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Soli-lunar cycles in Greek research and Jewish revelation Ridgway, Walter Sydney 1946

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SOLI-LUNAR CYCLES IN GREEK RESEARCH AND JEWISH REVELATION by Walter Sydney Ridgway **** A Thesis Submitted i n Partial Fulfilment of The Requirements for the Degree of. MASTER OF ARTS in the Department of CLASSICS The University of Br i t i s h Columbia September, 1946 TABLE OF CONTENTS p a g Q Introduction 1 - 2 Physical Cycles . . . • 3 -31 Definitions 3 - 4 Results of Greek Research 5 - 9 Tables of Cycles 10 - 31 1. Cycles of the Solar Year and the Lunar Year 11 - 12 2. Cycles of -the Solar Year and the Lunar Month IS - 23 3. Soli-Lunar-Anomalistic Cycles 24 - 26 4. Soli-Lunar-Nodical Cycles . . . . 27 - 29 5* Soli-Lunar-Anomalistic-Nodical Cycles 30 6. Solar Year Sidereal Month Cyoles 31 Moral Cycles 32-88 The Seventy Weeks 32 - 44 The Setting of the Other Moral Cycles .45 - 53 Daniel 7 45-47 Daniel 8 48 - 49 Daniel 11 and 12 49 The Book of the Revelation . . . 51 - 53 The Chronologic Prophecies 54 - 63 Introduction - The Development of the Year - Day Prinoiple... 54-56 The 1260 Years , 57 - 58 The 2300 Years 59 - 60 The 150 Years 60 The 391 Years 61 The 2520 Years 61 - 63 Adjustment of the Physioal Cycles to the Moral 64 - 72 M. DeCheseaux's Discoveries... 64 - 65 Dr. .Guinness' .Discoveries 66 Dr. W. Bell Dawson1 a Disoovery 67 Evaluating the Biblical Cycles 68 - 71 Guinness' Anticipations 72 - 88 Conclusion • . 88-91 Appendix A 92-95 Bibliography 96-98 1. SOLI-LUNAR CYCLES in GREEK RESEARCH and JEWISH REVELATION Those who are acquainted with the work of the Foundation for the Study of C y c l e s ^ or who have otherwise investigated the subject know that rhythmic fluctuations or cycles pervade not only inanimate nature but also many departments, of human act i v i t y and thought. The present treatise is concerned with discoveries which indicate that such cyclic relationships extend into the realms of the moral and the theological. Physical and moral phenomena are, of course, i n some ways quite distinct. Modern investigation has demonstrated that in many spheres the moral bears l i t t l e or no causal relation to the physical. Injustice does not occasion an eclipse, nor envy an earthquake. Physical elevation not moral depravation attracts lightning. Physical phenomena occur i n accord-ance with established and uniform physical principles. So, likewise, the physical i s no criterion of the moral. Degrees of holiness and sin cannot be measured by a ruler. Size i s no criterion of moral worth. It is only figuratively that a man's character can be weighed in the balances. Moral phenomena are governed by moral laws. Nevertheless, the moral and the physical are not entirely (1) A purely secular scientific organization "created to pursue and foster research into rhythmic fluctuations i n a l l branches of natural and social phenoma" and numbering amongst i t s members some of the greatest scientists of Britain and America. 2 . separate realms. They do exist together and, however we explain i t , must bear some inter-relationship. Either the moral has arisen from the physical, as materialists say, or the underlying substance of things has both physical and moral potentialities, or both the physical and moral realms owe their existence to a Divine Author. That there is some inter-relationship no one w i l l deny. Further, i t is evident that i n time we have an element common to both realms. There i s a physical time order. "The sun knoweth his going down." The moon and the planets have their appointed seasons. Eclipses occur at fixed times. Ancient Greek research long ago brought to light the fundamental elements of these physical cycles. But time i s related also to the moral realm. The righteous are not always oppressed. "The time of the promise draws nigh." "The fulness