Editing Julian day (section)

== History ==
===Julian Period <span class="anchor" id="Julian period"></span>===
The ''Julian day number'' is based on the ''Julian Period'' proposed by [[Joseph Justus Scaliger|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:

{{block indent|1=28 ([[Solar cycle (calendar)|solar cycle]]) × 19 ([[Metonic cycle|lunar cycle]]) × 15 ([[indiction|indiction cycle]]) = 7980 years}}

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, {{nowrap|4713 BC}}, as {{nowrap|year 1}}, which was chosen to be before any historical record.<ref>Richards 2013, pp. 591–592.</ref>

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&nbsp;BC or year&nbsp;0 was Julian Period {{nowrap|(JP) 4713}}. He knew that 1&nbsp;BC or year&nbsp;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&nbsp;years, each year numbered 1–28) and 28 lunar cycles (each of 19&nbsp;years, each year numbered 1–19), he determined that the first two numbers, 9 and 1, occurred at its year&nbsp;457. He then calculated via [[modulo operation|remainder division]] that he needed to add eight 532-year Paschal cycles totaling 4256&nbsp;years before the cycle containing 1&nbsp;BC or year&nbsp;0 in order for its year&nbsp;457 to be indiction 3. The sum {{nowrap|4256 + 457}} was thus JP&nbsp;4713.<ref>Grafton 1975, p. 184</ref>

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).<ref>de Billy 1665</ref> [[John Herschel|John F. W. Herschel]] gave the same formula using slightly different wording in his 1849 ''Outlines of Astronomy''.<ref>Herschel 1849</ref>

{{blockquote|text=Multiply the ''Solar'' Cycle by 4845, and the ''Lunar'', by 4200, and that of the ''Indiction'', by 6916. Then divide the Sum of the products by 7980, which is the ''Julian Period'': The ''Remainder'' of the Division, without regard to the ''Quotient'', shall be the year enquired after.|author=Jacques de Billy}}

[[Carl Friedrich Gauss]] introduced the [[modulo operation]] in 1801, restating de Billy's formula as: 
{{block indent|1=Julian Period year = (6916''a'' + 4200''b'' + 4845''c'') MOD 15×19×28}}
where ''a'' is the year of the indiction cycle, ''b'' of the lunar cycle, and ''c'' of the solar cycle.<ref>Gauss 1966</ref><ref>Gauss 1801</ref>

[[John Collins (mathematician)|John Collins]] described the details of how these three numbers were calculated in 1666, using many trials.<ref>Collins 1666</ref> A summary of Collin's description is in a footnote.<ref>
{| class=wikitable
|+ Calculation of 4845, 4200, 6916 <br> by Collins
|-
| || align=center | ''Try'' 2+ until ||
|-
| align=center | {{sfrac|7980|28}} = 19×15 = 285 
| align=center | {{sfrac|285×''Try''|28}} = <br> {{nowrap|remainder 1}} 
| align=center | 285×17 = 19×15×17 = 4845
|-
| align=center | {{sfrac|7980|19}} = 28×15 =  420 
| align=center | {{sfrac|420×''Try''|19}} = <br> {{nowrap|remainder 1}} 
| align=center | 420×10 = 28×15×10 = 4200
|-
| align=center | {{sfrac|7980|15}} = 28×19 = 532 
| align=center | {{sfrac|532×''Try''|15}} = <br> {{nowrap|remainder 1}} 
| align=center | 532×13 = 28×19×13 = 6916
|}</ref>
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.<ref name="Reese, Everett and Craun 1981">Reese, Everett and Craun 1981</ref>

The specific cycles used by Scaliger to form his tricyclic Julian Period were, first, the indiction cycle with a first year of 313.{{efn|All years in this paragraph are those of the Anno Domini Era at the time of Easter}}<ref>Depuydt 1987</ref> 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,<ref>Neugebauer 2016, pp. 72–77, 109–114</ref> or a first year of 532 according to [[Dionysius Exiguus]].<ref name="Dionysius Exiguus 2003/525">Dionysius Exiguus 2003/525</ref> Finally, Scaliger chose the post-Bedan solar cycle with a first year of 776, when its first quadrennium of [[concurrent (Easter)|concurrent]]s, {{nowrap|1 2 3 4}}, began in sequence.{{efn|1=The concurrent of any Julian year is the weekday of its March{{nbsp}}24, numbered from Sunday=1.}}<ref>''De argumentis lunæ libellus'', col. 705</ref><ref>Blackburn and Holford-Strevens, p. 821</ref><ref>Mosshammer 2008, pp. 80–85</ref> 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&nbsp;3268, because both remainder and modulo usually return the lowest positive result. Thus 7980&nbsp;years must be subtracted from it to yield the first year of the present Julian Period, −4712 or 4713&nbsp;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|Julian day numbers]].<ref name="Herschel 1849, p. 634">Herschel 1849, p. 634</ref> Specifically, the monk and priest Georgios wrote in 638/39 that the Byzantine year 6149&nbsp;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&nbsp;BC, the Byzantine Creation.<ref>Diekamp 44, 45, 50</ref> 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.<ref name="Dionysius Exiguus 2003/525"/>

