193 



quently, Monday; and, as the series of days of the week was not in- 

 terrupted, nor intended to be, by the reform, in order to make the 

 15th of October, in the new style, coincide with Friday, it is obvious 

 that we must go back three days; that is, we must subtract 3 from 

 the Juhan Solar Equation 5, leaving 2, which will thus become the 

 Gregorian Solar Equation for the remainder of the 16th century. 

 This equation would suit all succeeding centuries, were it not for 

 the second step taken at the reformation, of directing that after 1600, 

 which continued bissextile in both Calendars, every succeeding hun- 

 dredth year, whose centurial figures were not divisible by four, with- 

 out a remainder, should cease to be leap years. 



As each of the years, 1700, 1800, and 1900, loses consequently a 

 day, the number expressive of the solar equation is diminished by 

 one at each change of the centurial figure; but for 2000, and for 

 every succeeding 400th year, whose centurial figures are divisible 

 by four without a remainder, the equation continues, like that of 

 1600, the same as the preceding one, and these years only are 

 marked on the civil side of the column of Eras with an asterisk. 



Thus column A, consisting of fewer figures (and these symmetri- 

 cally disposed in a cycle of 7,) than have ever been used in con- 

 structing any table of Dominical letters for either style, completes a 

 Civil Calendar of simple form, and unlimited extent. In the present 

 century, whose solar equation is 0, the computation will be found 

 particularly easy. 



Mr. M'llvaine then proceeds to explain the construction of the Ec- 

 clesiastical side of his Calendar, and the means which he adopted 

 for connecting it with Table B of the other side, as well as for mak- 

 ing a single additional column C, serve as a convenient substitute for 

 the Extended Table of Epacts now in use. 



From the descriptions given in Mr. Galloway's article on the Calen- 

 dar, in the seventh edition of the Encyclopedia Britannica, and in one, 

 by Lord Macclesfield, published in the Philosophical Transactions for 

 1750, Mr. M'llvaine inferred, that the golden numbers, as remain- 

 ders, on division by 19 of the year plus 1, might be dispensed with, 

 and their place, in computation, conveniently supplied by adding to 

 11 times tlie year, the 19th part of the year used as a quotient, or 

 whole number, (taking care only that when the j^ear happens to be 

 a multiple of 19, one less than the 19th part shall be added,) and then 

 rejecting thirties from the sum. This easy formula, equivalent to the 

 rule at the head of the tablet, yielded him, without a faihire, the con- 

 stantly recurring 19 epacts that mark the Julian Calendar. Now 



