||Discourse on correctly determining the sixtieth day after Tishrei by R. David Friedländer. This R. Friedländer should not be confused with the maskil of the same name, for the second page has approbations from six leading Orthodox rabbis, namely R. Azriel Hildesheimer, R. Mordecai Amram Hirsch, R. Saul ben David Zevi, R. Nathan Adler, R. Meir Kristanfeller, and R. Feivel Palut. The first page is a detailed exposition of the issue, that is, determining the molad and tekufot. R. Friedländer addresses the problem, difficulties, and possible errors. On the final two pages he presents his calculations.
The present Jewish calendar is lunisolar, the months being reckoned according to the moon and the years according to the sun. A month is the period of time between one conjunction of the moon with the sun and the next. The conjunction of the moon with the sun is the point in time at which the moon is directly between the earth and the sun (but not on the same plane) and is thus invisible. This is known as the îåÉìÈã, molad ("birth," from the root éìã). The mean synodic month (or lunation) is 29 days, 12 hours, 44 minutes, and 3⅓ seconds (793 parts (halakim); in the Jewish system the hour is divided into 1,080 parts each of which is 3⅓ seconds). The solar year is 365 days, 48 minutes, and 46 seconds, which means that a solar year exceeds a lunar one (12 months) by about 11 days. The cycles of 12 lunar months must therefore be adjusted to the solar year, because although the Jewish festivals are fixed according to dates in months, they must also be in specific (agricultural) seasons of the year which depend on the tropical solar year. Without any adjustment the festivals would "wander" through the seasons and the "spring" festival (Passover), for example, would be celebrated eventually in winter, and later in summer. The required adjustment is realized by the addition of an extra month (Adar II) in each of seven out of the 19 years that constitute the small (or lunar) cycle of the moon (mahazor katan or mahazor ha-levanah). In 19 years the solar cycle exceeds the lunar by about 209 days, which are approximately 7 months. In Temple times this intercalation was decided upon in the individual years according to agricultural conditions (Tosef., Sanh. 2:2; Sanh. 11b); later, however, it was fixed to be in the years 3, 6, 8, 11, 14, 17, and 19 of the cycle.
In the calendar month only complete days are reckoned, the full (îÈìÅà, male) months containing 30, and the defective (çÈñÅø, haser) months 29 days. The months Nisan, Sivan, Av, Tishri, Shevat and (in a leap year) Adar I are always male; Iyyar, Tammuz, Elul, Tevet, and Adar (Adar II in a leap year) always haser, while Heshvan and Kislev vary. Hence, the common year contains 353, 354, or 355 days and the leap year 383, 384, or 385 days. For ritual purposes, e.g., in reckoning the times fixed for prayers or the commencement and termination of the Sabbath, the day is deemed to begin at sunset or at the end of twilight, and its 24 hours (12 in the day and 12 in the night) are "temporary" hours varying in length with the respective length of the periods of light and darkness. But in the reckonings of the molad the day is the equatorial day of 24 hours of unvarying length and is deemed to commence at 6 P.M., probably in terms of local Jerusalem time.