so ROYAL SOCIETY OF CANADA 



As these cycles-values fall within the narrow limits of uncertainty 

 in the data themselves, the cycles are exact at these epochs, as we pro- 

 posed to show. Any outstanding uncertainty attaches rather to the 

 epochs than to the cycles themselves; for there is a margin of several 

 centuries, in the vicinity of these epochs, in which the cycle-values would 

 still fall within the limits assigned to the secular acceleration of the sun 

 and moon. 



It is also noteworthy that these epochs not only lie 'w-ithin the 

 bounds of the human period, but also within the narrower limits of the 

 twenty-five centuries that include the periods on Avhich these cycles 

 are based. The cycles standing next to these in accuracy, are the two 

 leading solar and lunar calendar cycles, the Gregorian and Mahommedan; 

 but their epochs of exactitude are much more remote. Our Gregorian 

 year is made exact by the solar acceleration, at the epoch 3010 B.C.; 

 and at the higher rate of 9" for the lunar acceleration, the Mahommedan 

 calendar cannot become exact until 12,710 A.D. providing also that the 

 rate of secular acceleration remains constant for that lehgtli of time. 

 Next again to these in accuracy, are the Calippic and Metonic cycles; 

 and the best cyclical relations which these afford, have been already 

 indicated. The epochs at which these would be made exact by secular 

 acceleration at its present rate are more than 85,000 and 190,000 years 

 respectively, in the past. 



Concluding remarks. — We thus find that the only three cycles which 

 exceed the high accuracy of one day in 10,000 years, are those deduced 

 from the prophetic numbers. They thus cover the entire human period 

 with less than one day of error. 



This results from a comparison with our best modern data, at the 

 present epoch; but when secular acceleration is taken into account, 

 the cycles are found to transcend the limits of accuracy in the data 

 themselves. 



These cycles are not hidden in the prophetic numbers in any recon- 

 dite or abstruse way; but their periods are simply a multiple, or a 

 difference, or an arithmetical mean between them. 



Can it then be deemed unreasonable to believe that these periods 

 were revealed by the Creator, who originally appointed the sun and the 

 moon for times and seasons; and that he should use such periods to 

 mete out human destinies, is but to correlate man with the works of 

 creation which surround him. 



Note A. — The number 2,300 occurs in Daniel VIII, 14; and the 

 expression, A time, times, and a half, in Daniel XII, 7. In Révélation 

 XII, 6 and 14, this expression is stated to be equivalent to "1,260 days," 

 as will be seen by comparing these two verses. The expression. Times 



