7 | |Frid.|Thur.|Wed. |Tues.|Mon. |Sun. |Sat. |
| 7 | 14 | 21 | 28 | |Sat. |Frid.|Thur.|Wed. |Tues.|Mon. |Sun. |
+---+----+----+----+----+-----+-----+-----+-----+-----+-----+-----+

By means of the lunar cycle the new moons of the calendar were indicated
before the Reformation. 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 19 years will serve for any year whatever when we know
its number in the cycle. This number is called the _Golden Number_, either
because it was so termed by the Greeks, or because it was usual to mark it
with 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 Nicaea. The cycle is
supposed to commence with the year in which the new moon falls on the 1st
of January, which took place the year preceding the commencement of our
era. Hence, to find the Golden Number N, for any year x, we have N = ((x +
1) / 19)_r, which gives the following rule: _Add 1 to the date, divide the
sum by 19; the quotient is the number of cycles elapsed, and the remainder
is the Golden Number._ When the remainder is 0, the proposed year is of
course the last or 19th of the cycle. 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 deg., and thereby cause the new moon to
arrive on the second day before or after its mean time.

_Dionysian Period._--The cycle of the sun brings back the days of the month
to the same day of the week; the lunar cycle 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 letters, 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, familiarly styled "Denys the Little," in determining Easter
Sunday. It was, however, first proposed by Victorius of Aquitain, who had
been appointed