We have already seen the prophetic nature of Daniel’s _seventy_ weeks, and it now only remains to notice his other prophetic periods. In Dan. xii. 14, mention is made of “a time, times and half a time,” which should be accomplished, before the wonders he had seen should come to an end. This period is clearly shown by writers on the prophecies, to signify _three and a-half_ prophetic years, _forty-two_ prophetic months, or 1260 prophetic days; and this view is confirmed by the mention of 1290 and 1335 prophetic days, in the context. Again, in Dan. viii. 14, we read of 2300 prophetic days, after the lapse of which, “the sanctuary shall be cleansed.” That these periods are all connected with each other, and that they each signify so many years, has been long known and generally admitted; but, that they are connected with the revolutions of the heavenly bodies, appears to be but a very recent discovery! Mr. Birks, of Trinity College, Cambridge, in his “Elements of Prophecy,” just published, has very properly remarked, in p. 368, that, “It seems to have been first unfolded by M. de Chesaux, a French writer, purely as a curiosity of science; but it is Mr. Cuninghame who has revived attention to this interesting topic.” The fact is, that the original work of M. de Chesaux might have lain for ever on the shelves of the library of the University of Lausanne, had not Mr. Cuninghame searched it out with his wonted industry, and republished the author’s discovery anew in his work on the “Jubilean Chronology.” We shall endeavour to give our readers some idea of this curious discovery. 2. Lengths of the tropical year and the synodical period of the moon, according to Sir John Herschel—Application of the method of _continued fractions_ to the determination of their approximating ratios—Various lunisolar cycles—The Octaëteris of the Greeks—The cycle of nineteen discovered by Meton, but probably known to the Hebrews—The period of Calippus—Proof that the numbers of Daniel are lunisolar cycles—Remarks of Mr. Birks in his “Elements of Prophecy”—Observations of Mr. Cuninghame in his “Scientific Chronology”—Proof that the prophetic month and the jubilean period are lunisolar cycles. The latest determinations of the lengths of the tropical year, and the lunar month, or synodical period of the moon, are, according to Sir John Herschel, 365 days, 5 hours, 48 minutes, 49·7 seconds; and 29 days, 12 hours, 44 minutes, 2·87 seconds. “Astronomy,” pp. 205, 224. By the method of _Continued Fractions_,[34] we find that the continually approximating ratios of these periods are represented by the following series of fractions: Numbers, (1) (2) (3) (4) (5) (6) (7) (8) (9) Ratios, ¹⁄₁₂, ²⁄₂₅, ³⁄₃₇, ⁸⁄₉₉, ¹¹⁄₁₃₆, ¹⁹⁄₂₃₅, ³³⁴⁄₄₁₃₁, ³⁵³⁄₄₃₃₆, ⁶⁸⁷⁄₈₄₉₇, &c.