Popular Science Monthly/Volume 18/April 1881/History of Chronology
|←Physical Education IV||Popular Science Monthly Volume 18 April 1881 (1881)
History of Chronology
By E. S. Burns
|Some Notes on a Doctor's Liability→|
By Professor E. S. BURNS.
CHRONOLOGY is the science of the measurement of time, of ascertaining and fixing dates, which constitute the landmarks by which the mind is guided in its backward course through the long vista of years, and enabled to locate and fix the events of history, the knowledge of which would otherwise be a confused and wellnigh useless attainment. The advanced state of astronomical science and the experience of those who have gone before us have enabled us to reduce all that pertains to this subject to so complete a system that we lose sight of its magnitude and importance; we forget the slow progress and toilsome research which the great minds of past centuries had to undergo to reach the present state of correctness. To appreciate even faintly this magnitude, we must transport ourselves backward a few thousand years, and forget, if we can, the improvements of modern astronomy, the developments of mathematics, and, above all, the universality and ubiquity of modern almanacs.
The first and most obvious division of time is the day—the time required for a revolution of the earth upon its axis—which could not have been a very difficult matter to ascertain with sufficient correct- ness. But to mark and fix the time of the sun's apparent revolution through the heavens among the stars was a matter of so great diffi- culty that it was not exactly ascertained even at the time of the refor- mation of the calendar in 1582; yet so uniform is the motion of the earth in its orbit that the results of modern experiments render it next to absolutely certain that the time of orbital revolution has never varied even the fraction of a second. In the infancy of astronomy, many ingenious expedients were adopted to ascertain this and other matters connected with the times and motions of the planets and other heavenly bodies, one of which may be mentioned even at the risk of tediousness. To ascertain the exact time of the revolution of the con- cave of the heavens, two vessels were placed over each other, the upper filled with water, the lower empty. At the moment of the appearing of a certain star above the horizon, the water was permitted to flow from the upper into the lower vessel, and the flow was continued until the same star appeared the next night, when the flow was stopped. The whole concave of the heavens had then made one revolution. The water which had flowed out during this time was then divided into twelve equal parts, and smaller vessels were made each to hold just one of those parts, and on the following evening they repeated the operation, filling successively six of those vessels, and noting carefully what stars rose above the horizon during the time required to fill each of them. Each group of stars which rose during the time of filling one small ves- sel was called a statioti or house of the sun. They then postponed oper- ations upon the other half of the heavens for six months, when they repeated it, and thus divided the path of the sun through the whole heavens into twelve divisions, to most of which they gave the names of certain animals: hence the term zodiac, the propriety of which could have been seen only by the fertile fancies of the childhood of the race. The whole ancient method of dividing and naming the constellations is to us utterly absurd, and is really a hindrance to a knowledge of the stars. Fanciful forms of snakes and dogs and lions and bulls and w^agons and scorpions convey to us no idea but one of confusion and perplexity, and they are tolerated for the same reasons that we tolerate our bungling orthography: we are loath to break away from the associations of antiquity; we are loath to sever the giabt strides of Science, in its strength and manhood, from the feeble totterings of its infancy.
The time required by the sun to pass through one of these groups or signs is nearly equal to a lunar month; the time required to pass through three of them was called a season, as we have it now. All this was done by the Chaldeans or Egyptians, centuries before Greece or Rome had inhabitants or a name.
The Greeks divided the year into twelve lunar months, but, as this lunar year differed from the true year by about eleven days, they corrected the error, after many other devices, by intercalating three months every eight years, making every eighth year consist of fifteen months a method used by them for many years, perhaps centuries. It is said, however, that the length of the year was known, as early as the time of Solon, to be three hundred and sixty-five and one quarter days. Prior to the time of Numa, the Roman year consisted of ten months. He divided it into twelve lunar months, and to correct the error of eleven days a month was intercalated every second year. The management of this matter was intrusted to the priests, who added days whenever they deemed them necessary. But, owing to their ignorance of astronomy, this method proved irregular and erroneous, and the winter months were gradually carried back into autumn, the autumn months into summer, etc.
