KASTKR SUNDAY AND THK DOMINICAL LKTTKR. 1 5 



exactly round to the place of beginning. Coincidence is 

 restored, the same day of week, day of month and letter falling 

 together once more, and the same order recurring. The period 

 is called the Dominical Cycle, and as the secular suppressions 

 are not made in the Julian Calendar this is a new condition 

 introduced by the Gregorian reformation, and the rule gives 

 for the years previous to 1582 results which must be modified 

 to fit the facts. It is now clear that we shall in dividing any 

 date by 400 get certain Dominical Cycles which do not concern 

 us and a remainder of centuries which is to be dealt with. 



So then, suppress the last two figures of the date and 

 divide by four. This will give the same result as dividing the 

 entire date by 400, and be more convenient. The result is a 

 quotient of Dominical Cycles and a remainder either of o or of 

 certain centuries the final years of which are not leap years. 

 In each of these remainder centuries then (if any) there are 

 twenty-four leap years instead of twenty-five, which gives vir- 

 tually 124 common years in each of which the letter backs 

 one. Then, dividing by seven, get a quotient of sevens and a 

 remainder of five backward places. But to back five is the 

 same as to advance two. We choose the latter course, double 

 our remainder from dividing the centuries by four and sub- 

 tract from six. 



The reason for subtracting from six has been hinted above. 



The six is used merely to reach a base or bench mark, and 

 has nothing to do with the change of letter occasioned by 

 change of year. We have, namely, not yet fixed upon a 

 starting point for the calculation. To this end it is matter 

 of course to go back to the beginning of the Christian Era 

 and set out from the historical fact, already mentioned, that 

 our year One began on Saturday, January first. This makes 

 B the letter of the year, and C the letter of the year preceding. 

 We have thus advanced three letters from G before beginning 

 to count years. Moreover, on reaching 1582 w^e are ten letters 

 short of where we ought to be if our calculation of hitherto is 

 to be adjusted to our calculation of hereafter. In- 1582, namely. 



