112 MEMOIR EXPLANATORY OF A NEW PERPETUAL CALENDAR. 



ceeding hundredth year whose centurial figures were not divisible by 4 without a remain- 

 der, should cease to be leap years, but that every 400th year whose centurial figures were 

 multiples of 4, should continue to be leap years. These multiples, 16, 20, 24, &c, are, 

 accordingly all marked on the Civil side of the Calendar with asterisks, but the interme- 

 diate centurial figures 17, 18, 19, and 21, 22, 23, &c, on the same side, are left unmarked. 



Now whenever an asterisk occurs, no change takes place in the solar equation; but at 

 each of the three other centurial figures that equation is diminished by a unit, on account 

 of the one day lost at each successive non-intercalation of the 29th of February. The 

 equation 2 beside 15, continues, of course, to be 2 at 16. From 16 downwards, the equa- 

 tions limited by the weekly cycle of 7, (which number is always represented by in 

 column A,) fall into sets of four each, in a receding series, each new set of four beginning 

 with the same figure with which the last set ended; and 2 followed by 2 reappears at the 

 centurial figures 43, 44, &c, and at 71, 72, &c, thus returning after Jour times seven, or 

 twenty-eight centuries, to the same figure, or Solar Equation 2, and so on ad infinitum. 



Column A, consisting of fewer figures (and these symmetrically disposed in a cycle of 7) 

 than have ever been used in constructing any Table of Dominical Letters for cither style, 

 completes, accordingly, A CIVIL CALENDAR of simple form and unlimited range. 



From the terms of the Rule, it is obvious that the Remainder on division by 7 of the 

 first three items, (viz., the given year, its fourth part, and the secular correction in column 

 A,) forms a standing number, which, being once obtained and noted on New Year's day, 

 may serve a convenient purpose throughout that year. This Remainder is universally the 

 complement to 8 of the Dominical number for the year, and might be called the Yearly 

 Number. 



Then, supposing the Monthly Numbers well fixed in the memory, (a task which the 

 division of Table B into a thick-lined polygon, resembling a carpenter's square, containing 

 twice 3, 6, 0; and a thick-lined square containing a 5, leaving an interval composed of 

 squares less strongly marked, but numbered in regular order, 1, 2, 3, 4, 5, greatly facili- 

 tates,) the day of the week will be readily found without resort to an Almanac, by adding 

 together the Yearly No., the Monthly No., and the Day of the Month, and rejecting the 

 sevens from their sum. Since this sum never exceeds 43, the whole process may be 

 ■mentally performed without difficulty, after a little practice. During the present century, 

 Avhose solar equation is 0, the computation is particularly easy; for instance, 



The Remainder or Yearly No. for 1845, to be kept in mind is ( 1845 +^ 61 ±-° =) 3 



What day of the week, then, is August the 15th? Add that day of the month, . . 15 



And the Monthly Number, 2 



The sum is 20 

 which, divided by 7, (or mentally rejecting the sevens,) leaves the Remainder . . 

 or Friday. In leap years the exceptions respecting January and February must, of course, 

 be attended to. Those exceptions might, instead of referring to the preceding day of the 

 week, have been equally well provided for by the following direction, viz., " In January 

 and February of leap Years, use the monthly numbers of July and August, in each case 

 six months distant." 