These errors had become so troublesome in the time of Julius Csesar that he undertook, with the aid of an eminent astronomer (Sosigenes), to correct the calendar, which was done as follows: The Roman civil year had lost about ninety days. These were added to the year of three hundred and fifty-five days, making that year consist of four hundred and forty-five days, which is known in history as the " year of confusion." The year henceforward was made to consist of three hundred and sixty-five days, by adding ten days distributively to as many months. The odd quarter of a day was not noted until every fourth year, when the sum of these fourths made one day, and that year consisted of three hundred and sixty-six days. This odd day M^as inserted after the sixth day before the kalends of March, i. e., after the 24th of February, and was not counted as an addition to the year, but as a sort of appendix. Hence the sixth of the kalends of March was called bissextus, or double sixth, which root is still retained in our word bissextile, though the day is now added at the end of February. This arrangement would have been entirely correct had the year con- sisted of exactly three hundred and sixty-five and one quarter days. It was, however, in course of time, discovered to be erroneous, and an- other correction was made, which we will consider by and by. This new system went into effect on January 1, 46 b. c.
The subdivisions of the Roman month were apparently arbitrary. The days were not numbered as we have them, but the first day of every month was called the calends, the fifth the nones, and the thir- teenth the ides, except in the months of March, May, July, and Octo- ber, when the nones fell on the seventh and the ides on the fifteenth. From these points the days were counted backward i. e., the last of February was called Prid., Kal., Mar., etc.
Names of Months. The division of days into weeks was invented at a very early day by the Chaldeans, and was afterward adopted by almost all civilized nations, and by the Romans about the third century A. c. The principle upon which the days were named is odd enough to deserve especial notice. The order of the planets, according to the Ptolemaic system, was: 1. Saturn; 2. Jupiter; 3. Mars; 4. Sun; 5. Venus; 6, Mercury; 7. Moon. The Clialdeans called the twenty- four hours of the day by the names of these planets in their order, and named each day from the first hour of the day. Thus, first hour of first day was Saturn; last hour (or twenty-fourth) was Mars; first hour of next day was Sun, hence called Sunday; first hour of next day Moon, hence called Monday, etc. Our Saxon ancestors named the days from their corresponding gods. Thus, what the Romans called Mars- day, the Saxons called Tuisco-day (whence Tuesday), Tuisco being their god of war as Mars was among the Romans, and so of the rest.
The early Romans began the year with March, but in the time of Caesar it began with January. The early Christian Church began it on March 25th, and this was the beginning of the civil and ecclesiastical year in England and her American colonies until 1752, when it was changed by act of Parliament to January 1st.
Cycles. To facilitate computation of time, to fix the recurrence of moons and days, and to establish epochs as standpoints of chronology, recourse was had to cycles, which we will now examine. The word cycle is derived from a Greek word which signifies a circle here it signifies a circle of time. The first and most important among them was the Cycle of the Moon, the object of which was to accommodate t^e computation of time by the moon to that of the sun. It was in- i^ented about 430 b. c, by an Athenian named Meton, whence it was called also the Metonic Cycle, and was used to fix the times of the Grecian festivals, but fell into disuse with these festivals and was afterward restored by the Council of Nice, a. d. 325, being best adapted of all to fixing the time of Easter.
This cycle, at the time of its invention, was deemed entirely correct, and was so much superior to any other that had been attempted that each year was written in letters of gold in the public marts of Greece, from which cause it has ever since been known as the " golden number." It was constructed as follows: It had been discovered that the lunar year was eleven days shorter than the solar year; so that, if a new moon occurred upon any given day of any solar year, on the same day of the next solar year the moon would be eleven days old, on the same day of the second year twenty-two days old, etc. Examination showed that the new moon would again occur upon the same day of the solar year in the course of nineteen years. Hence the lunar cycle consists of nineteen years. The other ancient cycles are unimportant for our present purpose; the other cycles that we shall consider are the in- ventions of modern chronolosrers.
Solar Cycle. Chronologers have affixed to the seven days of the week the first seven letters of the alphabet, as follows: To January 1, A; January 2, B, etc., and whichever letter the first Sunday of the year happens to fall upon is called the dominical or Sunday letter for that year. The object of this cycle is to find (without reference to the almanac) what day of the week corresponds to any day of any month of any year, and it is constructed in this manner.