of time comes." In this moral realm the sacred literature of the Jews i s supreme. Here we find professed revelations of great moral cycles, times appointed for the duration of empires and kings and for the deliverance of the righteous. Centuries of independent research in regard to these appointed times or cycles of the physical and moral realms have culminated in the discovery of certain curious relationships between them. These relation-ships constitute the burden of this thesis and, we humbly hope, may seem of sufficient significance to some to strengthen their f a i t h in a theological interpretation of nature and history. 3. Physical Cycles The real and apparent motions of sun, moon, and planets form the basis of nature's time order. The day, the lunar month, the year, and the planetary periods are the principal units. The matter i s complicated, however, by the fact that each of these heavenly luminaries possesses more than one type of periodic motion. The moon, for example, has four main periodic elements a l l producing easily observable effects, and a l l known centuries before the time of Christ. Each planet has two principal periods. The four lunar periods or months are the sidereal, the synodic, the anomalistic, and the nodical. The sidereal month i s simply one complete revolution of the moon about the earth or, in other words, the mean time taken for the moon to return to the same place i n regard to the fixed stars. The synodic month is the mean time taken for the moon to re-turn to the same position i n relation to the earth and the sun. And as the earth i t s e l f i s in motion about the sun, this does not correspond to the sidereal month. The synodic month is the time from f u l l moon to f u l l moon or from new moon to new moon. The anomalistic month is the time taken for the moon to return to the corresponding point on i t s e l l i p t i c a l orbit. And as the ellipse i t s e l f i s in motion the anomalistic month is not the same i n length as the sidereal. The anomalistic fluctuation is the prinoipal cause of the considerable difference i n length observable between individual synodic months. It also affects the nature of eclipses. When a f u l l solar eclipse occurs with the moon at apogee the eclipse i s total, but when a f u l l solar eclipse occurs with the moon at perigee the eclipse is annular. The nodical month is fundamental to eclipses. The moon in i t s revolution about the earth does not revolve i n the same plane that the earth does in i t s revolution about the sun, but in a plane at an angle to i t . The nodical month is the time taken for the moon to return to the corresponding point i n i t s plane. And as the plane is i n motion neither does this period correspond to the sidereal month. It i s obvious, further, that eclipses can occur only when the sun, earth, and moon are in a straight l i n e . Two conditions are therefore necessary: (1) The moon must be f u l l (for a lunar eclipse) or new (for a solar eclipse); (2) The moon must be at a node, i.e., i t must be cutting the e c l i p t i c , the plane in which the earth revolves about the sun. Hence i t is evident that eclipses w i l l recur only at intervals which are synodic nodical cycles. The two principal planetary periods are the^sidereal and the synodic. The sidereal period i s the mean time taken by the planet to complete one revolution about the sun. The synodic period is the mean time taken for the planet to return to the same position In relation to the earth and the sun. Of these various units in nature's time order the most important are those which are suited to calendareographical uses, viz., the day, the synodic month, and the tropical year. It is well known, further, that these units are not commensurate. One tropical year, for example, does not contain an exact number of synodic months. It is possible, however, to find periods which do contain