came up with the idea of the so-called “Julian period”. He named this method of calculation in honor of his father Julius Caesar Scaliger (1484 – 1558), the famous humanist and scholar.
Joseph Scaliger suggested a chronological scale against which any historical date could be aligned. The starting point for counting the “Julian days” (JDN=0) was set to January 1, 4713 BNE, which was the era “from the foundation of the world” according to Scaliger. Then, the JDN value would increase by one every day. So, January 2, 4713 BNE equals to JDN=1 and so on. For example, January 1 of the 1st year NE is JDN=1721424.
In 1849, John Herschel (1792 – 1871) suggested expressing all the dates though the JD value, which is the number of days that passed since the beginning of the Scaliger cycle. The difference between the Julian date (JD) and the Julian day number (JDN) is that the former contains a fractional part which indicates the time of 24-hour day. It was agreed that the beginning of the Julian day would be noontime according to Greenwich Mean Time. So, the midnight of January 1 of the 1st year NE corresponds to JD=1721423.5. Note that the JD=1721424 will accumulate only by the noon of the specified day, because the count was started at noon January 1, 4713 BNE (the “zero point”). To make our calculations easier, we will use the rounded value of the Julian date or the Julian day number (JDN).
The procedure for calculating the Julian day number (JDN) for a specific Julian calendar date is as follows:
1) a= [(14-month) /12].
2) y=year+4800-a.
3) m=month+12a-3.
4) Julian day number:
JDN=day+ [(153m+2) /5] +365y+ [y/4] -32083.
Where “year” is the year of NE; “month” is the number of the month; “day” is the day of the month; value in brackets is the integer part.
Knowing the JDN, you can find the day of the week by calculating the remainder of the division of JDN by 7. Based on the remainder value, the days of the week are distributed as follows: 0 – Monday, 1 – Tuesday, 2 – Wednesday, 3 – Thursday, 4 – Friday, 5 – Saturday, 6 – Sunday.
For example, let us calculate the Julian day number for the Jewish Passover in 2016 (April 10 in the Julian calendar):
1) a=0.
2) y=6816.
3) m=1.
4) JDN=2457502.
Remainder of division (JDN mod 7) =5, therefore, it is Saturday.
Finding dates based on the Julian days
The method of calculation based on the Julian days can be useful, for example, for finding the date for Tisri 1. We don’t know the interval between Nisan 15 and Tisri 1 within one year. But the interval between Tisri 1 of the year to be found and Nisan 15 of the previous year is always 163 days because Nisan, Iyyar, Siwan, Tammuz, Ab, and Elul have an unchanging number of days. If you know the Julian day number for Nisan 15, you can, by adding 163, find the Julian day number for Tisri 1 of the following year.
For example, based on the Gauss formulas, Nisan 15 of the year 5775 in the Jewish calendar corresponds to March 22, 2015, in the Julian calendar. Now we can calculate JDN for this date (JDN =2457117). Consequently, Tisri 1 of the year 5776 corresponds to JDN=2457280. The remainder of division is 0. Therefore, the day is Monday. We have already determined that Nisan 15 of the year 5776 in the Jewish calendar (2016 NE) falls on Saturday. Using Table 3 (see above), we see that the year 5776 of the Jewish calendar is embolismic, that is, its duration is 385 days (an excessive year).
The procedure for converting a Julian day number (JDN) into a Julian calendar date is as follows:
1) c=JDN+32082.
2) d= [(4c+3) /1461].
3) e=c- [1461d/4].
4) m= [(5e+2) /153].
5) day=e- [(153m+2) /5] +1.
6) month=m+3—12* [m/10].
7) year=d-4800+ [m/10].
Where year is the year of NE; month is the number of the month; day is the day of the month; value in brackets is the integer part.
For example, let us convert the Julian day number JDN=2457280 (Tisri 1 of the year 5776 in the Jewish calendar) into a Julian calendar date:
1) c=2489362.
2) d=6815.
3) e=184.
4) m=6.
5) day=1.
6) month=9.
7) year=2015.
Consequently, Tisri 1 of the year 5776 in the Jewish calendar falls on September 1 2015 of the Julian calendar, or September 14 of the Gregorian calendar.
The Julian day and the Egyptian calendar
To convert a Jewish calendar date into a Julian calendar date, we should first find the the Julian day number:
JDN= (N-1) *365+ (M-1) *30+ (D-1) +1448638,
where “N” is the year of the Nabonassar era; “M” is the ordinal number of the Egyptian calendar month; “D” is the date of the month.
The calculation procedure of date is the same as the one described in the previous chapter.
Для For example, let us calculate the day of the Julian calendar corresponding to Pharmuthi 25 of the year 777 of the Nabonassar era.
Julian day number:
JDN= (777—1) *365+ (8—1) *30+ (25—1) +1448638=1732112.
Julian calendar date:
1) c=1764194.
2) d=4830.
3) e=37.
4) m=1.
5) day=7.
6) month=4.
7) year=30.
So, Pharmuthi 25 of the year 777 of the Nabonassar era falls on April 7th 30 NE.
Calculations simplified
Chronology calculations became so much easier now that we have computers. The above algorithms can be effectively implemented using popular computational programs or programming language scripts. Also, there are ready-to-use programs and online services designed specifically for calendar calculations; some of them are described in the Addendum.
Section 2. The Old Testament chronology
Speaking of the challenges of calculating dates in the era “from the foundation of the world”, or “from Adam” in Section 1, we didn’t mention
