One-Page Learn · The Halachos at a glance
קִדּוּשׁ הַחֹדֶשׁ
Sanctification of the New Month 15
Sefer Zemanim · Turning the mean positions into a true one: the elongation doubled, the table that corrects the moon's course, and the single threshold at 180 degrees that decides whether the correction is added or taken away
5
Degrees, the least the double elongation can ever be
62
Degrees, the most it can ever be on a sighting night
9
Degrees, the largest addition made to the mean course
5° 8'
The greatest angle of the course, reached at 100 degrees
Part 1The elongation, and why it is doubled
- Three means, then one subtraction. To find the true position of the moon on a given date, calculate the mean of the moon at the time of the sighting, the mean of the moon within its path, and the sun's mean, then subtract the sun's mean from the moon's mean and double the remainder; the result is the double elongation. (15:1)
- A built in check on the arithmetic. Since the intent of every calculation in these chapters is to know how to sight the moon, the size of this figure matters: on the night of a sighting it can never be less than five degrees or more than sixty-two, and it will never exceed or fall short of those numbers. (15:2)
- The farther from the sun, the larger the correction. Five degrees or thereabouts needs no increase; six to eleven adds one degree, twelve to eighteen two, nineteen to twenty-four three, twenty-five to thirty-one four, thirty-two to thirty-eight five, thirty-nine to forty-five six, forty-six to fifty-one seven, fifty-two to fifty-nine eight, and sixty to sixty-three nine. (15:3)
- The figure that results has a name. The mean of the moon within its path, once these additions have been made, is called the correct course, and it is the quantity every later step operates on. (15:3)
RememberNothing in this chapter locates the moon by itself. The first move is to measure its distance from the sun and double it.
Part 2The angle of the course, and which way it points
- The threshold at 180 reverses the operation. If the correct course is less than 180 degrees the angle of the course is subtracted from the mean of the moon at the time of sighting; if it is more than 180 degrees the angle is added, and what remains is the true position of the moon. (15:4)
- At an even 180 or 360 there is no angle at all. In those two cases the mean position of the moon at the time of sighting simply is its true position, with nothing to add or subtract. (15:5)
- The correction peaks in the middle and dies at the ends. Ten degrees of course gives 50 minutes, forty gives 3 degrees 6 minutes, eighty gives an even 5 degrees, one hundred gives the maximum of 5 degrees 8 minutes, and it then falls back through 4 degrees 40 minutes at 120 and 59 minutes at 170 to nothing at 180. (15:6)
- Above 180, and between the tens. A correct course greater than 180 is subtracted from 360 to obtain its angle, as with the sun, and a course carrying units as well as tens is handled by taking the average increase per degree and adding the proportionate amount to the lower figure. (15:7)
RememberCrossing 180 degrees does not change the size of the correction. It reverses its direction, and every figure on the sheet still looks reasonable.
Part 3The worked example, start to finish
- Three starting figures, twenty-nine days out. For Friday night, the second of Iyar in the year taken as the starting point, the sun's mean is 35 degrees 38 minutes 33 seconds, the moon's mean at sighting is 53 degrees 36 minutes 39 seconds, and the mean within its path is 103 degrees 21 minutes 46 seconds. (15:8)
- Elongation, doubled, then five degrees added. Subtracting the sun's mean gives an elongation of 17 degrees 58 minutes 6 seconds, which doubles to 35 degrees 56 minutes 12 seconds, falling in the band that calls for five degrees, so the correct course is 108 degrees and 21 minutes. (15:8)
- The minutes of the course are discarded on purpose. As with the sun, the minutes are of no consequence in the calculation of the course, so the twenty-one minutes are dropped and the angle is taken for a course of 108. (15:8)
- Subtract, round the seconds, and read the constellation. The angle for 108 is 5 degrees and 1 minute, and since the course is below 180 it is subtracted from the moon's mean, leaving 48 degrees 35 minutes 39 seconds; the seconds are counted as a minute, placing the moon at 18 degrees 36 minutes of the nineteenth degree of Taurus. (15:9)
RememberHe carries seconds through five operations and then throws away twenty-one minutes, because he knows which precision buys an answer.