As every common year consists of fifty-two weeks and one day, supposing the 1st of January of any year to fall upon Sunday, A will be the Sunday letter for that year. The last day of that year will also be Sunday, and Monday will be the 1st of January of next year; and, as A is always affixed to the first day of the year, G will become the Sunday letter for that year. The next year will begin with Tues- day, which will make its Sunday letter F, etc.; hence, if there were no leap-year, the Sunday letter of each succeeding year would be removed one letter further backward, and in seven years the cycle would be complete, and the Sunday letter of the eighth year would again be A. But, as every leap-year has fifty-two weeks and two days, the letter C, which always belongs to the 28th of February, is also affixed to the 29th, which puts the Sunday letter for the remainder of the year one letter further back. Leap-year has therefore two Sunday letters instead of one, as in common years. This change takes place every four years; the other, as we have seen, would take place in seven years. Hence a complete cycle of the Sunday letter consists of the miiltiple of seven and four = twenty-eight years; i. e., in any given century, the Sunday letters will again follow each other in exactly the same order every twenty-eight years.
Indiction Cycle. This is a cycle of fifteen years established by the Emperor Constantine, at the termination of which a tax was lev- ied to pay the soldiers whose term of enlistment was fifteen years. It was afterward ordered by the Council of Nice that this cycle, beginning A. D. 312, should be substituted as the epoch from which all dates should be reckoned instead of that of the Olympiads, which, until that time, seems still to have been used in the Eastern Emj)ire of the Romans.
The epoch from which we now compute years i. e., the birth of Christ was not used until about the year 500. The universal adop- tion of this by all Christendom has obviated the necessity of many of the cycles and epochs used prior to that time, and it is impossible for ns now to estimate the difficulties the earlier chronologists had to encounter in their attempts to locate events and to regulate them by some fixed standard (illustrated by different modern weights and meas- ures). The Greeks reckoned by Olympiads cycles of four years beginning 776 b. c. The Romans' great epoch was the founding of their city, 752 b. c. They also used the lustrum, a cycle of four years; and events are very frequently recorded to have occurred in the con- sulship of such or such a one. The later Jews used the era of the Seleucidse, 312 b. c, which era the Nestorians, it is said, still use. Prior to the adoption of our own era, the Christians used the era of Diocletian, 284 a. d.
To harmonize the conflicting and troublesome eras, one Scaliger, an historian of the early ages of the Church, invented a new cycle to which chronologers might refer all dates. It consisted of the mul- tiple of the years of the three cycles of the sun, moon, and indiction, 28x19x15 = 7,890, and taking these cycles, as settled by the early Church councils, and tracing them backward, he found they would begin together in the year 710 before the creation of the world, ac- cording to our received account. This cycle would have been of great value and importance, had it not been superseded by the adoption of the Christian epoch, which, as already said, has made the use of all former epochs and eras unnecessary. The cycle just described is known by the name of the " Julian period."
Several of the ancient cycles were, however, used by the early Church in fixing what are called the ^^ movable feasts"; these being regulated not by the solar year, as Christmas or the 4th of July is, but by the lunar year. But, as most of these feasts depend upon or are regulated by Easter, we need consider this one only. In the early days the churches of Asia kept their Easter upon the day on which the Jews celebrated their passover, i. e., on the fourteenth day of their fii-st month, which began with the new moon next after the vernal equinox. The Western churches celebrated on the Sunday following the Jewish festival, both to celebrate the day and to distinguish between Jews and Christians. This difference having finally caused great dissensions in the Church, Constantine had a canon passed at the Council of Nice, that Easter should everywhere be observed upon the same day; and, to prevent disputes thereafter, four j)aschal canons were also passed, to the effect that " Easter shall always be observed on the first Sunday after the full moon which happens on or next after the 21st of March, which was then the time of the vernal equinox; and, if this full moon happen on Sunday, the Sunday following shall be Easter Sunday."
Then was called into requisition the lunar cycle, and tables were made showing the day of every month in every year, of the cycle on which a new moon would occur, and this table would have been cor- rect for ever had the Julian year been correct and had the moon's cycle been nineteen years to the hour. The former, we have already seen, was not quite correct; and the new moon, although it occurs on the same day of the year every nineteenth year, does not occur at the same hour, but about one and a half hour earlier, which difference in a long course of years makes the tables all wrong and useless. In 1582, when the calendar was corrected, the computed equinoxes had been brought forward ten days, so that the full moon, on or after the 21st of March, was not always the first moon after the true vernal equinox i. e., was not the moon which the Church canon prescribed. The reformation of the calendar, by dropping ten days, brought back the equinox to March 21st, as it was at the time of the Nicene Council.
