Halakhah for Eruvin 111:2
והא תניא נראה צנון נראה סם המות לא קשיא כאן בעלין כאן באמהות כאן בימות החמה כאן בימות הגשמים
if radish appears a life-giving drug has appeared. Was it not, however, taught: If radish appears a drug of death has appeared? - This is no contradiction, the latter might deal with the leaves while the former with the roots, or the latter might refer to the summer while the former might refer to the winter. Rab Judah citing Rab said: In a town which abounds with ascents and descents men and beasts die in the prime of their lives.<span class="x" onmousemove="('comment',' Lit., 'in the half of their days'.');"><sup>4</sup></span>
The Sabbath Epistle
We find the solar cycle of Shmuel32 A scholar of the Talmud (’amora) who lived around 300 C.E. in Neharde‘a, Babylonia. Shmuel was well acquainted with astronomy and declared “The paths of the heavens are as clear to me as the paths of Neharde‘a” (Berachot 58b). to be exactly 365¼ days, not more nor less.33 Shmuel said that each of the four seasons is 91 days and 7.5 hours (‘eruvin 56a). Thus a solar year consists of 365 days and 6 hours. In his days that was close to the truth,34 Although Shmuel’s solar cycle is excessive, relative to the currently accepted value of a solar year, by about one day every 128 years (see Appendix A), however, Shmuel also set the first (virtual) vernal equinox at the time of Creation about seven days before the accepted date. Hence, at the time of Shmuel the discrepancy in his approximation of the vernal equinox (and hence of the solar calendar) and the actual vernal equinox was not great. To see this we calculate (see Appendix A): Shmuel lived around the year 4010 Anno Mundo (A.M.) (250 C.E.), the first year of the 212th mahzor. Multiplying the character of a mahzor by 211 (the number of past mahzorim), we obtain 211 ׳ (1 hour, 485 halaqim) = 12 days, 17 hours, and 815 halaqim. Subtracting the starting interval of 7 days, 9 hours, and 642 halaqim, we have the span between molad Nisan and the vernal equinox for the year 4010 of approximately 5 days. So according to Shmuel, the vernal equinox took place about the fifth of Nisan, which corresponds with March 25, 250 in the Gregorian calendar. This is quite close to the true vernal equinox (March 21). and he cited a figure appropriate for his students. He did a similar thing in a Bereita,35 See Bereita of Shmuel, ch. 5 (p. 29). Apparently Ibn Ezra is of the opinion that the author of Bereita of Shmuel was the ’amora Shmuel, the same scholar quoted in the Talmud regarding the seasons. where, in calculating the mean lunar month, he did not include the 73 halaqim36 One heleq (part) is 1⁄1080 of an hour. We have the following conversions: 1 hour (h) = 1080 halaqim (p), 1 minute (m) = 18p, 1 second (s) = 0.3p. Also 1 heleq is 3 and ⅓ seconds. which are in addition to ⅔ of an hour.37 According to the Talmud, a mean lunar month consists of 29 days, 12 hours, 40 minutes, and 73 halaqim (Rosh haShana 25a). In the Bereita of Shmuel the 73 halaqim are omitted. It is also written that there are two cycles, the cycle of Rav Adda38 Rav Adda bar Ahava, a third-century Babylonian ’amora. He composed a treatise on the calendar titled Bereita deRav Adda. in private and the cycle of Shmuel in public. The reason that Rav Adda’s figure was in private was because of prognostications, lest their scholars know the true cycle.39 If unscrupulous astrologers would know the true solar cycle, they might use the information for nefarious purposes. (See Sefer ha‘ibbur, p. 6b.)
