1. It is well-known and obvious that although the calculations indicate that the moon should be sighted on [a particular] night, its sighting is [only] probable. It is, however, also possible that it will not be sighted, because it is covered by clouds, because the place [from where it could be sighted] is in a valley,¹Since the moon is always low on the horizon at the beginning of the month, it is possible that the individuals dwelling in a valley will not be able to see it. For the horizon that appears to them is always higher in the sky than the actual horizon. or because there is a tall mountain in the west,²At the beginning of the month, the moon will always be sighted in the west, for it will have completed most of its daily circuit before nightfall, and will set within a few hours of the setting of the sun. blocking [view of] the people in the place [from where it could be sighted], and it will be as if they are in a valley.

For the moon will not be able to be sighted by a person in a low place, even when [its crescent] is large. Conversely, it will be possible for a person on a high and lofty mountain to sight [the moon], even though [its crescent] is very small. Similarly, sighting it will be possible for a person dwelling on the seashore, or a person travelling on a ship in the Mediterranean Sea, even though [its crescent] is very small.

2. Similarly, in the rainy season, on a clear day, the visibility of the moon will be greater than it is in the summer. For on a clear day in the rainy season, the air is clear and the heavens appear more brilliant, because there is no dust clouding the air. In the summer, by contrast, the air is like smoke, because of the dust. Therefore, the moon will appear small.

3. When the two limits [mentioned] with regard to the arc of sighting and the first longitude are short, [the crescent of] the moon will be small, and sighting the moon will be possible only from a very high altitude. If the arc of sighting and the first longitude are long, and [several] degrees were added to their minimal limits, the moon will appear large. Its size and the extent of its visibility will increase according to the length of the arc [of sighting] and the first longitude.

4. Therefore, the court should always have its attention focused on the following two matters: a) the season when [the moon] was sighted, and b) the place [where the witnesses were located]. [The judges] should ask the witnesses, "Where were you when you saw the moon?" For if the arc of sighting was short, and according to the calculations there is only a limited opportunity to see the moon, [more care is taken regarding their testimony].

For example, the arc of sighting was nine degrees and five minutes, and the first longitude was exactly thirteen degrees, and witnesses came, [claiming] that they saw [the moon]: If this occurs in the summer, or if the [witnesses] were located in a low place, we suspect [the veracity of] their [testimony] and subject them to much cross-examination.

In the rainy season, or in a very high place, [under such circumstances, the moon] would surely be sighted unless clouds obscured it.

5. [Let us examine a hypothetical situation:] Witnesses saw the new moon at the appropriate time.³I.e., on the night between the twenty-ninth and thirtieth days of the month, as mentioned in Chapter 1, Halachah 4. They came [to the court], and gave testimony. The court accepted their [testimony] and sanctified this first month.

Afterwards, they counted twenty-nine days from the day that was sanctified. On the night of the thirtieth, the moon was not sighted, either because sighting it was impossible, or because it was covered by clouds. The court waited the entire thirtieth day, as we have explained,⁴Chapter 1, Halachah 6. [but] witnesses did not arrive. [Therefore,] they added a day to the month, and thus, Rosh Chodesh of the second month was on the thirty-first day, as explained.⁵Ibid.

6. They began to count twenty-nine days from the day of Rosh Chodesh in the second [month], but the moon was not sighted. If you would say that [again] a day should be added to the month - i.e., the following day would be the thirtieth of the month, and the thirty-first day should be Rosh Chodesh of the third month [an undesirable situation would arise]. For it is possible that the moon would not be sighted on the night of the thirtieth of this month as well. Thus, [hypothetically, we could see an] ongoing [pattern, in which] a day is added and the new month begins after thirty days throughout the year. Thus, in the last month, it would be possible for the moon to be seen on the night of the twenty-fifth or the night of the twenty-sixth.⁶Since there are slightly more than twenty-nine and one half days in a lunar month, after an entire year the conjunction of the moon would fall approximately five and one sixth days earlier than the previous year. There could be no more ludicrous and demeaning situation than this.

7. Nor can one say that the [hypothetical situation described] - that the moon is never sighted throughout the year - is an infrequent occurrence [that need not be considered]. The contrary [is true]; it is very likely [to take place]. This often occurs in countries that have long rainy seasons and cloudy [skies]. For the intent is not that the moon will never be seen throughout the year, but that it will not be sighted at the beginning of the month, and will be sighted only afterwards.

[In certain months] it will not be sighted, because sighting it is impossible, and in the months when sighting it is possible, it possibly will not be sighted because of the clouds, or because its [crescent] was very small, and no one focused [his attention] on sighting it.

8. [These difficulties were avoided due to the following] tradition which existed among our Sages, [having been] transmitted from one to another in a chain extending back to Moses our teacher: When the moon was not sighted at the beginning of the months, month after month, the court establishes [the following sequence], one full month with thirty days, one lacking month with twenty-nine days. In this manner, they would calculate and establish one full month and one lacking month - establishing these months, but not sanctifying them.⁷I.e., although the court would declare the beginning of a new month, they would not follow the practice of sanctifying the new month described in Chapter 2, Halachah 8. For the sanctification of the months is dependent solely on the sighting [of the moon]. At times they would have a full month follow another full month, or a lacking month follow another lacking month, depending on the results of their calculations.

