One-Page Learn · The Halachos at a glance
קִדּוּשׁ הַחֹדֶשׁ
Sanctification of the New Month 9
Sefer Zemanim · From the moon to the sun: the length of the solar year, the four seasons of the sun, and the exact procedures for finding the hour, the weekday, and the date of any equinox or solstice
365
Days in the solar year, plus a quarter
91
Days from one season to the next, plus 7.5 hours
28
Years in the cycle that fixes the equinox weekday
4
Hours each season is permitted, and no others
Part 1A disputed year, a cycle remainder, and a fixed starting point
- Nobody settled the length of the year. Some Sages of Israel hold the solar year is 365 days and a quarter, meaning six hours; others hold it is slightly less, and the wise men of Greece and Persia disagree about it as well. (9:1)
- One hour and 485 parts per cycle. On the view that the year is exactly 365 and a quarter days, every nineteen year cycle leaves that remainder, and between the start of one season and the next there are 91 days and seven and a half hours, so that knowing one season lets you compute every following season forever. (9:2)
- Four seasons, four constellations. The equinox of Nisan is the hour and unit the sun enters the beginning of Aries, the solstice of Tammuz the beginning of Cancer, the equinox of Tishrei the beginning of Libra, the solstice of Tevet the beginning of Capricorn. (9:3)
- Seven days, nine hours, 642 parts. In the first year of creation the vernal equinox fell that far before the conjunction of Nisan, and every computation in the chapter runs back through that constant, subtracting it after the cycles have been totalled. (9:3, 9:4)
RememberThe chapter opens by admitting the number is disputed and then computes to the part anyway.
Part 2The procedures, and the four hours the sun is allowed
- Cycles, then years, then months. Add an hour and 485 parts for each completed nineteen year cycle; for each completed year inside the current cycle add 10 days, 21 hours, and 204 parts; group parts into hours and hours into days, subtract the creation constant, divide out lunar months of 29 days, 12 hours, and 793 parts, and add the remainder to that year's conjunction of Nisan. (9:4)
- Each season may fall at only four hours. The vernal equinox always at nightfall, midnight, daybreak, or noon; the summer solstice always at 7:30 or 1:30, morning or night; the autumn equinox always at nine or three, day or night; the winter solstice always at 10:30 or 4:30. (9:4)
- A separate 28 year cycle for the weekday. Divide the years since creation into groups of 28, add one day and six hours for each remaining year, add three days, divide into weeks, and count the remainder from nightfall on the first day of the week; the three days are added because the first equinox of creation fell at the beginning of the fourth day. (9:4)
- The worked example, checked against itself. For year 4930 the vernal equinox falls on the night of the fifth day at midnight, and adding seven and a half hours each time gives the summer solstice an hour and a half after daybreak, the autumn equinox nine hours after daybreak, and the winter solstice four and a half hours after nightfall. (9:5)
RememberIf your computed solstice lands on an hour the season is not allowed, the error is in your arithmetic, not in the sky.
Part 3From weekday to calendar date, and the audit at the end
- Eleven days a year, plus seven in this era. To find the date of the vernal equinox, determine its weekday and the weekday of Rosh Chodesh Nisan, add eleven days for each completed year of the nineteen year cycle, add a further seven in the present time, divide the sum by thirty, and count the remainder forward from Rosh Chodesh Nisan. (9:6)
- Then walk forward to the right weekday. If the day you reach is not the weekday on which the equinox falls, add one, two, or three days until you arrive at it, and the date you land on is the date of the equinox. (9:6)
- The eighth of Nisan. For year 4930, the ninth year of the 260th cycle, eight completed years give 88, plus seven gives 95, divided by thirty leaves five; five days past Rosh Chodesh Nisan is Monday, and walking forward to Thursday, the weekday of the equinox, gives the eighth of Nisan. (9:7)
- More than four days means you erred. One should never have to add more than one, two, or three days, or in a most unusual case four; if more are needed, know that a mistake was made in the reckoning and go back and calculate carefully. (9:8)
RememberThe chapter ends by handing the student a way to know his answer is wrong before he knows where he went wrong.