Slonimski formula

The Slonimski formula is a calculation system that was developed by Chajim Slonimski (1810–1904) and that allows the “character” (Kebioth) of the year in question to be calculated directly from the number of a Jewish year. The character of a year in the Jewish calendar indicates whether it is a diminished, regular or excessive common or leap year with 353, 354 or 355 or 383, 384 or 385 days. Furthermore, the weekday of the first day of this year ( Rosh Hashanah , 1st Tishri ) is given. From the six different lengths of the year and the four possible days of the week for the beginning of the year (Monday, Tuesday, Thursday and Saturday), there are in principle 24 possibilities for the character, of which only 14 occur. These 14 possibilities are also known as the normal calendar. The character of a year can alternatively also be determined by first entering the date of the Passover festival in the year A you are looking for or the New Year's festival in the following year A + 1, e.g. B. with the Gaussian Passover formula determined. Furthermore, one determines the date of the Passover or New Year celebrations in the previous year (year A -1 or A). By determining the daily difference or from the days of the week, the character of the relevant year results. In contrast, the Slonimski formula has the advantage that the character of the relevant year can be calculated directly from a given year.

Description of the Slonimski formula

A is a year of the Jewish era .

Calculate: and denote the remainder of the division by r. ${\displaystyle ((7A-6):19)}$

If r <12, then year A is a common year, otherwise for r 12 it is a leap year. ${\displaystyle \geq }$

Furthermore, we calculate: . Only the fractional part of k is taken into account (0 ≤ k ‹1). ${\displaystyle k=0{,}178117458A+0{,}7779654r+0{,}2533747}$

The character of year A now results from r and k.

For common years with r <5 applies:

character	k ${\displaystyle \geq }$	k ${\displaystyle <}$
2m	0	0.090410
2u	0.090410	0.271103
3r	0.271103	0.376121
5r	0.376121	0.661835
5u	0.661835	0.714282
7m	0.714282	0.752248
7u	0.752248	1

For common years with 5 r <7 applies: ${\displaystyle \leq }$

character	k ${\displaystyle \geq }$	k ${\displaystyle <}$
2m	0	0.090410
2u	0.090410	0.271103
3r	0.271103	0.376121
5r	0.376121	0.661835
5u	0.661835	0.714282
7m	0.714282	0.804693
7u	0.804693	1

For common years with 7 r <12 applies: ${\displaystyle \leq }$

character	k ${\displaystyle \geq }$	k ${\displaystyle <}$
2m	0	0.090410
2u	0.090410	0.285711
3r	0.285711	0.376121
5r	0.376121	0.661835
5u	0.661835	0.714282
7m	0.714282	0.804693
7u	0.804693	1

For leap years (r 12) the following applies: ${\displaystyle \geq }$

character	k ${\displaystyle \geq }$	k ${\displaystyle <}$
2M	0	0.157466
2U	0.157466	0.285711
3R	0.285711	0.428570
5 M	0.428570	0.533590
5U	0.533590	0.714282
7M	0.714282	0.871750
7U	0.871750	1

The number in the indication of the character indicates with which of the possible four days of the week the relevant year begins, e.g. B. means 2 Monday, 3 Tuesday, 5 Thursday and 7 Saturday. m denotes a poor, r a regular and u an excessive common year. Accordingly, M denotes a deficient leap year, R a regular and U an excessive leap year. You can see that 14 different characters (normal calendar) are possible for a year, seven for common and seven for leap years. In addition, in Jewish calendars the day of the week of the first day of the Passover festival (15th Nisan) is specified, for reduced, regular and excessive common or leap years 1, 2 or 3 or 3, 4 or 5 days of the week must be added to the weekday of New Year's Day must be added. This results in the following assignments:

character	more complete character (Kebioth Hashanah)		character	more complete character (Kebioth Hashanah)
2m	2m3		2M	2M5
2u	2u5		2U	2U7
3r	3r5		3R	3R7
5r	5r7		5 M	5M1
5u	5u1		5U	5U3
7m	7m1		7M	7M3
7u	7u3		7U	7U5

5U3 thus means that an excessive leap year (U, 385 days) begins on a Thursday (5) and the first day of the Passover festival of that year is on a Tuesday (3).

Calculations

Application of the Slonimski formula

As an example, the character of the year A = 5778 AM should be calculated.

According to the Gaussian Passover formula , the year A -1 = 5777 results in April 11, 2017 in the Gregorian calendar as the first day of the Passover festival (beginning with sunset on April 10, 2017) and from this September 21, 2017 greg. (Beginning with sunset on September 20, 2017) as New Year's Day ( Rosh Hashanah ) of the following year A = 5778.

With A = 5778, r = 8 and k = 0.63977022 according to the Slonimski formula. This results in the character 5r or 5r7. The year 5778 AM is therefore a regular common year (r) and begins on a Thursday (5) (September 21, 2017 greg., See above) and the first day of the Passover festival in 5778 AM is a Saturday (7) ( March 31, 2018 according to the Gaussian Passover formula for the year 5778 AM).

It is thus clear that the entire Jewish calendar for each year can be determined relatively easily using the Gaussian Passover formula and the Slonimski formula and can be related to the Julian or Gregorian calendar .

Explanation of the Slonimski formula

Schwarz and Kistner give a detailed derivation and explain the background to the formula. Note: There is an error in the formula for calculating the size k for black (0.779654 r instead of 0.7779654 r).

Individual evidence

1. ↑ Chajim Slonimski: Yesode Haibbur . Warsaw 1852, p. 21-25 .
2. ^ ^{A b c} Karl Friedrich Ginzel: Handbook of mathematical and technical chronology . Ed .: Hinrichs. tape 2 . Leipzig 1911, p. 93-96 .
3. ^ ^{A b} Adolf Schwarz: The Jewish calendar historically and astronomically examined . Ed .: Schletter'sche Buchhandlung. Breslau 1872, p. 73-75 .
4. ↑ Adolf Kistner: The calendar of the Jews . Verlag der Hofbuchhandlung Friedrich Gutsch, Karlsruhe 1905, p. 32-36 .