Immediately after this council the Bishop of Alexandria, in Egypt, was appointed to give notice to the Pope, and other dignitaries in va- rious parts of the Christian world, of the time when Easter should be celebrated each year, until a perfectly correct cycle should be estab- lished. The most prominent cycle framed for this purpose was one by a mathematician named Victorinus. It consisted of the product of the lunar and solar cycle i. e., 19 X 28 = 532. If this calculation had been without defect, any given day would have been the same day of the year, month, moon, and week, that it was five hundred and thirty- two years before or would be five hundred and thirty-two years after.
The Council of Orleans, a. d. 541, decreed that the feast of Easter should be celebrated every year, according to the table of Victorinus. But the tables derived from these data answer only for a limited time on account of the above-mentioned errors in the year and in the lunar cycle. Accordingly, the books which contain tables for finding Easter are good only until the y6ar 1900, when new ones must be made for another period.
As the cycles were fixed by the Latin Chnrch, the era of Christ began in the tenth year of the solar cycle and in the second year of the lunar cycle. Therefore, to find what year of the solar cycle any given year of our Lord is, we add 9 to the number of the year and di- vide by 28; the remainder, if any, will indicate the number of the year of the cycle. The year of the lunar cycle, i. e., the golden number, is found in a similar manner, by adding 1 to the given year and dividing by 19; the remainder will indicate the year of the lunar cycle.
After the Julian calendar had been used several centuries, the im- proved state of astronomy disclosed the fact that computed time did not keep pace with actual time, because the year did not consist of three hundred and sixty-five days ^nd six hours but was about eleven minutes ten seconds less. Hence, by inserting an extra day for leap- year, we gain upon true time forty-four minutes, forty seconds, which makes an error of a day in about one hundred and thirty-one years; and hence, in 1582, when the correction of the calendar was undertaken by Pope Gregory, the error had amounted to ten days; i. e., instead of counting just 1,582 years it ought to have been 1,582 years and ten days. A correction was accordingly made by taking a leap of ten days and calling October 5th of that year October 15th. This change, as elsewhere stated, brought the vernal equinox to the 21st of March, where it was at the time of the Nicene Council. To prevent the recurrence of the same error in future, it was ordered that every fourth year should be a leap-year as before, but centurial years, though multiples of 4, should not be leap-years unless they were multiples of 400. The loss of \\\ minutes yearly in time, as computed by the Julian method, amounts in 100 years to 18*6 hours. Calling this one hundredth year a common year gives a gain of one day, or 24 hours, which puts com- puted time ahead of actual time, 24 18-6 = 5-4 hours, which, in 400 years, equals 21-6 hours, gain. Calling the four hundredth a leap-year brings back computed time 24 2r6 = 2'4 hours behind real time. To lose a whole day at this rate will require 10X400 = 4,000 years.
This arrangement seems simple enough to us now, but it required a convention of astronomers, summoned to Rome for this purpose, ten years to effect the adjustment. This is called the change from Old to New Style. It also changed the dominical letter, which occurred in this wise:
The dominical letter of 1582 was G, and, A being always the let- ter for the 1st of October, that day must have been Monday, and in regular order the 17th would have been Tuesday, whose letter was C. The change was made by calling the 5th day, which was Friday, the 15th, whence Saturday became the 16th and Sunday the 17th, whose letter we have just seen was C, whence C instead of G became the dominical letter for that year, N. S., and by this all subsequent Sun- day letters were regulated. C is the fourth letter in backward order from G, hence the dominical letter of any year, N. S., was four letters backward from the letter belonging to that year O. S., and remained so until 1700, after which IST, S. is but the third letter from O. S. because, according to N. S., 1700 is not a leap-year and has but one dominical letter. In O. S. it would be leap-year, and would have two letters. For the same reason, after 1800 N. S. it is only the second letter back- ward from O. S., after 1900 only the first backward, and so continues until 2100 the year 2000 making no difference, as it is a leap-year in both styles. After 2100, Sunday letter N. S. is the same as that of O. S., and gains one letter each succeeding century, except those which are multiples of four hundred, so that, in every nine hundred years after 2100, the N. S. and O. S. Sunday letter correspond. This furnishes a perpetual almanac.
