CORRESPONDENCE, 1846-55. 205 



there was leap-year every fourth year, but does not say from 1849. 

 whence the years were reckoned. 



We have no authority for saying which particular years 

 were leap-years either in the pre- Augustan piece of the Julian 

 Calendar, or at the start made after the Augustan reformation. 



Nevertheless, I think a little train of reasoning will bring us 

 to the following theorem. 



The Julian Calendar starts with what, by reckoning back, we 

 should call January 1 of the year 45, on the supposition that 

 does not exist, but that we pass from 4-1 to 1 consecutively, 

 on the supposition that every fourth year is leap-year. 



There is much reason to suppose that Caesar began his year 

 on January 1 because there was a new moon on this day. Other- 

 wise it is likely he would have commenced it on the shortest day 

 preceding. He is thought to have gratified the feelings of the 

 Romans by making his start on a new moon day, and Macrobius, 

 in the words ' Annum civilem Caesar habitis ad unam dimensi- 

 onibus constitutum, edicto palam proposito publicavit,' is held 

 to have alluded to this. Now the fact is that January 1, 45, 

 back-reckoned as before noted, is found to have been a day 

 of new moon. Dr. Smith's Dictionary of Greek and Roman 

 Antiquities (a book you ought to have there is a good article 

 on the Calendar) says it was at 6h. 16m. P.M. My rough 

 calculation gives lOh. 55m., which I take to be within a quarter 

 of an hour. 



Now, as our tables reckon back (old style) upon the suppo- 

 sition of uninterrupted leap-year every four years, I take it that, 

 as to the interval, we may depend upon knowing the exact 

 number of days that have elapsed. 



But how are we to explain the dropping into leap-year 

 at +4? 



Diagram I. shows us 



J. Julian leap-year. 

 P. Priests' mistaken leap-years. 

 A. Augustan leap-year after the suspension. 

 At the end of the year 4, the priests' leap-years and one 

 Augustan make 13, just what there ought to haye been by our 

 back-reckoning. If, then, +4 was Augustan leap-year, we are 

 all right. I assume that the first year of the reckoning was cer- 

 tainly not a corrected year. Accordingly the first priests' leap- 

 year was 42 J., showing the Julian intention was never carried 

 into effect. 



