הלכה על ראש השנה 41:6

Today Shmuel’s cycle is not correct.⁴⁰ In the year 4919, the year that Ibn Ezra wrote The Sabbath Epistle, the vernal equinox according to Shmuel should have been April 1, about ten days later than the true vernal equinox (see Appendix A, Table 7). Thus, referring to the vernal equinox for the year 4918, Ibn Ezra writes: “Even the simplest of simpletons can see that the day and night were equal close to eleven days ago” (Ha‘ibbur, p. 8b). The daily shadow in each place is positive proof for the scholar.⁴¹ Thus for example, at the time of the winter solstice it is easily observed that the true solstice does not coincide with Shmuel’s calculation. A sundial would be useful for these observations. Also it is written “If you see that the winter season extends until the sixteenth of Nisan, do not hesitate to intercalate that year” (Rosh haShana 21a). Now, according to Shmuel’s calculation, last year (4918) spring began on the 25th of Nisan.⁴² See Appendix A, Table 7. So we transgressed the words of our Sages. Heaven forbid! We certainly observed the holiday in its correct time. Thus the cycle of Rav Adda is more exact than that of Shmuel, for the beginning of spring will not go beyond the given date (16 days in Nisan).⁴³ See Appendix B, Table 5. In Sefer ha‘ibbur (p. 3b), Ibn Ezra sets Rav Adda’s figure for a tropical year as 365 days, 5 hours, 997 halaqim, and 48 rega‘im (secondary parts, s), where 76 rega‘im constitute one heleq. This is equivalent to 365 days, 5 hours, 55 minutes, and 25 + 25⁄57 seconds, approximately 365.2468 days. This value is obtained by equating 19 tropical years to 235 mean lunar months. 235 months calculates to 6939d, 16h, 595p. Dividing by 19, we arrive at Rav Adda’s figure. (See Appendix B.) This same figure is given by Maimonides in Mishne Torah, Laws of Sanctification of the New Moon 10:1. Note that earlier Ibn Ezra set a tropical year at approximately 365.2423 days (see note 13). Summarizing, we have the following opinions for the length of a tropical year: Shmuel: 365.25 days (exact), Rav Adda: 365.2468 days (rounded off), Ibn Ezra: 365.2423 days (rounded off), Current value: 365.2422 days (rounded off). Thus Shmuel’s cycle differs from the currently accepted approximate value by 0.78 day per century, or about ¾ of a day per century. Rav Adda’s figure differs from the currently accepted approximate value by about 0.46 day per century, or about ½ day per century. So it is difficult to understand why Ibn Ezra is so critical of Shmuel’s cycle and not that of Rav Adda. At the time of Ibn Ezra (4919), Rav Adda’s cycle had fallen behind by over 22 days; Shmuel’s cycle had fallen behind by over 38 days. Note that Ibn Ezra’s figure differs from the currently accepted figure by less that ½ day over the 49 centuries since Creation. Also, looking at Table 6 of Appendix B, we see that Rav Adda’s date for the vernal equinox differs from the true current vernal equinox by about seven days.

When we investigate the Torah’s year, we find written “This month shall be for you the beginning of months” (Exodus 12:2), so it is first of the months of the year. It is also written “This day you depart, in the month of ripening” (ibid. 13:4), and “Observe the month of ripening” (Deuteronomy 16:1). The explanation is that Israel counts by lunar months, and the month in which the barley ripens in the Land of Israel is the first of the year’s months. The beginning of that month is the beginning of the year, whether the equinox has passed or not. However, in order to perform the waving of the Omer ⁷⁸ The Omer waving took place on the second day of Passover, the sixteenth of Nisan (Leviticus 23:10–11). the court should ensure that Passover will occur when the barley has ripened.⁷⁹ There are exceptions to this requirement. See Ibn Ezra’s commentary to Exodus 12:2 and to Deuteronomy 15:1. Most years the ripening coincides with the equinox, but sometimes they are separated slightly because of an abundance of rain or because of drought.