Part 35

410. The time measured by twelve Revolutions of the Moon, from the Sun to the Sun again, is called the _Lunar Year_; it contains 354 days 8 hours 48 minutes 37 seconds; and is therefore 10 days 21 hours 0 minutes 20 seconds shorter than the Solar Year. This is the foundation of the Epact.

[Sidenote: Civil Year.]

411. The _Civil Year_ is that which is in common use among the different nations of the world; of which, some reckon by the Lunar, but most by the Solar. The Civil Solar Year contains 365 days, for three years running, which are called _Common Years_; and then comes in what is called the _Bissextile_ or _Leap-Year_, which contains 366 days. This is also called the _Julian Year_ on account of _Julius Cæsar_, who appointed the Intercalary-day every fourth year, thinking thereby to make the Civil and Solar Year keep pace together. And this day, being added to the 23d of _February_, which in the _Roman_ Calendar, was the sixth of the Calends of _March_, _that_ sixth day was twice reckoned, or the 23d and 24th were reckoned as one day; and was called _Bis sextus dies_, and thence came the name _Bissextile_ for that year. But in our common Almanacks this day is added at the end of _February_.

[Sidenote: Lunar Year.]

412. The _Civil Lunar Year_ is also common or intercalary. The common Year consists of 12 Lunations, which contain 354 days; at the end of which, the year begins again. The _Intercalary_, or _Embolimic_ Year is that wherein a month was added, to adjust the Lunar Year to the Solar. This method was used by the _Jews_, who kept their account by the Lunar Motions. But by intercalating no more than a month of 30 days, which they called _Ve-Adar_, every third year, they fell 3-3/4 days short of the Solar Year in that time.

[Sidenote: _Roman_ Year.]

413. The _Romans_ also used the _Lunar Embolimic Year_ at first, as it was settled by _Romulus_ their first King, who made it to consist only of ten months or Lunations; which fell 61 days short of the Solar Year, and so their year became quite vague and unfixed; for which reason, they were forced to have a Table published by the High Priest, to inform them when the spring and other seasons began. But _Julius Cæsar_, as already mentioned, § 411, taking this troublesome affair into consideration, reformed the Calendar, by making the year to consist of 365 days 6 hours.

[Sidenote: The original of the _Gregorian_, or _New Style_.]

414. The year thus settled, is what we still make use of in _Britain_: but as it is somewhat more than 11 minutes longer than the _Solar Tropical Year_, the times of the Equinoxes go backward, and fall earlier by one day in about 130 years. In the time of the _Nicene Council_ (A. D. 325.) which was 1431 years ago, the vernal Equinox fell on the 21st of _March_: and, if we divide 1431 by 130, it will quote 11, which is the number of days the Equinox has fallen back since the Council of _Nice_. This causing great disturbances, by unfixing the times of the celebration of _Easter_, and consequently of all the other moveable Feasts, Pope _Gregory_ the 13th, in the year 1582 ordered ten days to be at once struck out of that year; and the next day after the fourth of _October_ was called the fifteenth. By this means the vernal Equinox was restored to the 21st of _March_; and it was endeavoured, by the omission of three intercalary days in 400 years, to make the civil or political year keep pace with the Solar for time to come. This new form of the year is called the _Gregorian Account_ or _New Style_; which is received in all Countries where the Pope’s Authority is acknowledged, and ought to be in all places where truth is regarded.

[Sidenote: Months.]

415. The principal division of the year is into _Months_, which are of two sorts, namely _Astronomical_ and _Civil_. The Astronomical month is the time in which the Moon runs through the _Zodiac_, and is either _Periodical_ or _Synodical_. The Periodical Month is the time spent by the Moon in making one compleat Revolution from any point of the Zodiac to the same again; which is 27^d 7^h 43^m. The Synodical Month, called a _Lunation_, is the time contained between the Moon’s parting with the Sun at a Conjunction, and returning to him again; which is in 29^d 12^h 44^m. The Civil Months are those which are framed for the uses of Civil life; and are different as to their names, number of days, and times of beginning, in several different Countries. The first month of the _Jewish Year_ fell according to the Moon in our _August_ and _September_, Old Style; the second in _September_ and _October_, and so on. The first month of the _Egyptian Year_ began on the 29th of our _August_. The first month of the _Arabic_ and _Turkish Year_ began the 16th of _July_. The first month of the _Grecian Year_ fell according to the Moon in _June_ and _July_, the second in _July_ and _August_, and so on, as in the following Table.

