48 ROYAL SOCIETY OF CANADA 



our data can yet determine. The term exact we use always in this 

 sense. 



The epochs chosen, at which to verify the exactitude of these cycles, • 

 are not unreasonable ones from a prophetic standpoint; and an ex- 

 planation of a rational character for their choice can only be given from 

 that point of view. The best expositors throughout the eighteenth and 

 nineteenth centuries have shown that the periods represented by the 

 numbers cited from Daniel and Revelation are due to run out m these 

 times; or say between 1800 and 2000 A.D. This wide margin is 

 suflEiciently near for our present purpose, as we are dealing with cen- 

 turies; and to leave it so, will also obviate a closer discussion of inter- 

 pretation, periods, and dates. The epoch 1900 A.D. is thus the ap- 

 proximate mean terminus of the periods; and at this epoch one of the 

 cycles is exact. The next epoch, 50 A.D., is the middle of the first 

 century of the Christian era, which is a noteworthy time. The epoc'.i 

 600 B.C., is at the beginning of the twenty-five centuries extending back 

 from their approximate terminus in 1900 A.D. to the time of Daniel. 

 [Under Note C, references are given to some leading expositors and 

 early authors, on whose writings are founded the modern explanation 

 of the prophetic periods.] 



The solar year at the various epochs. — The secular variation in 

 the length of the tropical year, as given in the Annuaire, Bureau des 

 Longitudes, is applied to Leverrier's value which corresponds with the 

 Annuaire; and Kewcomb's determination of the variation is applied 

 to his own value. The mean of the two is then taken. As this varia- 

 tion is a decrease with the forward progress of time, the year is, of 

 course, longer in former centuries than at present. 



Epoch 1900 A.D. Leverrier. . . . 365.24219340) Mean alreadj- adopted :— 

 Newcomb. . . . 365 . 24219879 * 365 . 24219G1 



Epoch 50 A.D. 



Leverrier 365.24219340 + (18^ x .00000624) = 365.2423088 



Newcomb 365.24219879 + (18.^ x .00000614) = 365.2423124 



Mean.... 365.2423106 



Epoch 600 B.C. (Same method as above) Leverrier = 365.2423494 



Newcomb = 365.2423523 



Mean.... 365.2423508 



Cycle-values for the lunar year. — Computed from the foregoing 

 determinations of the length of the solar year at each epoch, by means 

 of the ratios of the lunar 3'ear to the solar year, as afforded by the cycles. 



