A Budget of Paradoxes, Volume I

by Augustus De Morgan

VIII. Divide one more than the given year by 19, the remainder (or 19 if no remainder) is the golden number. (15).

XII. Divide 3 less than 11 times VIII. by 30; the remainder (or 30 if there be no remainder) is the epact. (12).

When the Epact is 23, or less. XIII. Subtract XII., the epact, from 45. (33). XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7, if there be no remainder, (1).

When the Epact is greater than 23. XIII. Subtract XII., the epact, from 75. XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7, if there be no remainder.

XV. To XIII. add VII., the dominical number, (and 7 besides if XIV. be greater than VII.,) and subtract XIV., the result is the day of March, or if more than 31, subtract 31, and the result is the day of April, on which Easter Sunday (old style) falls. (37; Easter Day is April 6).

These rules completely represent the old and new Calendars, so far as Easter is concerned. For further explanation we must refer to the articles cited at the commencement.

The annexed is the table of new and full moons of the Gregorian Calendar, cleared of the errors made for the purpose of preventing Easter from coinciding with the Jewish Passover.

The second table (page [370]) contains epacts, or ages of the moon at the beginning of the year: thus in 1913, the epact is 22, in 1868 it is 6. This table goes from 1850 to 1999: should the New Zealander not have arrived by that time, and should the churches of England and Rome then survive, the epact table may be continued from their liturgy-books. The way of using the table is as follows: Take the epact of the required year, and find it in the first or last column of the first table, in line with it are seen the calendar days of new and full moon. Thus, when the epact is 17, the new and full moons of March fall on the 13th and 28th. The result is, for the most part, correct: but in a minority of cases there is an error of a day. When this happens, the error is almost always a fraction of a day much less than twelve hours. Thus, when the table gives full moon on the 27th, and the real truth is the 28th, we may be sure it is early on the 28th.

	Jan.	Feb.	Mar.	Apr.	May	June	July	Aug.	Sep.	Oct.	Nov.	Dec.
1	29	27	29	27	27	25	25	23	22	21	20	19	1
	14	13	14	13	12	11	10	9	7	7	5	5
2	28	26	28	26	26	24	24	22	21	20	19	18	2
	13	12	13	12	11	10	9	8	6	6	4	4
3	27	25	27	25	25	23	23	21	20	19	18	17	3
	12	11	12	11	10	9	8	7	5	5	3	3
4	26	24	26	24	24	22	22	20	19	18	17	16	4
	11	10	11	10	9	8	7	6	4	4	2	2,31
5	25	23	25	23	23	21	21	19	18	17	16	15	5
	10	9	10	9	8	7	6	5	3	3	1	1,30
6	24	22	24	22	22	20	20	18	17	16	15	14	6
	9	8	9	8	7	6	5	4	2	2,31	30	29
7	23	21	23	21	21	19	19	17	16	15	14	13	7
	8	7	8	7	6	5	4	3	1	1,30	29	28
8	22	20	22	20	20	18	18	16	15	14	13	12	8
	7	6	7	6	5	4	3	2,31	30	29	28	27
9	21	19	21	19	19	17	17	15	14	13	12	11	9
	6	5	6	5	4	3	2	1,30	29	28	27	26
10	20	18	20	18	18	16	16	14	13	12	11	10	10
	5	4	5	4	3	2	1,31	29	28	27	26	25
11	19	17	19	17	17	15	15	13	12	11	10	9	11
	4	3	4	3	2	1,30	30	28	27	26	25	24
12	18	16	18	16	16	14	14	12	11	10	9	8	12
	3	2	3	2	1,31	29	29	27	26	25	24	23
13	17	15	17	15	15	13	13	11	10	9	8	7	13
	2	1	2	1,30	30	28	28	26	25	24	23	22
14	16	14	16	14	14	12	12	10	9	8	7	6	14
	1,31	—	1,31	29	29	27	27	25	24	23	22	21
15	15	13	15	13	13	11	11	9	8	7	6	5	15
	30	28	30	28	28	26	26	24	23	22	21	20
16	14	12	14	12	12	10	10	8	7	6	5	4	16
	29	27	29	27	27	25	25	23	22	21	20	19
17	13	11	13	11	11	9	9	7	6	5	4	3	17
	28	26	28	26	26	24	24	22	21	20	19	18
18	12	10	12	10	10	8	8	6	5	4	3	2	18
	27	25	27	25	25	23	23	21	20	19	18	17
19	11	9	11	9	9	7	7	5	4	3	2	1,31	19
	26	24	26	24	24	22	22	20	19	18	17	16
20	10	8	10	8	8	6	6	4	3	2	1,31	30	20
	25	23	25	23	23	21	21	19	18	17	16	15
21	9	7	9	7	7	5	5	3	2	1,31	29	29	21
	24	22	24	22	22	20	20	18	17	16	15	14
22	8	6	8	6	6	4	4	2	1,30	30	28	28	22
	23	21	23	21	21	19	19	17	16	15	14	13
23	7	5	7	5	5	3	3	1,31	29	29	27	27	23
	22	20	22	20	20	18	18	16	15	14	13	12
24	6	5	6	5	4	3	2	1,30	29	28	27	26	24
	21	19	21	19	19	17	17	15	14	13	12	11
25	5	4	5	4	3	2	1,31	29	28	27	26	25	25
	20	19	20	19	18	17	16	15	13	13	11	11
26	4	3	4	3	2	1,30	30	28	27	26	25	24	26
	19	18	19	18	17	16	15	14	12	12	10	10
27	3	2	3	2	1,31	29	29	27	26	25	24	23	27
	18	17	18	17	16	15	14	13	11	11	9	9
28	2	1	2	1,30	30	28	28	26	25	24	23	22	28
	17	16	17	16	15	14	13	12	10	10	8	8
29	1,31	—	1,31	29	29	27	27	25	24	23	22	21	29
	16	15	16	15	14	13	12	11	9	9	7	7
30	30	28	30	28	28	26	26	24	23	22	21	20	30
	15	14	15	14	13	12	11	10	8	8	6	6
	Jan.	Feb.	Mar.	Apr.	May	June	July	Aug.	Sep.	Oct.	Nov.	Dec.