+----+--------------------------+----++----+-----------------------+----+ |N^o | The Jewish year. |Days||N^o | The Egyptian year. |Days| +----+--------------------------+----++----+-----------------------+----+ | 1 |Tisri Aug.-Sept.| 30 || 1 |Thoth August 29 | 30 | | 2 |Marchesvan Sept.-Oct.| 29 || 2 |Paophi Septemb. 28 | 30 | | 3 |Casleu Oct.-Nov. | 30 || 3 |Athir October 28 | 30 | | 4 |Tebeth Nov.-Dec. | 29 || 4 |Chojac Novemb. 27 | 30 | | 5 |Shebat Dec.-Jan. | 30 || 5 |Tybi Decemb. 27 | 30 | | 6 |Adar Jan.-Feb. | 29 || 6 |Mechir January 26 | 30 | | 7 |Nisan _or_ Abib Feb.-Mar. | 30 || 7 |Phamenoth Februar. 25 | 30 | | 8 |Jiar Mar.-Apr. | 29 || 8 |Parmuthi March 27 | 30 | | 9 |Sivan April-May | 30 || 9 |Pachon April 26 | 30 | | 10 |Tamuz May-June | 29 || 10 |Payni May 26 | 30 | | 11 |Ab June-July | 30 || 11 |Epiphi June 25 | 30 | | 12 |Elul July-Aug. | 29 || 12 |Mesori July 25 | 30 | +----+--------------------------+----++----+-----------------------+----+ | Days in the year |354 || _Epagomenæ_ or days added | 5 | +-------------------------------+----++----------------------------+----+ |In the __Embolimic_ year after | || Days in the year |365 | | _Adar_ they added a month | || | | | called _Ve-Adar_ of 30 days. | || | | +-------------------------------+----++----------------------------+----+ +---+-------------------------+----++---+----------------------------+----+ |N^o|The _Arabic_ and |Days||N^o|The ancient _Grecian_ year. |Days| | | _Turkish_ year. | || | | | +---+-------------------------+----++---+----------------------------+----+ | 1 |Muharram July 16 | 30 || 1 |Hecatombæon June-July | 30 | | 2 |Saphar August 15 | 29 || 2 |Metagitnion July-Aug. | 29 | | 3 |Rabia I. Septemb. 13 | 30 || 3 |Boedromion Aug.-Sept. | 30 | | 4 |Rabia II. October 13 | 29 || 4 |Pyanepsion Sept.-Oct. | 29 | | 5 |Jomada I. Novemb. 11 | 30 || 5 |Mæmacterion Oct.-Nov. | 30 | | 6 |Jomada II. Decemb. 11 | 29 || 6 |Posideon Nov.-Dec. | 29 | | 7 |Rajab January 9 | 30 || 7 |Gamelion Dec.-Jan. | 30 | | 8 |Shasban February 8 | 29 || 8 |Anthesterion Jan.-Feb. | 29 | | 9 |Ramadan March 9 | 30 || 9 |Elapheloblion Feb.-Mar. | 30 | |10 |Shawal April 8 | 29 ||10 |Munichion Mar.-Apr. | 29 | |11 |Dulhaadah May 7 | 30 ||11 |Thargelion April-May | 30 | |12 |Dulheggia June 5 | 29 ||12 |Schirrophorion May-June | 29 | +---+-------------------------+----++---+----------------------------+----+ | Days in the year |354 || Days in the year |354 | +-----------------------------+----++--------------------------------+----+ |The _Arabians_ add 11 days at the end of every year, which keep the same | | months to the same seasons. | +-------------------------------------------------------------------------+

[Sidenote: Weeks]

416. A month is divided into four parts called _Weeks_, and a Week into seven parts called _Days_; so that in a _Julian_ Year there are 13 such Months, or 52 Weeks, and one Day over. The Gentiles gave the names of the Sun, Moon, and Planets to the Days of the Week. To the first, the Name of the _Sun_; to the second, of the _Moon_; to the third, of _Mars_; to the fourth, of _Mercury_; to the fifth, of _Jupiter_; and to the sixth, of _Saturn_.

[Sidenote: Days]

417. A Day is either _Natural_ or _Artificial_. The Natural Day contains 24 hours; the Artificial the time from Sun-rise to Sun-set. The Natural Day is either _Astronomical_ or _Civil_. The Astronomical Day begins at Noon, because the increase and decrease of Days terminated by the Horizon are very unequal among themselves; which inequality is likewise augmented by the inconstancy of the horizontal Refractions § 183: and therefore the Astronomer takes the Meridian for the limit of diurnal Revolutions; reckoning Noon, that is the instant when the Sun’s Center is on the Meridian, for the beginning of the Day. The _British_, _French_, _Dutch_, _Germans_, _Spaniards_, _Portuguese_, and _Egyptians_, begin the Civil Day at mid-night: the antient _Greeks_, _Jews_, _Bohemians_, _Silesians_, with the modern _Italians_, and _Chinese_, begin it at Sun-setting: And the antient _Babylonians_, _Persians_, _Syrians_, with the modern _Greeks_, at Sun-rising.

