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A. If. W. DOWNING, 31. A., D.SC, F.R.S., ON 



days, it is evident that from one common year to the next, the 

 Sunday Letter retrogrades one place, whilst after a leap year 

 the Sunday Letter retrogrades two places. It appears, then, that 

 knowing the Sunday Letter for any year — knowing for instance 

 (as all chronologists ought to know) that January 1, A.D. 1, was 

 a Saturday, with corresponding Sunday Letter B — it is easy to 

 write down a formula from which the Sunday Letter for any 

 other year may be found. A number, occurring in this formula, 

 has to be modified from time to time so as to adapt it to cases 

 of the occurrence, or non-occurrence, of leap years in centennial 

 years of the Gregorian calendar. This formula, translated into 

 ordinary language, with the necessary modifications during 

 successive periods, and the corresponding scale, is given in the 

 Prayer Book calendar. It is not necessary, therefore, to dwell 

 further on this point, except to note that in leap years the 

 Sunday Letter so found will be the second letter for the year, 

 the first being the preceding one in the Prayer Book scale 

 referred to above. 



We now come to the most complicated of the problems con- 

 nected with the determination of Easter Day. To carry into 

 effect the decree of the Council of Nicaea it was necessary to 

 determine the fourteenth day of the moon. But the Council 

 did not say how this fourteenth day was to be found, the duty 

 of determining it being assigned to the Bishop of Alexandria. 

 This arrangement naturally caused a good deal of dissatisfaction 

 to the ecclesiastical authorities at Pome. It was considered 

 derogatory to the Papal See, and efforts were made to render 

 the Western Church independent of Alexandria. This 

 eventuated, in a.d. 437, in the decision arrived at by Hilarius 

 (afterwards Pope), that the moon which governed the date of 

 Easter should not be the real moon of the heavens, but should 

 be an artificial moon supposed to move regularly, and that the 

 full moon should be accounted as occurring on the fourteenth 

 day. The phases of this artificial moon were to be computed 

 by means of the Golden Numbers of the Metonic Cycle, on the 

 assumption that 235 lunations are equivalent to 19 solar years. 

 This artificial moon, and the corresponding Golden Numbers, 

 are still used in the reformed ecclesiastical calendar in the way 

 that must now be explained. 



The Golden Numbers are the numbers attached to each year 

 of a cycle of nineteen years, after which the calendar new 

 moons fall on the same days of the Julian year. Thus, if a new 

 moon falls on January 1 in any year, it will again fall on 

 January 1 after a lapse of nineteen Julian years, and to each 



