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. 431/2 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 ma