Our Calendar Part 8

1924 " " " Fridays.

1928 " " " Wednesdays.

It will be seen from this table that in 1804 February had five Wednesdays; and then again in 1832, 1860 and 1888; then suppressing the intercalation in the year 1900 suppresses the 29th of February; so opposite 1900 in the table is blank, and the 29th of February does not occur again till 1904, and the five Wednesdays do not occur again till 1928--that is, 40 years from 1888, when it last occurred.

Again taking the five Mondays which occurred first in this century, in 1808, and then again in 1836, 1864 and in 1892, you will see, for reasons already given, that it will occur again in 12 years, that is, in 1904; and so on with all the days of the week, when it will be seen what is peculiar concerning the 29th of February.

But attention is particularly called to the five Thursdays, which occur first in this century 1816, and then again in 1844 and 1872, the last date being within 28 years of the close of the century. Suppressing the intercalation suppresses the 29th of February; consequently the five Thursdays do not occur again till 1912, that is 40 years from the preceding date, after which the cycle will be continued for two hundred years.

Hence it may be seen that the dominical or solar cycle of 28 years is so interrupted at the close of these centuries by the suppression of the leap-year, that certain events do not occur again on the same day of the week under 40 years, while others are repeated again on the same day of the week in 12 years; also the number of years in the cycle, that is 28 + 12 = 40.

And again the change of style in 1582, causes all events which occur between 28 and 8 years of that change, to fall again on the same day of the week in 36 years, and all that occur within 8 years of that change to be repeated again on the same day of the week in 8 years, after which the cycle of 28 years is continued for 100 years; also that the number of years in the cycle, that is, 28 + 8 = 36.

CHAPTER VII.

RULES FOR FINDING THE DAY OF THE WEEK OF EVENTS THAT TRANSPIRED PRIOR TO THE CHRISTIAN ERA.

First, it should be understood that the year 4 is the first leap year in our era, reckoning from the year 1 B. C., which must necessarily be leap year; so that the odd numbers 1, 5, 9, 13, etc., are leap years. Hence every year that is divisible by four and one remainder, is leap year; if no remainder, it is the first year after leap-year; if 3, the second; if 2, the third, thus:

45 4 = 11, remainder, 1, 44 4 = 11, no remainder, 43 4 = 10, remainder, 3, 42 4 = 10, remainder, 2, 41 4 = 10, remainder, 1,

and so on, every year being divided by four and 1 remainder is leap-year of 366 days. It should be borne in mind that the same calendar was in use without any correction from the days of Julius Caesar 46 B. C. to Pope Gregory XIII in 1582; consequently the method of finding the dominical letter is, in some respects, similar to the one already given on the 44th page. But in some respects the one is the reverse of the other, for we reckon backward and forward from a fixed point--the era; that is the numbers increase each way from the era. Also the dominical letters occur in the natural order of the letters in reckoning backward, but exactly the reverse in reckoning forward. See table on the 73d page, where the dominical letter is placed opposite each year from 45 B. C. to 45 A. D.

Now we use the same number 3, because C, the third letter is dominical letter for the year 1 B. C., the point from which we reckon. But instead of taking the remainder, after dividing by 7, _from_ 3 or 10, to find the number of the letter, as in Part Second, Chapter IV, (q. v.) we add the remainder _to_ 3; hence we have the following:

RULE.

Divide the number of the given year by 4, neglecting the remainders, and add the quotient to the given number, divide this amount by 7, and add the remainder to 3, and that amount will give the number of the letter, calling A, 1; B, 2; C, 3, etc.; except the first year after leap-year, (which is the year exactly divisible by 4), the number of the letter is one less than is indicated by the rule.

This rule gives the dominical letter for January and February only, in leap-year, while the letter that precedes it, is the letter for the rest of the year. If the amount be greater than seven, we should reckon from A to A or B again.

