Other Evidences of a Continuous Rotation
Three times in the year all the twenty-four orders of priests were alike entitled to share the pieces of offerings of the festival, and in the shewbread; and on the Feast of Pentecost the distributors say to each priest: “Here is leavened bread for thee, and here is unleavened bread for thee.” The order of priests whose regular time of service occurs in the festivals offer the continual daily offerings, vows, and voluntary offerings, and all congregational offerings, and every sacrifice.
Suk 5:5
This means that a division on duty does not serve a part week, skip a week, and then serve a part week during a festival season. That idea was the basis of N1AS. If the shortest length lunar year is worked out, it will be seen that skipping weeks at the three feasts makes it take 51 weeks to complete the rotations (24*2+3=51). But a lunar year can be as short as 50 weeks and 3 days. It is quite clear that the year can be cut short at 23 divisions, and then start again at 1, omitting the 24th, in an N1AS system. The disorderliness of serving part weeks also does not make sense.
Jack Finegan states:
A saying of Rabbi Abbahu (AD c. 300) recorded in the Jerusalem Talmud (y. Sukka 5.7-8) appears to imply supposition (no. 2) of unbroken succession of the courses. It was a Jubilee-year custom that a piece of arable land previously owned by a particular priestly course would revert to the priesthood as a whole and then be assigned for the next Jubilee period of 49...years to the course which was on duty at the beginning of the new Jubilee. Abbahu made a calculation and found that, at the beginning of each new Jubilee year, a different course was on duty until each of the twenty-four had had a turn, a situation which would not follow if the sequence of courses always began at the same time (a new year) each year. Thus, the system of unbroken succession would provide equal fairness to each of the priestly courses, and Abbahu believed that this bore witness to the wisdom of David...The supposition is accepted, for example by Lewin in his Fasti Sacri.
Finegan, §242, Handbook of Biblical Chronology, rev. ed.
Rabbi Abbahu certainly believed that the courses were continuous. For his conjecture would be obviously wrong if T1A, N1A, or N1AS were used. In any case the issue behind his conjecture was a supposed tradition, and his calculations were wrong. With CRT, in a space of 24 Jubilees (both 49 and 50 year versions) the same division comes up twice on the day of atonement multiple times while others are left out completely. Here is the test, where I calculate 24 Jubilees using the 49 year method and the 50 year method, and then determine who is on duty on the Day of Atonement, when the Jubilee trumpet is blown, using the rotation formula for the first Temple. Rabbi Abbahu’s calculation is incorrect.
49 Yr Method 50 Yr Method
BC………… NO JD of Yom Kippur D#………… BC…… Yom Kippur D#
1004 1 1354973 11 1003 1355357 17
955 2 1372897 4 953 1373607 8
906 3 1390793 16 903 1391885 3
857 4 1408512 4 853 1410136 18
808 5 1426584 17 803 1428415 14
759 6 1444480 6 753 1446664 5
710 7 1462376 19 703 1464915 20
661 8 1480271 7 653 1483195 15
612 9 1498166 19 603 1501444 6
563 10 1516062 8 553 1519724 2
514 11 1533957 20 503 1537974 17
465 12 1551854 9 453 1556223 8
416 13 1569748 21 403 1574503 3
367 14 1587644 10 353 1592753 18
318 15 1605540 23 303 1611032 14
269 16 1623435 11 253 1629282 5
220 17 1641331 24 203 1647532 20
171 18 1659226 12 153 1665812 15
122 19 1677122 1 103 1684062 7
73 20 1695017 13 53 1702341 2
24 21 1712913 2 3 1720591 17
26 22 1730808 14 54 1741055 12
75 23 1748734 7 104 1759305 4
124 24 1766599 15 154 1777585 23
Even though this Rabbi was incorrect in his calculations, at least he believed the rotations were continuous. Of course, if the rotations had been otherwise (as in T1A, N1A) then the results would have been worse, since the same division would always be on duty at the beginning of Tishri.
The first argument that Beckwith brings against Lewin, on the issue of continuous rotations is that there is no way keep it orderly:
[He alleges that the CRT method] gave them no yardstick for checking which course ought to be on duty at a particular time, should doubt or disagreement arise.
Calendar & Chronology, Jewish & Christian, pg. 79
Beckwith has not given this much sensible thought. Firstly, the plain method of counting 24 weeks from ones last service to one’s next service works as long as one is diligent to count. The Law requires counting of Sabbaths, counting of the Sabbatical year, counting of the Jubilee, and counting of weeks, days, and Sabbaths to the feast of Weeks. The Egyptians managed to count twelve thirty day months, with 5 leaps days, in their calendar, for centuries after centuries, without any anchor in the actual new moon or the actual year. Their calendar wandered the seasons, yet they managed to keep the sequence of days without missing one! The fact that we can locate the 25 year lunar cycles in their calendar shows that they kept it straight. Also Israel managed to count the days of the week to the Sabbath from the beginning to the present, without missing a day. I show several points where modern astronomical calculation confirms that the count has not been lost.