very nearly exact 5. numbers of both tropical years and synodic months. Such periods are called soli-lunar cycles^) and are of f i r s t importance i n the formation of calendars based on the motions both of sun and moon. The f i r s t cycle of this sort to be used in G r e e c e w a s the eight years' cycle or octaeteris. Commenting upon the origin and nature of this cycle Geminus t e l l s u s ^ ) that the period was considered to contain 99 months (of which 3 were intercalary) and 2922 days. These numbers were arrived at, he says, on the assumption that the lunar year contains 354 days^) and the solar year 365 1/4 days. Thus the epact would be 11 l/4 days, which in eight years would amount to a whole number of days and a whole number of months; viz., 90 days or 3 months. In other words, 8 solar years exceed 8 lunar years by 3 lunar months. If, then, the lunar years are not to lag farther and farther behind the solar, i t w i l l be necessary i n the course of every eight years to make three of the lunar years leap years of 13 instead of 12 lunar months. Geminus then proceeds to note certain modifications of the 8 years' cycle suggested by a more accurate estimate of the length of the lunar month. The true length of the lunar month i s , he says, 29 l/2 plus l/33 days.( 5) Hence 99 months contain not 2922 days but 2923 l/2 days. Thus, he says, every 16 years 3 days w i l l have to be added i n (1) Censorinus calls them great years (anni magni) cf. De Die Natali, 18/5. (2) It was also the f i r s t cycle employed by the Babylonians i n their calendar and the f i r s t cycle employed by the early Christians for fixing the date of Easter. (3) Gemini Elementa Astronomiae 8/27 f . Manitius' edition p.110, 1. 21, f . Geminus flourished i n Rhodes c. B.C. 77. (4) The lunar year consisted of 12 months alternately " f u l l " and "hollow", i.e. of alternately 30 and 29 days. (5) 29 l/2 + l/33 s 29.5303 days, which is not far from 29.5306 days, the actual length of the synodic month. 6. order to harmonize the days with the lunar months. But since 8 solar years do contain 2922 d a y s , ^ i n 16 years the months w i l l be i n excess of the years by the 3 added days. This excess w i l l increase to a f u l l lunar month i n 10 of the 16 year periods or i n 160 years, when a f u l l month w i l l have to be dropped out to correct the cycle.(2) Finally, Geminus notices the 19 years' or Metonic cycle and i t s modifications. This cycle equates 19 years, 235 months (7 of which are intercalary), and 6940 days. In order to obtain the correct proportion of " f u l l " and "hollow" months the Greeks dropped every 64th day from an hypothetical calendar containing 235 months of 30 days each. Thus the omitted day i n the "hollow" months did not always come at the end of the month. The 64th day was arrived at by dividing 7050 (the number of days in 235 months of 30 days each) by 110 (the difference between 7050 and 6940 and hence the number of days that had to be dropped o u t ) / 4 ) Callipus suggested that the error of Meton's cycle could be corrected by dropping one day after four cyclic periods or 76 years. (1) Actually 2921.94 days. (2) This system of correcting the octaeteris on the basis of a 160 years' cycle seems to have been f i r s t suggested by the great Greek geometrician and astronomer, Eudoxus, and a system based upon i t to have been actually introduced i n Athens possibly i n 381 or 373 B.C., cf. Heath, Aristarchus p.293. Judged by accurate modern values the 160 years' cycle has an error of s l i g h t l y more than two days: 160 years r 58,438.75 days 1979 months s 58,441.03 days (3) Named after Meton who discovered i t c. 432 B.C. It has an error of less than a day (19 years - 6939.60 days, 235 months = 6939.69 days) and came to be the most widely used of a l l calendareographical cycles of the tropical year and the synodic month. It is s t i l l used i n the Jewish calendar and also, for fixing the date of Easter, in our own calendar. (4) Heath, Aristarchus, p.293. Geminus 8/50-56. 