It has already been stated in Part First, Chapter III, (q. v.), that a change was made by Augustus Caesar about 8 B. C., in the number of days in the month; and, as this change effects the day of the week on which certain events fall, it becomes necessary that they should be presented as they were arranged by Julius Caesar, and as corrected by Augustus. Julius Caesar gave to February 29 days in common years, and in leap-year 30. This arrangement was the very best that could possibly be made, but, as has already been shown, it was interrupted to gratify the vanity of Augustus.

The left hand column in the table on the 72d page represents the number of days in each month from the days of Julius Caesar to Augustus, a period of 37 years. The right hand column represents the number of days in the months as they now are, and have been since the change was made by Augustus, 8 B. C. Consequently the rule for finding the day of the week on which events have fallen for the 37 years prior to the last mentioned date, is not perfectly exact, and needs a little explanation here.

The rule itself is given, and fully explained in Part Second, Chapter V, (q. v.) but cannot be applied to the 37 years without some correction. In all the months marked with a star, events fall one day later in the week than that which is indicated by the rule. This should be borne in mind, and make the event one day later in the week than that which is found by the rule. For example, Julius Caesar was a.s.sa.s.sinated on the 15th of March, 44 B. C. By giving to February 28 days the first day of March would fall on Wednesday, and, of course, the 15th would be Wednesday. But Caesar gave to February 29 days, so that the first day of March fell on Thursday, and the 15th was Thursday.

Hence, every event from March to September will fall one day later in the week than the rule indicates. But the rule is applicable to September, for it will make no difference whether there are 29 days in February or 31 in August, there are the same number of days from February to September. But the 31 days in September will cause all events to fall one day later in the week during the month of October, but they coincide again during the month of November. The order is interrupted again in December by giving 31 days to November. See following table:

_As Arranged by Julius_ _As Corrected by Augustus,_ _Caesar._ _8 B. C._ January, 31 January, 31 February, 29 February, 28 March, 31* March, 31 April, 30* April, 30 May, 31* May, 31 June, 30* June, 30 July, 31* July, 31 August, 30* August, 31 September, 31 September, 30 October, 30* October, 31 November, 31 November, 30 December, 30* December, 31

---------+-----+---------+-----+---------+-----+---------+----- Dominical Year. Dominical Year. Dominical Year. Dominical Year.

Letter. Letter. Letter. Letter. ---------+-----+---------+-----+---------+-----+---------+----- B. C. B. C. A. D. A. D.

cb 45 b 22 b 1 c 23 a 44 ag 21 a 2 ba 24 g 43 f 20 g 3 g 25 f 42 e 19 fe 4 f 26 ed 41 d 18 d 5 e 27 c 40 cb 17 c 6 dc 28 b 39 a 16 b 7 b 29 a 38 g 15 ag 8 a 30 gf 37 f 14 f 9 g 31 e 36 ed 13 e 10 fe 32 d 35 c 12 d 11 d 33 c 34 b 11 cb 12 c 34 ba 33 a 10 a 13 b 35 g 32 gf 9 g 14 ag 36 f 31 e 8 f 15 f 37 e 30 d 7 ed 16 e 38 dc 29 c 6 c 17 d 39 b 28 ba 5 b 18 cb 40 a 27 g 4 a 19 a 41 g 26 f 3 gf 20 g 42 fe 25 e 2 e 21 f 43 d 24 dc 1 d 22 ed 44 c 23 c 45 ---------+-----+---------+-----+---------+-----+---------+-----

PART THIRD.

CYCLES--JULIAN PERIOD--EASTER.

HEBREW CALENDAR.

CHAPTER I.

THE SOLAR CYCLE.

Cycle, (Latin _Cyclus_, ring or circle). The revolution of a certain period of time which finishes and re-commences perpetually. Cycles were invented for the purpose of chronology, and for marking the intervals in which two or more periods of unequal length are each completed a certain number of times, so that both begin exactly in the same circ.u.mstance as at first. Cycles used in chronology are three: The solar cycle, the lunar cycle, and the cycle of indiction.

