by Pope Hilary to revise and correct the church calendar.
Hence it is also called the _Victorian Period_. It continued in use till
the Gregorian reformation.

_Cycle of Indiction._--Besides the solar and lunar cycles, there is a third
of 15 years, called the cycle of indiction, frequently employed in the
computations of chronologists. This period is not astronomical, like the
two former, but has reference to certain judicial acts which took place at
stated epochs under the Greek emperors. Its commencement is referred to the
1st of January of the year 313 of the common era. By extending it
backwards, it will be found that the first of the era was the fourth of the
cycle of indiction. The number of any year in this cycle will therefore be
given by the formula ((x + 3) / 15)_r, that is to say, _add 3 to the date,
divide the sum by 15, and the remainder is the year of the indiction_. When
the remainder is 0, the proposed year is the fifteenth of the cycle.

_Julian Period._--The Julian period, proposed by the celebrated Joseph
Scaliger as an universal measure of chronology, is formed by taking the
continued product of the three cycles of the sun, of the moon, and of the
indiction, and is consequently 28 x 19 x 15 = 7980 years. In the course of
this long period no two years can be expressed by the same numbers in all
the three cycles. Hence, when the number of any proposed year in each of
the cycles is known, its number in the Julian period can be determined by
the resolution of a very simple problem of the indeterminate analysis. It
is unnecessary, however, in the present case to exhibit the general
solution of the problem, because when the number in the period
corresponding to any one year in the era has been ascertained, it is easy
to establish the correspondence for all other years, without having again
recourse to the direct solution of the problem. We shall therefore find the
number of the Julian period corresponding to the first of our era.

We have already seen that the year 1 of the era had 10 for its number in
the solar cycle, 2 in the lunar cycle, and 4 in the cycle of indiction; the
question is therefore to find a number such, that [v.04 p.0994] when it is
divided by the three numbers 28, 19, and 15 respectively the three
remainders shall be 10, 2, and 4.

Let x, y, and z be the three quotients of the divisions; the number sought
will then be expressed by 28 x + 10, by 19 y + 2, or by 15 z + 4. Hence the
two eq