7. The Callipio cycle thus equates 76 years, 940 months, and 27,759 days (instead of 27,760.)^ About 125 B.C. Hipparchus devised a s t i l l further correction, dropping another day after four Callipic cycles, thus equating 304 years, 3760 months and 111,035 days (instead of 111,036). ( 2) Thus the practical necessity of devising an accurate calendar led the Greeks and other ancient peoples to investigate the relationship between the synodic month and the tropical year. Scientific interest led them on to investigate other more profound mysteries of nature's time measurements: the remaining elements of the moon's motion, (elements which affect the time and character of eclipses), and the periodicity of the planets. The b r i l l i a n t results of this research are set forth i n Claudius P t o l e m y ' g r e a t Syntaxis Mathematioa or "Almagest" the greatest extant astronomical work of antiquity, a work "which for fourteen centuries was the authoritative 'scripture of astronomy.*"^^ (5) In discussing the motions of the moon Ptolemy t e l l s us^ ' that the ancient mathematicians sought for a period which would harmonize the Moon's various incommensurate motions, and that, through observations of (1) Actually 76 years = 27,758.41 days and 940 months - 27,758.75 days (2) Cf. Eeath, Aristarchus, p.296,7. Actually 304 years = ill,033.63 days 3760 months - 111,035.01 days (3) Ptolemy flourished at Alexandria about A.D. 140. (4) Astronomy, Russel, Dugan, Stewart,, p.243. (5) Ptolemy, Syn. Math. 4/2. The extent of the errors of the cycle may be seen from the following figures: 223 synodic months s 6585.32 days 239 anomalistic months = 6585.54 days 242 nodical months - 6585.36 days 241 sidereal months s 6584.52 days 8. lunar eclipses, discovered that 6585 1/3 days (18 years 11 days) was such a period, for i t contained 223 synodic months, 239 anomalistic months, 242 nodical months, and 241 sidereal months. In later times this remarkable period came to be known as the "saros". Amongst the shorter periods i t is the fundamental eclipse cycle. Each saros contains a series of eclipses very similar to that i n the previous saros. After t e l l i n g us that some tripled this period of 6585 l/3 days i n order to eliminate the fraction, Ptolemy proceeds to recount that Hipparchus, (1) by making use of Chaldean observations as well as his own discovered another distinot and very remarkable eolipse cycle, a cycle which equates 345 years, 4267 synodic months, 4573 anomalistic months, 4630.5 nodical months,^ and 4612 sidereal months. Two other lunar cycles are mentioned by Ptolemy, the one a synodic anomalistic cycle equating 251 synodic and 269 anomalistic months4*' the other a synodic nodical oycle equating 5458 synodio and 5923 nodical months. (5) In modern times the search for eclipse cycles has been taken (1) Hipparchus flourished c. B.C. 130. (2) Ptolemy does not note the number of nodical months i n the period though i n the very nature of the case, as an eclipse interval, i t must contain either an integral or (as i n this case) a semi-integral number of nodical months. (3) The errors of the cycle may be seen from the following: 345 years = 126,008.56 days 4267 synodic mo. a 126,007.02 4573 anomalistic mo. s 126,006.96 days 4630.5 nodical mo. s 126,006.18 days 4612 sidereal mo. = 126,007.50 days (4) A very accurate cycle 251 synodic months n 7412.178 days • 269 anomalistic months • 7412.174 days (5) Another very accurate cycle 5458 synodic months = 161,177.95 days 5923 nodical months - 161,177.98 days 9. taken up by the well-known astronomer Simon Newcomb. ^  He discovered that 358 synodic months and 388.5 nodical months form a cycle.