VOL. XLVI.] PHILOSOPHICAL TRANSACTIONS. 37 



that number only, and not 11, is to be added to the epact of the preceding, to 

 form the epact of that, the then present year , by which a new set of epacts will 

 be introduced, all less by one than their precedent corresponding epacts : and 

 the golden numbers nmst be set a day forwarder in the calendar ; that is, be 

 prefixed to the day following that against which they stood in the precedent hun- 

 dred years. 



This method would preserve a sort of regularity between the solar and the 

 lunar years ; and, by means of the rules and directions before mentioned, the 

 days of the new moons might be pointed out, either by the golden numbers or 

 by the epacts, placed in the calendar for that purpose ; according to the Julian 

 account for ever, and according to the Gregorian account till the year 4199 in- 

 clusive, after which there must be some little variation made in the 4 last precepts 

 or rules; but it would be to little purpose now, to attempt the framing of a new 

 set of rules for so distant a time. 



The Gregorians have chosen to make use of the epacts to determine the days 

 of the new moons, and follow pretty nearly the niles prescribed above ; except 

 that they order the epacts to have an additional augmentation of a unit 8 times 

 in 2500 years, beginning with the year 1 800, as at the end of 400 years ; to which 

 400 years if there be added 3 times 700, or 2100 years, the period of 2500 years 

 will be completed in the year 3Q00. After which they do not make their extra- 

 ordinary augmentation of a unit in the epacts, till at the end of another term of 

 400 years ; which defers that augmentation from the year 4200 to the year 

 4300. And this is the reason that the rules above delivered will require a vari- 

 ation in the year 4200 ; whereas it is directed in this paper that the epacts should 

 be augmented, or (which is the same thing) the golden numbers be set back in 

 the calendar Q times in 2800 years. This arises from the Gregorians supposing, 

 that the difference between 19 solar and as many lunar years, would not amount 

 to a whole day in less than 312^ years ; whereas it has appeared above, that it 

 would amount to a whole day in 310.7 years. But though the rule prescribed in 

 this paper comes much nearer the truth, yet the error in either case is very in- 

 considerable, being so small as not to amount to a whole day in many thousand 

 years; and therefore is not worth regarding. 



Of fading Easter. — From what has been said, a method may be obtained for 

 fixing, with sufficient exactness, the time of the celebration of the feast of Easter, 

 which is governed by the vernal equinox, and by the age of the moon nearest 

 to it. The former of which, when once rightly adjusted, may, (by the corrections 

 mentioned in that part of this paper which relates to the solar year) be made to 

 continue to fall at very near the same time with, or at most not to differ a whole 

 day from the true equinox : and the same rules and directions which, as before 

 shown, would without any great error, point out the times of the first day of the 



