The Cycle of the Sun

If there were just fifty-two weeks in a year, each year would invariably commence on the same day of the week. As a common year consists of fifty-two weeks and one day, if all the years were thus constituted, when a given year commences on Sunday, the second year would commence on Monday, the third on Tuesday, the seventh on Saturday, and the eighth on Sunday again-bringing the commencement of the year on a given day of the week once in a cycle of seven years.ASC 9.3

As this order is interrupted once in four years by the Bissextile, or “leap year,” which has two days over even weeks, the year following each Bissextile must commence two days later in the week than its preceding one; while common years commence but one day later.ASC 10.1

Therefore, if the first year commence on Wednesday, as does the first year of the present cycle, which commenced in 1840, that being a Bissextile, the second year would commence on Friday, the fourth on Sunday, and the fifth on Monday, which, (1844,) being a Bissextile, the sixth would commence on Wednesday; and so on through a cycle of 4 times 7 = 28 years, in the following order:-ASC 10.2

S.	M.	T.	W.	T.	F.	S.
			1		2	3
4	5		6	7	8	9
	10	11	12	13		14
15	16	17		18	19	20
21		22	23	24	25
26	27	29

At the end of the cycle of twenty-eight years, there is a recurrence of years commencing on days of the week in the same order. This order is, however, varied by every year, which, ending a century, is reckoned as a common year, ^{1In New Style, the last year of centuries which can be divided by 400 without a remainder are reckoned as Bissextile; the last year of other centuries, as common years.}-the current years of each cycle then commence one day in the week earlier than the corresponding years of the cycles of the preceding century. It is thus varied three days in each 400 years.ASC 10.3

This is sometimes called the cycle of the Dominical, or Sunday letter. On whatever day of the week the first day of any year falls, that day of the week is indicated by the letter a, the succeeding day by b, and so on to the first Sunday: and the letter that falls on that day is the Dominical, or Sunday letter, for the year, excepting in the Bissextile. In that year, as one day is added to the month of February, if g is the Dominical for the first two months, f would be for the last ten, and then e for the next year. But with common years, if g is the Dominical letter for the first, f would be for the second. The first seven letters of the alphabet are called the Dominical letters, and succeed each other-one in each common year, and two in each Bissextile-five times during the solar cycle of 28 years, when they again commence, and succeed each other in the following order: ^{2Except as this order is varied by the common year at the end of centuries.}ASC 11.1

G	F	E	D	C	B	A
		1	1	2	3	4
5	5	6	7	8	9	9
10	11	12	13	13	14	15
16	17	17	18	19	20	21
21	22	23	24	25	25	26
27	28

As each year begins later in the week than its preceding one, there are less days between its first day and its first Sabbath. Consequently, if its first day is represented by a, a letter nearer to a will fall on Sunday than in the preceding year.ASC 12.1

To find the Dominical letter for any year of the Christian Era, previous to the change of the year from Old to New Style, or from the Julian to the Gregorian year:ASC 12.2

Add to any given year one fourth of its number, (omitting fractions,) and 5 to that sum: divide this result by 7: if there is no remainder, a is the Dominical letter. If there is a remainder, the letter below, which stands under the number corresponding with the remainder, is the letter sought.ASC 12.3

0	6	5	4	3	2	1
A	B	C	D	E	F	G

If in the division of the given year by four, to get its fourth part, there is no remainder, the year is a Bissextile or leap year, ^{3Unless it be the last year of a century, when to be a Bissextile, see note on p. 11.} and the letter thus found is only the Dominical letter for the last ten months of that year-the letter following, in the above line, being that for the first two.ASC 12.4

To find the Dominical letter for any year since the adoption of the Gregorian year: add to any given year its fourth part, (excepting fractions,) and instead of adding 5, as before, add 2 to the sum, for any year in the 16th and 17th centuries, 1 for each year in the 18th, and nothing for the present century. Then divide by 7, and find the letter by the remainder, as before.ASC 12.5

The first year of the Christian era commenced with Monday-so that five days intervened between it and the first Sunday, and are required to be added, to make even weeks. As the addition during the leap years is balanced by the addition of one fourth of the current years, 5 should be added to each Julian year. When the Gregorian year was introduced, ten days were omitted for that number of years which had been reckoned as leap years which should have been considered common years. This being a week and three days, left but two days to be added till the 18th century, when, another fourth year being a common year, but one was to be added. The year 1800 being considered a common year, leaves none to add for the present century.ASC 13.1

The Gregorian year was adopted in Catholic countries in 1582, but was not adopted in Great Britain and her colonies till 1752. In Sweden it was adopted in 1753, and in Germany in 1777. Russia only retains the Old Style, which now differs twelve days from the New.ASC 13.2

The Dominical letter being found, the day of the week on which any given day of any year falls, is ascertained by a simple process.ASC 13.3

If there were four weeks in each month, the first days of each would commence on the same day of the week during the year. Varying from even weeks, the first day of each month will be on days of the week varying from that on which January commences, as the following letters vary from each other:-ASC 13.4

A	D	D	G	B	E	G	C	F	A	D	F
Jan.,	Feb.,	Mar.,	Apr.,	May,	June,	July,	Aug.,	Sept.,	Oct.,	Nov.,	Dec.

The order of these letters may be easily remembered by the following familiar couplet:ASC 14.1

Jan.,	Feb.,	Mar.,	Apr.,	May,	June,
“At	Dover	dwells	George	Brown,	Esquire,
July,	Aug.,	Sept.,	Oct.,	Nov.,	Dec.
Good	Caleb	Fitch,	And	Doctor	Friar.”

To find the day in the week on which any month begins, find the letter which corresponds to the given month, as in the above couplet. If the letter thus found is the Dominical letter for the year, the month begins on Sunday. If it is a different letter, the day of its commencement varies from Sunday, as many days as the letter found varies from the Dominical letter for the year, in the following order:-ASC 14.2

A,

B,

C,

D,

E,

F,

G.

The day of the week on which the month commences, being found, that on which any corresponding day of the month falls is found by subtracting one from the given day of the month, and dividing the difference by seven. The remainder gives the number of days in the week, which the given day varies from Sunday.ASC 14.3

Thus, on what day of the week did the dark day occur-May 19th, 1780 ? 1780 ÷ 4 = 445. Add 1780, it equals 2225. Add 1, it equals 2226. Divide by 7, it equals 318, with no remainder. Or it might thus be stated: (1780 ÷ 4 + 1780 + 1) ÷ 7 = 318. Then a is the Dominical letter for the last ten months-it being a Bissextile. b is the letter which corresponds with May in the above couplet, which varies one from a, so that the 1st of May for that year falls on Monday.ASC 14.4

Then (19 - 1) ÷ 7 = 2, with 4 remainder. Four days from Monday is Friday, on which was the Dark Day.ASC 15.1