letters, constructed for
twenty-eight years, will serve to show the dominical letter of any given
year from the commencement of the era to the Reformation. The cycle, though
probably not invented before the time of the council of Nicaea, is regarded
as having commenced nine years before the era, so that the year _one_ was
the tenth of the solar cycle. To find the year of the cycle, we have
therefore the following rule:--_Add nine to the date, divide the sum by
twenty-eight; the quotient is the number of cycles elapsed, and the
remainder is the year of the cycle._ Should there be no remainder, the
proposed year is the twenty-eighth or last of the cycle. This rule is
conveniently expressed by the formula ((x + 9) / 28)_r, in which x denotes
the date, and the symbol r denotes that the remainder, which arises from
the division of x + 9 by 28, is the number required. Thus, for 1840, we
have (1840 + 9) / 28 = 66-1/28; therefore ((1840 + 9) / 28)_r = 1, and the
year 1840 is the first of the solar cycle. In order to make use of the
solar cycle in finding the dominical letter, it is necessary to know that
the first year of the Christian era began with Saturday. The dominical
letter of that year, which was the tenth of the cycle, was consequently B.
The following year, or the 11th of the cycle, the letter was A; then G. The
fourth year was bissextile, and the dominical letters were F, E; the
following year D, and so on. In this manner it is easy to find the
dominical letter belonging to each of the twenty-eight years of the cycle.
But at the end of a century the order is interrupted in the Gregorian
calendar by the secular suppression of the leap year; hence the cycle can
only be employed during a century. In the reformed calendar the intercalary
period is four hundred years, which number being multiplied by seven, gives
two thousand eight hundred years as the interval in which the coincidence
is restored between the days of the year and the days of the week. This
long period, however, may be reduced to four hundred years; for since the
dominical letter goes back five places every four years, its variation in
four hundred years, in the Julian calendar, was five hundred places, which
is equivalent to only three places (for five hundred divided by seven
leaves three); but the Gregorian calendar suppresses exactly three
intercalations in four hundred years, so that after four hundred years the
dominical letters must again return in the