110 



MEMOIR EXPLANATORY OF A NEW PERPETUAL CALENDAR. 



The rule of the Tablet is therefore perfectly consonant with the well-known law of the 

 Solar Cycle and Dominical Letters in the Julian Calendar, and it is evident to the mere 

 arithmetician, that the part which the Equation 5 plays, in the type or first cycle of that 

 Calendar, just exhibited at large in connexion with the initial and final day of the year, 

 would be equally well performed by it, in conjunction with any intermediate ordinal day of 

 those years, or with any other Old Style year, without limitation. 



But thus far we have not considered the year as divided into months and days of the 

 month, both of which are embraced as elements of computation in our general rule. 



On carrying out the plan of the foregoing Table, and introducing every month, it will 

 hf seen that the first days of each month are equivalent to the following ordinals of the 

 common year, placed in the upper line of 



Series II. — First Days of the Months. 



Now these Twelve Remainders disposed in Quarters of a year, (and in a form and 

 order quite as easily remembered as the usual tabular index to the Dominical Letters,) 

 constitute Table B of the Perpetual Calendar. They are called Nos. for the respective 

 months, and on being substituted for the corresponding ordinals of the year standing in 

 the upper line, will, when the first day of the month comes to be added with them to the 

 year and the constant 5, yield the very same remainders, and so indicate correctly the 

 day of the week on which each month of the first year of the Christian Era begins. 



0, the monthly number for January, marks the true zero of the civil year, or the mid- 

 night between the old and the new year: and this No. added to the day of the month, 

 equals throughout January the ordinal day of the year. The rest of the monthly Nos. 

 mark the midnights preceding the first day of each subsequent month, expressed in the 

 odd days over full weeks, counted from the same zero-point: and this distance, together 

 with the days of each month in succession, must, of course, equal the other ordinals 

 throughout, the year. But since the rejection of entire weeks (or division by 7,) docs not 

 affeel the day of the week, the sum of the monthly No. and the day of the month, may be 

 substituted uniformly lor those ordinals. Thus the 31st of December, whose monthly No. 

 is 5, added to the year 1. its fourth part 0, and the constant 5 = 42, which sum divided 

 l>\ 7 gives us 0, or Saturday, the same result as when calling it the 365th day in Series f. 

 Either an additional year, or an additional day of the month, or an additional 29th of 

 Februarj in every fourth year, advances by 1 the day of the week as regularly and per- 

 manently, through an infinite succession of weekly cycles, as we have already found them 

 to do. m the computations connected with that series, in which 0, the No. for January, 

 with 1, the ,|;i\ of the month, might have been used as equivalent to 1. the day of the 

 j lar. 