This ai-rangement of the calendar, whose complete cycle is four hundred years, is called the Gregorian, from the name of Pope Greg- ory, through whose instrumentality it was made. It was adoj^ted shortly afterward by all the Catholic countries of Europe; but Protes- tant countries refused to adopt it, notwithstanding its obvious superi- ority and correctness, because it was originated by Catholics. En- lightened public sentiment compelled its adoption in course of time, and an act was accordingly passed by the British Parliament in 1752, almost two centuries later, ordering that the 3d of September should be called the 14th, the error having by that time amounted to eleven days. The change was, however, not popular among the masses, be- cause it changed the time of long-established festivals, and members of Parliament were insulted in the streets by the rabble calling after them: "What have you done with the days?" "Give us back the days you stole!"
We have already seen that tables were constructed showing on what days each new moon would fall in the whole lunar cycle, but, though they would in nineteen years fall upon the same day of the month, they fell about an hour and a half earlier in the day, and this in sixteen cycles, or about three hundred and twelve years, would make a difference of one day. As these tables were published by ecclesiasti- cal and secular authority, and could not be changed without such au- thority, another method was resorted to to find the times of the moon without the use of these tables. This method was called the epact, which we will now proceed to consider.
The lunar year, as we have already seen, differs from the solar year by about eleven days, i. e., if a new moon occur January 1st of any year, on January 1st of the next year the moon will be eleven days old, on the same day of the next year twenty-two days old, the next thirty- three days old, which equals a whole lunation plus three days. This cycle corresponds with the lunar cycle, and is constructed as follows:
3 4 5 6 7 8 9 10
3 14 25
6 17 28
March 30 j
April 15 j
Epact. Paschal Limits.
April 1 2
From this table the astronomical moons not only for Easter but for the whole year can be found without variation of more than a day for about three hundred and twelve years, at the end of which time the new moon will fall one day earlier, when a new set of epacts must be made, the first of which will be 1 instead of 0, and the succeeding ones will be changed correspondingly. To find the age of the moon for any day of the year, we add to the epact the date of the month, and one for every month from March inclusive, the epact for a year being eleven days, or a day a month nearly. This sum, casting out thirty if required, will give the age of the moon at the given day: e. g., suppose it be required to find the moon's age on Chi'istmas-day of the year 1868. We find, by the method already explained, that 1868 was the seventh year of the lunar cycle, whose epact in the table we found to be 6, to which adding 25 and 10 gives 41; from this deduct one lunation (29 days) = 12 days for the moon's age on that day. The epacts are calculated to show the moon's age on March 1st in any year of the cycle.
The rule for finding the Sunday letter of any year, as given in the "Book of Common Prayer," is constructed upon this principle: The dominical letter of the year of Christ, according to N. S., would have been B A. Then for any year from 1800 to 1899 the number of letters used equals the number of years + 1⁄4 the number of years (that number being leap-years) — 14 for centurial years which are not leap-years. This number divided by 7 gives the number of times all the letters have been used, and if the remainder is the dominical letter is the same as that of the year 0, i, e., A (from March). Any remainders, 1, 2, 3, etc., will give corresponding letters, G, F, E, etc., as in the years 1, 2, 3, etc., a. c. Upon the same principle the dominical letter for the years of any other century can be found. But, as the number to be deducted for centurial years, not leap-years (equal 14), is an exact multiple of 7, the remainder will be the same whether it is deducted or not, and hence no account need be made of it, for it is by the remainder and not by the quotient that the Sunday letter is fixed. The above-mentioned rule will, therefore, not answer for any century but this one until the twenty-eighth century, when it can again be used, because the centurial number to be deducted will then be 21, which, being also a multiple of 7, may be disregarded.
In addition to these tables, another was constructed showing at a glance what letter corresponds to any day of the year; but, as this table is cumbersome and unwieldy, a device has been substituted which is very simple and answers all the purposes of a table. The letter for the first day of every month is always the same. These letters being known, together with the Sunday letter for any year, we can readily find what the first day of any month is, and consequently what day of the week any other day of the month is. The letters for the first of each are as follows, beginning with January: A, D, D, G, B, E, G, C, F, A, D, F, and, to assist the memory in retaining them, they have been woven into the following couplet: