the year is embolismic when R < 7.
The calendar is constructed on the assumptions that the mean lunation is 29
days 12 hours 44 min. 3-1/3 sec., and that the year commences on, or
immediately after, the new moon following the autumnal equinox. The mean
solar year is also assumed to be 365 days 5 hours 55 min. 25-25/57 sec., so
that a cycle of nineteen of such years, containing 6939 days 16 hours 33
min. 3-1/3 sec., is the exact measure of 235 of the assumed lunations. The
year 5606 was the first of a cycle, and the mean new moon, appertaining to
the 1st of Tisri for that year, was 1845, October 1, 15 hours 42 min.
43-1/3 sec., as computed by Lindo, and adopting the civil mode of reckoning
from the previous midnight. The times of all future new moons may
consequently be deduced by successively adding 29 days 12 hours 44 min.
3-1/3 sec. to this date.
To compute the times of the new moons which determine the commencement of
successive years, it must be observed that in passing from an ordinary year
the new moon of the following year is deduced by subtracting the interval
that twelve lunations fall short of the corresponding Gregorian year of 365
or 366 days; and that, in passing from an embolismic year, it is to be
found by adding the excess of thirteen lunations over the Gregorian year.
Thus to deduce the new moon of Tisri, for the year immediately following
any given year (Y), when Y is
ordinary, subtract (10)(11) days 15 hours 11 min. 20 sec.,
embolismic, add (18)(17) days 21 hours 32 min. 43½ sec.
the second-mentioned number of days being used, in each case, whenever the
following or new Gregorian year is bissextile.
Hence, knowing which of the years are embolismic, from their ordinal
position in the cycle, according to the rule before stated, the times of
the commencement of successive years may be thus carried on indefinitely
without any difficulty. But some slight adjustments will occasionally be
needed for the reasons before assigned, viz. to avoid certain festivals
falling on incompatible days of the week. Whenever the computed conjunction
falls on a Sunday, Wednesday or Friday, the new year is in such case to be
fixed on the day after. It will also be requisite to attend to the
following conditions:--
If the computed new moon be after 18 hours, the following day is to be
taken, and if that happen to be Sunday, Wednesday or Friday, it must be
further postponed one day. If, for an ordinary year, the new moon falls on
a Tuesday, as late as 9 hours 11 min. 20 sec., it is not to be observed
thereon; and as it may not be held on a Wednesday, it is in such case to be
postponed to Thursday. If, for a year immediately following an embolismic
year, the computed new moon is on Monday, as late as 15 hours 30 min. 52
sec., the new year is to be fixed on Tuesday.
After the dates of commencement of the successive Hebrew years are finally
adjusted, conformably with the foregoing directions, an estimation of the
consecutive intervals, by taking the differences, will show the duration
and character of the years that respectively intervene. According to the
number of days thus found to be comprised in the different years, the days
of the several months are distributed as in Table VI.
The signs + and - are respectively annexed to Hesvan and Kislev to indicate
that the former of these months may sometimes require to have one day more,
and the latter sometimes one day less, than the number of days shown in the
table--the result, in every case, being at once determined by the total
number of days that the year may happen to contain. An ordinary year may
comprise 353, 354 or 355 days; and an embolismic year 383, 384 or 385 days.
In these cases respectively the year is said to be imperfect, common or
perfect. The intercalary month, Veadar, is introduced in embolismic years
in order that Passover, the 15th day of Nisan, may be kept at its proper
season, which is the full moon of the vernal equinox, or that which takes
place after the sun has entered the sign Aries. It always precedes the
following new year by 163 days, or 23 weeks and 2 days; and Pentecost
always precedes the new year by 113 days, or 16 weeks and 1 day.