form began on the 106 day after the first of Janua Ty, i, e. on the 16th of April, and that the 1037 Yezdegerdick commenc'd from Oct. 1, or the 274th day from the first of January. $.8. The Gelalean year is admirably well adapt- The Gelaed to the Solar Motions; and was inftituted for the lean year. regular celebration of the feftival called Neurux, as the Gregorian was for that of Eafter. It takes in a leap day every fourth year, but every fixth or feventh turn it throws it forward to the fifth year, by which means the Equinoxes and Solftices are fix'd to almost the fame days of the Months. §. 9. The Syriack year confifts of 365 days and fix hours, being divided into 12 Months of equal extent with thofe of the Julian year to which they correfpond. This year begins Oct. 1. fo that the firit Month called Tifrin correfponds to October, and the Month called Shabat which correfponds to February has 28 days or 29 in a leap year. The Syri ack year. year. §. 10. In the infancy of Aftronomy, the Athenians The Attick taking it for granted that the Moon finifh'd its courfe in 30 days, divided their year into 12 tricenary Months; and at the fame time out of regard to the Suns motion, added a fupernumerary Month of 30 days to every o ther year. But when the annual and menftrual converfions of the Stars came to be better known; they made a Common year of 12 Lunar Periods, and an Embolifmal one of 13. The beginning of their year was computed not from the real New Moon, but aò Ths gastos from the first appearance of the New Moon. Months. §. 11. Forafmuch as a Lunar Month confifts of 29 The length days, 12 hours and 44', the odd twelve hours make and order up a day in two Revolutions; and for that reafon of the A- | all the Attick Months are Cavi and Pleni by turns, thenian that is, one has 29 and the next in order 30 days. At this rate their Common year contained 354 days; but in that called Embolismal an additional Month was joyned to rosedev, and fo the Month called Pofideon was doubled. The Embolifmal years in a Decennoval Cycle, or the courfe of nineteen years are 3, 5, 8, 11, 14, 16, 19. All the reft being fitil'd Common. The frit day of every Month was called, vanvía, and the laft was known by the name of 'n na via, i. e. the old and the new, alluding to its divided relation to the new New and the Old Moon. The Athenians divided their Months into three parts, namely isauére, iì fixa and DívovTos; by reference to which they pointed out every day as the Romans did by their Calends, Nones and Ides. S. 12. The beginning of the Athenian year is reckonmencement ed from that New Moon, the Full Moon of which of the At- comes next after the Summer Solitice. Now the ancitick year. ent Grecians, in the time of Meto and Eudoxus, fix'd The com donian year. the Summer Solftice in the 8th degree of Cancer or on the 8th of July: But afterwards, when Timocharis and Hipparchus flourish'd, 'twas thrown upon the 27 of Fune. If this be duly confidered, 'twill be eafie to reduce the Attick New years day or the first day of Hecatombeon, to its correfponding place in the Fulian form. For if the Attick year proposed runs before the 4400 year of the Fulian Period, we reckon from that New Moon, the Full Moon of which came next after the 8th of July: But if the year propofed falls later than the 4400 year of the Fulian Period, we reckon from that New Moon, the Full Moon of which followed next after the 27th of Fune. The begin. §.13.The MacedonianLunar year agrees with the Athening of nian, excepting that the former takes its beginning not the Mace from theSummer Solstice,but from the Autumnal Equinox. S. 14. The fews calculated their Months by the motion of the Moon, and their years by that of the Sun, The Jewish as well as the Athenians; from whence it came to pafs Aftronomi- that they fometimes threw in an Embolifm to keep the eal year. Lunar year from ranging wide of the Equinoctial points, X The order that the Paffover might be celebrated at the appointed Seafons. Each Month confifting of 29 days, 12 hours and 793 Helakim, i. e. 44′, 3", 20" it follows by confequence that the common year contained 354 days, 8 hours and 876 Helakim, to which if you add an Embolifmal Month, it makes 383 days, 21 hours and 589 Helakim. A Hélek or jewish Scruple contains 18 common Minutes. S. 15. The Jewish Months are twelve in number, befides the Embolifmal call'd Veadar. They were Pleni and length and Cavi by turns, i. c. the firft 30, the 2d 29, the of the Jew- 3d 30 again and fo on. In the Ecclefiaftical Computaif Months tion we make Nifan the first Month; though tis plain that in Mofes's time the Jews made Tibri the firft Month, and fo it continues in the Aftronomical and the the Civil years. The Embolismal was called Veadar, because of its intercalation after the Month, which was the fixth in order. It confifts of 30 days. cles. §. 16.In the Decennoval Cycle of femish years, twelve The diffeare common and feven Embolifmal. The Embolifmal rence beare 3, 6, 8, 11, 14, 17, 19. In that space of nineteen tween the years the Julian Cycle out-runs the Jewish by I Julian and hour, 26′ 56" 40". So that in finding out the day of Jewish Cythe Julian year that correfponds to the first day of a Jewish Month, we must take off for each Jewish Cycle 1 hour 26 56" 40"". The head of the Jewish Epocha of years commences from the New Moon that happen'd on the 7th of October in the 593d year of the fuLian Period. §. 