EPACT

, in Chronology, the excess of the solar month above the lunar synodical month; or of the solar year above the lunar year of 12 synodical months; or of several solar months above as many synodical months; or of several solar years above as many dozen of synodical months.

The Epacts then are either Annual or Menstrual.

Menstrual Epacts, are the excesses of the civil calendar month above the lunar month. Suppose, for example, it were new moon on the first day of January: then since the month of January contains 31 days,

and the lunar month	29ds	12h	44m	3s;
the menstrual Epact is	1	11	15	57

Annual Epacts, are the excesses of the solar year above the lunar. Hence,

as the Julian solar year is	365ds	6h	0m	0s,
and the Julian lunar year	354	8	48	38,
the annual Epact will be	10	21	11	22,

that is, almost 11 days. Consequently the Epact of 2 years, is 22 days; of 3 years, 33 days; or rather 3, since 30 days make an embolismic, or intercalary month. Then, adding still 11, the Epact of 4 years is 14 days; and so of the rest as in the following table, where they do not become 30, or 0 again, till the 19th year; so that at the 20th year the Epact is 11 again; and hence the cycle of Epacts expires with the Golden Number, or Lunar Cycle of 19 years, and begins with the same again.

Table of Julian Epacts.
Golden Numb.	Epacts	Golden Numb.	Epacts	Golden Numb.	Epacts
I	11	VIII	28	XV	15
II	22	IX	9	XVI	26
III	3	X	20	XVII	8
IV	14	XI	1	XVIII	19
V	25	XII	12	XIX	30
VI	6	XIII	23		or 0
VII	17	XIV	4

Again, as the new moons are the same, or fall on the same day, every 19 years, so the difference between the solar and lunar years is the same every 19 years. And because the said difference is always to be added to the lunar year, to adjust or make it equal to the solar year; hence the said difference respectively belonging to each year of the moon's cycle, is called the Epact of the said year, that is, the number to be added to the said year, to make it equal to the solar year. Upon this mutual respect between the cycle of the moon and the cycle of the Epacts, is founded this

Multiply the Golden Number, or the given year of the Moon's Cycle, by 11, and the product will be the Epact if it be less than 30; but if it exceed 30, then throw out as many 30's as the product contains, and the remainder will be the Epact.

1st, The difference between the Julian and Gregorian years being equal to the difference between the solar and lunar year, or 11 days, therefore the Gregorian Epact for any year is the same with the Julian Epact for the preceding year; and hence the Gregorian Epact will be found, by subtracting 1 from the golden number, multiplying the remainder by 11, and rejecting the 30's. This rule will serve till the year 1900; but after that year, the Gregorian Epact will be found by this rule: Divide the centuries of the given year by 4; multiply the remainder by 17; then to this product add 43 times the quotient, and also the number 86, and divide the whole sum by 25, reserving the quotient: next multiply the golden number by 11, and from the product subtract the reserved quotient, so shall the remainder, after rejecting all the 30's contained in it, be the Epact sought.

The following table contains the Golden Numbers, with their corresponding Epacts, till the year 1900.

Table of Gregorian Epacts.
Golden Numb.	Epacts	Golden Numb.	Epacts	Golden Numb.	Epacts
I	0	VIII	17	XV	4
II	11	IX	28	XVI	15
III	22	X	9	XVII	26
IV	3	XI	20	XVIII	7
V	14	XII	1	XIX	18
VI	25	XIII	12	I	0
VII	6	XIV	23

On the subject of Epacts, see Wolfius's Elementa Chronologiæ, apud Opera, tom. 4, pa. 133; also Philos. Trans. vol. 46. pa. 417, or numb. 495, art. 5.