( 2) He further noticed that the third multiple of this cycle has the addition-a l feature of being an anomalistic cycle: 1074 synodic months, 1165.5 nodical months, and 1151 anomalistic months are a l l of very nearly the same length.( 3) Finally Mr. Newcomb noticed that in i t s eighteenth multiple the cycle possesses the yet additional feature of embracing an integral number of Julian years. Thus 521 Julian years, 6444 synodic months, and 6993 nodical months are equated. Newcomb illustrated the cycle h i s t o r i c a l l y by measuring 521 year intervals from the Nineveh eclipse of June 15th, 763 B.C. Thus eclipses recur on June 15th by the Old Style or Julian Calendar of the years 763, 242 B.C., A.D. 280, 801, 1322, and 1843. However, June 15th, 1843, Old Style i s the same as June 27th, 1843 by the Gregorian or present day calendar. It must be remembered, therefore, that this cycle is remarkable simply i n regard to the a r t i f i c i a l Julian year hut not i n regard to the true tropical year. It should be noticed, too, that i n this form (521 years) the anomalistic error of the cycle has increased to such an extent that i t can no longer be regarded as an anomalistic cycle. (1) Cf. Newcomb's arti c l e , Eclipse, in the eleventh edition of the Encyclopaedia Britannica. (2) 358 synodic months - 10,571.951 days 388.5 nodical months - 10,571.947 days (3) 1,074 synodic months - 31,715.85 days 1,165.5 nodical months - 31,715.84 days 1,151 anomalistic months - 31,715.29 days (4) 521 Julian years - 190,295.25 days 6444 synodic months - 190,295.11 days 6993 nodical months - 190,295.05 days 521 tropical years - 190,291.19 days 6906 anomalistic months - 190,291.72 days TABLES OF CYCLES The oalendareographical and eclipse cycles that we have been discussing above are units i n nature's time order, some of them remarkable and important units, but they are not the only units, nor the only remarkable units. In order, therefore, to obtain a more comprehensive grasp of nature's time order and i n order to provide a basis of comparison by which we may judge of the relative accuracy and unusualness of various cyclical periods, we shall set forth i n tabular form some of the main types of cycles. 11. TABLE 1 Cycles of the Solar Year and the Lunar Year The epact between one solar year and one lunary year i s 10.8751 days. This epact increases to a f u l l lunary year i n 354.3671 10 '8751" = 5 2 , 5 8 5 2 s o l a r years. That i s , i n 32.5852 solar years there are 32.5852 lunar years plus one lunar year. Henoe a l l multiples of 32.5852 w i l l contain integral epaots, and those multiples which are themselves integral w i l l be true cycles of the solar year and the lunar year, that i s , w i l l contain integral numbers of each. By this method we have located the solar year lunar year cycles found i n the following table. The table contains a l l cycles shorter than 4,000 years with errors less than a day. The bracketed number of the primary cycle appears after cycles which are not themselves primary. In calculating the errors of the cycles the values employed are: for the tropical year, 365.24219879 days; for the lunary year, 354.3670582 days, which are the values for the epoch A.D. 1900. The effect of secular acceleration on the error is such that i n past centuries oycles with a lunar-greater-than-solar error had somewhat smaller errors, but those with a solar-greater-than-lunar error had somewhat larger. The effect i s so slight, however, that for our present purposes we shall only occasionally need to draw attention to i t . TABLE 1. Cycles of the Solar Year and the Lunar Year 12 Solar Years Lunar Years Days in the Lunar Differ-Solar Period ence (days) 163 168 59,534.48 am .81 391 403 142,809.70 + .22 554 571 202,344.18 - .59 782 (391) 806 285,619.40 + .45 945 974 345,153.88 - .36 1,175 (391) 1,209 428,429.10 + .67 1,336 1,377 487,963.58 - .14 1,499 1,545 547,498.06 - .95 1,564 (391) 1,612 571,238.80 .90 1,727 1,780 630,773.28 + .09 1,890 (945) 1,948 690,307.76 - .73 2,118 2,183 773,582.98 + .31 2,281 2,351 833,117.46 - .50 2,509 2,586 916,392.68 + .54 2,672 (1,336) 2,754 975,927.16 - .28 2,900 2,989 1,059,202.38 + .76 3,063 3,157 1,118,736.85 - .05 3,226 3,325 1,178,271.33 - .86 3,291 3,392 1,202,012.08 + .99 3,454 (1,727) 3,560 1,261,546.55 + .17 3,617 3,728 1,321,081.03 am .64 3,845 3,963 1,404,356.25 + .40 13 TABLE 2. Cyoles of the Solar Year and the Lunar Month The epact between one solar year and one lunar year increases . 