This is a “Rough 'n Ready” computation, somewhat mechanical. This scholastic exercise may not take in some subtle features that may have occurred for those Calendar Dates.
1. Jehoiarib is on Duty during the Destruction of the Second Temple as given in the Babylonian Talmud:
“Whence do we know that the second Temple was also destroyed on the 9th of Abh? We have learned in a Boraitha: " A happy event is credited to the day on which another happy event happened. while a calamity is ascribed to the day when another calamity occurred: and it was said that when the first Temple was destroyed it was on the eve preeeding the 9th of Abh, which was also the night at the close of the Sabbath and also the close of the Sabbatical year. The watch at the time was that of Jehoyoreb, and the Levites were chanting in their proper places...This happened also at the destruction of the second Temple….”
Josephus, Wars…, 6, 4, 5:
“So Titus retired into the tower of Antonia, and resolved to storm the temple the next day, early in the morning, with his whole army, and to encamp round about the holy house. But as for that house, God had, for certain, long ago doomed it to the fire; and now that fatal day was come, according to the revolution of ages; it was the tenth day of the month Lous, [Ab,] upon which it was formerly burnt by the king of Babylon...”
There may yet be some interesting math here with Josephus, but let's move on.
2. http://www.cgsf.org/dbeattie/calendar/?roman=70 .
http://aa.usno.navy.mil/data/docs/JulianDate.php
Look at the chart and find the Tenth of Ab. It's listed as August 5, 70. Lets convert to a Julian Day:
“The Julian date for CE 70 August 5 00:00:00.0 UT is
JD 1746841.500000”
Jehoiarib rotates in on August 4, 70, “Sunset to Sunset”. If August 5 is JD 1746841.500000, then August 4 is JD 1746840.5 This an Anchor Date for the entire Work. If there are Blocks of 168 Days for Mishmarot Rotation, we still have no one Date to fit to the Rotation. The Course of Jehoiarib at the Destruction of the Temple gives us that Anchor Date.
If we compute another date based on the Sabbath, we will get some Mishmarot Group coming to Duty. Let's continue with Jehoiarib. If a Julian Date is given for that Sabbath, subtract the Julian Date from the Sabbath Date of Jehoiarib at the fall of the Temple (Make decision as to the Start of the Week or the End of the Week) Divide by 168. If the remainder is Zero, that means that Jehoiarib started (or ended) the week on that date.
Jehoiarib 1720128
JD 1720128.500000 is
BCE 4 June 16 00:00:00.0 UT Saturday
1746840 – 1720128 = 26712. 26712 / 168 = 159. NO REMAINDER.
Jehoiarib was on Duty for the week of June 16, 4 BCE.
The question now becomes, “When did Immer have Mishmarot Service and was it during Passover?
Immer is 7 weeks “ahead” of Jehoiarib – for ease of calculating – and that is 63 days.
1720128 – 63 = 1720065.
JD 1720065.500000 is
BCE 4 April 14 00:00:00.0 UT Saturday
The Dates for Passover: http://www.observadores-cometas.com/com ... sover.html
Compare with the Hebrew/ Roman Calendar, given above. No differences for computational purposes.
April 11, 4 BCE.
Immer was on Duty for Passover Week, 4 BCE.
It is easy to show that Immer was on Duty for the 9 CE Passover as well.
Eisenman and Wise, The Dead Sea Scrolls Uncovered, ISBN-13 978-15661-9623-9, p 108:
“In all their timekeeping, the authors of the Qumran Calendars reckoned not only by months, but also by the rotation of the Priestly Courses (mishmarot)...Qumran texts relied upon this 'eternal cycle' not only for their calendar units, but for their chronography and historiography...Every sabbath, month, year and feast bore the name of a priestly family.”