הלכה על ראש השנה 40:11

There are those of our generation who calculate the Hebrew calendar. Because they know the calculation based on 1:12:793,⁸ A mean lunar month is 29 days, 12 hours and 793 halaqim. If we discard the four complete weeks from this figure, we have the “character” of 1 day, 12 hours, and 793 halaqim (1d, 12h, 793p). This is the amount of time that the molad proceeds through the week from month to month. Thus the molad advances monthly by 1d, 12h, 793p of a week. they think that they have discovered the principle of the calendar. They then examine the duration between the molad and the beginning of the night, and they tell the uncircumcised (Christians) when the moon will be visible.⁹ I do not know why the Christians, who use a solar calendar, need to know when the moon will be visible. Perhaps there is an error here in our texts and it should read “Arabs.” When they see that in their place the duration [between molad and sighting] is sometimes less that six hours,¹⁰ It sometimes happens that the molad is less than six hours before sunset yet the moon is visible that evening. they think that the time given for the molad applies to the location of each individual calculator. However, there are times when the moon is seen at the beginning of the night and sometimes there are seven or eight hours between the molad and dusk, and the moon is still not visible. Therefore, they think that the calculation of our calendar is incorrect. Heaven forbid! Rather they err, for they think they are wise. For a scholar cannot know when the moon will be visible until he does as I shall explain: He must know the moment of the molad. He should not assign to the night twelve hours. Rather he should begin to count from the beginning of the night until the moment of conjunction so many and so many hours.¹¹ He should count night followed by day on a 24-hour clock and not begin a new count with dawn. He should know where conjunction will take place as to the minute of the degree of the zodiacal sign. He should see if the sun’s path is long or short, and how long the path of the moon is. He should then add or subtract until he knows the moment of true conjunction for Jerusalem. He should then calculate how far this conjunction is from the beginning of the night by hours and minutes. If he is west of Jerusalem he should add to those hours the hours of his distance in longitude, or subtract hours if he is east of Jerusalem. He should know the daily distance that the sun travels in hours and add it to the place of the sun at the moment of true conjunction. He should do similarly for the position of the new moon based on its orbit. Then he should record in a chart the degrees of the zodiacal signs in his land, and take those degrees that he will find relative to the position of the sun. He should similarly do this in degrees relative to the moon, and subtract the smaller from the larger. Then he will find the arc of the chord (between the sun and the moon). He should find the positions of the nodes,¹² The nodes are the two points at which the moon crosses the ecliptic. They are called the “head” and the “tail” of the “dragon.” Berry (p. 48) explains: “The moon’s path on the celestial sphere is slightly inclined to the ecliptic, and may be regarded as a great circle cutting the ecliptic in two nodes, at an angle which Hipparchus was probably the first to fix definitely at about 5÷. Moreover, the moon’s path is always changing in such a way that, the inclination to the ecliptic remaining nearly constant, the nodes move slowly backwards from east to west along the ecliptic, performing a complete revolution in about 19 years.” so that he will know the latitude of the moon,¹³ There is a difference in the time of visibility of the moon if it is north of the ecliptic or if it is south of the ecliptic. in order to correct this arc. Then he should adjust the arc based on the correction of the sighting, both in longitude and in latitude. Then we will know the true arc of vision.¹⁴ This is the arc between the longitude of the sun and that of the moon. In order for the moon to be visible, an arc of vision of at least 12÷ is necessary. Then he will know when the moon will appear in each place for any desired month. One who knows these matters can understand the principle “If it is born before noon” (Rosh haShana 20b).¹⁵ The Talmud states: “If it [the moon] is born before noon, it will be seen before sunset; if it is not born after noon, it will not be seen before sunset.” In Sefer ha‘ibbur (p. 10b) Ibn Ezra explains this statement.

