Page:Encyclopædia Britannica, Ninth Edition, v. 4.djvu/745

here given, this distinction is made by means of an accent placed over the last figure.

At the reformation the epacts were given by the line D. The year 1600 was a leap year; the intercalation accordingly took place as usual, and there was no interruption in the order of the epacts; the line D was employed till 1700. In that year the omission of the intercalary day rendered it necessary to diminish the epacts by unity, or to pass to the line C. In 1800 the solar equation again occurred, in consequence of which it was necessary to descend one line to have the epacts diminished by unity; but in this year the lunar equation also occurred, the anticipation of the new moons having amounted to a day: the new moons accordingly happened a day earlier, which rendered it necessary to take the epacts in the next higher line. There was, consequently, no alteration; the two equations destroyed each other. The line of epacts belonging to the present century is therefore C. In 1900 the solar equation occurs, after which the line is B. The year 2000 is a leap year, and there is no alteration. In 2100 the equations again occur together and destroy each other, so that the line B will serve three centuries, from 1900 to 2200. From that year to 2300 the line will be A. In this manner the line of epacts belonging to any given century is easily found, and the method of proceeding is obvious. When the solar equation occurs alone, the line of epacts is changed to the next lower in the table; when the lunar equation occurs alone, the line is changed to the next higher; when both equations occur together, no change takes place. In order that it may be perceived at once to what centuries the different lines of epacts respectively belong, they have been placed in a column on the left hand side of the following table.

Table III.—Extended Table of Epacts.

Years.			Index.	Golden Numbers.
				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

 

The use of the epacts is to show the days of the new moons, and consequently the moon's age on any day of the year. For this purpose they are placed in the calendar (Table IV.) along with the days of the month and dominical letters, in a retrograde order, so that the asterisk stands beside the 1st of January, 29 beside the 2nd, 28 beside the 3rd, and so on to 1, which corresponds to the 30th. After this comes the asterisk, which corresponds to the 31st of January, then 29, which belongs to the 1st of February, and so on to the end of the year. The reason of this distribution is evident. If the last lunation of any year ends, for example, on the 2nd of December, the new moon falls on the 3rd; and the moon's age on the 31st, or at the end of the year, is twenty-nine days. The epact of the following year is therefore twenty-nine. Now that lunation having commenced on the 3rd of December, and consisting of thirty days, will end on the 1st of January. The 2nd of January is therefore the day of the new moon, which is indicated by the epact twenty-nine. In like manner, if the new moon fell on the 4th of December, the epact of the following year would be twenty-eight, which, to indicate the day of next new moon, must correspond to the 3rd of January.

When the epact of the year is known, the days on which the new moons occur throughout the whole year are shown by Table IV., which is called the Gregorian Calendar of Epacts. For example, the golden number of the year 1832, is $\left({\frac {\scriptstyle 1832+1}{\scriptstyle {\text{19}}}}\right)_{r}$ = 9, and the epact, as found in Table III., is twenty-eight. This epact occurs at the 3rd of January, the 2nd of February, the 3rd of March, the 2nd of April, the 1st of May, &c.; and these days are consequently the days of the ecclesiastical new moons in 1832. The astronomical new moons generally take place one or two days, sometimes even three days, earlier than those of the calendar.