420. A Cycle is a perpetual round, or circulation of the same parts of time of any sort. The Cycle of the Sun is a revolution of 28 years, in which time, the days of the months return again to the same days of the week; the Sun’s Place to the same Signs and Degrees of the Ecliptic on the same months and days, so as not to differ one degree in 100 years; and the leap-years begin the same course over again with respect to the days of the week on which the days of the months fall. The Cycle of the Moon, commonly called the Golden Number, is a revolution of 19 years; in which time, the Conjunctions, Oppositions, and other Aspects of the Moon are within an hour and half of being the same as they were on the same days of the months 19 years before. The Indiction is a revolution of 15 years, used only by the Romans for indicating the times of certain payments made by the subjects to the republic: It was established by Constantine, A.D. 312.

To find the Years of these Cycles.

421. The year of our Saviour’s Birth, according to the vulgar Æra, was the 9th year of the Solar Cycle; the first year of the Lunar Cycle; and the 312th year after his birth was the first year of the Roman Indiction. Therefore, to find the year of the Solar Cycle, add 9 to any given year of Christ, and divide the sum by 28, the Quotient is the number of Cycles elapsed since his birth, and the remainder is the Cycle for the given year: if nothing remains, the Cycle is 28. To find the Lunar Cycle, add 1 to the given year of Christ, and divide the sum by 19; the Quotient is the number of Cycles elapsed in the interval, and the remainder is the Cycle for the given year: if nothing remains, the Cycle is 19. Lastly, subtract 312 from the given year of Christ, and divide the remainder by 15; and what remains after this division is the Indiction for the given year: if nothing remains, the Indiction is 15.

The deficiency of the Lunar Cycle, and consequence thereof.

422. Although the above deficiency in the Lunar Cycle of an hour and half every 19 years be but small, yet in time it becomes so sensible as to make a whole Natural Day in 310 years. So that, although this Cycle be of use, when rightly placed against the days of the month in the Calendar, as in our Common Prayer Books, for finding the days of the mean Conjunctions or Oppositions of the Sun and Moon, and consequently the time of Easter; it will only serve for 310 years Old Style. For as the New and Full Moons anticipate a day in that time, the Golden Numbers ought to be placed one day earlier in the Calendar for the next 310 years to come. These Numbers were rightly placed against the days of New Moon in the Calendar, by the Council of Nice, A. D. 325; but the anticipation which has been neglected ever since, is now grown almost into 5 days: and therefore, all the Golden Numbers ought now to be placed 5 days higher in the Calendar for the O.S. than they were at the time of the said Council; or six days lower for the New Style, because at present it differs 11 days from the Old.

Days Jan.Feb.MarchAprilMayJuneJulyAugustSept.Octob.Nov.Dec.
1 9 917176 11 19
2 17 61414311 19
3 176176 311 1988
4 6 614143 198 16
5 14 31111198 16
6 143143 19 1655
7 3 3111119 816 13
8 11 1988165513
9 11191119 13 2
10 19881616513 210
11 198 5132210
12 816816165 10 18
13 51313210 187
14 165165 21018187
15 5 513132 7 15
16 13 21010187 15
17 132132 187 1544
18 2 2101018 15 12
19 10 1877154412
20 10181018 15 1211
21 187715 412 9
22 187 154412119
23 715715 12 91717
24 154412 19 6
25 154 12 1917176
26 4 412 1 6 14
27 12 1199176 14
28 12112 9 176141433
29 1 19 17 3 11
30 1766143 11
31 9 9 143 11 19

How to find the day of the New Moon by the Golden Number.

423. In the annexed Table, the Golden Numbers under the months stand against the days of New Moon in the left hand column, for the New Style; adapted chiefly to the second year after leap-year as being the nearest mean for all the four; and will serve till the year 1900. Therefore, to find the day of New Moon in any month of a given year till that time, look for the Golden Number of that year under the desired month, and against it, you have the day of New Moon in the left hand column. Thus, suppose it were required to find the day of New Moon in September 1757; the Golden Number for that year is 10, which I look for under September and right against it in the left hand column I find 13, which is the day of New Moon in that month. N. B. If all the Golden Numbers, except 17 and 6, were set one day lower in the Table, it would serve from the beginning of the year 1900 till the end of the year 2199. The first Table after this chapter shews the Golden Number for 4000 years after the birth of Christ, by looking for the even hundreds of any given year at the left hand, and for the rest to make up that year at the head of the Table; and where the columns meet, you have the Golden Number (which is the same both in Old and New Style) for the given year. Thus, suppose the Golden Number was wanted for the year 1757; I look for 1700 at the left hand of the Table, and for 57 at the top of it; then guiding my eye downward from 57 to over against 1700, I find 10, which is the Golden Number for that year.

A perpetual Table of the time of New Moon to the nearest hour, for the Old Style.

424. But because the lunar Cycle of 19 years sometimes includes five leap-years, and at other times only four, this Table will sometimes vary a day from the truth in leap-years after February. And it is impossible to have one more correct, unless we extend it to four times 19 or 76 years; in which there are 19 leap years without a remainder. But even then to have it of perpetual use, it must be adapted to the Old Style, because in every centurial year not divisible by 4, the regular course of leap-years is interrupted in the New; as will be the case in the year 1800. Therefore, upon the regular Old Style plan, I have computed the following Table of the mean times of all the New Moons to the nearest hour for 76 years; beginning with the year of Christ 1724, and ending with the year 1800.