Editing Nisan (section)

==Table of civil dates when 1 Nisan occurs==
The list below gives a time which can be used to determine the day the Jewish ecclesiastical (spring) year starts over a period of nineteen years. These are not Nisan ''molad'' times, although the offset necessarily remains constant. (The fractions shown are fractions of a minute.)

:17:49 Wednesday, 22 March 2023
:15:21 <math>\tfrac{13}{18}</math> Tuesday, 9 April 2024
:00:10 <math>\tfrac{7}{18}</math> Sunday, 30 March 2025
:08:59 <math>\tfrac{1}{18}</math> Thursday, 19 March 2026
:06:31 <math>\tfrac{14}{18}</math> Wednesday, 7 April 2027
:15:20 <math>\tfrac{8}{18}</math> Sunday, 26 March 2028
:00:09 <math>\tfrac{2}{18}</math> Friday, 16 March 2029
:21:41 <math>\tfrac{15}{18}</math> Wednesday, 3 April 2030
:06:30 <math>\tfrac{9}{18}</math> Monday, 24 March 2031
:15:19 <math>\tfrac{3}{18}</math> Friday, 12 March 2032
:12:51 <math>\tfrac{16}{18}</math> Thursday, 31 March 2033
:21:40 <math>\tfrac{10}{18}</math> Monday, 20 March 2034
:19:13 <math>\tfrac{5}{18}</math> Sunday, 8 April 2035
:04:01 <math>\tfrac{17}{18}</math> Friday, 28 March 2036
:12:50 <math>\tfrac{11}{18}</math> Tuesday, 17 March 2037
:10:23 <math>\tfrac{6}{18}</math> Monday, 5 April 2038
:19:12 Friday, 25 March 2039
:04:00 <math>\tfrac{12}{18}</math> Wednesday, 14 March 2040
:01:33 <math>\tfrac{7}{18}</math> Tuesday, 2 April 2041

Every nineteen years this time is 2 days, 16 hours, 33 1/18 minutes later in the week. That is either the same or the previous day in the civil calendar, depending on whether the difference in the day of the week is three or two days. If 29 February is included fewer than five times in the nineteen – year period the date will be later by the number of days which corresponds to the difference between the actual number of insertions and five. If the year is due to start on Sunday, it actually begins on the following Tuesday if the following year is due to start on Friday morning. If due to start on Monday, Wednesday or Friday it actually begins on the following day. If due to start on Saturday, it actually begins on the following day if the previous year was due to begin on Monday morning.

The table below lists, for a Jewish year commencing on 23 March, the civil date of the first day of each month. If the year does not begin on 23 March, each month's first day will differ from the date shown by the number of days that the start of the year differs from 23 March. The correct column is the one which shows the correct starting date for the following year in the last row. If 29 February falls within a Jewish month the first day of later months will be a day earlier than shown.

{|class="wikitable"
|+ Civil date of first day of Jewish months
|-
!Length of year: ||353 days||354 days||355 days||383 days||384 days||385 days
|-
|First month||colspan="6"| 23 March
|-
|Second month||colspan="6"| 22 April
|-
|Third month||colspan="6"| 21 May
|-
|Fourth month||colspan="6"| 20 June
|-
|Fifth month||colspan="6"| 19 July
|-
|Sixth month||colspan="6"| 18 August
|-
|Seventh month||colspan="6"| 16 September
|-
|Eighth month||colspan="6"| 16 October
|-
|Ninth month||colspan="2"| 14 November||15 November||colspan="2"| 14 November||15 November
|-
|Tenth month||13 December||14 December||15 December||13 December||14 December||15 December
|-
|Eleventh month||11 January||12 January||13 January||11 January||12 January||13 January
|-
|Added month||colspan="3" {{N/A}} ||10 February||11 February||12 February
|-
|Twelfth month||10 February||11 February||12 February||12 March||13 March||14 March
|-----------------------------------------------------------------------------------------
|First month||11 March||12 March||13 March||10 April||11 April||12 April
|}

For long period calculations, dates should be reduced to the [[Julian calendar]] and converted back to the civil calendar at the end of the calculation. The civil calendar used here (Exigian) is correct to one day in 44,000 years and omits the leap day in centennial years which do not give remainder 200 or 700 when divided by 900.<ref>{{cite web |last=Cassidy |first=Simon |title=Re: How long is a year..EXACTLY? East Carolina University Calendar discussion List CALNDR-L |url=http://hermetic.ch/cal_stud/cassidy/howlong.htm |access-date=11 March 2023 |date=25 October 1996}}</ref> It is identical to the Gregorian calendar between 15 October 1582 CE and 28 February 2400 CE (both dates inclusive).{{efn|This calendar was devised to provide specific advantages over the Revised Julian calendar, which was itself devised to provide specific advantages over the Gregorian calendar. These are: historical identity of dates with the Gregorian (see above for range); when projected back to before the Christian era the leap year rule remains unchanged; in the Finnish Orthodox Church, which currently uses the Gregorian Paschalion, five Easter tables would be used in the next 900 years (involving six switches) because two tables are used twice. There would be no change over any 900-year cycle if the Revised Julian calendar were used, but the Exigian calendar (so named to avoid having to describe it every time it came up in discussion) requires only four switches because no table is used twice.}}