29.53059 n „,,_ T T to a f u l l lunar month i n n • - 2.715 solar years. Hence a l l 10.8701 multiples of 2.715 w i l l contain integral numbers of lunar months and those multiples which are themselves integral w i l l be true oyoles of the solar year and the lunar month, that i s , they w i l l contain integral numbers of each. By this method we have located the solar year lunar month cycles found in the following table. The table contains a l l cycles shorter than 3000 years which have errors less than a day. Below 100 years a l l cycles whose errors are less than two days are included. The value of the synodic month employed in calculating the errors is that for the epoch 1900, viz., 29.53058818 days. The bracketed number of the primary cycle appears after cycles whioh are not themselves primary. TABLE 2 14. Cycles of the Solar Year and the Lunar Month Solar Years Lunar Months Days in the Lunar Differ-Solar Period ence (days) 8 99 2,921.94 + 1.59 11 136 4,017.66 - 1.50 19 235 6,939.60 + .09 27 334 9,861.54 + 1.68 30 371 10,957.27 - 1.42 38 (19) 470 13,879.20 + .17 46 569 16,801.14 + 1.76 49 606 17,896.87 - 1.33 57 (19) 705 20,818.81 + .26 65 804 23,740.74 + 1.85 68 829 24,836.47 - 1.24 76 (19) 940 27,758.41 + .35 84 1,039 30,680.34 + 1.94 87 1,076 31,776.07 - 1.16 95 (19) 1,175 34,698.01 + .43 114 (19) 1,410 41,637.61 + .52 125 1,546 45,655.27 - .99 133 (19) 1,645 48,577.21 + .61 144 1,781 52,594.88 - .90 152 (19) 1,880 55,516.81 + .69 163 2,016 59,534.48 - .81 171 (19) 2,115 62,456.42 + .78 182 2,251 66,474.08 - .73 TABLE 2. Cycles of the Solar Year and the Lunar Month 15 Solar Years Lunar Months Days i n the Lunar Differ-Solar Period enoe (days) 190 (19) 2,350 69,396.02 + .86 201 2,486 73,413.68 mm .64 209 (19) 2,585 76,335.62 + .95 220 2,721 80,353.28 - .55 239 2,956 87,292.89 - .47 258 3,191 94,232.49 - .38 277 3,426 101,172.09 - .29 296 3,661 108,111.69 - .21 315 3,896 115,051.29 • - .12 334 4,131 121,990.89 .03 353 4,366 128,930.50 + .05 372 4,601 135,870.10 + .14 391 4,836 142,809.70 + .22 410 5,071 149,749.30 + .31 429 5,306 156,688190 + .40 448 5,541 163,628.51 + .48 467 5,776 170,568.11 .57 478 (239) 5,912 174,585.77 - .93 486 6,011 177,507.71 + .66 497 6,147 181,525.37 - .85 505 6,246 184,447.31 + .74 516 (258) 6,382 188,464.97 - .76 TABLE 2. 16. Cycles of the Solar Year and the Lunar Month Solar Years Lunar Months Days i n the Lunar Differ-Solar Period ence (days) 524 6,481 191,386.91 + .83 535 6,617 195,404.58 - .67 543 6,716 198,326.51 + .92 554 (277) 6,852 202,344.18 - .59 573 7,087 209,283.78 - .50 592 (296) 7,322 216,223.38 - .42 611 7,557 223,162.98 - .33 630 (315) 7,792 230,102.59 - .24 649 8,027 237,042.19 - .16 668 (334) 8,262 243,981.79 - .07 687 8,497 250,921.39 + .02 706 (353) 8,732 257,860.99 + .10 725 8,967 264,800.59 + .19 744 (372) 9,202 271,740.20 + .28 763 9,437 278,679.80 + .36 782 (391) 9,672 285,619.40 .45 801 9,907 292,559.00 + *54 812 10,043 296,576.67 - *97 820 (410) 10,142 299,498.60 + *62 831 (277) 10,278 303,516.-27 - .38 839 10,377 306,438.20 + i l l 850 10,513 310,455.87 — iBO TABLE 2. Cycles of the Solar Year and the Lunar Month 17. Solar Years Lunar Months Days i n the Lunar Differ-Solar Period once (days) 858 (429) 10,612 313,377.81 + . .80 869 10,748 317,395.47 - .71 877 10,847 320,317.41 + .88 888 (296) 10,983 324,335.07 - .62 896 (448) 11,082 327,257.01 + .97 907 11,218 331,274.67 - .54 926 11,453 338,214.28 - .45 945 (315) 11,688 345,153.88 - .36 964 11,923 352,093.48 - • .28. 