OF THE REFORMATION

2Z3

the epact cannot possibly exceed thirty ; in thiscafe, therefore, thirty must be subtracted; sothat instead of thirty-three, at the beginning ofthe fourth year, the epact will be only three.And by observing this rule, through a period ofnineteen years, the epacts will stand in the fol-lowing order, o, n, 22, 3, 14, 25, 6, 17, 28, 9,20, 1, 12, 2 Z, 4, 15, 26, 7, 18.

These epacts being placed against the days ofthe month in the calendar, on which the newmoons fell in each year, would have answeredthe same purpose with the golden numbers ; andhad the Metonic cycle been complete, the formwould have required no alteration : but this isnot the cafe; for after about sixteen of theseperiods, or three hundred years, the new moons,arriving sooner by twenty-four hours, wouldhappen on the preceding day; and therefore theepacts answering to those new moons, ought tobe augmented by unity. For supposing, thatthe second year of the lunar cycle had eleven forthe epact, then because the new moon, the pre-ceding year, arrived eleven days before the endof December, after three hundred years, thesame new moon, of the first year of the cycle,would arrive twelve days before the end of theyear ; and, consequently, the second year oughtnow to have twelve for the epact.

This number twelve, therefore, will be theindex of the new moons in that second year;

1 and