To find how many days the civil calendar is ahead of the Julian in any year from 301 BCE (the calendar is proleptic [assumed] up to 1582 CE) add 300 to the year, multiply the hundreds by 7, divide by 9 and subtract 4. Ignore any fraction of a day. When the difference between the calendars changes the calculated value applies on and from 1 March (civil date) for conversions to Julian. For earlier dates reduce the calculated value by one. For conversions to the civil date the calculated value applies on and from 29 February (Julian date). Again, for earlier dates reduce the calculated value by one. The difference is applied to the calendar one is converting '''into'''. A negative value indicates that the Julian date is ahead of the civil date. In this case it is important to remember that when calculating the civil equivalent of 29 February (Julian), 29 February is discounted. Thus if the calculated value is −4 the civil equivalent of this date is 24 February. Before 1 CE use astronomical years rather than years BCE. The astronomical year is (year BCE) – 1.

Up to the 4th century CE, these tables give the day of the Jewish month to within a day or so and the number of the month to within a month or so. From the 4th century, the number of the month is given exactly and from the 9th century the day of the month is given exactly as well.

In the Julian calendar, every 76 years the Jewish year is due to start 5h 47 14/18m earlier, and 3d 18h 12 4/18m later in the week.

;Example calculation

On what civil date does the eighth month begin in CE 20874–5?

20874=2026+(248×76). In (248×76) Julian years the Jewish year is due to start (248×3d 18h 12 4/18m) later in the week, which is 932d 2h 31 2/18m or 1d 2h 31 2/18m later after removing complete weeks. Allowing for the current difference of thirteen days between the civil and Julian calendars, the Julian date is 13+(248×0d 5h 47 4/18m) earlier, which is 72d 21h 28 16/18m earlier. Convert back to the civil calendar by applying the formula.

:20874+300=21174
:211×7=1477
:1477/9=164 remainder 1
:164−4=160.
:160d−72d 21h 28 16/18m=87d 2h 31 2/18m.

So, in 20874 CE, the Jewish year is due to begin 87d 2h 31 2/18m later than in 2026 CE and 1d 2h 31 2/18m later in the week. In 20874 CE, therefore, the Jewish year is due to begin at 11.30 3/18 am on Friday, 14 June. Because of the displacements, it actually begins on Saturday, 15 June. Odd months have 30 days and even months 29, so the starting dates are 2, 15 July; 3, 13 August; 4, 12 September; 5, 11 October; 6, 10 November; 7, 9 December, and 8, 8 January.

The rules are based on the theory that Maimonides explains in his book ''Rabbinical Astronomy''.<ref>{{cite book |last=Feldman |first=W M |title=Rabbinical Mathematics and Astronomy |series=Judaic Studies Library; no. SHP 4 |isbn=978-0872030268 |publisher=Hermon Press |edition=3rd |location=New York |year=1978}}</ref>{{efn|No allowance is made for the secular (centennial) decrease of ½ second in the length of the mean tropical year and the increase of about four yards in the distance between the Earth and the Moon resulting from tidal friction because astronomy was not sufficiently developed in the 12th century (when Maimonides wrote his book) to detect this.}} The times in the list are those calculated by [[Carl Friedrich Gauss|Gauss]]<ref>C F Gauss, ''Berechnung des jüdischen Osterfestes'', Monatliche Correspondenz zur Beförderung der Erd- und Himmels-Kunde, 5, herausgegeben vom Freiherrn von Zach, Mai 1802, pp 435–437; reprinted in: Carl Friedrich Gauss Werke (Königlichen Gesellschaft der Wissenschaften, Göttingen, 1874), vol. 6, pp. 80–81.</ref> with an offset of −14 days as his calculation gives the civil date of Passover rather than the start of the month. Gauss's calculation has been rigorously proved.<ref>{{cite web |last=Burnaby |first=Sherrard Beaumont |year=1901 |title=Elements of the Jewish and Muhammedan calendars with rules and tables and explanatory notes on the Julian and Gregorian calendars. Chapter 8: The formula of Dr. Gauss for finding the Christian date of the Jewish Passover |url=http://www.archive.org/details/elementsofjewish00burnuoft/page/218/mode/2up |pages=219–239 |location=London}}</ref>