128 MEMOIR EXPLANATORY OF A NEW PERPETUAL CALENDAR. 



APPENDIX TO MR. McILVAINE'S MEMOIR. 

 Read July 16th, 1S47. 



I beg the Society's acceptance of the accompanying Cards, containing a new plan of 

 a Perpetual Civil Calendar, &c, in which, still dispensing with Dominical Letters, and 

 substituting for them Yearly Numbers, (always their complement to 8, if we read as 

 equal to 7,) the same results may be obtained by mere inspection, as those requiring com- 

 putation according to the scheme heretofore presented by me. The equivalence of the 

 two methods will be readily recognised by the following comparison of them, which is 

 universally applicable. 



The Yearly Number, by the former plan, would be the Remainder on division by 7 of 

 the Sum of the Year, its fourth part (omitting fractions,) and the secular Equation in 

 Column A; which Remainder, for the New Style year 1847, after Christ, is 5, the same 

 as the Yearly Number here standing in Table C, at the intersection of the line of A with 

 the column of B. The same line (be it observed) answers for a whole century. 



Now for the names of the months of Table E in this plan, substitute the Monthly 

 Numbers 0, 1, 2, 3, 4, 5, 6, of Table B in the former, and the two processes become 

 virtually identical, thus: 



The 1 8th of June, 1847, found by the former, would bef J ~*~ — J = (—J = or Friday. 



By the present, counting 5 onwards from 18 in Table C, we reach a column containing 23; 

 then descending the column to Table E, we find in the line of June the Day of the Week 

 to be Friday, corresponding with the Remainder 6. If, in the blank space between the 

 Examples and Table E, and in line with the respective months, their seven monthly num- 

 bers were so arranged as to form a short column, it would, perhaps, be more clearly seen 

 how and why, the relative position of the several Tables of page 129 effects the same 

 object as the Rule on the Civil side of the Perpetual Calendar, at page 106. 



I have given no examples of New Style years, either before the Christian Era, or 

 between it and the year 1582, because that mode of reckoning, though well calculated to 

 reveal, and to measure approximately, the chief defect of the Julian Calendar, is not cus- 

 tomary in chronology, and, being somewhat speculative, might perplex, rather than assist 

 an inquirer; but, in Old Style years before Christ, and in New Style years until the Gre- 

 gorian reckoning shall be modified, the wide range of these five Tables may be very satis- 

 factorily shown by two of the examples which have been already worked in a different 

 manner, namely the 1st of January, in the astronomical year (5857, B. C, at page 125, 

 and the 10th of April, a. n 50000, at page 123. Both their centurial figures lie beyond 

 the limits of Table A; but 08, yielding, on division by 7, the Remainder 5, belongs to the 

 same line with 5, o.s. n.c; and 500, yielding, on division by 4, the Remainder 0, belongs 

 to the same line with 10, n.s. a.c. The Yearly Number in the first case, (using, agree- 

 ably to the 2d Exception, 43 instead of 57, in Table B,) is 1, and the answer is Monday. 

 The Yearly Number, in the second case, is 0, and the answer is Sunday. 



This device is accordingly verified by the formulae of Delambre to the same extent as 

 the one from which it has been drawn; and I solicit permission to occupy, with a copy of 

 it, an additional page of the Transactions. 



