same order. Hence the following
table of dominical letters for four hundred years will serve to show the
dominical letter of any year in the Gregorian calendar for ever. It
contains four columns of letters, each column serving for a century. In
order to find the column from which the letter in any given case is to be
taken, strike off the last two figures of the date, divide the preceding
figures by four, and the remainder will indicate the column. The symbol X,
employed in the formula at the top of the column, denotes the number of
centuries, that is, the figures remaining after the last two have been
struck off. For example, required the dominical letter of the year 1839? In
this case X = 18, therefore (X/4)_r = 2; and in the second column of
letters, opposite 39, in the table we find F, which is the letter of the
proposed year.

It deserves to be remarked, that as the dominical letter of the first year
of the era was B, the first column of the following table will give the
dominical letter of every year from the commencement of the era to the
Reformation. For this purpose divide the date by 28, and the letter
opposite the remainder, in the first column of figures, is the dominical
letter of the year. For example, supposing the date to be 1148. On dividing
by 28, the remainder is 0, or 28; and opposite 28, in the first column of
letters, we find D, C, the dominical letters of the year 1148.

_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 [v.04 p.0993] 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 happens 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 t