17. To find out the day of the Julian year that How to recorrefponds to the first day of Tifri, i.e. The fewish duce the New years day, we must first multiply all the paft first day of compleat Jewish Cycles by 1 hour and 485 Hela- a Jewish kimi.e. 26 56" 40"; that being the excels of the year to the Julian Cycle above the Jewish. Then we muft mul- Julian tiply all the common compleat years by 10 days, 21 form. hours and 204 Helakim, and the Embolifmal compleat years by 18 days 15 hours and 589 Helakim; the former multiplyer being the excess of the Fulian year above the fewifh common year, and the latter the excess of the Embolifmal above the Julian. This done we must fubftract the Product of the laft or third Multiplication from the Product of the second, because the excess of the Fulian year above the fewish decreases in proportion to the rifing of the Jewish Embolismal above the Fulian. But after all, the Remainder of this Subftraction must be .. added to the Product of the first Multiplication, that the joynt fumm may give the whole excess of the fulian above the fewish, whether in Cycles or in compleat years. To conclude the operation this last fum mult be fubftracted from Oct. 7. (i. e. its numeral character from Fan. 1.) on which day the Jewish Epocha commences, and the Remainder gives you the day requir'd. After the Neomenia of Tifhri is found, the term of the Paffover is found by fubftracting 163 from the former. §. 18. In regard that the Femith Aftronomical year The Jewish takes in the odd hours and minutes, the computation Civil year. of which is inconvenient for Civil ufe; the Fems made use of a Civil year in their publick Bufi nels nefs, which confifted only of days; and to make it bear fome correfpondence with the Attronomical, fometimes added and fometimes lop'd off a day. The Jewish §. 19. The fews divided their Solar year into three Solar year parts call'd Tekupha, or Cardinal points. The Tekuand their pha of Tifhri correfponded to the Autumnal Equinox, Tekuphx. that of Tebeth to the Winter Solstice, that of Nifan contri to the Spring Equinox, and that of Tamuz to the Summer Solstice Thefe four terms were observed by that People with the utmost fuperftition. In §. 20. The Arabian year is called Mahumetan from The name, Mahomet their falfe Prophet. 'Tis likewife ftil'd the form and year of the Hegira, because the calculation of thefe vance of years runs from the Epocha of the Hegira, i. e. Mathe Arabi- homer's flight from Mecca to Medina. The Arabian an years. Aftronomical Months were (each of 'em) less than the Jewish by one Helek,fo that their Aftronomical year being Lunar contained 354 days, 8 hours and 48. their Civil Computation they left out the odd hours and minutes, and to make it even afterwards they divided their years into τριακονταετήριδες or Cycles of thirty years, eleven of which had an additional day a piece. In the courfe of the thirty years, the Embolifmal years run in this order, 2, 5, 7, 10, 13, 15, 18, 21, 24, 26, 29, all the reit being common years. They pitch'd upon Cycles of thirty years, because thirty Aftronomical Arabian years made a compleat number of days without any fractional hours or minutes. Their Embolismal day was added to the end of the year; fo that their laft Month Dulheggia had in their leap year 30 days inftead of 29. .. The Arabian Months. §. 21. The Arabians had twelve civil Months in a year, which contain'd 29 days and 30 days by turns, abating for their leap years in which the Month D heggia has always 30. Their Months commence not from the real New Moon, but from its first appearance after its coition. Now this appearance happening always in the Evening or at Night, 'tis plain that the Ma-, hometans as well as the fews and Athenians and all others that us'd Lunar Months,reckon'd the beginning' of their days from Sun-fet. But the Mahometans in particular, compute their time by fuch and fuch a number of nights and not days. After the twentieth day of the Month they reckon backwards as the Athenians and Romans did. CHAP. 1. Under the Name of Epacts, we usually understand are 12. 4. The Aftronomical Epacts may be termed thofe Days, Hours and Minutes, which are intercepted between the Common Lunar year, and the mean or equal Julian year, which are 10 days 12 hours 11'. 22'. 16'. S. 1. THE word Epact is derived from the Greek The EtyTáy, which, befides other things, figni- mology of fies to intercalate: In which fenfe Plutarch in Numa the word ufes it; and in the Egyptian Nabonaffarear Computa- Epact. tion, the 5 days over and above the 12 Months confifting of 30 days, added to compleat the year, are termed the ἡμέρας Ἐπαγωμέναι or added days, and therefore fince the Epacts are days that are to be added to the Lunar year, this Denomination is no ways abfurd. S. 2. The reafon of the Epacts, is the difference of The reafon the quantity between the Lunar and Julian year: For of the Ethe common Lunar year being not Equal to,but lefs than pacts. the Fulian, and both being made ufe of in the Eccle fiaftical Computation, fome Authors bethought themfelves of reducing the one to the other, which they effected by appointing the Epacts. he §. 3. A difference indeed was ever between the Lunar and Julian year; but becaufe Sofygenes the Author of the Fulian Calendar, in that form of a year Propofed to Cafar, little regarded the Moons Motion;" It is probable that the ufe of the Epacts was anciently unknown E 1. The time! when firft known. |