108 G. H. KNIBBS. 



To obtain a normal periodic fluctuation it would be pre- 

 ferable, were it practicable, to combine the results, each 

 for a series of years such as would give Easter an identical 

 distribution. In the period such a series is, however, im- 

 practicably long. Hence in the case of marriage, migration 

 etc., we must consider the actual effect on the periodic 

 fluctuation studied. The effect of Easter is to reduce the 



I denoting the letter belonging to the day on which the 15th 



of the "paschal moon" falls 

 p denoting the number of direction or number of days from 

 21st March to Easter day 

 then a subscript r following brackets denoting that the remainder 

 only is to be taken, and a subscript w in a similar position denot- 

 ing that only the whole number in the quotient is to be taken, we 

 shall have 

 N = /Y+\\ . . ,0-17 



19 )*'. \ 25 Jw 



E = ^+10(A'-D \ _ , c _ 16) _l - 1 6\ , C i .0 - a 



L = 7* 



30 r \ 4 jw 



in which m is an integer such as will give a product not more than 

 6 greater than the number following in the brackets. 



When^<24:{ , 2 7-JF\ * > 24 : \ % _ /57 -E 



I 7. )r 7 )r 



p = P + L - I. 

 Hence the number of days from the beginning of the year is: — 

 81 + p for leap years, and 80 + p for common years : 

 common years being such as are not exactly divisible by 4, or 

 being divisible by 4 are also divisible by 100 but not by 400 ; 

 excepting that years divisible by 4000 are also common years. 

 Leap years are years exactly divisible by 4, unless divisible also 

 by 100 and not by 400 ; and further if divisible by 4000 they are 

 common years. 



