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. CHAPTER IV. CYCLE OF INDICTION, AND THE JULIAN PERIOD. The cycle of Indiction or Roman Indiction, is a period of fifteen years; not astronomical like the two former, but entirely arbitrary. Its origin and the purpose for which it was established are alike uncertain; but it is conjectured that it was introduced by Constantine the Great, about the year 312 of the common era, and had reference to certain judicial acts that took place under the Greek emperors at stated intervals of fifteen years. In chronological reckoning, it is considered as having commenced on the first day of January of the year 313. By extending it backward, it will be found that the cycle commenced three years before the beginning of our era. In order, therefore, to find the number of any year in the cycle of indiction, we have this rule: Add three to the date, divide the number by fifteen; and the remainder is the year of the indiction. Should there be no remainder, the proposed year is the fifteenth or last of the cycle. Thus, for the year 1892, we have (1892 + 3) / 15 = 126, remainder 5. Therefore, 5 is the number in the cycle. The Julian period, proposed by the celebrated Joseph Scaliger, as an universal measure of chronology, is a period of 7980 years, and is formed by the continual multiplication of the three numbers, 28, 19 and 15; that is, of the cycle of the sun, the cycle of the moon, and the cycle of indiction. Thus, (28 x 19 x 15) = 7980. In the course of this long period no two years can be expressed by the same numbers in all the three cycles.