Julian Period The
Julian day number is based on the
Julian Period proposed by
Joseph Scaliger, a classical scholar, in 1583 (one year after the Gregorian calendar reform) as it is the product of three calendar cycles used with the Julian calendar: Its epoch occurs when all three cycles (if they are continued backward far enough) were in their first year together. Years of the Julian Period are counted from this year, , as , which was chosen to be before any historical record. Scaliger corrected chronology by assigning each year a tricyclic "character", three numbers indicating that year's position in the 28-year solar cycle, the 19-year lunar cycle, and the 15-year indiction cycle. One or more of these numbers often appeared in the historical record alongside other pertinent facts without any mention of the Julian calendar year. The character of every year in the historical record was unique – it could only belong to one year in the 7980-year Julian Period. Scaliger determined that 1 BC or year 0 was Julian Period . He knew that 1 BC or year 0 had the character 9 of the solar cycle, 1 of the lunar cycle, and 3 of the indiction cycle. By inspecting a 532-year
Paschal cycle with 19 solar cycles (each of 28 years, each year numbered 1–28) and 28 lunar cycles (each of 19 years, each year numbered 1–19), he determined that the first two numbers, 9 and 1, occurred at its year 457. He then calculated via
remainder division that he needed to add eight 532-year Paschal cycles totaling 4256 years before the cycle containing 1 BC or year 0 in order for its year 457 to be indiction 3. The sum was thus JP 4713. A formula for determining the year of the Julian Period given its character involving three four-digit numbers was published by
Jacques de Billy in 1665 in the
Philosophical Transactions of the Royal Society (its first year).
John F. W. Herschel gave the same formula using slightly different wording in his 1849
Outlines of Astronomy.
Carl Friedrich Gauss introduced the
modulo operation in 1801, restating de Billy's formula as: where
a is the year of the indiction cycle,
b of the lunar cycle, and
c of the solar cycle.
John Collins described the details of how these three numbers were calculated in 1666, using many trials. A summary of Collin's description is in a footnote. Reese, Everett and Craun reduced the dividends in the
Try column from 285, 420, 532 to 5, 2, 7 and changed remainder to modulo, but apparently still required many trials. The specific cycles used by Scaliger to form his tricyclic Julian Period were, first, the indiction cycle with a first year of 313. Then he chose the dominant 19-year Alexandrian lunar cycle with a first year of 285, the
Era of Martyrs and the Diocletian Era epoch, or a first year of 532 according to
Dionysius Exiguus. Finally, Scaliger chose the post-Bedan solar cycle with a first year of 776, when its first quadrennium of
concurrents, , began in sequence. Although not their intended use, the equations of de Billy or Gauss can be used to determined the first year of any 15-, 19-, and 28-year tricyclic period given any first years of their cycles. For those of the Julian Period, the result is AD 3268, because both remainder and modulo usually return the lowest positive result. Thus 7980 years must be subtracted from it to yield the first year of the present Julian Period, −4712 or 4713 BC, when all three of its sub-cycles are in their first years. Scaliger got the idea of using a tricyclic period from "the Greeks of Constantinople" as Herschel stated in his quotation below in
Julian day numbers. Specifically, the monk and priest Georgios wrote in 638/39 that the Byzantine year 6149 AM (640/41) had indiction 14, lunar cycle 12, and solar cycle 17, which places the first year of the
Byzantine Era in 5509/08 BC, the Byzantine Creation. Dionysius Exiguus called the Byzantine lunar cycle his "lunar cycle" in argumentum 6, in contrast with the Alexandrian lunar cycle which he called his "nineteen-year cycle" in argumentum 5. which Reese, Everett and Craun translate as "We have termed it Julian because it fits the Julian year".
John F. W. Herschel then developed them for astronomical use in his 1849
Outlines of Astronomy, after acknowledging that Ideler was his guide. At least one mathematical
astronomer adopted Herschel's "days of the Julian period" immediately.
