--_1st_, Easter
must be celebrated on a Sunday; _2nd_, this Sunday must _follow_ the 14th
day of the paschal moon, so that if the 14th of the paschal moon falls on a
Sunday then Easter must be celebrated on the Sunday following; _3rd_, the
paschal moon is that of which the 14th day falls on or next follows the day
of the vernal equinox; _4th_ the equinox is fixed invariably in the
calendar on the 21st of March. Sometimes a misunderstanding has arisen from
not observing that this regulation is to be construed according to the
tabular full moon as determined from the epact, and not by the true full
moon, which, in general, occurs one or two days earlier.
From these conditions it follows that the paschal full moon, or the 14th of
the paschal moon, cannot happen before the 21st of March, and that Easter
in consequence cannot happen before the 22nd of March. If the 14th of the
moon falls on the 21st, the new moon must fall on the 8th; for 21 - 13 = 8;
and the paschal new moon cannot happen before the 8th; for suppose the new
moon to fall on the 7th, then the full moon would arrive on the 20th, or
the day before the equinox. The following moon would be the paschal moon.
But the fourteenth of this moon falls at the latest on the 18th of April,
or 29 days after the 20th of March; for by reason of the double epact that
occurs at the 4th and 5th of April, this lunation has only 29 days. Now, if
in this case the 18th of April is Sunday, then Easter must be celebrated on
the following Sunday, or the 25th of April. Hence Easter Sunday cannot
happen earlier than the 22nd of March, or later than the 25th of April.
Hence we derive the following rule for finding Easter Sunday from the
tables:--_1st_, Find the golden number, and, from Table III., the epact of
the proposed year. _2nd_, Find in the calendar (Table IV.) the first day
after the 7th of March which corresponds to the epact of the year; this
will be the first day of the paschal moon, _3rd_, Reckon thirteen days
after that of the first of the moon, the following will be the 14th of the
moon or the day of the full paschal moon. _4th_, Find from Table I. the
dominical letter of the year, and observe in the calendar the first day,
after the fourteenth of the moon, which corresponds to the dominical
letter; this will be Easter Sunday.