A TABLE for reducing A TABLE for reducing Avoirdupois weight; Trov wt. to Avoirdupois. Troy lb. lb. oz.pw gr. into Troy. ar.10. oz. pw. gr. 2 11 16 0 2051 4 622 1 5 7.77 6 932 7 1084 291 8 8 1244 9 33 9 1 9 14 6 167 234678 23456 4 10 6 16 3 10 8 6 I 16 98 13 10 11 S O O 8 *44 Jb. 9 12 1 16 16 10 6.06 48 7 3 13 8 o 616 3 8 o O 16 16 77 9 7 6 78615 17 2 I 8097 2 23 84 w. I 0.88 10 8 3 10 5202 5C3 24 10 1554 20 16 7 30 4이 32 14 100S 123 0 18 5:5 90 109 4 10 100 121 6 6 16 200 243 0 13 8 31 2 14 16.5 300 364 7 3 12 22 2 4:57 74 0 13.62 55 -30 4 II 3.5 I 400 486 616 500 607 7 13 600 729 2 0 o 700 850 8 616 800 972 2 13 8 a 8 702 200 164 9 979 8 300 246 13 1142 9 7 5 20 4 15 9 2 7 6 137 11 10 0 12.5 685 10 8.78 400 329 2 4'52 12 10 18 18 2.28141 1513 16 900 740 9 14 15 1 I 900 1093 9 10001215 3 616 2000 2430 6 13 8 3000 3645 10 4000 4861 50006076 4 13 5000 7291 8 O I 616 8 of AN ACCOUNT of the Gregorian or New Style, together with some Chronological Problems, for finding the Epact, Golden Number, Moon's Age, &c. POPE GREGORY the XIIIth. made a reformation of the calendar. The Julian calendar, or old style, had, before that time, been in general use all over Europe. The year, according to the Julian calendar, consists of three hundred and sixty five days and six hours; which six hours being one fourth part of a day, the common years consisted of three hundred and sixty five days, and every fourth year, one day was added to the month of February, which made each of those years three hundred and sixty six days, which are usually called leap years. This computation, though near the truth, is more than the solar year by eleven minutes, which, in one hundred and thirty one years, amounts to a whole day. By which the Vernal Equinox was anticipated ten days, from the time of the general council of Nice, held in the year 325 of the Christian Era, to the time of Pope Gregory; who therefore caused ten days to be taken out of the month of October in 1582, to make the Equinox fail on the 21st of March, as it did at the time of that council. And, to prevent the like variation for the future, he ordered that three days should be abated in every four hundred years, by reducing the leap year at the close of each century, for three successive centuries, to common years, and retaining the leap year at the close of each fourth century only. This was at that time esteemed as exactly conformable to the true solar year; but Dr. Halley makes the solar year to be three hundred and sixty five days, five hours, forty eight minutes, fifty four seconds, forty one thirds, twenty seven fourths, and thirty one fifths: According to which, in four hundred years, the Julian year of three hundred and sixty five days and six hours will exceed the solar by three days, one hour and fifty five minutes, which is near two hours, so that in fifty centuries it will amount to a day. Though the Gregorian calendar, or new style, had long been used throughout the greatest part of Europe, it did not take place in Great Britain and America till the first of January, 1752; and in September following, the eleven days were adjusted by calling the third day of that month the fourteenth, and continuing the rest in their order. CRONOLOGICAL PROBLEMS. PROBLEM I. As there are three leap years to be abated in every four centuries: to show how to find in which century the last year is to be a leap year, and in which it . is not. RULE.-Cut off two cyphers, and divide the remaining figures by 4; if nothing remain, the year is a leap year. The first and second examples, having remainders, shew the years to be common years of three hundred and sixty-five days; but the third and fourth, having no remainders, are leap years of three hundred and sixty-six days. PROBLEM II. To find, with regard to any other years, whether any given year be leap year, and the contrary. RULE. Divide the proposed year by 4, and if there be no remainder, after the division, it is leap year; but if 1, 2 or 3 remain, it is the first, second or third after leap year. To find the Dominical Letter for any year, according to the Julian method of calculation. RULE. Add to the year its fourth part and 4, and divide that sum by 7: if nothing remain, the Dominical Letter is G; but if there be any remainder, it shews the letter in a retrograde order from G, beginning the reckoning with F; or, if it be subtracted from 7, you will have the index of the letter from A, accounting as follows: To find the Dominical Letter for any year according to the Gregorian computation. RULE. Divide the year and its fourth part, less 1 (for the present century) by 7; subtract the remainder after the division, from 7, and this remainder will be the index of the Dominical Letter, as before; if nothing remain it is G. *Here it is to be obferved, that every leap year has two Dominical Letters; that, found by this rule, is the Dominical Letter from the twenty-fifth day of February to the end of the year; and the next in the order of the alphabet ferves from the first of January to the twenty-fourth of February. In the 2d. Example, D is the Dominical Letter for the year; but E, the next in the order of the alphabet, is the Dominical Letter for January and February. From this interruption of the Dominical Letter every fourth year, it is twenty-eight years before the Dominical Letter returns to the fame order, which, were it not for the leap years, would return to the fame every feven years. This Cycle of twenty-eight years is called the Cycle of the Sun. PROBLEM V. To find the Prime, or Golden Number. RULE. Add 1 to the given year; divide the sum by 19, and the remainder, after the division, will be the Prime; if nothing remain, then 19 will be the Golden Number. EXAMP. For the year 1786. Add 19)1787(94 171 77 1 Golden Number.. The Golden Number, or Lunar Cycle, is a period of 19 years, invented by Meton, an Athenian, and from him called the Metonick Cycle. The use of this cycle is to find the change of the moon; because, after 19 years, the changes of the moon fall on the same days of the month as in the former 19 years; though not at the same time of the day, there being an anticipation of one hour, twenty-seven minutes, forty-one seconds, and thirty-two thirds; which, in 312 years, amount to a whole day. Hence, the Golden Number will not show the true change of the moon for more than three hundred and twelve years, without being varied. But the golden number is not so well adapted to the Gregorian, as the Julian calendar: The epact being more certain in the new style, to find which, the golden number is of use. PROBLEM VI. To find the Julian Epact. RULE. First find the Golden Number, which multiply by 11, and the product, if less than 30, will be the number required; if the product exceed 30, then divide it by 30, and the remainder is the epact. EXAMP. 1. For the year 1786. Golden Number 1 and 1x 11 11 the Julian Epa&. |