One-Page Learn · The Halachos at a glance
קִדּוּשׁ הַחֹדֶשׁ
Sanctification of the New Month 10
Sefer Zemanim · The second reckoning of the solar year, the seasons that follow from it, and the Rambam's own admission of where it fails
19
Year cycle that closes with no remainder at all
76
Rega'im in a single chelek of an hour
91
Days in a season, plus 7 hours 519 chalakim 31 rega'im
2
Days the true equinox precedes either calculation
Part 1The shorter solar year, and a cycle that closes
- A year of 365 days, 5 hours, 997 chalakim, 48 rega'im. This is the figure held by those Sages who reckon the solar year as less than 365 and a quarter days, where a rega is a seventy sixth of a chelek. (10:1)
- The solar year exceeds the lunar by 10-21-121-48. Ten days, twenty one hours, one hundred twenty one chalakim and forty eight rega'im is the yearly surplus that the added months must absorb. (10:1)
- No remainder after nineteen years. On this reckoning the cycle leaves nothing over, and the solar years correspond exactly to the combination of ordinary and full lunar years. (10:1)
- A season is a quarter of that year. Ninety one days, seven hours, five hundred nineteen chalakim and thirty one rega'im, so that knowing one season's beginning yields the next by simple addition. (10:2)
RememberAn hour cut into eighty two thousand pieces, so that nineteen years can close without a crumb left over.
Part 2An anchor at creation, and the procedure that follows
- The first spring, nine hours and 642 chalakim early. On this calculation the vernal equinox of the first year of creation fell that far before the conjunction of Nisan. (10:3)
- The same offset heads every cycle. In the first year of every nineteen year cycle the vernal equinox stands nine hours and 642 chalakim before the Nisan conjunction. (10:3)
- Add a season at a time through the cycle. From the first year of a cycle, add 91 days, 7 hours, 519 chalakim and 31 rega'im for each successive season until the cycle ends. (10:4)
- To find any year's vernal equinox. Add 10-21-121-48 for each complete year elapsed in the cycle, group rega'im into chalakim, chalakim into hours and hours into days, subtract 9 hours and 642 chalakim, divide by a lunar month, and add the remainder to that year's conjunction of Nisan. (10:5)
RememberHe does not hand you a table, he hands you the method, so any reader with a pen can check the court.
Part 3What the court relied on, and what neither reckoning can do
- It appears to me, says the Rambam. He rules that the Sages relied on this calculation of the seasons for instituting a leap year in the era when the High Court sat, and he marks the ruling as his own inference. (10:6)
- Why this one and not the other. This reckoning is the more accurate of the two and bears a greater resemblance to what the astronomers have established than the opinion that the year is exactly 365 and a quarter days. (10:6)
- Both figures are mean values. Each calculation is an approximation resting on the mean rate of the sun's progress rather than its actual position in the celestial sphere. (10:7)
- The real equinox arrives about two days early. Measured against the sun's actual position the vernal equinox falls roughly two days before the computed time, and this holds on both opinions alike. (10:7)
RememberThe reckoning the court used to fix the festivals is, by its own author's admission, two days ahead of the sky.