But there are additional ways that the priests can double check their counting. Firstly, every other division is counting also to their week of service. So one can always cross check with someone of another division what week they are on. Also the chief priests in the Temple surely had accounts and a calendar to mark off daily and weekly.
If the priests wanted to, they could estimate the calendar date that they were due to return. Firstly they take note of the month and day on which their last service began. Now there are 168 days between services of the divisions (24 x 7 = 168). Every division serves 168 days from its last service, or 24 weeks. The priest who wishes a calendar date of his next service adds 5 months and 20 days to his last date of service (29.5 * 5 + 20 = 167.5). Say that the date of the Sabbath beginning the last service was 10/22 (22nd day of the 10th month). Adding 5 to the 10th month is 15, and adding 20 to the 22nd day is 42. If needed Subtract 30 days and add 1 month. It is needed in this case, result: 16/12. If the month number is greater than 12, adjust for Adar II. That is necessary in this case. In the case of no Adar II, subtract 12 from the months: 4/12. The next service will be the sabbath nearest to 4/12 of the next year. In the case of Adar II subtract 13 from the months: 3/12. The next service will be the Sabbath nearest to 3/12 next year. If this is hard for any priests in 28/30 cases the math brain in the Temple can give them a date nearest to their next Sabbath of service.
The reason that there are 2/30 cases in which a date cannot be given, is because Adar II is in doubt when the Spring Equinox falls on Nisan 4-5. Coming round a year from Nisan 4 takes one 11 days past the Nisan 4 to the next equinox, and lands it right on Nisan 15 or 16. The case is too close to call a year in advance in those days. The assumed Nisan might have to become an Adar II. They had to observe so as to make sure Passover would fall in the new year. If the last year began on Nisan 4 or Nisan 5, (i.e. the spring equinox, 11 days before Passover, as the lunar year is 11 days shorter than the solar), then no one can really tell if there will be an Adar II until the 13th new moon is seen. In this case the priests just remember their return day without the Adar II (4/12 in the example above), and if one happens, they subtract one month. The amount of time is exactly the same in either case. It is just arithmetic to confirm weekly counting and double check it. Probably most people calculated without Adar II, and then they simply adjusted for it when it happened. The lunar clock is regular enough that it is always clear which Sabbath lands closest to the date. There are a few other ways of counting. If the people are required to count seven weeks once a year, then surely the priests who teach them that can handle 24! And if they mess up, the scribes and teachers in the Synagogues have been noting the weeks of each priestly course every Sabbath.
It has been suggested that Israel would forget the order of the priestly rotations with a disruption like that of Antiochus Epiphanes. The Temple was made desolate by him for a little over three years. Did the people forget when the Sabbath was during those years? No. Then why should the priests who rotate in and out on the Sabbaths forget their position. Three years is not enough time for hope of return to die. The Law and Prophets make it clear that counting is necessary to keep it. Accurate counting is a religious duty and part of orderliness, which is next to Godliness. Even after the destruction of the Second Temple, the order of the divisions was recounted for at least the next half century, and remembered by scholars for the next hundred years after that. And not only that, but they wrote down the date of the last division to serve in the Temple.
Recovering the order of the divisions is remarkably easy if one is armed with certain facts. Firstly, one needs a standard era that is in practice. The books of Maccabees used the Seleucid Era. Next one needs only note which division was serving at the spring equinox in a given year, and which day of the week the sun set due west. Then using the knowledge of the Babylonians or the Greeks on the length of the year (better than 365.25 which is good enough), one can work out the weekly position of the divisions for the next hundred years without anyone having to count during the whole time. I know this because I simulated it using 365.25 days and simply adding the weeks of the divisions from equinox to equinox. As long one avoids the borderline numbers, the correct rotation can be worked out. This is because the real year (365.2422) does not deviate enough from the schematic year to upset the weekly synchronization in the space of 100 years. It would take about 300 years to screw everything up. But I do not think that any such measure was ever taken, because it was never needed. During the short periods of disruption (three years was the longest) by the Greeks and the Romans (before AD 70) the priests were diligent to keep their rotations in place, even when they were prevented from serving.
The Qumran Scribes regarded the rotations as a method of dating. For that is how they chronicled events in 4Q323-4Q324. See Eiseman and Wise, The Dead Sea Scrolls Uncovered, “Aemilius Kills” (pg. 119). Aemililus was Pompey’s General Scaurus. Also mentioned are Queen Shalome, John Hyrcanus, and other figures familiar from Josephus’ Antiquities. If keeping a calendar of the times of the priestly rotations was such a difficult task for the Jews as Beckwith suggests, then it really begs the question why they used it for dating events surrounding the time of Pompey’s vandalism of the Temple in 64 or 63 BC.