MEMOIR EXPLANATORY OF \ NEW PERPETUAL CALENDAR. 127 



In the first example, the difference between the styles is 12 days, and in the second^it 

 is 18 days. It so happens, therefor.', that, in both these cases, the Julian and Gregorian 

 Easters will be celebrated on the very same day. The year 2698 is the last, according to 

 Mr. De Morgan, in which such a coincidence will occur. See note at the foot of page 19, 

 in hi- Essaj 'Mi the Ecclesiastical Calendar. Sec also page 105 of this Memoir. 



The Rule for the Gregorian Epact, it will he perceived, becomes universally the following, 



To 11 limes the Cyclic No. add tin Equation in Column C ; and reject 30sfroiyi the'Sum. 



The Rule for the Feria, (or day of the week,) though not attended with an equal eco- 

 nomy of Figures, suggests the practical convenience of marking for remembrance, in any 

 current century, those years which terminate cycles of 28, (such as 1820, 1818, and 1876, 

 in the present century.) in which case the Cyclic No. for any intermediate year, may be 

 promptly known, and the day of the week be thence deduced by an easy mental process. 

 For instance, the Cyclic No. for 1817 is 27, (or 27 years beyond 1820,) and the other 

 figures to be added to it are so few and small, that ordinary questions may be solved by 

 the Rule without putting pen to paper, more especially in the present century, whose 

 secular equations are, on both sides of the Tablet, null until 1900. 



A similar expedient might be adopted with the years 1S05, 1821, 1843, 1862, 1881, 

 each cndin<i cycles of 19, and the Epacts for intermediate years be mentally computed 

 with like facility. Thus the Cyclic No. for 1817 i< 1, (or four years beyond 1813,) and 

 the Epact is II, or *1 times 11 lessened by 30. 



Without departing, however, from the original form of the Tablet, the work may be 

 somewhat abbreviated by noting those years only which close at once, centuries and 

 cycles, (such as 1 100, 1800, &c, on one side, and 1900, 3800, &c, on the other.) and by 

 using, in computation, the years beyond those epochs respectively. Thus 1 17. 1 18, vSjc, 

 yield the same feriao as A. D. 1847, 1848, &c; and, in the coming century, 1, 2. :!. &c., 

 will yield the same Epacts as A. D. 1901, 1902, &c. 



\lh. .1 Rule for the Solution, by the foregoing Tablet, of Converse Questions, viz.. 



To find nn what day of the Month a given Daj of the Week first Falls in any Month in any \ ear. 

 < )mit the day of the Month in the fifth line, and dh ide the Sum of the four other lines h\ ? : 

 Subtract the Remainder from the numerical Day qftht Week, increased, if needful, 1>\ 7. 

 The Difference will be the Answer. Hut in January and February of Leap Year 

 take the Remainder from the succeeding day of the Week, increased, if needful, in like manner. 



EXAMPLES. 



What Day of the Month was the first Monday in Dec. What /)<>i/ of the Month wot the first Thursday in 



1846, the day of the meeting of Congress? Feb., 18441 being a Leap Yrar.) 



I Remainder, by the above Rule, will be . . . 2 The Remainder b\ the above Rale, will be 5 



Monday 2 — '2 = 0: Increase, therefore, the day by 7. 5 taken from 6, (Friday) leaves lor the answer I 



I — 2=7. Answer, December the 7th. or tho first da} ol thai Month. 



Proof — The Tablet shows that the month began on Ti\ S<n De Men' Essay, page 16, Example 2d. 



— Any reference, in Leap Years, either t" preceding or n lt;,\s of the Week in January and 



i raary may !><■ avoided by substituting the Monthly No. of July for January, and that <<i August for February, 

 eacli No. being half a year distant from that which it t:ikc>< the place of. 



In the last example, for instanee, had the kugUSl No. 2 been used instead of the February N" •'. thl Rl maindl i 

 woidd ha\e been i. which taken from Thursday, or 5, would have given lha tan 



