Astronomy Explained Upon Sir Isaac Newton's Principles / And made easy to those who have not studied mathematics

by James Ferguson

The year 1800 begins a new Cycle.

Easter Cycle, deficient.

425. The Cycle of Easter, also called the Dionysian Period, is a revolution of 532 years, found by multiplying the Solar Cycle 28 by the Lunar Cycle 19. If the New Moons did not anticipate upon this Cycle, Easter-Day would always be the Sunday next after the first Full Moon which succeeds the 21st of March. But, on account of the above anticipation § [422], to which no proper regard was had before the late alteration of the Style, the Ecclesiastic Easter has several times been a week different from the true Easter within this last Century: which inconvenience is now remedied by making the Table which used to find Easter for ever, in the Common Prayer Book, of no longer use than the Lunar difference from the New Style will admit of.

Number of Direction.
To find the true Easter.

426. The earliest Easter possible is the 22d of March, the latest the 25th of April. Within these limits are 35 days, and the number belonging to each of them is called the Number of Direction; because thereby the time of Easter is found for any given year. To find the Number of Direction, according to the New Style, enter [Table V] following this Chapter, with the compleat hundreds of any given year at the top, and the years thereof (if any) below an hundred at the left hand; and where the columns meet is the Dominical Letter for the given year. Then, enter [Table I], with the compleat hundreds of the same year at the left hand, and the years below an hundred at the top; and where the columns meet is the Golden Number for the same year. Lastly, enter [Table II] with the Dominical Letter at the left hand and Golden Number at the top; and where the columns meet is the Number of Direction for that year; which number, added to the 21st day of March shews on what day either of March or April Easter Sunday falls in that year. Thus, the Dominical Letter New Style for the year 1757 is B ([Table V]) and the Golden Number is 10, ([Table I]) by which in [Table II], the Number of Direction is found to be 20; which, reckoned from the 21st of March, ends on the 10th of April, and that is Easter Sunday in the year 1757. N. B. There are always two Dominical Letters to the leap-year, the first of which takes place to the 24th of February, the last for the following part of the year.

Dominical Letter.

427. The first seven Letters of the Alphabet are commonly placed in the annual Almanacks to shew on what days of the week the days of the months fall throughout the year. And because one of those seven Letters must necessarily stand against Sunday it is printed in a capital form, and called the Dominical Letter: the other six being inserted in small characters to denote the other six days of the week. Now, since a common Julian Year contains 365 Days, if this number be divided by 7 (the number of days in a week) there will remain one day. If there had been no remainder, ’tis plain the year would constantly begin on the same day of the week. But since one remains, ’tis as plain that the year must begin and end on the same day of the week; and therefore the next year will begin on the day following. Hence, when January begins on Sunday, A is the Dominical or Sunday Letter for that year: then, because the next year begins on Monday, the Sunday will fall on the seventh day, to which is annexed the seventh Letter G, which therefore will be the Dominical Letter for all that year: and as the third year will begin on Tuesday, the Sunday will fall on the sixth day; therefore F will be the Sunday Letter for that year. Whence ’tis evident that the Sunday Letters will go annually in a retrograde order thus, G, F, E, D, C, B, A. And in the course of seven years, if they were all common ones, the same days of the week and Dominical Letters would return to the same days of the months. But because there are 366 days in a leap-year, if this number be divided by 7, there will remain two days over and above the 52 weeks of which the year consists. And therefore, if the leap-year begins on Sunday, it will end on Monday; and the next year will begin on Tuesday, the first Sunday whereof must fall on the sixth of January, to which is annexed the Letter F, and not G as in common years. By this means, the leap-year returning every fourth year, the order of the Dominical Letters is interrupted; and the Series does not return to its first state till after four times seven, or 28 years: and then the same days of the month return in order to the same days of the week.

To find the Dominical Letter.

428. To find the Dominical Letter for any year either before or after the Christian Æra[^[87]]: In [Table III] or IV for Old Style, or V for New Style, look for the hundreds of years at the head of the Table, and for the years below an hundred (to make up the given year) at the left hand: and where the columns meet you have the Dominical Letter for the year desired. Thus, suppose the Dominical Letter be required for the year of Christ 1758, New Style, I look for 1700 at the head of [Table V], and for 58 at the left hand of the same Table; and in the angle of meeting, I find A, which is the Dominical Letter for that year. If it was wanted for the same year Old Style, it would be found by [Table IV] to be D. But to find the Dominical Letter for any given year before Christ, subtract one from that year and then proceed in all respects as just now taught, to find it by [Table III] Thus, suppose the Dominical Letter be required for the 585th year before the first year of Christ, look for 500 at the head of [Table III], and for 84 at the left hand; in the meeting of these columns is FE, which were the Dominical Letters for that year, and shews that it was a leap-year; because, leap-year has always two Dominical Letters.

To find the Days of the Months.