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MEMOIR EXPLANATORY OF A NEW PERPETUAL CALENDAR. 



The point of view in which the subject presented itself will probably be best understood 

 by expanding my original course of reasoning into figures in the following way: 



The 1st day of year 1 of Christ, having the Sunday letter B, was Saturday, or the 

 7th day of the week; which number 7 agreeing with that of the weekly cycle, (never to 

 be interrupted,) suggests this plan of freeing the calendar from Dominical Letters. 



If (referring to the following Table, Series I.,) to the 1st day of the year 1 we add 5, 

 in order to reach and include the 7th or last day of that cycle, the sum 7 divided by 7. 

 gives us the remainder 0; which remainder being always taken as the equivalent of 7, the 

 divisor (conformably to arithmetical usage in the case of all other cycles,) becomes a fit 

 expression for Saturday: and 0, or a week completed, will thus represent perpetually thai 

 day of the week in the scale of time. 



The same process with the succeeding ordinal days of the year, exhibits a perfectly 

 correct expression for the other six intermediate days of the week, as in 



Series I. — Days of the Common Year. 



Showing that 

 Year 1 begins and ends (52 entire weeks, or 364 days intervening) on or Saturday. 

 A like Table for succeeding years would show 

 in year 2, its Jirst and last day, . . . by the Remainder 1 to be Sunday, 

 in year 3, its Jirst and last day, . . -by the Remainder 2 to be Monday. 



Year 4 is a leap year, but not until the 29th of February; 

 its first day, therefore, would be shown . . by the Remainder 3 to be Tuesday, 

 and its last, or 365th day, . . . -by the Remainder 4 to be Wednesday. 



This result for the end of the year 4 would be the same if, instead of calling its last 

 the 366th day, . . we add to the 365th day of a common year, 

 the year ...... 4 



then, by the general rule, its fourth part 1 for the first Leap Year of the Era, 

 and constant ..... 5 



The sum ..... 375 divided by 7, gives Remainder 4 or Wednes- 

 day for the 31st of December. But this rule, as applied to the beginning or 1st day of 

 January of the year 4, would make it also to be Wednesday, which is not the true day, 

 hut Tuesday is, as we have seen above. Hence the exception stated in regard to the 

 months of January and February in leap years, viz., to take the preceding as the true 

 day, since no intercalation occurs until the 29th of February. I proceed to show the 

 effect of seven such quadrennial intercalations to advance by exactly a week, the day of 

 the week, after going through the first complete cycle of the Julian Era. 



