Q & A: The Lunar Leap Year (Part II)


Photo Credit: Jewish Press

Question: Why is there an extra month in the Jewish calendar every few years? And who decides whether a particular year should be a leap year or not?

Name Withheld
Toronto, Ontario


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Answer: Many years ago, my uncle HaRav Sholom Klass, zt”l, was asked a similar question. His reply can be found in his book Responsa of Modern Judaism Vol. I: Below we excerpt, with minimal adaptation, portions of his response that are relevant to our discussion:

“The history of the Jewish calendar goes back to the time of the Bible. It is divided into three periods: the Biblical, the post-Biblical, and the post-Talmudic. The first rested purely on the observation of the sun and the moon, the second on both observation and reckoning, and the third entirely on reckoning.

“The study of astronomy was largely due to the need to fix the dates of the festivals. The command (Deuteronomy loc. cit.) “You shall observe the month of springtime (Aviv)” made it necessary to be acquainted with the position of the sun, and the command “Also observe the moon and sanctify it” made it necessary to study the phases of the moon.

“The Torah does not provide any names for the Jewish months; it merely designates them by a number (for example, “Observe the first month”). The Talmud Yerushalmi (Rosh Hashana 1:2) explains that the Jews began to use names for the months during the time of the Babylonian exile. The ancient Babylonians were sufficiently advanced in astronomy to enable them to draw up almanacs in which the eclipses of the sun and the moon and the times of the new and full moon were predicted.

“There is no mention of an intercalary month in the Torah, and it is not known how the correction was applied in ancient times. In post-Talmudic times, Nissan, Sivan, Av, Tishrei, Kislev, and Shevat each had 30 days, and Iyar, Tammuz, Elul, Cheshvan, and Adar each had 29 days. In leap years Adar I had 30 days and Adar II had 29 days. According to Pirkei D’Rabbi Eliezer, there was a lunar-solar cycle of 48 years; i.e., the lunar and solar calendars were synchronized every 48 years. The Hellenists, Essenes, and early Christians followed this cycle.

“It appears from the Talmud (Rosh Hashana 23b) that in the times of the Second Temple the priests had a court to which witnesses came and reported. This function was afterward taken over by the civil court.

“The fixing of the lengths of the months and the intercalation of months was the prerogative of the Sanhedrin, which was headed by a Nasi, or patriarch. The entire Sanhedrin was not called upon to act in this matter; the decision was left to a special court of three. The Sanhedrin met on the 29th day of each month to await the report of the witnesses.

“Certain rules were in effect before the destruction of the Temple. The new moon could not occur before a lapse of 29 and a half days and two-thirds of an hour. If the new moon could not be determined exactly, one month was to have 30 full days and the next 29. (A month with 30 days is known as a “full month.”)

“The full months were not to be less than 4 in number nor more than 8, so the year could not be less than 352 days nor more than 356. After the destruction of the Temple (70 C.E.), R. Johanan ben Zakkai, the Nasi of the Sanhedrin, removed the Sanhedrin to the city of Yavneh. To this body he transferred decisions concerning the calendar which had previously belonged to the Nasi. After this, the witnesses of the new moon came directly to the Sanhedrin.

“Every two or three years, depending on the circumstances, an extra month was intercalated. The intercalation seems to have depended on actual calculation of the relative lengths of the solar and lunar years, which were handed down by tradition in the Nasi’s family. It was also possible to judge by the grain harvest. Moreover, if the month of Nissan arrived and the sun was at such distance from the vernal equinox that the equinox would not be reached by the 16th of the month, then this month was not called Nissan, but Adar II (Adar Sheni).

“On the evening before the announcement of the intercalation, the Nasi assembled certain scholars who assisted in this decision. It was then announced to the various Jewish communities by letters. To this epistle was added the reason for that intercalation. An example of one such letter of R. Gamaliel is described in Sanhedrin 11b: It once happened that R. Gamaliel was sitting on a step of the Temple hill and the well-known scribe Johanan was standing before him.

“’Take a sheet and write the following,’ said R. Gamaliel. ‘To our brethren, the Exiles of Babylon, and to those in Medea and to all the other exiled sons of Israel: May your peace be great forever! We beg to inform you that the doves are still tender and the lambs still too young and that the crops are not yet ripe. It seems advisable to me and to my colleagues to add thirty days to this year.’

“The country people and the inhabitants of Babylon were informed of the beginning of the month by fire signals, which were readily carried from station to station in the mountain country. These signals could not be carried to the exiles in Egypt, Asia Minor, and Greece, who, accordingly being left in doubt, celebrated two days as the new moon.

“Due to the weather, it was frequently impossible to observe the new moon. In order to remove any uncertainty with regard to length of the year on this account, it was ordained that the year should not have less than 4 nor more than 8 full months. After the fixing of the calendar, it was settled that the year should not have less than 5 nor more than 7 full months.

