One-Page Learn · The Halachos at a glance
קִדּוּשׁ הַחֹדֶשׁ
Sanctification of the New Month 16
Sefer Zemanim · The two invisible points where the moon's orbit crosses the sun's, the bounded band of five degrees the moon is never permitted to leave, and the table of angles that turns a course into a latitude
2
Points where the orbits intersect; at either one the moon has no latitude
5
Degrees, the greatest latitude ever reached, north or south
180
Degrees of course; below it northerly, above it southerly
7
Constellations between the head and the tail, always and exactly
Part 1The head, the tail, and their schedule
- Two tilted circles, two crossings. The moon's orbit meets the sun's orbit at an angle, part of it inclined north of the sun's orbit and part south, and there are two points opposite one another where they intersect. Standing at either point, the moon revolves in the same plane as the sun. The point at which it begins to incline north is the head, and the point from which it begins to incline south is the tail. (16:1)
- The head runs against the order of the constellations. It revolves at a uniform pace in opposition to the movement of the sphere of the constellations, from Pisces toward Aquarius, without increase or decrease, and it continuously follows that pattern. (16:1)
- The mean motion table. The head's mean movement in one day is 3 minutes and 11 seconds; in ten days 31 minutes 47 seconds; in one hundred days 5 degrees 17 minutes 43 seconds; in one thousand days 52 degrees 57 minutes 10 seconds; in twenty nine days 1 degree 32 minutes 9 seconds; in a regular year 18 degrees 44 minutes 42 seconds. Its mean on the Thursday night that begins these calculations is 180 degrees 57 minutes 28 seconds. (16:2)
- The worked position, and the seconds discarded. For Friday night, the second of Iyar, twenty nine days from the starting point, the mean of the head is 182 degrees 29 minutes 37 seconds and the head itself stands at 177 degrees 30 minutes, the seconds being of no consequence, which is 27 degrees and 30 minutes within Virgo. (16:5)
- The tail is never anywhere but opposite. There is always an even half of the celestial sphere between the head and the tail, so wherever the head stands, the tail stands seven constellations further along at exactly the same degrees and minutes. On that same night the tail is at 27 degrees and 30 minutes within Pisces. (16:5, 16:6)
RememberNothing occupies the head or the tail. They are crossings, and the whole chapter measures the moon against a point that has no body.
Part 2Latitude, and the ceiling it can never break
- North or south, read off the head and the tail. Once the head, the tail and the true position of the moon are known, compare them: if the moon stands at the head or the tail in degrees and minutes it inclines neither way; if it has passed the head and is proceeding toward the tail it inclines north of the sun's orbit; if it stands before the tail and is proceeding toward the head it inclines south. (16:7)
- The name of the quantity. The moon's inclination north or south is called its latitude, northerly or southerly accordingly, and at either crossing point it has no latitude at all. (16:8)
- Five degrees, and the pattern is fixed. The latitude never exceeds five degrees, north or south. From the head the moon diverges slightly and the divergence grows until it reaches five degrees, then it closes until there is no latitude at the tail; then it diverges again to five degrees and closes again to nothing. (16:9)
- The course of the latitude, and what its size decides. Calculate the position of the head and the true position of the moon for the date, then subtract the head from the moon, and the remainder is called the course of the latitude. Between 1 and 180 degrees the latitude is northerly; more than 180 degrees and it is southerly; an even 180 or an even 360 and the moon has no latitude at all. (16:10)
RememberThe moon is always leaving the sun's plane and always returning, and it is never permitted more than five degrees away from it.
Part 3The table of angles and the worked night
- The angle for each ten degrees of course, to ninety. A course of 10 gives 52 minutes; 20 gives 1 degree 43 minutes; 30 gives 2 degrees 30 minutes; 40 gives 3 degrees 13 minutes; 50 gives 3 degrees 50 minutes; 60 gives 4 degrees 20 minutes; 70 gives 4 degrees 42 minutes; 80 gives 4 degrees 55 minutes; 90 gives an even 5 degrees. (16:11)
- Units are interpolated, as with the sun and the moon. Where the course carries units as well as tens, take the average increase per degree and add the proportionate amount to the lower figure. A course of 53 falls between 50, whose angle is 3 degrees 50 minutes, and 60, whose angle is 4 degrees 20 minutes, a difference of 30 minutes or 3 minutes per degree, so its angle is 3 degrees 59 minutes. (16:12)
- One quarter of the circle carries the other three. A course between 90 and 180 is subtracted from 180 and the angle of the remainder is taken; a course between 180 and 270 has 180 subtracted from it; a course between 270 and 360 is subtracted from 360. Thus 150 gives the angle of 30, which is 2 degrees 30 minutes; 200 gives the angle of 20, which is 1 degree 43 minutes; 300 gives the angle of 60, which is 4 degrees 20 minutes. (16:13, 16:14, 16:15, 16:16, 16:17, 16:18)
- The second of Iyar, start to finish. The true position of the moon that night is 18 degrees 36 minutes within Taurus and the head stands at 27 degrees 30 minutes within Virgo. Subtracting the head from the moon leaves a course of the latitude of 231 degrees 6 minutes, and the minutes are of no consequence for the course, so the angle works out to 3 degrees 53 minutes. That is the latitude of the moon that night, and it is southerly, because the course is larger than 180 degrees. (16:19)
RememberThe answer is not a place. It is how far the moon has drifted off the sun's plane, and in which direction, and that is the number a sighting depends on.