40 PHILOSOPHICAL TRANSACTIONS. [aNNO 1750. 



should be deducted from those 1 1 days, by which the golden numbers ought 

 otherwise to be advanced; and the golden number 14 should not be placed against 

 the 11th, but the 8th day of March; which being reckoned the first day of the 

 moon, if we count on to the 14th day of the same inclusive, that would be 

 found to fall on the 21st day of March; on which day the Gregorian paschal 

 limit or full moon will happen, when the golden number is 14. And the like 

 course should be taken with the rest of the IQ golden numbers ; which ought to 

 be placed 8 days forwarder than they now stand, if they are to point out the new 

 moon; or 21 days forwarder than they are at present, if they are to mark the 

 14th day of the moon, or the full moon ; the latter of which, as has been shown, 

 would be more eligible, than to prefix those numbers to the days on which the 

 new moons happen. 



Thus may the rule and method now used in the church of England, be most 

 easily adapted to show the time of Easter, as it is observed by the Gregorians, 

 till the year IQOO; 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 to the foregoing rules and directions for that purpose, they will 

 continue to show the new or the full moons of the church of Rome, or the Gre- 

 gorian 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 direc- 

 tions. There is however one exception to those general rules and directions, 

 which will be taken notice of in the next paragraph. 



On these principles is framed the table accompanying this paper, and showing, 

 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 41 99 

 inclusive. Which space of time is there divided into 1 6 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 1 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 5 th of April, to show the paschal new moons, or 

 against the 17th or 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 pre- 

 ceding 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: while others, on the contrary, generally stand single and by them- 



