The Julian and the Gregorian Calendars | |
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by Peter Meyer |
(i) The Julian Calendar
For many European institutions, we can thank the Romans (for good or for bad, though they too had their predecessors in the Greeks, Egyptians and Babylonians). So with the solar calendar currently in widespread use.Originally the Romans numbered years ab urbe condita, that is, "from the founding of the city" (of Rome, where much of the character of the modern world had its beginnings). Had this old calendar remained in use, 1996-01-14 would have been New Years Day in the year 2749 a.u.c.
Following his conquest of Egypt in 48 B.C.E. Julius Caesar consulted the Alexandrian astronomer Sosigenes about calendar reform (since the a.u.c. calendar then used by the Romans was completely inadequate to the needs of the emerging empire, which Caesar was poised to command, briefly as it turned out). The calendar which Julius Caesar adopted in the year 709 a.u.c. (what we now call 46 B.C.E.) was identical to the Alexandrian Aristarchus' calendar of 239 B.C.E., and consisted of a solar year of twelve months and of 365 days with an extra day every fourth year. It is unclear as to where or how Aristarchus arrived at this calendar, but one may speculate that Babylonian data or theory was involved.
As we can read in the excellent article, "The Western Calendar and Calendar Reforms" in the Encyclopedia Brittanica, Sosigenes decided that the year known in modern times as 46 B.C.E. should have two intercalations. The first was the customary intercalation of 23 days following February 23, the second, "to bring the calendar in step with the equinoxes, was achieved by inserting two additional months between the end of November and the beginning of December. This insertion amounted to an addition of 67 days, making a year of no less than 445 days and causing the beginning of March, 45 B.C.E. in the Roman republican calendar, to fall on what is still called January 1 of the Julian Calendar."
According to a contributor to the CALNDR-L mailing list, Julius Caesar wanted to start the year on the Spring Equinox or the Winter Solstice, but the Senate, which traditionally took office on January 1st, the start of the Roman civil calendar year, wanted to keep January 1st as the start of the year, and Caesar yielded in a political compromise.
The Roman date-keepers at first erroneously added a leap day every third year, rather than every fourth, as we do today. This practice was continued to 9 B.C.E., when the Emperor Augustus (Caesar's nephew Octavian) decreed that leap years should not be observed for awhile (they were resumed in 8 A.D.).
Another source of uncertainty regarding exact dating of days at this time derives from changes made by Augustus to the lengths of the months. According to some accounts, originally the month of February had 29 days and in leap years 30 days (unlike 28 and 29 now). It lost a day because at some point the fifth and six months of the old Roman calendar were renamed as Julius and Augustus respectively, in honor of their eponyms, and the number of days in August, previously 30, now became 31 (the same as the number of days in July), so that Augustus Caesar would not be regarded as inferior to Julius Caesar. The extra day needed for August was taken from the end of February. However there is still no certainty regarding these matters, so all dates prior to A.D. 8, when the Julian Calendar finally stabilized, are uncertain.
Subsequently the Julian Calendar became widespread as a result of its use throughout the Roman Empire and later by the Christian Church, which inherited many of the institutions of the Roman world.
The system of numbering years A.D. (for "Anno Domini", "in the year of Our Lord") was instituted in the year 525 by the Roman abbot Dionysus Exiguus (who was off by about about 6 years in his indentification of the year of the birth of Christ). It endured for one and a half millennia. Because of its specifically Christian meaning this designation is now often replaced by the more neutral C.E. (for "Common Era"), and B.C. ("Before Christ") is now often written B.C.E. (for "Before Common Era").
(ii) The Gregorian Reform
The average length of a year in the Julian Calendar is 365.25 days (one additional day being added every four years). The length of the year in the Julian Calendar exceeds the length of the mean solar year (365.24219 mean solar days to five decimal places) by 11.2 minutes. This error accumulates so that after 128 years the calendar is out of sync with the equinoxes and solstices by one day. Thus as the centuries passed the Julian Calendar became increasingly inaccurate with respect to the seasons. This was especially troubling to the Christian Church because it affected the determination of the date of Easter, which, by the 16th Century, was well on the way to slipping into Summer.
