the year beginning again at A, there will be two, A, A, falling together, Dec. 31. and fan. 1. and if one of them, (the former) happen to be Sunday, the other in courfe muft ftand for Monday; and then reckoning onward, Sunday muft fall upon the first following G, and G will be the Dominical that enfuing year. Thus the odd day fhifts back the Dominical Letter every year by one Letter. And this Revolution would be terminated in 7 years, But fecondly, there comes in another odd day every 4th year, being Leap-year. And in that year there are confequently two fuch fhifts; the Sunday Letter being changed twice: Once at the beginning of the year,and the 2d time towards the latter end of February, by Interpofition of the Biffextile, or intercalar day called Biffextile, becaufe the 6th of the Calends of March is twice repeated. And the reafon why this was done in that Month, and not rather at the end of the year, feems to be, because by Numa's Inftitution for the better regulating the year, (in imitation of what the Greeks had done before) there had been an intercalation of feveral days, at that very time in Febru ary. To take a more eafie Account of thefe Changes, there is appropriated a Cycle, which comprehends in order all the variations of the Sunday Letter: and is therefore called, the Cycle of the Sun; compofed of 4, which makes the Leap-year, and 7, the change of one odd day, throughout the Septimana, or Week; 4 times 7 gives 28. This Cycle begins at that Leapyear, wherein G and F are the Sunday Letters, and is terminated at 28, Additions Additions to the foregoing Chapter Collected from Dr. Beveridges's Inftitutiones Chronologicæ. RULES. 1. The Dominical Letter is one or two of thefe Letters A, B, C, D, E, F, G; which point to the Sunday through the whole courfe of the Solar Cycle. 2. The Dominical Letters shift backwards, fo that they ftand thus G, F, E, D, C, B, A. S. 1.THAT Letter which answers to the first Sun- The occaday of the year, or to New years day (fup- fion of the pofing it to begin on a Sunday) will ftand for Sunday double Doall the year round, if it be a Common year. But in a minical Biffextile year there are two Dominical Letters, the Letters. first of which points to Sunday all along from the beginning of the year to the time of intercalation, viz. Feb. 24. and the other does the fame fervice for the reft of the year. Now, there being feven intercalations or leap days in the space of 28 years or a Solar Cycle, it follows that the Dominical Letter is feven times double in this Cycle. §. 2. The Dominical Letters fhifting in a retrograde The order order, it follows that if this year have G for its Domiof Domini nical, F will answer to the next, and fo on: And in the cal Letter leap years which have double Dominicals the fame whether Retrograde order is obferved, as, if F and G be the fingle or Dominicals, 'tis not fet F G. but G F. §. 3. Tho' double. Every year of the Selar Cycle is call'd a Cycle in a Numeral order. year, and §. 3. Though the Cycle of the Sun, properly fpeaking, fignifies the whole Circle of 28 years, yet every year of that Circle or Revolution is called the Cycle of the Sun; fo that the first year is called the firft Cycle of the Sun, the 2d the fecond Cycle of the Sun, and fo forth. $.4. To find the Cycle of the Sun, and the DomiHow to nical Letter depending upon it, for any year, take the find theCy-propofed year of the Julian Period, and divide it by 28; cle for any the Quotient fhews you how many Cycles are pait its Domi- from the beginning of that Period to the year pronical. pofed, and the Remainder upon the Divifion is the Cycle; or if it be o, 28 is the Cycle. If the year propos'd be of the Chriftian Era, we add 9 to it, and proceed as before in dividing the fum by 28. The reafon of the addition of 9, is, that the Christian Æra began in the tenth Cycle of the Sun, fo that there were 9 compleat Cycles before it. Thus you'll find that the year 6380 of the Fulian Period has 24 for its Cycle, and that the year of Chrift 1671, leaving no Remainder upon the Divifion, has 28 for its Cycle. As for the correfponding Dominical Letters: See Strauchius's Tables. How to $. 5. To find the Feria or day of the Week that find the Fe- answers to any day of the year; find out the Solar ria or day Cycle and Dominical for that year (as above,) then obof the ferve what Character or Letter anfwers to the proWeek that pos'd day in the Kalendar, fo reckon the number of anfwers days from the Dominical found to the Character of the to any day day inclufive, in a direct Order. Thus, the Dominiof the year. nical of the year being F, and the Character of the propos'd day E, feven is the number of the Feria, i. e. Saturday. How to re §. 