from F to E. If E be the Dominical Letter this Year, D will be the next. * To find the Dominical Letter for Year. any Divide the Cent'ries by 4; and twice what does remain Take from 6; and then add to the Number you gain The odd Years and their 4th; which dividing by Seven, What is left take from 7, and the Letter is *Every common Year brings the Dominical Letter one backward, and every Leap Year two; therefore to any Number of Years, under 100, add its 4th Part for the Leap Years, omitting Fractions; and the Sum will be the Number of Times the Letter has fhifted backward during that Number of Years, which being divided by 7, the Remainder will be the Number of the Letter of the prefent Year, reckoning from the Letter belonging to the last centeffimal Year in a retrograde Order; or the Complement of the Remainder to 7 will be the prefent Dominical Letter in a direct Order, as will appear by the in Example. Let By the Dominical Letter, you may compute on what Day of the Week any Day of the Month will fall throughout the Year, by the following Canon. At Let the Letter of the last centeffimal Year be G, and fuppofe the given Year to be 77. When the centeffimal Year, which is the last of the Century, is common, that Century will bring the Dominical Letter two forward; (100 Years + 24 Leap Years 124; 1247 Remains 5, 7-5=2). But when the lat Year is Leap Year, that Century will bring the Dominical Letter but one forward (100 Years + 25 Leap Years = 125; 1257, Remains 6; 7-6-1). Confequently, 4 Gregorian Centuries will compleat a Revolution of the Letter: Thus the Dominical Letter is for the Year 1600 A; 1700 C; 1800 E; 1900 G; 2000 A; &c. Now as A, the fixth Letter backward from G, is the Dominical Letter of a Biffextile centeffimal Year, (which is when the Number of Centuries is divifible by 4 without any Remainder) the Rule to find it until the next hundredth Year will be, To divide the odd Years, their 4th Part, and 6, by 7; and the Remainder fubftracted from 7, will give the Number of the Letter, reckoning A 1, B 2, &c. But as the firft common Century brings it two Letters forward from A, or two lefs backward from G, the Remainder, after dividing the Centuries by 4, must be doubled; then 6-2=4, therefore 4 must be added to the odd Years and their 4th in order to find the Dominical Letter till the laft Year of the second common Century; and, for the fame Reason, 2 must be added in the next Century, and o in the fourth. Whence it easily appears, that the Rule for finding the Dominical Letter may be abridged during the prefent Century to this: Divide the odd Years, their fourth and four by seven, What is left substract from seven the Letter is given. 8 9 ΙΟ II 12 7 Where the 12 Words answer to the 12 Months; the first Letter of each Word ftands in the Calendar against the first Day of the corresponding Month, as A against January the ift, D against February the ift, &c. Suppofe B is the Dominical Letter, I would know on what Day of the Week June the 24th falls that Year, E ftands against June the 1ft, per Canon, Remember that the 1ft, 8th, 15th, 22a, 29th, is the fame Day of the Week in each Month. Now if B be Sunday, E is Wednefday; therefore June the 22 is Wednesday, and the 24th is Friday. C CHA P. III. Of CYCLES. YCLES, or Periods, are fuch Spaces of Time as revolve into themselves again; of which Sort the most confider able are, of the Sun, The Cycle of the Moon, of the Roman Indiction. EXAMPLE for 1766. 66+16+4786÷7=123, or 2 remains. 1. The 7-25 E, the Dominical Letter; and fubftituting 2 for 4 in the first Line, the Rule will hold for the next Century, 1. The Cycle of the Sun confists of 28 Years, which contain all the poffible Combinations of the Dominical Letters, in refpect to their fucceffive Order, as pointing out common Years and Leap Years: fo that after the Expiration of the Cycle, the Days of the Month return in the fame Order to the fame Days of the Week, throughout the next Cycle. Except that upon every centeffimal Year, which is not a Leap Year, the Letters must all be removed one Place forward, to make them answer to the Years of the Cycle. For Inftance, If the Year 1800 were a Leap Year, as every centeffimal Year is in the Julian Account, the Dominical Letters would be ED, and C would be the Dominical Letter of the next Year; but as it is a common Year in the Gregorian Account, D is the Dominical Letter of 1801, which answers to the 18th of the Cycle; C to the 19th &c. until the next centeffimal Year. The Dominical Letter of each Year in this Cycle, until the Year 1800, appears in the following Table. Part III, 2. The Cycle of the Moon is a Period of 19 Years, after which the new and full Moons return on the fame Days of the Months; only 1 Hour 28 Minutes fooner; So that on whatever Days the new and full Moons fall this Year, they will happen 19 Years hence on the fame Days of the Months. Except when a centeffimal common Year falls within the Cycle, that will remove the new and full Moons a Day later in the Calendar, than otherwise they would have fallen; so that a new Moon which fell, before the centerfimal Year, fuppofe on March 10th, will fall 19 Years afterwards on March 11th. The Number of the Years in this Cycle is called the Prime, from its ufe in pointing out the first Day of the Moon (Primum Luna) and the Golden Number, as deferving to be writ in Letters of Gold. The Golden Numbers are thofe placed in the firft Column of the Calendar, betwixt March 21 and April 18", both inclusive, to denote the Days upon which those full Moons fall, which happen upon or next after March 21ft in thofe Years, of which they are refpectively the Golden Numbers. The day of fuch full Moon, or the Number of Days from March 1ft to that Day inclufive, is called the Pafchal Limit, the next Sunday after which is Eafter Day. From whence it appears that Easter can never fall fooner 3 1 |