Pope Paul III recruited several astronomers to come up with a solution, principally the Jesuit Christopher Clavius (1537-1612) who built upon calendar reform proposals by the astronomer and physician Luigi Lilio (d. 1576). When Pope Gregory XIII was elected he found various proposals for calendar reform before him, and decided in favor of that of Clavius. On 1582-02-24 he issued a papal bull, Inter Gravissimas, establishing what is now called the Gregorian Calendar reform. The Gregorian Calendar is the calendar which is currently in use in all Western and Westernized countries.
The Gregorian reform consisted of the following:
- Ten days were omitted from the calendar, and it was decreed that the day following (Thursday) October 4, 1582 (which is October 5, 1582, in the old calendar) would thenceforth be known as (Friday) October 15, 1582.
- The rule for leap years was changed. In the Julian Calendar a year is a leap year if it is divisible by 4. In the Gregorian Calendar a year is a leap year if (a) it is divisible by 4 and (b) if it is divisible by 100 then it is divisible by 400. In other words, a year which is divisible by 4 is a leap year unless it is divisible by 100 but not by 400 (in which case it is not a leap year). Thus the years 1600 and 2000 are leap years, but 1700, 1800, 1900 and 2100 are not.
- New rules for the determination of the date of Easter were adopted (the old rule relied on the Jewish calendar).
- The first day of the year (New Years Day) was set at January 1st.
- The position of the extra day in a leap year was moved from the day before February 25th to the day following February 28th.
The term "leap year" derives from the fact that the day of the week on which certain festivals were held normally advanced by one day (since 365 = 7*52 + 1), but in years with an extra day the festivals would "leap" to the weekday following that.
It may be noted that there was no necessity for ten days, rather than, say, twelve days to have been omitted from the calendar. In fact, the calendar could have been reformed without omitting any days at all, since only the new rule for leap years is required to keep the calendar synchronized with the vernal equinoxes. The number of days omitted determines the date for the Spring equinox, an omission of ten days resulting in a date usually of March 20th.
The average length of the vernal equinox year during the last 2000 years is 365.242 days. The average length of the Julian year (365.25 days) differs from this value by 0.008 days. So from the year 1 to the year 1582 the calendar drifted off the mean solar year by 1581*0.008 = 12.6 days. Why didn't Pope Gregory remove twelve days, instead of just ten? It has to do with the First Council of Nicea, which was held in Nicea (now Iznik, Turkey) in the year 325. One of the matters settled by this council was the method for determining the date of Easter. From the 325 to 1582 the calendar diverged by 1257*0.008 = 10.1 days, so ten days were removed so as to restore the date of Easter to the same time of the year at which it had occurred at the time of the Council of Nicea.
(iii) Adoption of the Gregorian Calendar
The Gregorian Calendar was adopted immediately upon the promulgation of Pope Gregory's decree in the Catholic countries of Italy, Spain, Portugal and Poland, and shortly thereafter in France and Luxembourg. During the next two years most Catholic regions of Germany, Belgium, Switzerland and the Netherlands came on board. Hungary followed in 1587. The rest of the Netherlands, Denmark, Germany and Switzerland made the change during 1699 to 1701.By the time the British were ready to go along with the rest of Europe, the old calendar had drifted off by one more day, requiring a correction of eleven days, rather than ten, to locate the Spring equinox at March 21. The Gregorian Calendar was adopted in Britain (and in the British colonies) in 1752, with September 2, 1752, being followed immediately by September 14, 1752.
In many countries the Julian Calendar was used by the general population long after the official introduction of the Gregorian Calendar. Thus events were recorded in the 16th - 18th Centuries with various dates, depending on which calendar was used. Dates recorded in the Julian Calendar were marked "O.S." for "Old Style", and those in the Gregorian Calendar were marked "N.S." for "New Style".
