| 4,000 | years is | (1d. 0h. 52m.) - 1 day = | 52m. |
| 100,000 | " " | (52m. × 25) = | 21h. 40m. |
J.—PAGE [89].
Lilius, author of the “Extended Table of Epacts,” says, when the full moon falls on the 10th of March, the following moon, which happens 29 days later, is the paschal moon, making the 18th of April its latest possible date. For, says he, because of the double epact that occurs on the 4th and 5th of April that lunation has only 29 days. It may have been very convenient for Lilius, in his peculiar method of determining the date of the paschal moon, to give to that lunation only 29 days; but nevertheless, when he did so, it was at the expense of accuracy, for he makes a difference of 12 days in the date of the paschal moon of that year, and the year preceding, and only 10 days difference between that year and the succeeding year; whereas the difference is uniformly 11 days from year to year through the whole cycle of 19 years.
By referring to the table on the 93d page, it will be seen that, in fixing the date of the paschal moon, six times in a cycle of 19 years the full moon falls before the 21st of March, and in every instance except this one the following moon is reckoned by Lilius 30 days later. By this uniform method of determining the date of the paschal moon, we make the 19th of April instead of the 18th, its latest possible date; so it should be borne in mind that whenever the 19th of April is the date of the paschal moon, as indicated in the tables commencing with the 93d page, that Lilius, and probably most, if not all other authors, have the 18th.
Now it is admitted that notwithstanding the cumbersome apparatus employed by Lilius in his calculations, the conditions of the problem are not always satisfied, nor is it possible that they can be always satisfied by any similar method of proceeding. We admit that none of these calculations are perfectly exact, but the sum of the solar and lunar inequalities is compensated in the whole period, or corrections made at the end of certain periods, not by interrupting the order of a uniform method during the cycle of 19 years.
Now the table of epacts was introduced by Lilius himself, making the excess of the solar year beyond the lunar, in round numbers 11 days. Then why interrupt this order every 19 years, for a period of 114 years; that is from 1596 to 1710, by making the epact 12 days for one year, and the following year only 10? After which, from 1710 to 1900, a period of 190 years, according to Lilius’ own calculations, the epact is uniformly 11 days, coinciding exactly with the calculations made in this work.
Then again after the year 1900, he gives to that particular lunation, in every lunar cycle for a period of 304 years, only 29 days; and having done so, he is under the necessity of giving only 29 days to another lunation in the same cycle, and also to all the cycles in the period to avoid the absurdity of making the paschal moon fall twice on the same day in the course of a lunar cycle.
By reference to the 101st page, opposite the year 1905, it will be seen that the date of the paschal moon is the 19th of April. Lilius, by giving to that lunation only 29 days, makes its date the 18th; and then again in the year 1916, lest he should make the paschal moon fall twice on the 18th of April in the course of a lunar cycle, (a thing which cannot really occur) he for the first time in more than 400 years, gives only 29 days to a second lunation in the same cycle and of course to all the cycles in the period of 304 years. Now the epacts for a lunar cycle of 19 years are represented thus:
| 26 | ||||||||||||||||||||
| 0, | 11, | 22, | 3, | 14, | 25, | 6, | 17, | 28, | 9, | 20 | ||||||||||
| 27 | ||||||||||||||||||||
| 1, | 12, | 23, | 4, | 15, | 26, | 7, | 18 | |||||||||||||