983 12,158 359,033.08 - .19. 1,002 (334) 12,393 365,972.68 •a .10 1,021 12,628 372,912.28 - .02' 1,040 12,863 379,851.89 + .07-1,059 (353) 13,098 386,791.49 + .16* 1,078 13,333 393,731.09 + .24 1,097 13,568 400,670.69 + .33 1,116 (372) 13,803 407,610.29 + .41 1,135 14,038 414,549.90 + .50 1,154 14,273 421,489.50 + .59 1,165 14,409 425,507.16 - .92 1,173 (391) 14,508 428,429.10 + .67 1,184 (296) 14,644 432,446.76 ' .83 TABLE 2. Cycles of the Solar Year and the Lunar Month 18 Solar Years Lunar Months Days i n the Lunar Differ-Solar Period enoe (days) 1,192 14,743 435,368.70 + .76 1,203 14,879 439,386.37 - .74 1,211 14,978 442,308.30 + .85 1,222 (611) 15,114 446,325.97 - .66 1,230 (410) 15,213 449,247.90 + .93 1,241 15,349 453,265.57 - .57 1,260 (315) 15,584 460,205.17 - .48 1,279 15,819 467,144.77 - .40 1,298 (649) 16,054 474,084.37 - .31 1,317 16,289 481,023.98 - .22 1,336 (334) 16,524 487,963.58 - .14 1,355 16,759 494,903.18 - .05 1,374 (687) 16,994 501,842.78 + .03 1,393 17,229 508,782.38 + .12 1,412 (353) 17,464 515,721.98 + .21 1,431 17,699 522,661.59 + .29 1,450 (725) 17,934 529,601.19 .38 1,469 18,169 536,540.79 + .47 1,488 (372) 18,404 543,480.39 + .55 1,499 18,540 547,498.06 .95 1,507 18,639 550,419.99 + .64 1,518 18,775 554,437.66 .86 TABLE 2 19. Cycles of the Solar Year and ihe Lunar Month Solar Years Lunar Months Days i n the Lunar Differ-Solar Period enoe (days) 1,526 (763) 18,874 557,359.60 + .73 1,537 19,010 561,377.26 - .78 1,545 19,109 564,299.20 + .81 1,556 19,245 568,316.86 - .69 1,564 (391) 19,344 571,238.80 + .90 1,575 (315) 19,480 575,256.46 - .61 1,583 19,579 578,178.40 + .99 1,594 19,715 582,196.06 - .52 1,613 19,950 589,135.67 - .43 1,632 20,185 596,075.27 - .35 1,651 20,420 603,014.87 - .26 1,670 (334) 20,655 609,954.47 - .17 1,689 20,890 616,894.07 - .09 1,708 21,125 623,833.68 - .00 1,727 21,360 630,773.28 + .09 1,746 21,595 637,712.88 + .17 .1,765 (353) 21,830 644,652.48 + .26 1,784 22,065 651,592.08 + .35 1,803 22,300 658,531.68 + .43 1,822 22,535 665,471.29 + .52 1,833 (611) 22,671 669,488.95 - .99 1,841 22,770 672,410.89 + .60 TABLE 2. Cycles of the Solar Year and the Lunar Month 20. Solar Years Lunar Months Days i n the Lunar Differ-Solar Period enoe (days) 1,852 (926) 22,906 676,428.55 - .90 1,860 (372) 23,005 679,350.49 + .69 1,871 23,141 683,368.15 - .81 1,879 23,240 686,290.09 + .78 1,890 (315) 23,376 690,307.76 - .73 1,898 23,475 693,229.69 . + .86 1,909 23,611 697,247.36 mm .64 1,917 23,710 700,169.30 + .95 1,928 (964) 23,846 704,186.96 - .55 1,947 (649) 24,081 711,126.56 - .47 1,966 ( 983) 24,316 718,066.16 - .38 1,985 24,551 725,005.76 - .29 2,004 (334) 24,786 731,945.37 - .21 2,023 25,021 738,884.97 - .12 2,042 (1,021) 25,256 745,824.57 - .03 2,061 (687) 25,491 752,764.17 .05 2,080 (1,040) 25,726 759,703.77 + .14 2,099 25,961 766,643.38 + .22 2,118 (353) 26,196 773,582.98 + .31 2,137 26,431 780,522.58 + .40 2,156 (1,078) 26,666 787,462.18 + .48 2,175 (725) 26, 901 794,401.78 + .57 TABLE "2. Cycles of the Solar Year and the Lunar Month 21. Solar Years Lunar Months Days in the Lunar Differ-Solar Period ence (days) 2,186 27,037 798,419.45 mm .93 2,194 (1,097) 27,136 801,341.38 + .66 2,205 (315) 27,272 805,359.05 - .85 2,213 27,371 808,280.99 + .74 2,224 27,507 812,298.65 - .76 2,232 (372) 27,606 815,220.59 + .83 2,243 27,742 819,238.25 - .67 2,251 27,841 822,160.19 + .92 2,262 27,977 826,177.85 - .59 2,281 28,212 833,117.46 - .50 2,300 28,447 840,057.06 - .42 2,319 28,682 846,996.66 - .33 2,338 (334) 28,917 853,936.26 - .24 2,357 29,152 860,875.86 - .-16 2,376 29,387 867,815.46 tm *07 2,395 29,622 874,755.07 + .02 2,414 29,857 881,694.67 + ao 2,433 30,092 888,634.27 + i l 9 2,452 30,327 895,573.87 + .