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Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4

Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4

Author: Various
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Chapter 1 4 , 7

Word Count: 3349    |    Released on: 06/12/2017

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n of one day in four years, and is considerably too gr

n twenty-nine years, and errs in defect, as it s

ve intercalations at the end of four years respectively, and the eighth at the end

ds of thirty-three years with one of twenty-nine, and would consequently be very convenient in applic

e true within much narrower limits. It has been stated by Scaliger, Weidler, Montucla, and others, that the modern Persians actually follow this method, and intercalate eight days in thirty-three [v.04 p.0991]years. The statement has, however, been contested on good authority; and it seems proved (see Delambre, Astronomie Moderne, tom. i. p.81) that the Persian intercalation combines the two peri

of the year was fixed at midnight preceding the day in which the true autumnal equinox falls. But supposing the instant of the sun's entering into the sign Libra to be very near midnight, the small errors of the solar tables might render it doubtful to which day the equinox really belonged; and it would be in vain to have recourse to observation to obviate the difficulty. It is therefore infinitely more commodious to determine the commencement of the year by a fixed rule of intercalation; and of the various methods which might be

asses through the whole circle of the seasons in about thirty-four lunar years. It is therefore so obviously ill-adapted to the computation of time, that, excepting the modern Jews and Mahommedans, almos

enedos, who flourished shortly after the time of Thales, to omit the biennary intercalation every eighth year. In fact, the 7? days by which two lunar years exceeded two solar years, amounted to thirty days, or a full month, in eight years. By inserting, therefore, three additional months instead of four in every period of eight years, the coincidence between the solar and lunar year would have been exactly restored if the latter had contained only 354 days, inasmuch as the period contains 354 × 8 + 3 × 30 = 2922 days, corresponding with eight solar years of 365? days each. But the true time of 99 lunations is 2923.528 days, which exceeds the above period by 1.528 days, or thirty-six hours and a few minutes. At the end of two periods, or six

sent date, 13 × 360° + 477644″.409; that of the sun being 360° + 27″.685. Thus the corresponding relative mean geocentric motion of the moon from the sun is 12 × 360° + 477616″.724; and

last formed the third, fifth, eighth, eleventh, thirteenth, sixteenth, and nineteenth years of the cycle. As it had now been discovered that the exact length of the lunation is a little more than twenty-nine and a half days, it became necessary to abandon the alternate succession of full and deficient months; and, in order to preserve a more accurate correspondence between the civil month and the lunation, Meton divided the cycle into 125 full months of thirty days, and 110 deficient months of twenty-nine days each. The number of days in

6939 days 14 hours 26.592 minutes; hence the period, which is exactly 6940 days, exceeds nineteen revolutions of the sun by nine and a half hours nearly. On the other hand, the exact time of a synodic revolut

uple the period of Meton, and deduct one day at the end of that time by changing one of the full months into a deficient month. The period of Calippus, therefore, consisted of three Metonic cycles of 6940 days each, and a period of 6939 days; and its error in respect of the moon, consequently, amounted only to six hours, or to one day

ample of the Jews, and adhered to the 14th of the moon; but these, as usually happened to the minority, were accounted heretics, and received the appellation of Quartodecimans. In order to terminate dissensions, which produced both scandal and schism in the church, the council of Nicaea, which was held in the year 325, ordained that the celebration of Easter should thenceforth always take place on the Sunday which immediately follows the full moon that happens upon, or next after, the day of the vernal equinox. Should the 14th of the moon, which is regarded as the day of full moon, happen on a Sunday, the celebration Of Easter was deferred to the Sunday following, in order to avoid concurrence with the Jews and the above-mentioned heretics. The observance of this rule renders it necessary t

day, the year following will begin with Tuesday. For the sake of greater generality, the days of the week are denoted by the first seven letters of the alphabet, A, B, C, D, E, F, G, which are placed in the calendar beside the days of the year, so that A stands opposite the first day of January, B opposite the second, and so on to G, which stands opposite the seventh; after which A returns to the eighth, and so on through the 365 days of the year. Now if one of the days of

