After reading Harold King's experience you might be wondering how he calculated the date of the Memorial by looking at the position of the moon from his prison cell. So I looked up some additional info about the spring equinox in relation to the establishment of the Lord's Evening Meal...but first, here's some backround info on the Jewish Calendar and agricultural timetable.
(Calendar on pg 9, of the 06/15/07 Watchtower)
NISAN (ABIB): March—April
IYYAR (ZIV): April—May
TISHRI (ETHANIM): September—October
HESHVAN (BUL): October—November
(The following excerpts from pgs 389-392 of the Insight on the Scriptures, Vol. 1)
Various calendar systems have been developed by men in the past, and a number continue in use today. Early calendars were mainly lunar calendars, that is, the months of the year were counted by complete cycles of the moon, as, for example, from one new moon to the next new moon. On the average, such lunation takes about 29 days, 12 hours, and 44 minutes. The months were usually counted as of either 29 or 30 days, but in the Bible record the term “month” generally means 30 days.—Compare De 21:13; 34:8; also Re 11:2, 3.
A year of 12 lunar months falls nearly 11 days short of a solar year of 365 1⁄4 days. Since the solar year determines the return of the seasons, there was need to adjust the calendar to this solar year, and this resulted in what are called lunisolar, or bound solar, years—that is, years in which the months were lunar but the years were solar. This was done by the addition of a number of days each year or of an additional month during certain years to compensate for the shortness of the 12 lunar months.
The Israelites used such a lunisolar, or bound solar, calendar. This is evident from the fact that Jehovah God established the beginning of their sacred year with the month Abib in the spring and specified the celebration of certain festivals on fixed dates, festivals that were related to harvest seasons. For these dates to have coincided with the particular harvests, there had to be a calendar arrangement that would synchronize with the seasons by compensating for the difference between the lunar and solar years.—Exodus 12:1-14; 23:15, 16; Leviticus 23:4-16.
Whereas the sacred year began in the spring with the month Abib (or Nisan) by God’s decree at the time of the Exodus (Ex 12:2; 13:4), the Bible record indicates that prior to this the Israelites had counted the year as running from fall to fall. God gave recognition to this arrangement so that, in effect, there was a dual system of a sacred and a secular or agricultural calendar used by his people. (Ex 23:16; 34:22; Le 23:34; De 16:13) In postexilic times, Tishri 1, in the last half of the year, marked the beginning of the secular year, and the Jewish New Year, or Rosh Hashanah (head of the year), is still celebrated on that date.
The Bible does not indicate what method was originally used to determine when additional days or an additional, or intercalary, month should be inserted. It is logical, however, that either the vernal or the autumnal equinox served as a guide to indicate when the seasons were falling behind sufficiently to require calendar adjustment. Though not specifically mentioned in the Bible, a 13th month that was added by the Israelites to accomplish this adjustment was called, in postexilic times, Veadar, or the second Adar.
We do not find record of a definitely fixed or standardized form of Jewish calendar until the fourth century of our Common Era (c. 359 C.E.), when Hillel II specified that the leap years of 13 months should be the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th of each 19 years. Such a 19-year cycle is commonly called the Metonic cycle, after the Greek mathematician Meton (of the fifth century B.C.E.), although there is also evidence that such a cycle was perfected before him by the Babylonians. (See Babylonian Chronology, 626 B.C.–A.D. 75, by R. A. Parker and W. H. Dubberstein, 1971, pp. 1, 3, 6.) This cycle takes into account that every 19 years the new and the full moons fall again on the same days of the solar year.
The Jewish months ran from new moon to new moon. (Isaiah 66:23) One Hebrew word, cho′dhesh, “month” (Genesis 7:11), comes from a root meaning “new,” while another word for month, ye′rach, means “lunation.”
(by-the-way, there's even more detailed info in the Insight book, if you want to do more 'indepth' research on this topic)
(the following info is from pg 268 of the Insight on the Scriptures Vol. 2)
The Lord's Evening Meal
Time of Its Institution: The Passover was always observed on Nisan (Abib) 14, being on or near the day of full moon, inasmuch as the first day of every month (lunar month) in the Jewish calendar was the day of the new moon, as determined by visual observation. Therefore the 14th day of the month would be about the middle of a lunation. The date of Jesus’ death is shown...to be Nisan 14, 33 C.E. Concerning the day of his death as reckoned on the Gregorian calendar, astronomical calculations show that there was an eclipse of the moon on Friday, April 3, 33 C.E. (Julian calendar), which would be Friday, April 1, on the Gregorian calendar. (Oppolzer’s Canon of Eclipses, translated by O. Gingerich, 1962, p. 344) Eclipses of the moon always occur at the time of full moon. This evidence strongly indicates that Nisan 14, 33 C.E., fell on Thursday-Friday, March 31–April 1, 33 C.E., on the Gregorian calendar.
It was on the evening before his death that Jesus observed his last Passover meal and afterward instituted the Lord’s Evening Meal. Even before the Memorial meal began, the traitorous Judas was sent out, at which time, according to the record, “it was night.” (John 13:30) Since the days of the Jewish calendar ran from evening of one day to evening of the next, the Lord’s Evening Meal was celebrated also on Nisan 14, on Thursday evening, March 31.
(So for calculating the day of the observance in modern times here's what the Reasoning Book says on pg 269):
Jehovah’s Witnesses observe the Memorial after sundown on Nisan 14, according to the reckoning of the Jewish calendar that was common in the first century. The Jewish day begins at sundown and extends until the following sundown. So Jesus died on the same Jewish calendar day that he instituted the Memorial. The beginning of the month of Nisan was the sunset after the new moon nearest the spring equinox became visible in Jerusalem. The Memorial date is 14 days thereafter. (Thus the date for the Memorial may not coincide with that of the Passover kept by modern-day Jews. Why not? The start of their calendar months is set to coincide with the astronomical new moon, not the visible new moon over Jerusalem, which may come 18 to 30 hours later. Also, most Jews today keep the Passover on Nisan 15, not on the 14th as did Jesus in harmony with what was stated in the Mosaic Law.)
*I'm gonna post some archaeological info on this subject tomorrow...