THE LUNAR CYCLE AND GOLDEN NUMBER.
In connecting the lunar month with the solar year, the framers of the
ecclesiastical calendar adopted the period of Meton, or lunar cycle, which
they supposed to be exact. A different arrangement has, however, been
followed with respect to the distribution of the months. The lunations are
supposed to consist of twenty-nine and thirty days alternately, or the
lunar year of 354 days; and in order to make up nineteen solar years, six
embolismic or intercalary months, of thirty days each, are introduced in
the course of the cycle, and one of twenty-nine days is added at the end.
This gives (19 x 354) + (6 x 30) + 29 = 6935 days, to be distributed among
235 lunar months.
But every leap-year one day must be added to the lunar month in which the
29th of February is included. Now if leap-year happened on the first,
second or third year of the period, there will be five leap-years in the
period, but only four when the first leap-year falls on the fourth. In the
former case the number of days in the period becomes 6940, and in the
latter 6939. The mean length of the cycle is, therefore, 6939-3/4 days,
agreeing exactly with nineteen Julian years. By means of the lunar cycle
the new moons of the calendar were indicated before the reformation in
1582. As the cycle restores these phenomena to the same days of the civil
month, they will fall on the same days in any two years which occupy the
same place in the cycle; consequently a table of the moon's phases for
nineteen years will serve for any year whatever when we know its number in
the cycle.
The number of the year in the cycle is called the Golden Number; either
because it was so termed by the Greeks, who, on account of its utility,
ordered it to be inscribed in letters of gold in their temples, or more
probably because it was usual to distinguish it by red letters in the
calendar. The Golden Numbers were introduced into the calendar about the
year 530, but disposed as they would have been if they had been inserted
at the time of the Council of Nice. The cycle is supposed to commence with
the year in which the new moon falls on the first day of January, which
took place the year preceding the commencement of our era.
Hence to find the Golden Number for any year, we have the following rule:
Add one to the date, divide the sum by nineteen; the quotient is the
number of cycles elapsed, and the remainder is the Golden Number. Should
there be no remainder, the proposed year is, of course, the last or
nineteenth of the cycle. Thus, for the year 1892, we have (1892 + 1) / 19
= 99, remainder 12; therefore, 99 is the number of cycles, and 12 the
number in the cycle, or the Golden number.
It ought to be remarked that the new moons determined in this manner, may
differ from the astronomical new moons sometimes as much as two days. The
reason is, that the sum of the solar and lunar inequalities which are
compensated in the whole period, may amount in certain cases to 10 degrees
and thereby cause the new moon to arrive on the second day before or after
its mean time.
The cycle of the sun brings back the days of the month to the same day of
the week; the cycle of the moon restores the new moons to the same day of
the month; therefore, 28 x 19 = 532 years, includes all the variations in
respect of the new moons and the dominical letter, and is consequently a
period after which the new moons again occur on the same day of the month
and the same day of the week. This is called the Dionysian or Great
Paschal Period, from its having been employed by Dionysius Exiguus in
determining Easter Sunday.