JHA, xxix (1998), 328-330
THE JULIAN AND MODIFIED JULIAN DATES

DENNIS D. MCCARTHY, U.S. Naval Observatory

For many astronomical and geodetic purposes it is important to know the time elapsed between the events under study. The calendar we use today, with its varying number of days in the month and complex rules governing leap years, is most inconvenient for this purpose, and so for much of the twentieth century astronomers have used the sequence of 'Julian day numbers' to denote the days (beginning with Greenwich mean noon) on which events occur. Instants within a given day are assigned a Julian Date (JD), which is the Julian day number plus the fraction of the day since the preceding noon, and the time elapsed between two events is simply the difference between their JDs.

That the Julian Day begins at noon is often inconvenient, since it implies that morning and afternoon on a given day in the civil calendar have different Julian day numbers. The 1973 General Assembly of the International Astronomical Union recommended that a Modified Julian Date be adopted which omitted the first two digits that were rarely of interest, and which began at midnight. This decision was however reversed by resolution of the 1994 General Assembly, which called for a return to Julian Dates.

The reversal nevertheless proved unacceptable to geodesists, among whom the Modified Julian Date was in widespread use, and the following year the International Union of Geodesy and Geophysics called on the IAU to reconsider the 1994 resolution. The IAU accordingly set up a Working Group with representatives from the relevant commissions. The Working Group's report resulted in a resolution adopted at the 1997 General Assembly that approved the parallel use of both systems but asked that the particular system in use in any application be clearly stated. During the deliberations of the Working Group, of which the author was a member, it became clear that many astronomers were unfamiliar with the origins of the system of Julian Dates, and therefore a short account of the system and how it arose may be of interest.

The modern use of Julian Days for continuous counts of days is rooted in the calendar reforms of the sixteenth century. Joseph Justus Scaliger (1540-1609), the son of Julius Caesar Scaliger, a famous physician and humanist, and himself an outstanding scholar,1 in 1583 began the process that led to the Julian day number count when he attempted to clarify the confusing calendars in use during the Middle Ages. Scaliger used three numbers of importance in early Christian calendrics:

    (i) In the calendar introduced by Julius Caesar and in use until the Gregorian Reform of 1582, the normal year had 365 days, and a leap year of 366 days occurred every fourth year without exception. The day of the week on which (say) 1 January fell therefore advanced by five weekdays every four years, and returned to its original weekday after 4×7 = 28 years.

    (ii) The 'Golden Number' Cycle, associated with Melon who flourished in Athens in the fifth century B.C., equated 19 years with 235 months, and this period of 19 years was used by Dionysius Exiguus in the sixth century A.D. as the basis of a cyclic solution to the problem of the dates of Easter.

    (iii) A tax cycle or 'indiction' of 15 years was used in the legal and financial organization of the Roman empire under Constantine and later emperors.

Scaliger reasoned that any year could be characterized by its position (S) within a 28-year solar cycle, its position (G) within the 19-year cycle of Golden Numbers, and its position (I) within the 15-year Roman tax cycle. Because 15, 19 and 28 have no common factors, a particular combination of S, G, and I would repeat only after 28 x 19x15= 7980 years. This period Scaliger called a Julian period, not in honour of his father as is frequently asserted,2 but because of the involvement of the Julian calendar. Knowing that the year 1 B.C. was characterized by S = 9, G = 1, and 1 = 3, Scaliger computed that the combination of S = 1, G = 1, I = 1 occurred for 4713 B.C. This provided him with the starting year from which to begin a continuous counting of years. Anthony Grafton translates the relevant passage from Scaliger's De emendatione temporum (1583) as follows:

To avoid any cumulative error due to the long series and interconnections of the epochs, I have devised a period which contains both [astronomical] cycles and the indictions. I shall call this the Julian Period. For to obtain it I multiplied the great 532-year period of Dionysius [obtained by multiplying 28 by 19] by 15.

    15×532 = 7980.

The period begins from the first year in both cycles and the indiction. Its last year, similarly, is the last one of the indiction and both cycles [the 'character' of JP 1 is 1.1.1; that of JP 7980 is 28.19.15]. For one cannot make the three cycles agree in this way in the course of a shorter period. The common year of the Lord 3267 has the last position in both cycles and the indiction. Therefore A.D. 3267 is JP 7980. Granted that, it is clear that the year 4713 of the same period is the one in which the birth of Christ falls, according to the normal Christian computation. Hence the current year, which is normally taken to be A.D. 1582, is JP 6295. If you divide 6295 by 19,28, and 15, the year will turn out to be 6 in the Dionysian lunar cycle, from March; 23 in the solar cycle from 1 January; 10 in the pontifical indiction of Constantine, from the 25th of last September. The utility of this period defies description. Not only can one see this from the epoch established below, but one can also do so by using it in practice to work out other chronological points. I have called the period Julian because it is laid out for the Julian year only. If the chronologer will arrange all historical epochs and tables of years with regard to this technical period, he will save himself and his readers much work.3

The advantages accruing from a continuous day count based on Scaliger's epoch were set out at length in 1849 by John Herschel, in his immensely influential Outlines of astronomy:

