34 ROYAL SOCIETY (JF CANADA 



times, and a half," an expression explained in Eevelation as meaning 

 1260; the prophetic "time" being 360 years. These numbers are the 

 most noteworthy, as they stand in relation to the age which is termed 

 in Scripture the Times of the Gentiles. In prophecy, the day stands 

 for a year; but it may be either an ordinary solar year or a lunar 

 year; and there is good reason to conclude, from the fuliilmeut of the 

 Messianic prophecies, that they are, to be reckoned in both these ways. 

 In general, the periods appear to be reckoned in lunar years when con- 

 nected with Eastern peoples, more especially the Jews; and an solar 

 years when connected with the western nations. In this way, the 

 various nations are reckoned in accordance with the calendar-systems 

 which they have themselves adopted. [For references on the points 

 here briefly mentioned, see Note A, appended]. 



To , those who believe the Book of Daniel to be authentic and trust- 

 worthy, there is thus reason to expect that these numbers should bear ' 

 a relation to solar and lunar periods; and it is this belief which has 

 brought ,to light cycles of three different types, which prove to have 

 such an extreme degree of accuracy as to transcend the best data which 

 modern observations have yet given us. 



On this account, it may be pardonable to be precise in definitions, 

 and explicit as to data used and assumptions made; so that the cal- 

 culations now submitted in proof of the accuracy of these cycles may 

 be revised, if other values are preferred ; or if the. data themselves can 

 be determined more accurately in future. At present, the uncertainty 

 in the length of the year, according to the determinations of dilferent 

 astronomers, is nearly half a second of time; and in a lunar year of 

 twelve lunar months, the uncertainty in the same sense amounts to about 

 a whole second. 



There are only two modern investigators who have taken up this 

 subject, so far as the writer has been able to learn. A Swiss astronomer, 

 M. de Cheseaux, in the eighteenth century, discovered a cycle based on 

 these prophetic numbers. Also, Mr. G. W. McCready, C.E., has com- 

 puted the time of the first full moon in the year, for every tenth year 

 during 4,000 years; based upon a cycle for the lunar month which is 

 obtained by combining the cycle of Cheseaux with one of my results. 



The two cycles derived from the prophetic numbers which we now 

 submit, are of two new types; and with the cycle of Cheseaux they 

 furnish cycles of three types out of the four which are possible, as we 

 will explain. 



Year, month and day. — It is unnecessary to describe the several 

 solar years and the several lunar months, as these are explained in any 

 work on astronomy. For the ordinary reckoning of time and the 



