1ET. XIV.

OF THE CALENDAR.

239

and it is easy to perceive, that all the new moonswhich happen sooner by a day, will take placeupon the day preceding that which in the formerperiod was marked eleven. After three hundredyears more, the epact will be thirteen, whichwill be a day still preceding that in the lattefperiod: and the same will happen with all theother epacts of the cycle. It was this kind ofanalysis, that gave Luilius the idea of placingthe epacts in their natural order, against thedays of the new moons in every year, for thefirst three hundred years ; and after that period,to place them in the order 1,12, 23, 4, 15, 26,7, 18, 29, xo, &c. instead of the former one:and so on.

This arrangement was simple and ingenious ;but the omission of three days in every fourhundred years, was a circumstance that occa-sioned some embarrassment. These years, hav-ing a day less than in the Julian account, thenew moons would happen a day later, and con*fequently the epact, at the end of the year, mustbe diminished accordingly. But as this orderis only interrupted once in a hundred years,Luilius imagined, that by subtracting unityfrom each of the epacts belonging to those newMoons, they might be made to serve for thesubsequent century. And as there are onlythirty possible series of these numbers, it wassufficient to shew by a table, what series be-

loneed