To complicate matters further New Year's Day, the first day of the new year, was celebrated in different countries, and sometimes by different groups of people within the same country, on either January 1, March 1, March 25 or December 25. January 1 (decreed by Pope Gregory) seems to have been the usual date but there was no standard observed. With the introduction of the Gregorian Calendar in Britain and the colonies New Year's Day was generally observed on January 1. Previously in the colonies it was common for March 24 of one year to be followed by March 25 of the next year. This explains why, with the calendrical reform, the year of George Washington's birth changed from 1731 to 1732. In the Julian Calendar he was born on 2/11/1731 but in the Gregorian Calendar his birthdate is 2/22/1732.
Sweden adopted the Gregorian Calendar in 1753, Japan in 1873, Egypt in 1875, Easterm Europe during 1912 to 1919 and Turkey in 1927. Following the Bolshevik Revolution in Russia it was decreed that thirteen days would be omitted from the calendar, the day following January 31, 1918, O.S. becoming February 14, 1918, N.S. Further information can be found in The Perpetual Calendar.
In 1923 the Eastern Orthodox Churches adopted a modified form of the Gregorian Calendar in an attempt to render the calendar more accurate (see below). October 1, 1923, in the Julian Calendar became October 14, 1923, in the Eastern Orthodox calendar. The date of Easter is determined by reference to modern lunar astronomy (in contrast to the more approximate lunar model of the Gregorian system).
(iv) Astronomical Year Numbering
Astronomers designate years B.C.E. by means of negative numbers. In order to avoid a hiatus between the year 1 and the year -1, there has to be a year 0. Thus astronomers adopt the following convention:
1 A.D. = year 1 1 B.C.E. = year 0 2 B.C.E. = year -1 and so on More generally, a year popularly designated n B.C.E. is designated by astronomers as the year -(n-1).
The rules for leap years, in both calendars, are valid for the year 0 and for negative years as well as for positive years.
Note that the rules for leap years in the two calendars work for years prior to 1 A.D. only if those years are expressed according to the astronomical system, not if expressed as years B.C.E. 4 A.D is a leap year in both calendars, 1 B.C = astronomical year 0, 5 B.C = year -4, 9 B.C = year -8, and so on, are all leap years. 101 B.C.E. = year -100 is a leap year in the (proleptic) Julian Calendar but not in the (proleptic) Gregorian Calendar. These statements, however, are only abstractly true, because (as noted above) prior to 8 A.D. the leap years were not observed correctly by the Roman calendrical authorities.
(v) The Proleptic Julian and Gregorian Calendars
Every date recorded in history prior to October 15, 1582 (Gregorian), such as the coronation of Charlemagne as Holy Roman Emperor on Christmas day in the year 800, is a date in the Julian Calendar, since on those dates the Gregorian Calendar had not yet been invented.We can, however, identify particular days prior to October 15, 1582 (Gregorian), by means of dates in the Gregorian Calendar simply by projecting the Gregorian dating system back beyond the time of its implementation. A calendar obtained by extension earlier in time than its invention or implementation is called the "proleptic" version of the calendar, and thus we obtain the Proleptic Gregorian Calendar. The Julian Calendar also can be extended backward as the Proleptic Julian Calendar.
For example, even though the Gregorian Calendar was implemented on October 15, 1582 (Gregorian) we can still say that the date of the day one year before was October 15, 1581 (Gregorian), even though people alive on that day would have said that the date was October 5, 1581 (the Julian date at that time). As another example, the date of the coronation of Charlemagne, December 25, 800, in the Julian Calendar, was December 29, 800, in the Proleptic Gregorian Calendar.
Similarly, dates after October 15, 1582 (Gregorian) have equivalent, but different, dates in the Julian Calendar. For example, this article was completed on October 10, 1992, in the Gregorian Calendar, but we could equally well say that it was completed on September 28, 1992, in the Julian Calendar. As another example, the date of the winter solstice in the year 2012 is December 21, 2012 (Gregorian), which is December 8, 2012 (Julian).
Thus any day in the history of the Earth, either in the past or in the future, can be specified as a date in either of these two calendrical systems. The dates will generally be different; in fact they will be the same only for dates from March 1st, 200, to February 28, 300. The dates in neither calendar will coincide with the seasons in the distant past or distant future, but that does not affect the validity of these calendars as systems for uniquely identifying particular days.