Different nations in different ages of the world have of course reckoned their time in different ways, and from different epochs, and it is therefore a matter of great convenience that astronomers and chronologists (as they have agreed on the uniform adoption of the Julian system of years and months) should also agree on an epoch antecedent to them all, to which, as to a fixed point in time, the whole list of chronological eras can be differentially referred. Such an epoch is the noon of the 1st of January, B.C. 4713, which is called the epoch of the Julian period, a cycle of 7980 Julian years.... The first year of the current Julian period, or that of which the number in each of the three subordinate cycles is 1, was the year 4713 B.C., and the noon of the 1st of January of that year, for the meridian of Alexandria, is the chronological epoch, to which, by all historical eras [sic], are most readily and intelligibly referred, by computing the number of integer days intervening between that epoch and noon (for Alexandria) of the day, which is reckoned to be the first of the particular era in question. The meridian of Alexandria is chosen as that to which Ptolemy refers the commencement of the era of Nabonassar, the basis of all his calculations.4

Herschel never refers to this continuous day count as the "Julian day", but rather as the "day in the Julian period". In fact, he uses the term "Julian Date" to refer to the year, month and day, of an event in the Julian Calendar in contrast to the "Gregorian Date" corresponding to the year, month and day in the Gregorian Calendar. He goes on in Outlines to provide a procedure for determining the day in the Julian period for any calendar date. Today, modern algorithms for converting between Gregorian calendar dates and Julian day numbers perform the same function.5

Herschel's arguments bore fruit as use of the Julian Date terminology became widespread around the turn of the century. Thus in 1890 J. G. Hagen6 gave observations of variable stars in both calendar and Julian dates, while in 1893 S. C. Chandler7 not only used both dating systems but provided a conversion table. The current definition, with the day beginning at Greenwich noon, was accepted as appropriate for use in astronomy.

A further development took place in 1948, when the Time Department of the Royal Greenwich Observatory began the use of continuous day numbers so as to reduce the confusion of dates associated with data reported to them for international time comparisons. Humphrey Smith, Secretary of IAU Commission 31 (Time), introduced this concept for discussion at the General Assembly of the IAU in 1955, and there the decision was taken to create a Modified Julian Date (MJD) by dropping the first two digits of the Julian day number as being for most purposes superfluous, and by making the correction of 0.5 days to bring the beginning of the day into agreement with Universal Time. At the 1973 General Assembly of the IAU, in recognition of the fact that a dating system in which the day began at midnight was useful for monitoring time signals and that such a system had been in use for some time, a resolution was passed recommending the use of MJD as the equivalent of JD-2400000.5. The Bureau International de l'Heure began to use MJD in its monthly circulars in October 1973, and in its Annual Report for 1973.

The General Assembly held in Kyoto in 1997 accepted the following definitions. The Julian day number (JDN) is the number assigned to a day in a continuous count of days beginning with the Julian day number 0 assigned to the day starting at Greenwich mean noon on 1 January 4713 B.C., in the Julian calendar extrapolated backwards ('proleptic'). The Julian Date (JD) of any instant is the Julian day number for the preceding noon plus the fraction of the day since that instant. A Julian Date begins at 12h Om Os, and the calendar date 2000 January 1, 12h 0m 0s (exactly) is equivalent to the Julian Date 2451545.0 (exactly). Finally, the Modified Julian Date (MJD) is defined as JD-2400000.5.

    Acknowledgements

It is a pleasure to acknowledge the members of the Working Group, as well as Humphrey Smith who provided the facts regarding the institution of the Modified Julian Date. Valuable comments were also received from Bernard Guinot. David Florkowski was instrumental in establishing early usage of Julian Dates in the literature.

REFERENCES

1. The ll-th edn of the Encyclopaedia Britannica (Cambridge, 1910-11), xxiv, 284, characterizes J. J.Scaliger as "the greatest scholar of modern times".
2. This belief is extraordinarily widespread; typical of many assertions is that of Atlas of the universe (London, 1961), 158: "Introduced by Scaliger in 1582 and named by him after his father (and therefore not related to the Julian calendar)."
3. Anthony Grafton, Joseph Scaliger: A study in the history of classical scholarship (Oxford, 1993), 249-50. With reference to the claim that Scaliger named the Julian Period after his father, Grafton cites the Latin of De emendatione temporum, "lulianum vocavimus, quia ad annum lulianum duntaxat accommodata est", and remarks in a footnote: "Is it necessary to point out that the name of the Julian Period, as this passage shows, was not derived from that of Scaliger's father?"

4. John F. W. Herschel, Outlines of astronomy (London, 1849), 632, 634.

5. H. F. Fliegel and T. C. Van Flandern, "A machine algorithm for processing calendar dates", Communications of the Association of Computing Machines, xi (1968), 657, reprinted in P. K. Seidelmann, Explanatory supplement to the Astronomical Almanac (Mill Valley, Calif., 1992), 604.

6. J. C. Hagen, "Light-variations of S Persei and T Arietis...", Astronomical journal, x (1890-91),115-18.

7. S. C. Chandler, "Second catalogue of variable stars", Astronomical journal, xiii (1893-94), 89-110.