Although many references say that the ''Julian'' in "Julian Period" refers to Scaliger's father, [[Julius Caesar Scaliger|Julius Scaliger]], at the beginning of Book V of his ''{{lang|la|Opus de Emendatione Temporum}}'' ("Work on the Emendation of Time") he states, "{{lang|la|Iulianam vocauimus: quia ad annum Iulianum accomodata}}",<ref>Scaliger 1629, p. 361</ref>{{refn|Scaliger used these words in his 1629 edition on p. 361 and in his 1598 edition on p. 339. In 1583 he used "{{lang|la|Iulianam vocauimus: quia ad annum Iulianum duntaxat accomodata est}}" on p. 198.}} which Reese, Everett and Craun translate as "We have termed it Julian because it fits the Julian year".<ref name="Reese, Everett and Craun 1981"/> Thus ''Julian'' refers to the [[Julian calendar]].

===Julian day numbers===
Julian days were first used by [[Christian Ludwig Ideler|Ludwig Ideler]] for the first days of the Nabonassar and Christian eras in his 1825 ''Handbuch der mathematischen und technischen Chronologie''.<ref>Ideler 1825, pp. 102–106</ref>{{refn|The Nabonassar day was elapsed with a typo – it was correctly printed later as 1448638. The Christian day (1721425) was current, not elapsed.}} [[John Herschel|John F. W. Herschel]] then developed them for astronomical use in his 1849 ''Outlines of Astronomy'', after acknowledging that Ideler was his guide.<ref>Herschel, 1849, p. 632 note</ref>

{{blockquote |text=The period thus arising of 7980 Julian years, is called the Julian period, and it has been found so useful, that the most competent authorities have not hesitated to declare that, through its employment, light and order were first introduced into chronology.<ref>Ideler 1825, p. 77</ref> We owe its invention or revival to Joseph Scaliger, who is said to have received it from the Greeks of Constantinople. 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 {{nowrap|4713 BC}}, and the noon of January 1 of that year, for the meridian of Alexandria, is the chronological epoch, to which all historical eras are most readily and intelligibly referred, by computing the number of integer days intervening between that epoch and the 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.<ref name="Herschel 1849, p. 634">Herschel 1849, p. 634</ref>}}

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 [[ephemeris|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 {{nowrap|18{{sup|h}} 51{{sup|m}} 48{{sup|s}}}} 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&nbsp;0, thus "–" means BC, including decimal fractions for hours, minutes, and seconds.<ref>Peirce 1853</ref> The same table appears in ''Tables of Mercury'' by Joseph Winlock, without any other Julian days.<ref>Winlock 1864</ref>

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&nbsp;years, increasing in 1899 to 3,000&nbsp;years.<ref>''Connaissance des Temps'' 1870, pp. 419–424; 1899, pp. 718–722</ref> The British ''Nautical Almanac'' began in 1879 with 2,000&nbsp;years.<ref>''Nautical Almanac and Astronomical Ephemeris'' 1879, p. 494</ref> The ''Berliner Astronomisches Jahrbuch'' began in 1899 with 2,000&nbsp;years.<ref>''Berliner Astronomisches Jahrbuch'' 1899, pp. 390–391</ref> The ''American Ephemeris'' was the last to add a multi-year table, in 1925 with 2,000&nbsp;years.<ref>''American Ephemeris'' 1925, pp. 746–749</ref> 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, {{lang|fr|italic=yes|Traité de Mécanique Céleste}}, in 1823.<ref>Laplace 1823</ref> Other astronomers added fractions of the day to the Julian day number to create Julian Dates, which are typically used by astronomers to date [[astronomy|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 [[N. R. Pogson|Norman Pogson]], which he stated was at the suggestion of John Herschel.<ref>Pogson 1860</ref> They were popularized for variable stars by [[Edward Charles Pickering]], of the [[Harvard College Observatory]], in 1890.<ref>Furness 1915.</ref>

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 clock]]s. Nevertheless, he double-dated most nighttime observations with both [[Egypt (Roman province)|Egyptian]] days beginning at sunrise and [[Babylonia]]n days beginning at sunset.<ref>Ptolemy {{Circa|150}}, p. 12</ref> 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 {{nowrap|January 1, 1925}}, 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&nbsp;day and the beginning of the 588,466th&nbsp;day (civil reckoning) of the Julian Period, or between {{nowrap|February 17 and 18}} JP&nbsp;1612 or 3102&nbsp;BC.<ref>Burgess 1860</ref><ref>Burgess was furnished these Julian days by US Nautical Alamanac Office.</ref> Robert Schram was notable beginning with his 1882 ''Hilfstafeln für Chronologie''.<ref>Schram 1882</ref> 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.<ref>Schram 1908</ref> 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.<ref>Richards 1998, pp. 287–342</ref>