One other percularity of the Jewish calendar is that 24-hour days are counted from sunset, not from midnight. This was believed to be the pattern of creation in the corresponding Genesis account: “And the evening and the morning were the first day” (Gen 1:5).

      The formulas of Gauss

      Around the year 1800, the German mathematician Carl Friedrich Gauss (1777 – 1855) introduced formulas for calculating the dates for Christian Easter and the Jewish Passover. These formulas made chonological calculations much easier.

      The procedure for calculating the date of the Jewish Passover (Nissan 15) is as follows:

      1) A=R+3660,

      where “A” is the year according to the Jewish calendar; “R” is the year NE.

      2) a= (12A+17) mod 19,

      where “mod 19” is the remainder of the division by 19.

      3) b=A mod 4.

      4) M+m= (32,0440933+1,5542418a+0,25b-0,00317779A),

      where “M” is the integer part, and “m” is the fractional part.

      5) c= (M+3A+5b+5) mod 7.

      So, three variants are possible:

      1) is c=1, a> b and m≥0.63287037, then the Jewish Passover (Nissan 15) falls on M+2 March in the Julian calendar.

      2) if c=2, 4 or 6, and also when c=0, a> 11 and m≥0,89772376, then the Jewish Passover falls on M+1 March.

      3) in all other cases it falls on M in March.

      If the resulting value is greater than the number of days in March, you should subtract 31. The result will correspond to a date in April.

      For example, let us calculate the date for the Jewish Passover in 2016:

      1) A=5776.

      2) a=17.

      3) b=0.

      4) M+m=40,11128886.

      M=40, m=0,11128886.

      5) c=6.

      Since c=6, you should add 1 to M=40 and subtract 31. So, in 2016, the Jewish Passover (Nissan 15) falls on April 10 in the Julian calendar, which corresponds to April 23 in the Gregorian calendar. As noted above, the 24-hour day in the Jewish calendar begins at sunset. That is why the 15th of Nissan in this case begins in the evening of April 9 and ends in the evening of April 10.

      The procedure for calculating the date of Christian Easter using the Gauss formula is as follows:

      1) a=R mod 19,

      where “R” is the year NE; “mod 19” is the remainder after the division by 19.

      2) b=R mod 4.

      3) c=R mod 7.

      4) d= (19a+15) mod 30.

      5) e= (2b+4c+6d+6) mod 7.

      Three variants are possible:

      1) if the sum of (d+e) does not exceed 9, then Christian Easter falls on March (22+d+e).

      2) is (d+e) ≥10, then Easter falls on April (d+e-9).

      For example, let us calculate the date for Easter in 2016:

      1) a=2.

      2) b=0.

      3) c=0.

      4) d=23.

      5) e=4.

      Since (d+e) exceeds 9, let us calculate (d+e-9) =18. So, in 2016, Orthodox Christian Easter falls on April 18 of the Julian calendar, which corresponds to May 1 in the Gregorian calendar.

      The Julian period and calendar

      Historians and annalists often deal with calendar calculations which involve various types of dates. To simplify the process for converting dates from one calendar to another, the “system of Julian days” or “continuous day count” was introduced. In 1583, the French scholar Joseph Justus Scaliger (1540 – 1609) 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