Benjamin Peirce of
Harvard University used over 2,800 Julian days in his
Tables of the Moon, begun in 1849 but not published until 1853, to calculate the lunar
ephemerides in the new
American Ephemeris and Nautical Almanac from 1855 to 1888. The days are specified for "Washington mean noon", with Greenwich defined as west of Washington (282°57′W, or Washington 77°3′W of Greenwich). A table with 197 Julian days ("Date in Mean Solar Days", one per century mostly) was included for the years –4713 to 2000 with no year 0, thus "–" means BC, including decimal fractions for hours, minutes, and seconds. The same table appears in
Tables of Mercury by Joseph Winlock, without any other Julian days. The national ephemerides started to include a multi-year table of Julian days, under various names, for either every year or every leap year beginning with the French
Connaissance des Temps in 1870 for 2,620 years, increasing in 1899 to 3,000 years. The British
Nautical Almanac began in 1879 with 2,000 years. The
Berliner Astronomisches Jahrbuch began in 1899 with 2,000 years. The
American Ephemeris was the last to add a multi-year table, in 1925 with 2,000 years. However, it was the first to include any mention of Julian days with one for the year of issue beginning in 1855, as well as later scattered sections with many days in the year of issue. It was also the first to use the name "Julian day number" in 1918. The
Nautical Almanac began in 1866 to include a Julian day for every day in the year of issue. The
Connaissance des Temps began in 1871 to include a Julian day for every day in the year of issue. The French mathematician and astronomer
Pierre-Simon Laplace first expressed the time of day as a decimal fraction added to calendar dates in his book, , in 1823. Other astronomers added fractions of the day to the Julian day number to create Julian Dates, which are typically used by astronomers to date
astronomical observations, thus eliminating the complications resulting from using standard calendar periods like eras, years, or months. They were first introduced into
variable star work in 1860 by the English astronomer
Norman Pogson, which he stated was at the suggestion of John Herschel. They were popularized for variable stars by
Edward Charles Pickering, of the
Harvard College Observatory, in 1890. Julian days begin at noon because when Herschel recommended them, the
astronomical day began at noon. The astronomical day had begun at noon ever since
Ptolemy chose to begin the days for his astronomical observations at noon. He chose noon because the transit of the Sun across the observer's meridian occurs at the same apparent time every day of the year, unlike sunrise or sunset, which vary by several hours. Midnight was not even considered because it could not be accurately determined using
water clocks. Nevertheless, he double-dated most nighttime observations with both
Egyptian days beginning at sunrise and
Babylonian days beginning at sunset. Medieval Muslim astronomers used days beginning at sunset, so astronomical days beginning at noon did produce a single date for an entire night. Later medieval European astronomers used Roman days beginning at midnight so astronomical days beginning at noon also allow observations during an entire night to use a single date. When all astronomers decided to start their astronomical days at midnight to conform to the beginning of the civil day, on , it was decided to keep Julian days continuous with previous practice, beginning at noon. During this period, usage of Julian day numbers as a neutral intermediary when converting a date in one calendar into a date in another calendar also occurred. An isolated use was by Ebenezer Burgess in his 1860 translation of the
Surya Siddhanta wherein he stated that the beginning of the
Kali Yuga era occurred at midnight at the meridian of
Ujjain at the end of the 588,465th day and the beginning of the 588,466th day (civil reckoning) of the Julian Period, or between JP 1612 or 3102 BC. Robert Schram was notable beginning with his 1882
Hilfstafeln für Chronologie. Here he used about 5,370 "days of the Julian Period". He greatly expanded his usage of Julian days in his 1908
Kalendariographische und Chronologische Tafeln containing over 530,000 Julian days, one for the zeroth day of every month over thousands of years in many calendars. He included over 25,000 negative Julian days, given in a positive form by adding 10,000,000 to each. He called them "day of the Julian Period", "Julian day", or simply "day" in his discussion, but no name was used in the tables. Continuing this tradition, in his book "Mapping Time: The Calendar and Its History" British physics educator and programmer Edward Graham Richards uses Julian day numbers to convert dates from one calendar into another using algorithms rather than tables. == Julian day number calculation ==