016 - הִלְכוֹת קִדּוּשׁ הַחֹדֶשׁ פֵּרֶק טז

Laws of Sanctifying the New Moon, Chapter 16

1. The circle in which the moon always revolves is inclined above the circle in which the sun always revolves—half of it is inclined to the north, and half of it is inclined to the south. There are two points on it, opposite each other, where the two circles intersect. Therefore, when the moon is at one of these two points, it is found to be revolving in the sun’s circle, directly opposite the sun. But if the moon passes out from one of these two points, it is found to be moving either to the north of the sun or to its south.

The point from which the moon begins to incline to the north of the sun is called the “head,” and the point from which the moon begins to incline to the south of the sun is called the “tail.” The head has a uniform motion, which has neither increase nor decrease; it moves through the constellations in a backward direction, from Aries to Pisces to Aquarius, and so it always revolves.

2. The mean motion of the head in one day is three chalakim and eleven seconds. Therefore, its motion in ten days is thirty-one chalakim and forty-seven seconds. Its motion in one hundred days is five degrees, seventeen chalakim, and forty-three seconds—its sign is 5, 17, 43. Its motion in one thousand days is fifty-two degrees, fifty-seven chalakim, and ten seconds—its sign is 52, 57, 10. The remainder of its motion in ten thousand days is one hundred sixty-nine degrees, thirty-one chalakim, and forty seconds—its sign is 169, 31, 40. Its motion in twenty-nine days is one degree, thirty-two chalakim, and nine seconds—its sign is 1, 32, 9. Its motion in a regular year is eighteen degrees, forty-four chalakim, and forty-two seconds—its sign is 18, 44, 42. The mean position of the head at the beginning of the night of Thursday, which is the principal time, was one hundred eighty degrees, fifty-seven chalakim, and twenty-eight seconds—its sign is 180, 57, 28.

3. If you wish to know the position of the head at any time you desire, you should calculate its mean position for that time in the same way you calculate the mean position of the sun and the mean position of the moon, and subtract the mean position from three hundred sixty degrees. What remains is the position of the head at that time; and directly opposite it will always be the position of the tail.

4. How is this done? For example, if we want to know the position of the head at the beginning of the night of Friday, which is the second day of the month of Iyar in this year, which is the principal year, and the number of complete days from the beginning of the principal night until the beginning of this night in which we want to know the position of the head is twenty-nine days—

5. You calculate the mean position of the head for this time as you have learned: add its motion for twenty-nine days to the principal value. The result is that the mean position of the head is one hundred eighty-two degrees, twenty-nine chalakim, and thirty-seven seconds—its sign is 182, 29, 37. Subtract this mean from three hundred sixty, and you are left with one hundred seventy-seven degrees, thirty chalakim, and twenty-three seconds—its sign is 177, 30, 23. This is the position of the head; do not pay attention to the seconds. The position of the head is found to be in the constellation of Virgo, at twenty-seven degrees and thirty chalakim; and the position of the tail, directly opposite it, is in the constellation of Pisces, at twenty-seven degrees and thirty chalakim.

6. There will always be exactly half the circle between the head and the tail. Therefore, whichever constellation you find the position of the head in, the tail will be in the seventh constellation from it, with the same number of degrees and chalakim. If the head is at ten degrees in a certain constellation, the tail will be at ten degrees in the seventh constellation from it.

Laws of Sanctifying the New Month, Chapter 16

7. Once you know the position of the head, the position of the tail, and the true position of the moon, consider all three: If you find the moon together with the head or with the tail at the same degree and part, you know that the moon is not inclined either to the north of the sun or to its south. But if you see the position of the moon before the position of the head and it is moving opposite the tail, you know that the moon is inclined to the north of the sun. And if the moon is before the position of the tail and is moving opposite the head, you know that the moon is inclined to the south of the sun.

8. The inclination of the moon to the north of the sun or to its south is called the latitude of the moon. If it is inclined to the north, it is called northern latitude; if it is inclined to the south, it is called southern latitude. If the moon is at either of the two points, it will have no latitude, as we have explained.