The solar cycle is a period of time after which the same days of the year recur on the same days of the week. If every year contained 365 days, then every year would commence one day later in the week than the year preceding, and the cycle would be completed in seven years. For if the first day of January, in any given year, fall on Sunday, then the following year on Monday, the third on Tuesday, and so on to Sunday again in seven years.

But this order is interrupted in the Julian calendar every four years by giving to February 29 days, and consequently the year 366. Now the number of years in the intercalary period being four and the days of the week being seven, their product is 4 7 = 28; twenty-eight years then is a period after which the first day of the year and the first day of every month recur again in the same order on the same day of the week. This period is called the solar cycle or the cycle of the sun, the origin of which is unknown; but is supposed to have been invented about the time of the Council of Nice, in the year of our Lord 325; but the first year of the cycle is placed by chronologists nine years before the commencement of the Christian era.

Hence the year of the cycle corresponding to any given year in the Julian calendar is found by the following rule: Add nine to the date and divide the sum by twenty-eight; the quotient is the number of cycles elapsed, and the remainder is the year of the cycle. Should there be no remainder, the proposed year is the twenty-eighth, or last of the cycle. Thus, for the year 1892, we have (1892 + 9) 28 = 67, remainder 25. Therefore, 67 is the number of cycles, and 25 the number in the cycle.

CHAPTER II.

THE LUNAR CYCLE.

The Lunar cycle, or the cycle of the moon, is a period of nineteen years, after which the new and full moons fall on the same days of the year as they did nineteen years before. This cycle was invented by Meton, a celebrated astronomer of Athens, and may be regarded as the masterpiece of ancient astronomy. In nineteen solar years there are 235 lunations, a number which, on being divided by nineteen, gives twelve lunations, with seven of a remainder, to be distributed among the years of the period.

The period of Meton, therefore, consisted of twelve years containing twelve months each, and seven years containing thirteen mouths each, and these 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 30 days, and 110 deficient months of 29 days each. The number of days in the period was, therefore, 6940; for (125 30) + (110 29) = 6940.

In order to distribute the deficient months through the period in the most equable manner, the whole period may be regarded as consisting of 235 full months of thirty days, or 7050 days, from which 110 days are to be deducted; for (235 30) = 7050; 7050 - 110 = 6940, as before. This gives one day to be suppressed in sixty-four, so that if we suppose the months to contain each thirty days, and then omit every sixty-fourth day in reckoning from the beginning of the period, those months in which the omission takes place will, of course, be the deficient months.

The number of days in the period being known, it is easy to ascertain its accuracy both in respect of the solar and lunar motions. The exact length of nineteen solar years is (365d, 5h, 48m, 49.62s.) 19 = 6939d, 14h, 27m, 42.78s.; hence, the period, which is exactly 6940 days, exceeds nineteen annual revolutions of the earth by a little more than nine and a half hours. On the other hand, the exact time of the synodic revolution of the moon is 29d, 12h, 44m, 2.87s.; 235 lunations, therefore, contain 235 (29d, 12h, 44m, 2.87s.) = (6939d, 16h, 31m, 14.45s.), so that the period exceeds 235 lunations by nearly seven and a half hours.

At the end of four cycles, or seventy-six years, the acc.u.mulation of the seven and a half hours of difference between the cycle and 235 lunations amounts to thirty hours, or one whole day and six hours. Calippus, therefore, in order to make a correction of the Metonic cycle, proposed to quadruple 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 to the moon, consequently, amounted to only six hours, or to one day in 304 years.

This period exceeds seventy-six true solar years by 14h, 9m, 8.88s., but coincides exactly with seventy-six Julian years; and in the time of Calippus the length of the solar year was almost universally supposed to be exactly 365-1/4 days.

CHAPTER III.

THE LUNAR CYCLE AND GOLDEN NUMBER.