or last of the cycle. This rule is conveniently expressed by the formula ((x + 9) / 28)r, in which x denotes the date, and the symbol r denotes that the remainder, which arises from the division of x + 9 by 28, is the number required. Thus, for 1840, we have (1840 + 9) / 28 = 66-1/28; therefore ((1840 + 9) / 28)r = 1, and the year 1840 is the first of the solar cycle. In order to make use of the solar cycle in finding the dominical letter, it is necessary to know that the first year of the Christian era began with Saturday. The dominical letter of that year, which was the tenth of the cycle, was consequently B. The following year, or the 11th of the cycle, the letter was A; then G. The fourth year was bissextile, and the dominical letters were F, E; the following year D, and so on. In this manner it is easy to find the dominical letter belonging to each of the twenty-eight years of the cycle. But at the end of a century the order is interrupted in the Gregorian calendar by the secular suppression of the leap year; hence the cycle can only be employed during a century. In the reformed calendar the intercalary period is four hundred years, which number being multiplied by seven, gives two thousand eight hundred years as the interval in which the coincidence is restored between the days of the year and the days of

mencement of the era to the Reformation. For this purpose divide the date by 28, and the letter opposite the remainder, in the first column of figures, is the dominical letter of the year. F

ar year of 354 days; and in order to make up nineteen solar years, six embolismic or intercalary months, of thirty days each, are introduced in the course of the cycle, and one of twenty-nine days is added at the [v.04 p.0993]end. This gives 19 × 354 + 6 × 30 + 29 = 6935 days, to be distributed among 235 lunar months. But every leap year one day must be added to the lunar month in which the 2

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1 Chapter 1 4 , 72 Chapter 2 No.23 Chapter 3 No.34 Chapter 4 No.45 Chapter 5 No.56 Chapter 6 E7 Chapter 7 E No.78 Chapter 8 E No.89 Chapter 9 D10 Chapter 10 11 39 67 9511 Chapter 11 E No.1112 Chapter 12 D No.1213 Chapter 13 E No.1314 Chapter 14 E No.1415 Chapter 15 22 50 7816 Chapter 16 E No.1617 Chapter 17 D No.1718 Chapter 18 28 56 8419 Chapter 19 D No.1920 Chapter 20 No.2021 Chapter 21 D No.2122 Chapter 22 D No.2223 Chapter 23 D No.2324 Chapter 24 D No.2425 Chapter 25 D No.2526 Chapter 26 27 Chapter 27 E No.2728 Chapter 28 E No.2829 Chapter 29 E No.2930 Chapter 30 E No.3031 Chapter 31 E No.3132 Chapter 32 133 Chapter 33 25 2634 Chapter 34 2735 Chapter 35 25′2536 Chapter 36 737 Chapter 37 2438 Chapter 38 2239 Chapter 39 1840 Chapter 40 1941 Chapter 41 18 No.4142 Chapter 42 1443 Chapter 43 1744 Chapter 44 1545 Chapter 45 1146 Chapter 46 1247 Chapter 47 11 No.4748 Chapter 48 2149 Chapter 49 1050 Chapter 50 851 Chapter 51 452 Chapter 52 553 Chapter 53 4 No.5354 Chapter 54 2855 Chapter 55 356 Chapter 56 1 No.5657 Chapter 57 27 No.5758 Chapter 58 No.5859 Chapter 59 E No.5960 Chapter 60 E No.6061 Chapter 61 E No.6162 Chapter 62 E No.6263 Chapter 63 E No.6364 Chapter 64 1 No.6465 Chapter 65 2366 Chapter 66 19 No.6667 Chapter 67 21 No.6768 Chapter 68 18 No.6869 Chapter 69 670 Chapter 70 14 No.7071 Chapter 71 1672 Chapter 72 12 No.7273 Chapter 73 14 No.7374 Chapter 74 11 No.7475 Chapter 75 1376 Chapter 76 7 No.7677 Chapter 77 978 Chapter 78 5 No.7879 Chapter 79 7 No.7980 Chapter 80 4 No.8081 Chapter 81 2082 Chapter 82 No.8283 Chapter 83 284 Chapter 84 28 No.8485 Chapter 85 No.8586 Chapter 86 27 No.8687 Chapter 87 27 No.8788 Chapter 88 23 No.8889 Chapter 89 25 2490 Chapter 90 19′2091 Chapter 91 D No.91