UBMOIB EXPLANATORY OF A NEW TERPETUAL CALENDAR. 123 



The facility of this method arises principally from the Gregorian Secular Equations, in 

 Columns A and C, being meehanically formed and tabulated. To obtain the same cor- 

 rections, arithmetically, no simpler rules than the following could perhaps be devised; and 

 a comparison of the two processes will therefore exhibit fairly the economy of time and 

 trouble which the Tablet effects, apart from what is saved b\ using Table B. 



Rule for Ji tiding, universally, the New Style Solar Equation of Column A. 



Divide the Centurial figures b\ 8, and the Remainder by 4. 



From the sum of the two Quotients (increased, if needful, by 7.) deduct the Remainder. 



The Difference (rejecting the sevens, if any.) will be the Equation wanted. 



(But since the final rejection of the sevens, is provided for by the Rule of the Tablet, 



the Difference itself will answer every purpose of that Equation.) 



Rules for finding the New Style hunisolar Equation of Column C, until a. d. 1899 inclusive. 



Divide the Centurial figures by both 3 and 4, and to the two Quotients add 8. 



from the Sum deduct the Centurial figures, the Difference will be the Equation wanted. 



From a. d. 1899 to a. d. 4199, both inclusive. 



Divide the Centurial figures by both 3 and 4, and to the two Quotients add 8. 

 From the Centurial figures deduct the Sum: Then take the Difference from the next 

 higher multiple of 30 (which, during this period, is alwaj s 30,) and the Second Difference 

 will be the Equation wanted. 



At and after a. d. 4200yb>- evt r. 

 The rule i< the same as the last, with this Exception only, viz. 



that the Centurial figures must be diminished by ( — — — ) = [ — ' — ] , 



9 ^ 25 Jw V loo Jw 



that is to say, by the Quotient arising from the division of " four times the Centurial 



figures" less 68, by LOO, before beiiiu' divided bj '■'<: but liny must be used, in the rest of 

 the work, exact!) in the manner there directed. 



The following results of the Rule and Tablet will be found in perfect accordance with 

 those derived from Delambre's formula; and Paschal Table, in determining Easter for 

 a.i). 50000. 



The Solar Equation of Column A = 3; and Lunisolar liquation of Column C = 3. 



The Dominical Letters are />' and A, and the Epact is 1. 



The 1 1th day of the Paschal Moon will fall on Sunday, the 9th of April, ami Easter, 

 of course, on the following Sunday, viz., the 10th of April. 



\ collateral proof of the correctness of these secular equations is derived from the fact, 

 lately observed 1>\ me, that the same mechanical expedient of the asterisks furnishes, 

 instantly, ;ill the Gregorian Corrections M anil \ of Gauss's formula, beginning with 22 

 ami 2, but in advancing series (the reverse of mine --i- given by M. Le Chevalier dr < 0-< -\ . 



in Vol. XXIV.. pai'e "?. ol'the Mel -of tin: Uo\al \e,i«|< iii> of Turin. 