9. The latitude of the moon will never be more than five degrees, whether to the north or to the south. Rather, this is its pattern: it begins at the head and moves away from it little by little, and the distance increases until it reaches five degrees; then it returns and draws closer little by little until it has no latitude when it reaches the tail; then it again moves away little by little, and the distance increases until it reaches five degrees; then it returns and draws closer until it has no latitude.

10. If you wish to know the latitude of the moon at any time you desire, and whether it is northern or southern, determine the position of the head and the true position of the moon for that time, and subtract the position of the head from the true position of the moon. The remainder is called the path of latitude. If the path of latitude is from one degree up to one hundred and eighty, you know that the latitude of the moon is northern; if the path is more than one hundred and eighty, you know that the latitude of the moon is southern. If it is exactly one hundred and eighty or exactly three hundred and sixty, the moon has no latitude at all. Then look again at the amount of the path of latitude, and that is the measure of its inclination to the north or to the south; and this is called the southern or northern latitude of the moon, as we have explained.

11. And what is the measure of the path of latitude? If the path of latitude is ten degrees, its measure is two degrees and fifty parts; if this path is twenty degrees, its measure is one degree and forty-three parts; if the path is thirty, its measure is two degrees and thirty parts; if the path is forty, its measure is three degrees and thirteen parts; if the path is fifty degrees, its measure is three degrees and fifty parts; if the path is sixty, its measure is four degrees and twenty parts; if the path is seventy, its measure is four degrees and forty-two parts; if the path is eighty, its measure is four degrees and fifty-five parts; if the path is ninety, its measure is five degrees.

12. If there are units together with tens, take what is appropriate for them according to the difference between the two measures, as you did with the path of the sun and the path of the moon. How so? If the path of latitude was fifty-three degrees—you already know that if the path was fifty, its measure would be three degrees and fifty parts, and if the path was sixty, its measure would be four degrees and twenty parts. The difference between the two measures is thirty parts, which is three parts for each degree. Therefore, according to the calculation for this path, which is fifty-three, its measure is three degrees and fifty-nine parts. In this manner, you should do for every number and number.

Laws of Sanctifying the New Moon, Chapter 16

13. After you know the portion of the wide path up to ninety, as we have informed you, you will know the portions for all the counts of the path: If the path is more than ninety up to one hundred and eighty, subtract the path from one hundred and eighty, and the remainder is the portion you will know.

14. Similarly, if the path is more than one hundred and eighty up to two hundred and seventy, subtract one hundred and eighty from it, and the remainder is the portion you will know.

15. And if the path is more than two hundred and seventy up to three hundred and sixty, subtract it from three hundred and sixty, and the remainder is the portion you will know.

16. How is this? If the path was one hundred and fifty, subtract it from one hundred and eighty; thirty remains. And you already know that the portion for thirty is two degrees and thirty chalakim; so too, the portion for one hundred and fifty is two degrees and thirty chalakim.

17. If the path was two hundred, subtract one hundred and eighty from it; twenty remains. And you already know that the portion for twenty is one degree and forty-three chalakim; so too, the portion for two hundred is one degree and forty-three chalakim.

18. If the path was three hundred, subtract it from three hundred and sixty; sixty remains. And you already know that the portion for sixty is four degrees and twenty chalakim; so too, the portion for three hundred is four degrees and twenty chalakim. And in this manner, for all the counts.

19. For example, if we want to know the width of the moon, and in which direction it is—whether north or south—at the beginning of the night of the second Shabbos evening of the month of Iyar of this year: You already know that the true position of the moon on this night was eighteen degrees and forty chalakim from the constellation Taurus—its sign is 18° 40'. And the position of the head at that time was twenty-seven degrees and thirty chalakim from the constellation Virgo—its sign is 27° 30'. Subtract the position of the head from the position of the moon; you will get a path width of two hundred and thirty-one degrees and ten chalakim—its sign is 231° 10'—since we do not pay attention to the chalakim in any path. And you will find the portion for this path, according to the methods we have explained in this chapter, is three degrees and fifty-three chalakim; and this is the width of the moon at the beginning of this night, and it is to the south—since the path is more than one hundred and eighty.