(vi) Variation in the Tropical Year
The tropical year (a.k.a. the mean solar year) corresponds to the cycle of the seasons. The exact definition of this concept is currently a matter of debate among some astronomers (see Simon Cassidy's Error in Statement of Tropical Year). All agree, however, that due to the gravitational dynamics of the Sun-Earth-Moon system the length of the tropical year (however defined) is changing slowly. The length of the tropical year on 2000-01-01 is calculated by some astronomers to be 365.24218967 days, but at this level of precision the value depends on the definition of the concept. The value changes significantly with the millennia, however, as follows (according to a formula in common use among astronomers):
Thus the value of the tropical year varies over this 10,000-year timespan by as much as .00052 days (about 45 seconds).
Year Length of tropical year in days -5000 365.24253 -4000 365.24250 -3000 365.24246 -2000 365.24242 -1000 365.24237 0 365.24231 1000 365.24225 2000 365.24219 3000 365.24213 4000 365.24207 5000 365.24201(vii) Accuracy of the Gregorian and Orthodox Calendars
As in any completely rule-based (or determinate) calendar, the Gregorian Calendar is not absolutely accurate. As noted above, the average mean solar year at 2000-01-01 is 365.24219 days, compared to the average length of the year in the Gregorian Calendar of 365.2425 days. The average length of the year in the Gregorian Calendar thus exceeds the mean solar value at present by about 11.23 seconds (compared to 11.2 minutes for the Julian). Were the length of the mean solar year to be constant this error would accumulate to one day after about 3,200 years. However, by the year 5000 the value of the mean solar year will have decreased from 365.24219 days to 365.24201 days. Since the value of the mean solar year during the period of -5000 to 5000 ranges from 365.24253 to 365.24201 it is difficult to estimate calendrical error precisely, but we can say that the Gregorian Calendar is becoming less accurate (with respect to the mean solar year) in the short term (a few thousand years) but may become more accurate in the long term (about 20,000 years), with further variations thereafter.However, astronomers distinguish between the mean solar year and the average vernal equinox year (a distinction considered by some to have not only astronomical but also political significance) and the Gregorian Calendar, according to some acute investigators, was intended to follow the latter rather than the former, a fact which has resulted in confusion among scholars who study the question of its accuracy.
Whereas in the Gregorian Calendar a century year is a leap year only if division of the century number by 4 leaves a remainder of 0, in the Eastern Orthodox system a century year is a leap year only if division of the century number by 9 leaves a remainder of 2 or 6. This implies an average calendar year length in the Orthodox Calendar of 365.24222 days. This is very close to the present mean solar value of 365.24219, and the Eastern Orthodox Calendar is at present significantly more accurate in this respect than the Gregorian. Were the mean solar year to remain constant, the Orthodox Calendar would be off by one day only after about 33,000 years. However over the next few millennia the Orthodox calendar, like the Gregorian, will become increasingly inaccurate with respect to the mean solar year until possibly recovering around 10,000 years from now. However, in terms of the vernal equinox year the Gregorian Calendar is more accurate than the Orthodox and will become more accurate in the near future.
(viii) True Length of the Tropical Year
The tropical year has been defined as "the time it takes the Sun to appear to travel around the sky from a given point of the tropical zodiac back to that same point in the tropical zodiac." As Simon Cassidy has pointed out (Error in Statement of Tropical Year) this value depends on where in the Earth's orbit one begins the measurement of one revolution about the Sun. If the point used is the point of the vernal equinox then the value is 365.2424 tropical days (so this is the value of the "vernal-equinox year"). If one wishes an average value that is the mean of the values obtained by using different orbital starting points, then a value of 365.24219 days emerges.Those interested in pursuing this question further should consult (in addition to the articles linked in the previous paragraph) the following:
Royal Greenwich Observatory Information leaflets Royal Greenwich Observatory Information Leaflet No. 48: Leap Years L. E. Doggett Calendars Simon Cassidy Implementing a correct 33-year calendar reform Simon Cassidy Re: How long is a year -- EXACTLY?
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