[Sidenote: Hours]

418. An _Hour_ is a certain determinate part of the Day, and is either equal or unequal. An equal Hour is the 24th part of a mean natural Day, as shewn by well regulated Clocks and Watches; but those Hours are not quite equal as measured by the returns of the Sun to the Meridian, because of the obliquity of the Ecliptic and Sun’s unequal motion in it § 224-245. Unequal Hours are those by which the Artificial Day is divided into twelve Parts, and the Night into as many.

[Sidenote: Minutes, Seconds, Thirds, and Scruples.]

419. An Hour is divided into 60 equal parts called _Minutes_, a minute into 60 equal parts called Seconds, and these again into 60 equal parts called _Thirds_. The _Jews_, _Chaldeans_, and _Arabians_, divide the Hour into 1080 equal parts called _Scruples_; which number contains 18 times 60, so that one minute contains 18 Scruples.

[Sidenote: Cycles, of the Sun, Moon, and Indiction.]

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.

[Sidenote: 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.

[Sidenote: 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.|Mar.|Apr.|May |Jun.|Jul.|Aug.|Sep.|Oct.|Nov.|Dec.| +----++----+----+----+----+----+----+----+----+----+----+----+----+ | 1 || 9 | | 9 | 17 | 17 | 6 | | | | 11 | | 19 | | 2 || | 17 | | | 6 | 14 | 14 | 3 | 11 | | 19 | | | 3 || 17 | 6 | 17 | 6 | | | 3 | 11 | | 19 | 8 | 8 | | 4 || 6 | | 6 | 14 | 14 | 3 | | | 19 | 8 | | 16 | | 5 || | 14 | | | 3 | 11 | 11 | 19 | 8 | | 16 | | +----++----+----+----+----+----+----+----+----+----+----+----+----+ | 6 || 14 | 3 | 14 | 3 | | | 19 | | | 16 | 5 | 5 | | 7 || 3 | | 3 | 11 | 11 | 19 | | 8 | 16 | | | 13 | | 8 || | 11 | | | 19 | 8 | 8 | 16 | 5 | 5 | 13 | | | 9 || 11 | 19 | 11 | 19 | | | | | | 13 | | 2 | | 10 || | | 19 | 8 | 8 | 16 | 16 | 5 | 13 | | 2 | 10 | +----++----+----+----+----+----+----+----+----+----+----+----+----+ | 11 || 19 | 8 | | | | | 5 | 13 | 2 | 2 | 10 | | | 12 || 8 | 16 | 8 | 16 | 16 | 5 | | | | 10 | | 18 | | 13 || | | | | 5 | 13 | 13 | 2 | 10 | | 18 | 7 | | 14 || 16 | 5 | 16 | 5 | | | 2 | 10 | 18 | 18 | 7 | | | 15 || 5 | | 5 | 13 | 13 | 2 | | | | 7 | | 15 | +----++----+----+----+----+----+----+----+----+----+----+----+----+ | 16 || | 13 | | | 2 | 10 | 10 | 18 | 7 | | 15 | | | 17 || 13 | 2 | 13 | 2 | | | 18 | 7 | | 15 | 4 | 4 | | 18 || 2 | | 2 | 10 | 10 | 18 | | | 15 | | | 12 | | 19 || | 10 | | | 18 | 7 | 7 | 15 | 4 | 4 | 12 | | | 20 || 10 | 18 | 10 | 18 | | | 15 | | | 12 | 1 | 1 | +----++----+----+----+----+----+----+----+----+----+----+----+----+ | 21 || | | 18 | 7 | 7 | 15 | | 4 | 12 | | | 9 | | 22 || 18 | 7 | | | 15 | 4 | 4 | 12 | 1 | 1 | 9 | | | 23 || 7 | 15 | 7 | 15 | | | 12 | | | 9 | 17 | 17 | | 24 || | | 15 | 4 | 4 | 12 | | 1 | 9 | | | 6 | | 25 || 15 | 4 | | | 12 | | 1 | 9 | 17 | 17 | 6 | | +----++----+----+----+----+----+----+----+----+----+----+----+----+ | 26 || 4 | | 4 | 12 | | 1 | | | | 6 | | 14 | | 27 || | 12 | | 1 | 1 | 9 | 9 | 17 | 6 | | 14 | | | 28 || 12 | 1 | 12 | | 9 | | 17 | 6 | 14 | 14 | 3 | 3 | | 29 || 1 | | 1 | 9 | | 17 | | | | 3 | | 11 | | 30 || | | | | 17 | 6 | 6 | 14 | 3 | | 11 | | +----++----+----+----+----+----+----+----+----+----+----+----+----+ | 31 || 9 | | 9 | | | | 14 | 3 | | 11 | | 19 | +----++----+----+----+----+----+----+----+----+----+----+----+----+

[Sidenote: 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.