“Rabban Gamaliel II (80-116 C.E.) used to receive the reports of the witnesses in person and showed them representations of the moon to test their accuracy (Rosh Hashana 24a). On one occasion, he fixed the first of Tishrei after the testimony of two suspected witnesses. The accuracy of the decision was disputed by R. Joshua, who was thereupon commanded by the Nasi to appear before him on the day which was according to R. Joshua’s calculation Yom Kippur, prepared for travel (to show that he had accepted the decision that this day was not in fact Yom Kippur). This was an order with which he most reluctantly complied (Rosh Hashana 25a).

“During the persecution under Hadrian and in the time of his successor Antoninus Pius, the martyr R. Akiva and his pupils attempted to lay down rules for the intercalation of a month.

“Under the patriarchate of Simon III (14-163 C.E.), a great quarrel arose concerning the feast days and the leap year, which threatened to cause a permanent schism between the Babylonian and the Palestinian communities – a result which was averted only by the exercise of much diplomacy.

“Under the leadership of R. Judah I, called ‘the Holy’ (163-193), the Samaritans, in order to confuse the Jews, set up fire signal at improper times and thus caused the Jews to fall into error with regard to the day of the new moon (Rosh Hashana 22b). R. Judah accordingly abolished the fire signals and employed messengers. The inhabitants of countries that could not be reached by messengers before the feast were thus in doubt, and used to celebrate two days of holidays. By this time, the fixing of the new moon according to the testimony of witnesses seems to have lost its importance, and astronomical calculations were in the main relied upon.

“One of the great figures in the history of the calendar was Samuel [born about 165, died about 250], who was named ‘Yarhinai’ because of his great knowledge of the workings of the moon. He was an astronomer and it was said that he knew the courses of the heavens as well as the streets of his city (Berachot 58b). He was a director of a school in Nehardea [Babylonia], and while there he arranged a calendar of the feasts so that his fellow countrymen might be independent of Judea. He also calculated the calendar for sixty years. His calculations greatly influenced the subsequent calendar of Hillel II. A contemporary of his, R. Adda (born 183), also wrote a treatise on the calendar.

“Mar Samuel reckoned the solar year at 365 days and 6 hours and R. Adda at 365 days, 5 hours, 55 minutes and 25/57 seconds.

“Under the leadership of R. Judah III (300-330), the testimony of the witnesses with regard to the appearance of the new moon was received merely as a formality; the settlement of the day depended entirely upon calculation. This innovation seems to have been viewed with disfavor by some members of the Sanhedrin who wrote to both the Babylonians and the Alexandrian communities, advising them to follow the customs of their fathers and continue to celebrate two days. This advice was followed and is still followed by the majority of the Jews living outside of Israel.

“Under the reign of Constantinus (337-361), the persecutions of the Jews reached such a height that all religious exercises, including the computation and the calendar, were forbidden under pain of death. The Sanhedrin was apparently prevented from inserting the intercalary month in the spring; it accordingly placed it after the month of Av (July-August).

“These persecutions finally caused the patriarch Hillel II (330-365) to publish rules for the computation of the calendar, which had hitherto been regarded as a secret science. The political difficulties attendant upon the meetings of the Sanhedrin became so numerous in this period that R. Huna bar Abin made known the following secret of the calendar of Raba in Babylonia: Whenever it becomes apparent that the winter will last till the sixteenth of Nissan, make the year a leap year without hesitation.

“This promulgation of the calendar, though it destroyed the hold of the Nasi on the scattered Judeans, fixed the celebration of the Jewish holidays upon the same day everywhere. Later Jewish writers agree that Hillel II fixed the calendar in the year 670 of the Seleucidan era; that is, 4119 [in the Jewish calendar] or 359 C.E. Some, however, e.g. Isaac Israeli, have fixed the date as late as 500 C.E. Saadia Gaon afterward formulated calendar rules, after having disputed the correctness of the calendar established by the Karaites.”

We have included the following chart to explain the differences between the lunar and solar years. These charts also demonstrate the high accuracy of our intercalatory procedure. The great wisdom of our Sages is clearly evident.

Lunar month = 29 days, 12 hours, 793 chalakim*
Lunar year = 354 days, 8 hours, 48 minutes
Lunar Leap year = 383 days, 21 hours, 32.4 minutes
Solar year = 365 days, 6 hours


19-Year Lunar Cycle

12 x Lunar Years = 4,252 days, 9 hours, 36 minutes
7 x Leap Lunar Year = 2,687 days, 6 hours, 45.36 minutes
Total: 19-year cycle = 6,939 days, 16 hour, 36.36 minutes


19-Year Solar Cycle

19 x Solar Year = 6,939 days, 18 hours
Difference: 1 hour, 24.5 minutes every 19 years.
(See Tur Orach Chayyim 428, Hilchot Rosh Chodesh-Luach Ibbur).

 * Chelek = 1/18 minutes.


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