Thus may the Rule and Method now used in the Church of England, be most easily adapted to shew the Time of Easter, as it is observed by the Gregorians, till the Year 1900; at which Time, and at the other proper succeeding Times, if the Golden Numbers in the Calendar shall either be advanced or set backward a Day, according the foregoing Rules and Directions for that Purpose, they will continue to shew us the New or the Full Moons, of the Church of Rome or the Gregorian Calendar with great Exactness, till the Year 4199: when, as has been already mentioned, there must be a little Variation made in those Rules and Directions.
There is however one Exception to those General Rules and Directions, which will be taken notice of in the next Paragraph.
Upon these Principles I framed the Table accompanying this Paper, and shewing, by means of the Golden Numbers, all the Gregorian Paschal Limits or Full Moons, from the Reformation of the Calendar, &c. by Pope Gregory to the Year 4199 inclusive. Which Space of Time is therein divided into sixteen unequal Portions or Periods; at the Beginning of each of which, all the Golden Numbers, when once they shall have been properly placed in the Calendar, must either be advanced or set back one Day, with respect to the Place where they stood in the preceding Period, agreeably to the foregoing Rules: Except those Numbers which shall happen to stand against the 4th and 5th of April to shew the Paschal New Moons, or against the 17th and 18th of the same Month to mark out the Paschal Full Moons; both which Numbers at some Times, and only one of them at others, must keep the same Place for that, which was allotted to them in the immediately preceding Period.
In order to determine at what Times, and on what Occasions, this Exception is to take Place; let it be observed, that, in the Months of January, March, May, and some others in our present Calendar, as well as in the Table above mentioned, some of the Golden Numbers stand double or in Pairs, and follow one the other immediately; whilst others, on the contrary, generally stand single and by themselves.
Now, when any of those Pairs, or two Numbers which usually accompany each other, happen, in pursuance of the foregoing Rules, to be prefixed the one to the 4th and the other to the 5th of April for the New Moons, or the one to the 17th and the other to the 18th of April for the Paschal Limits or Full Moons: And when any of those Numbers, which generally stand single, are prefixed, according to the said Rules, to the 5th of April for the New Moons, or to the 18th for the Full Moons: In these Cases those Pairs or single Numbers that are so situated; must not be set forward or advanced at the Beginning of the next Period, but must keep their Places during another Period, if the foregoing Rules direct all the Golden Numbers to be advanced a Day; which must be complied with in respect to all the other Golden Numbers, except those so situated as above. Instances whereof may be seen in the Table, under the respective Periods beginning with the Years 1900, 2600, 3100, and 3800.
But if, in Conformity to the foregoing Rules, all the Golden Numbers are to be set one Day backward; those Pairs or single Numbers, tho' situated as is above-mentioned, must not keep their Places, but must move one Day backward like all the other Golden Numbers; as they may be seen to do in the Periods beginning with the Years 2400 and 3600.
To give a plain and intelligible Account of the Reason, on which the Directions now given with respect to this Exception are founded, would extend this Paper, already too long, far beyond its due and proper Bounds. I shall therefore content myself with observing, that it depends chiefly upon the Nature of the Menses Pleni and Menses Cavi, into which the Lunar Year is usually divided: and that, in order to make use of the Golden Numbers for finding the Time of the Gregorian Easter, it will be necessary not only to conform to the general Rules laid down in the former Part of this Paper; but also to follow the Directions just now given, with respect to the above-mentioned Exception to those general Rules.
But I should not do Justice to Peter Davall of the Middle Temple, Esq; Secretary of the Royal Society, did I not here acknowledge, that, before I had so fully considered these Matters as I have since done, I had the first Hint of applying the Golden Numbers to find the Gregorian Paschal Limit or full Moon, from him; who has since that time composed and drawn up Tables, &c. which may possibly be of considerable and general Use in this Nation hereafter.
FINIS.