There are those of our generation who calculate the Hebrew calendar. Because they know the calculation based on 1:12:793,⁸ A mean lunar month is 29 days, 12 hours and 793 halaqim. If we discard the four complete weeks from this figure, we have the “character” of 1 day, 12 hours, and 793 halaqim (1d, 12h, 793p). This is the amount of time that the molad proceeds through the week from month to month. Thus the molad advances monthly by 1d, 12h, 793p of a week. they think that they have discovered the principle of the calendar. They then examine the duration between the molad and the beginning of the night, and they tell the uncircumcised (Christians) when the moon will be visible.⁹ I do not know why the Christians, who use a solar calendar, need to know when the moon will be visible. Perhaps there is an error here in our texts and it should read “Arabs.” When they see that in their place the duration [between molad and sighting] is sometimes less that six hours,¹⁰ It sometimes happens that the molad is less than six hours before sunset yet the moon is visible that evening. they think that the time given for the molad applies to the location of each individual calculator. However, there are times when the moon is seen at the beginning of the night and sometimes there are seven or eight hours between the molad and dusk, and the moon is still not visible. Therefore, they think that the calculation of our calendar is incorrect. Heaven forbid! Rather they err, for they think they are wise. For a scholar cannot know when the moon will be visible until he does as I shall explain: He must know the moment of the molad. He should not assign to the night twelve hours. Rather he should begin to count from the beginning of the night until the moment of conjunction so many and so many hours.¹¹ He should count night followed by day on a 24-hour clock and not begin a new count with dawn. He should know where conjunction will take place as to the minute of the degree of the zodiacal sign. He should see if the sun’s path is long or short, and how long the path of the moon is. He should then add or subtract until he knows the moment of true conjunction for Jerusalem. He should then calculate how far this conjunction is from the beginning of the night by hours and minutes. If he is west of Jerusalem he should add to those hours the hours of his distance in longitude, or subtract hours if he is east of Jerusalem. He should know the daily distance that the sun travels in hours and add it to the place of the sun at the moment of true conjunction. He should do similarly for the position of the new moon based on its orbit. Then he should record in a chart the degrees of the zodiacal signs in his land, and take those degrees that he will find relative to the position of the sun. He should similarly do this in degrees relative to the moon, and subtract the smaller from the larger. Then he will find the arc of the chord (between the sun and the moon). He should find the positions of the nodes,¹² The nodes are the two points at which the moon crosses the ecliptic. They are called the “head” and the “tail” of the “dragon.” Berry (p. 48) explains: “The moon’s path on the celestial sphere is slightly inclined to the ecliptic, and may be regarded as a great circle cutting the ecliptic in two nodes, at an angle which Hipparchus was probably the first to fix definitely at about 5÷. Moreover, the moon’s path is always changing in such a way that, the inclination to the ecliptic remaining nearly constant, the nodes move slowly backwards from east to west along the ecliptic, performing a complete revolution in about 19 years.” so that he will know the latitude of the moon,¹³ There is a difference in the time of visibility of the moon if it is north of the ecliptic or if it is south of the ecliptic. in order to correct this arc. Then he should adjust the arc based on the correction of the sighting, both in longitude and in latitude. Then we will know the true arc of vision.¹⁴ This is the arc between the longitude of the sun and that of the moon. In order for the moon to be visible, an arc of vision of at least 12÷ is necessary. Then he will know when the moon will appear in each place for any desired month. One who knows these matters can understand the principle “If it is born before noon” (Rosh haShana 20b).¹⁵ The Talmud states: “If it [the moon] is born before noon, it will be seen before sunset; if it is not born after noon, it will not be seen before sunset.” In Sefer ha‘ibbur (p. 10b) Ibn Ezra explains this statement.

Now, what value is there in calculating the seasons according Shmuel? Even if his division was correct, what benefit would there be for the people of this island in knowing the time of the season change, since it is determined based on Jerusalem. For the sun rises there around four equinoctial hours before it rises on this island.⁵³ This is not accurate. Jerusalem is located at a longitude of 35÷10ʹ E, while London is at 0÷3ʹ W, so the difference in longitude is 35÷13ʹ, about two hours and 21 minutes. (An arc of 15÷ represents one hour.) In Sefer ha‘ibbur (p. 8b), Ibn Ezra estimates the distance between Jerusalem and England at three or four hours. This agrees with the value that Claudius Ptolemy (The Geography, pp. 49 and 128) gave, setting the distance between Jerusalem and London at about 50÷ of longitude, or three and one third hours. Our Rabbis agree in this matter, for they used the terms “new” and “old,” “for us” and “for them” (Rosh haShana 20b).