[Sidenote: 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.

This Table may be made perpetual, by deducting 6 hours from the time of New Moon in any given year and month from 1724 to 1800, in order to have the mean time of New Moon in any year and month 76 years afterward; or deducting 12 hours for 152 years, 18 hours for 228 years; and 24 hours for 304 years, because in that time the changes of the Moon anticipate almost a complete natural day. And if the like number of hours be added for so many years past, we shall have the mean time of any New Moon already elapsed. Suppose, for example, the mean time of Change was required for _January_ 1802; deduct 76 years and there remains 1726, against which in the following Table under _January_ I find the time of New Moon was on the 21st day at 11 in the evening: from which take 6 hours and there remains the 21st day at 5 in the evening for the mean time of Change in _January_ 1802. Or, if the time be required for _May_, A. D. 1701, add 76 years and it makes 1777, which I look for in the Table, and against it under _May_ I find the New Moon in that year falls on the 25th day at 9 in the evening; to which add 6 hours, and it gives the 26th day at 3 in the Morning for the time of New Moon in _May_, A. D. 1701. By this addition for time past, or subtraction for time to come, the Table will not vary 24 hours from the truth in less than 14592 years. And if, instead of 6 hours for every 76 years, we add or subtract only 5 hours 52 minutes, it will not vary a day in 10 millions of years.

Although this Table is calculated for 76 years only, and according to the _Old Style_, yet by means of two easy Equations it may be made to answer as exactly to the _New Style_, for any time to come. Thus, because the year 1724 in this Table is the first year of the Cycle for which it is made; if from any year of CHRIST after 1800 you subtract 1723, and divide the overplus by 76, the Quotient will shew how many entire Cycles of 76 years are elapsed since the beginning of the Cycle here provided for; and the remainder will shew the year of the current Cycle answering to the given year of CHRIST. Hence, if the remainder be 0, you must instead thereof put 76, and lessen the Quotient by unity.

Then, look in the left hand column of the Table for the number in your remainder, and against it you will find the times of all the mean New Moons in that year of the present Cycle. And whereas in 76 _Julian_ Years the Moon anticipates 5 hours 52 minutes, if therefore these 5 hours 52 minutes be multiplied by the above found Quotient, that is, by the number of entire Cycles past; the product subtracted from the times in the Table will leave the corrected times of the New Moons to the _Old Style_; which may be reduced to the _New Style_ thus:

Divide the number of entire hundreds in the given year of CHRIST by 4, multiply this Quotient by 3, to the product add the remainder, and from their sum subtract 2: this last remainder denotes the number of days to be added to the times above corrected, in order to reduce them to the _New Style_. The reason of this is, that every 400 years of the _New Style_ gains 3 days upon the _Old Style_: one of which it gains in each of the centurial years succeeding that which is exactly divisible by 4 without remainder; but then, when you have found the days so gained, 2 must be subtracted from their number on account of the rectifications made in the Calendar by the Council of _Nice_, and since by Pope _Gregory_. It must also be observed, that the additional days found as above directed do not take place in the centurial Years which are not multiples of 4 till _February_ 29th, _O. S._ for on that day begins the difference between the _Styles_; till which day therefore, those that were added in the preceding years must be used. The following Example will make this accommodation plain.

_Required the mean time of New Moon in_ June, A.D. 1909, _N.S._

From 1909 take 1723 Years, and there rem. 186 Which divided by 76, gives the Quotient 2 and the remainder 34 Then, against 34 in the Table is _June_ 5^d 8^h 0^m Afternoon. And 5^h 52^m multiplied by 2 make to be subtr. 11 44 ------------- Remains the mean time according to the _Old Style_, _June_ 5^d 9^h 16^m Morning. Entire hundred in 1909 are 19, which divided by 4, quotes 4 And leaves a remainder of 3 Which Quotient multiplied by 3 makes 12, and the remainder added makes 15 From which subtract 2, and there remains 13 Which number of days added to the above time _Old Style_, gives _June_ 18^d 9^h 16^m Morn._N.S._