9. The intent of their calculations is always that it is possible to sight the moon in the following month at its proper time,⁸I.e., on the night between the twenty-ninth and thirtieth days of the month. or on the night following the added day, but not to sight it beforehand - e.g., on the night of the twenty-eighth.

Through the sighting calculations mentioned above, it is possible for you to determine when it will be possible [for the moon to be] sighted, and when it is possible that it will not be sighted. [The court] relies on [similar calculations] and [accordingly,] establishes two full months in succession, or two lacking months in succession.

Never should there be fewer than four full months in a year, nor should there ever be more than eight full months.⁹These figures apply in the era when the moon is sanctified according to the testimony of witnesses. According to the fixed calendar we follow at present, there are never more than seven, nor fewer than five, full months. When a full month is established according to calculations, a celebratory feast is also made in honor of the full month, as mentioned previously in Chapter 3.¹⁰Halachah 7.

10. Whenever you find statements in the Talmud¹¹E.g., Rosh HaShanah 20a. according to which it appears that the court relies on computations [rather than the testimony of witnesses], or that there is [a chain of tradition extending] from Moses at Sinai that this matter has been entrusted to them, and it is their decision whether to make the month lacking or full, and similarly, the fact that, during one year, Rabbi [Yehudah HaNasi] declared nine months as lacking¹²That year was a leap year, and Rabbi Yehudah HaNasi decided that it would be preferable for the additional month to be lacking rather than full (Arichin 9b). - these and all similar matters are dependent on this principle [and apply at] a time when the moon is not sighted at the appropriate time.

11. Similarly, the statements of our Sages¹³Rosh HaShanah, loc. cit. that a day is added to the month when necessary, applies in an instance when a full month [is declared] according to the calculations, [so that] one month is made lacking, and another month full.¹⁴Note the gloss of the Lechem Mishneh on Chapter 3, Halachah 15, which offers a different interpretation of that passage. They have the authority to declare full months in succession one after the other, and lacking months in succession.

[Only] when the moon is not seen at the appropriate time does [the court] declare full months when necessary. When, however, the moon is seen at the appropriate time - its first shining after its conjunction with the sun - it is always sanctified.

12. All the above concepts apply when there is a court that relies on the testimony of witnesses. In the present era, by contrast, we rely solely on the calculations based on the mean [motion of the sun and the moon] that are [simple and] widespread throughout Israel, as explained [previously] in these laws.¹⁵See Chapters 6-10.

13. It is explained in the texts of astronomical and geometrical calculations that if the moon is sighted in Eretz Yisrael, it will be sighted in all the lands in the world that are located to the west of Eretz Yisrael and are at the same latitude.¹⁶As one moves westward, the sun sets earlier, granting more time for the moon to be seen. If the calculations indicate that the moon will not be sighted in Eretz Yisrael, sighting it is, nevertheless, possible in those lands that are west of Eretz Yisrael and at the same latitude. Therefore, the fact that the moon is sighted in a country that lies west of Eretz Yisrael is not an indication of whether [or not] the moon will be sighted in Eretz Yisrael.¹⁷In this instance, our translation follows the version of the Mishneh Torah found in authoritative manuscripts and early printings. The standard printed text differs slightly.

14. If, however, the moon is not sighted on the mountains of the countries located west of Eretz Yisrael that are at the same latitude, the moon surely was not sighted in Eretz Yisrael.

15. Similarly, if the moon was not sighted in Eretz Yisrael, it certainly was not sighted in those countries that are east of Eretz Yisrael, and at the same latitude. If [the moon] was sighted in Eretz Yisrael, however, [there is no certainty whether it will be sighted] in these easterly lands; it may be sighted, and it may not be sighted.

Accordingly, if the moon was sighted in a country located to the east of Eretz Yisrael at the same latitude, the moon was surely sighted in Eretz Yisrael. If, however, the moon was not sighted in a country that lies east [of Eretz Yisrael], that is not an indication that the moon will not be sighted in Eretz Yisrael. On the contrary, it is possible that it will be sighted in Eretz Yisrael.

16. All the above statements apply when the countries to the west and to the east [of Eretz Yisrael] are at the same latitude as Eretz Yisrael - i.e., they are 30 to 35 degrees north [of the equator]. If they are located in a more northerly position, or in a less northerly position, different principles apply, for they are not parallel to Eretz Yisrael.

In the cities that are located to the east and west [of Eretz Yisrael], the statements we made [concerning the sighting of the moon are of abstract interest only], to clarify all the laws regarding the sighting [of the moon] to make the Torah great and glorious. [The intent is not that] the people living in the east or the west should depend on [their] sighting of the moon, or that [their sighting] should be of any consequence whatsoever. Instead, we rely only on the sanctification of the moon [performed] by the court in Eretz Yisrael, as we have explained several times previously.¹⁸See Chapter 1, Halachah 8; Chapter 5, Halachah 1.