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The Sabbath Epistle
Also, he divided the year into four seasons of equal length.48 Shmuel set each season at 91 days and 7½ hours (‘eruvin 56a). This is true in the solar sphere, but it is not true relative to the zodiacal sphere, since the sun’s speed changes depending if it is closer to or farther from its apogee.49 The ancients believed that the sun orbited the earth at a constant speed. However, since the center of the sun’s sphere differed from the earth’s center, the speed of the sun varied relative to an observer on earth. This apparent variation in speed is known as the “solar anomaly.” The sun’s apparent speed is least at its apogee and greatest at its perigee. In the days of Ibn Ezra the sun’s apogee was between the summer solstitial point and the autumnal equinoctial point. (See Evans, p. 211.) There are over 94 days and many hours from the moment of vernal equinox, which begins the spring season, until the sun is at the extreme north (summer solstice), which is the beginning of the changeable sign,50 The sign Cancer. The “changeable signs” are the signs that appear at the time of a season change, namely Aries (spring), Cancer (summer), Libra (autumn), and Capricorn (winter). for then the season ends and we have the longest day. The second season (summer) is approximately the same number of days. The two remaining seasons (autumn and winter) are approximately 177 days.51 Spring and summer together comprise 2 ׳ 94 = 188 days, leaving 365 – 188 = 177 days for autumn and winter. This is accurate with definitive proof.52 “The definitive values for the lengths of the seasons in antiquity were those of Hipparchus, measured around 130 b.c.e.: Spring 94½ days Summer 92½ days Autumn 88 and ⅛ days Winter 90 and ⅛ days” (Evans, p. 210).
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The Sabbath Epistle
Furthermore, assume that the seasons are relative to this island. Thus, if spring began at the beginning of the night, then summer would begin seven and one-half hours after nightfall. But night on this island is only seven hours in duration,54 The relation between the length of the night (N) at summer solstice for a certain position (S) on earth, with latitude (L), is given by the equation cos (7.5 ׳ N) = tan (23÷26ʹ) ׳ tan L (Evans, p. 120). London is at a latitude of L = 51÷30ʹ north, so N = 1⁄7.5 ׳ arccos (tan (23÷26ʹ) ׳ tan (51÷30ʹ)) = 7.60 hours. Thus the summer solstitial night is 7.60 hours in duration, and the day is 16.40 hours. This is approximately the value given by Ptolemy for Southern Brittania (Almagest ii, 6, p. 87). Ibn Ezra’s assertion that the summer solstitical night was only seven hours, might indicate that he was residing in the northern part of the British Isle, or the Halachic definition of night is different than the astronomical definition. so the season will begin after sunrise.55 Shmuel said (‘eruvin 56a) that the summer season always begins at 1½ hours or 7½ hours of the day or night. However, if spring began at sundown in England, then summer would begin at ½ hour of the day, since night is only 7 hours long. However, Jerusalem which is at 31÷47ʹ N, has a shortest night and shortest day of approximately 9.92 hours, so Shmuel’s statement would be valid. Anyone who says that the season is based on unequal (seasonal) hours, which are twelve in the day and also twelve in the night,56 The division of a day into “seasonal hours” divides the period of time from sunrise to sunset into 12 equal parts, called “daytime hours,” and also the period from sunset to sunrise into 12 equal parts, called “nighttime hours.” Daytime hours and nighttime hours are not necessarily of equal length. Thus the length of an “hour” varies over the year. This differs from “equinoctial hours,” which is the division of the period from one midnight to the following midnight into 24 equal hours, where each hour corresponds to 360÷ ק 24 = 15÷ of the sun’s daily revolution about earth. Thus, if Shmuel was speaking of seasonal hours, then whenever spring began at sundown in England, summer would begin (7½ hours ׳ 7⁄12) = 4.375 equinoctial hours after nightfall, or about 12:52 a.m. is more hopeless than a fool. For how is it possible that an arc that measures 105÷ at the equator should be like an arc that measures 255÷?57 At summer solstice in England, daytime extends for 17 equinoctial hours, an arc of 255÷. At winter solstice, daytime is only 7 equinoctial hours, an arc of 105÷. Ibn Ezra believed that it was not reasonable that an arc of 105÷ should be divided into the same number of parts (12) as an arc of 255÷. In Sefer ha‘ibbur (pp. 8b-9a) Ibn Ezra states his critique somewhat differently: “One cannot claim that Shmuel’s hours are seasonal hours, determined by each night and by each day, since he divided the year into equal quarters.”
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