6. If Gregory in the caftigation of the Fulian year had thrown out only days or a Week, the Domiduce the minical of nicals of the Gregorian had been ftill the fame with a Fulian the Fulian; but in regard that he lop'd off ten, which year to that is three above feven, we must take three Letters of of aGrego- the Fulian Dominical to make it Gregorian. If the Tian' Julian Dominical (for inftance) be F; reckoning in a first of these two, and throwing out three in a Retrograde order exclufive, take the two next Dominicals. Thus, if the Fulian Leap Dominicals be E D, I find A G. to be the Gregorian. But, you must take notice that after the year of Christ 1700, I throw out but two Letters, by reafon that a Leap day is then caft out in the Gregorian form, but retained in the fulian. From the year 1800 to 1900, another being omitted, I take but one Letter from the Dominical. From the year 1900 to 2100, there being one leap day more omitted in these two Centuries, the Gregorian Dominical is the very next Letter to the Fulian. From 2100 to 2200, 'ts exactly the fame with the Fulian; but from 2200 to 2300, the next Letter before the fulian in a Retrograde Order is the Gregorian Dominical; as if the Fulan Dominical be E the Gregorian will be F. if the former be ED, the latter will be FE. The next Century after that will be the fecond Letter and so on. CH A P. VI. Of the Lunar Cycle. RULE. 1. The Lunar Cycle or Golden Number is a Syftem of nineteen years, both Solar and Luna-Solar, of which laft 12 have 12 Months apiece, and 7 have 13. Thefe nineteen years being elapfed, the mean New Moons are fuppofed to return upon the fame Julian Day. which the §. 1.THE Greeks being taught by their Oracles, of the that their accuftomed Sacrifices were to be Number of offered navà gia, which they understood as if their years in Year were to be regulated by the Sun, and their Days and Months to be adjusted by the motion of the Moon; Moon coinwere always folicitous, how by certain Periods they cide. might reduce the difagreeing motions of the Luminaries to Sun and to a Third fomething in which they might agree, Hence in the ancient times they are faid to have used a Biennium, intercalating every other year: But fault was found with this, and 'twas fucceeded by a Quadriennium, upon the return of which the Olympic Games were celebrated. After this came the Octennium, of which mention is made in rehearfing the times of Cadmus by Apollod. Bibl. l. 3. Hyppolitus, Cleoftratus, Tenedus, Harpalus, and others of the Ancients feem to have interpolated this Period of years. See Eufeb. Hift. Eccl. 1.7. c. 20. Cenfor. de Die nat. c. 6. Macrob. Šaturn l. 1. c. 13. Scaliger de emend. temp. l. 2. p. 46. Petavius de doct.temp. Tom. 1.l.2.c.2. et in Uranologi. l. 4. c. 1. Next came the Duodennium, or 12 years, which feems to have been obferved by the Learned only, as may be gathered from Cenforinus c. 18. But amongst all the Cycles of the Ancients, there's none more famous than the 'Evven denarners of Meto the Athenian, which is ufed to be called the the great year of Meto, though it's uncertain whether Meto was the firft Author of this Cycle; for Livius feems to attribute the Invention to Numa Pompilius, and Geminas to Euctemon and Philippus. This is certain that this Cycle confifting of 19 years comprehends 6940 days, or 19 Solar years, and almoft fo many Lunar years, in which they intercalated 7 times, and that in this Order, according to Dionyfius Petavius, 3, 6, 8, 11, 14, 17, 19. But In the Courfe of this time Meto, or whoever was the Author of this Cycle, thought that 235 Lunations would be exactly compleated, making a hundred and ten New, and a hundred and twenty five Full Moons, or nineteen Solar years. Afterwards Calippus attempted to correct this Period by joining four Metonic Cycles, and giving to them 22759 days, taking away one day in the space of 76 years. In fine, Calippus found many other Cenfors and Correctors, as Democritus, Hipparchus, Ptolomy, and others: Who did not wholly reject, but only interpolated the Metonic Cycle. Why not aljo Chriftians at the beginning of the N. Teftament were fo follicitous about the Harmony of the Luna Solar Motions. of |