WHITSUNTIDE INDICTION. 



year 1855, we add 3, which gives 1858, and dividing by 15 

 we find the remainder 13, which is the Indiction. 



40. A common year of 365 days consists of 52 weeks and 1 

 day. It follows, therefore, that such a year is always followed 

 by one which begins one day later in the week. If seven such 

 years followed each other in uninterrupted succession, their first 

 days would be the seven successive days of the week. 



But a leap year consists of 52 weeks and 2 days ; therefore, the 

 first day of the year which succeeds it will be two days later in 

 the week than that of the leap year. Since in seven successive 

 years there must be one, and may be two leap years, it follows 

 that the first days of the years included in such a period will not 

 include all the days of tho week. 



To find the interval which must elapse between two years, each 

 day of which will fall upon the same day of the week, it will be 

 evidently necessary to find a number of years which will consist 

 of an exact number of weeks. If there were no leap years, this 

 number would evidently be 7, since the odd day which is con- 

 tained in each year, seven times repeated, would make up a week, 

 so that 7 years would consist of 4 times 52 weeks and 1 week, 

 that is 209 weeks exactly. But the recurrence of a year of 366 

 days every fourth year prevents this. 



Four years consist of 208 weeks and 5 days. It will be neces- 

 sary, therefore, to find how often this interval must be repeated 

 to make a complete number of weeks ; or, what is the same, how 

 often five days must be repeated to make a complete number of 

 weeks. Now this is evidently 7 times, which will make up 5 

 complete weeks. If 4 years, therefore, be repeated 7 times, 

 we shall obtain a number of years which will be also an exact 

 number of weeks. But this number of years is 28, and it con- 

 sists of 7 times 208 weeks, together with five weeks, making in 

 all 1461 weeks. 



After every successive period of 28 years, therefore, the same 

 days of the year will fall upon the same days of the week. 



This period of 28 years is called the SOLAR CYCLE. 



41. The first year of the Christian era being taken to be the 

 tenth of the current solar cycle, it follows, that to find the nume- 

 rical order of any proposed year in the current solar cycle, we 

 must add 9 to the year, and divide by 28 ; the remainder, if any, 

 will be the order of the year. If there be no remainder, the year 

 will be the last, or the 28th of the current cycle. Thus, for 

 example, to find the order of the year 1855 in the solar cycle, 

 adding 9, we have 1864, and dividing by 28, we obtain the 

 remainder 16, showing that 1855 is the 16th year of the cycle, and 

 the first year of the present cycle was therefore 1840. 



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