-28 2,471 (353) 30,562 902,513.47 + *36 2,490 30,797 909,453.07 + .45 2,509 31,032 916,392.68 + .54 TABLE 2. Cycles of the Solar Year and the Lunar Month 22. Solar Years Lunar Months Days in the Lunar Differ-Solar Period ence (days) 2,520 (315) 31,168 920,410.34 - .97 2,528 31,267 923,332.28 + .62 2,539 31,403 927,349.94 - .88 2,547 31,502 930,271.88 + .71 2,558 (1,279) 31,638 934,289.54 - .80 2,566 31,737 937,211.48 + .80 2,577 31,873 941,229.15 - .71 2,585 31,972 944,151.08 + .88 2,596 (649) 32,108 948,168.75 .62 2,604 (372) 32,207 951,090.69 + .97 2,615 32,343 955,108.35 - .54 2,634 (1,317) 32,578 962,047.95 - ;45 2,653 32,813 968,987.55 - *36 2,672 (334) 33,048 975,927.16 - .28 2,691 33,283 982,866.76 - .19 2,710 (1,355) 33,518 989,806.36 - .10 2,729 33,753 996,745.96 - .02 2,748 (687) 33,988 1,003,685.56 + .07 2,767 34,223 1,010,625.16 + .16 2,786 (1,393) 34,458 1,017,564.77 + .24 2,805 34,693 1,024,504.37 + .33 2,824 (353) 34,928 1,031,443.97 + .41 23 TABLE 2. Cycles of the Solar Year and the Lunar Month Solar Years Lunar Months Days in the Lunar Differ-Solar Period ence (days) 2,843 35,163 1,038,383.57 + .50 2,862 (1,431) 35,398 1,045,323.17 + •59 2,873 35,534 1,049,340.84 - .92 2,881 35,633 1,052,262.77 + .67 2,892 (964) 35,769 1,056,280.44 mm .83 2,900 (725) 35,868 1,059,202.38 + .76 2,911 36,004 1,063,220.04 - .74 2,919 36,103 1,066,141.98 + .85 2,930 36, 239 1,070,159.64 - .66 2,938 (1,469) 36,338 1,073,081.58 + .93 2,949 (983) 36,474 1,077,099.24 - .57 2,968 36,709 1,084,038.85 - .48 2,987 36,944 1,090,978.45 .40 24. TABLE 3. Soli-Lunar - Anomalistic Cyoles In the preparation of this table two separate tables of solar-synodic and solar-anomalistic tables were compared for cycles common to both. The resulting cycles are free from the considerable e r r o r ^ occasioned by the moon»s anomaly; that i s , i n these cycles the solar-synodic error is the only error of any magnitude and therefore comes very close to representing the actual error found i n practice. The table displays a l l numbers whose soli-lunar error is not appreciably greater than a day and whose lunar-anomalistio error is less than two days. (It should be remembered, of course, that a two day lunar-anomalistic error when reduoed to i t s observable effect upon the length of the synodic period amounts to a very small fraction of a day.) In the soli-lunar error column, plus and minus signs indicate whether the lunar period is greater or less than the solar. Similarly, i n the lunar-anomalistic error column, plus and minus signs indicate whether the anomalistic period is greater or less than the lunar. (1) Though the average value of the synodic month i s , as we have said, 29.53058818 days, the actual value varies nearly thirteen hours, mainly on account of the eccentricity of the lunar" orbit; that "is on account of the moon's anomalistic motion. See Russel-Pugan-Stewart, Astronomy p. 160. TABLE 3. Soli-Lunar-Anomalistic Cycles 25. Solar Years Lunar Anomalistic Soli-Lunar Lunar Anomalistic Months Months Error i n Error i n Days Days . 106 1,311 1,405 - 1.07 - .46 133 1,645 1,763 + .61 + .85 239 2,956 3,168 . - .47 + .40 372 4,601 4, 931 + ,14 + 1.25 478 (239) 5,912 6,336 - .93 + . .79 486 . 6,011 6,442 + .66 - 1.95 611 7,557 8,099 - .33 + 1.65 725 8,967 • 9,610 + .19 - 1.56 858 10,612 11,373 + .80 - .70 964 11,923 12,778 - .28 - 1.16 1,097 13,568 14,541 + .33 - .31 1,203 14,879 15,946 - .74 - .77 1,230 15,213 16,304 + .93 + .55 1,336 16,524 17,709 - .14 + .09 1,469 18,169 19,472 + .47 + .94 1,575 19,480 20,877 - .61 + .48 1,708 21,125 22,640 - .00 + 1.34 1,814 22,436 24,045 - 1.07 + .88 1,822 22,535 24,151 + .52 - 1.87 1,947 24,081 25,808 - .47 + 1.73 1,955 24,180 25,914 + 1.12 - 1.01 2,061 25,491 27,319 + .05 1.47 TABLE 3. Soli-Lunar-Anomalistic Cycles Solar Years Lunar Anomalistic Soli-Lunar Lunar Anoma-Months Months Error in l i s t i c Error Days i n Days 2,194 (1,097) 27,136 29,082 + .66 mm .62 2,300 28,447 30,487 .42 - i.oe 2,433 30,092 32,250 + .19 - .22 2,539 31,403 33,655 - .88 - .68 2,566 31,737 34,013 + .80 + .63 2,672 (1,336) 33,048 35,418 - .28 + .17 2,805 34,693 37,181 - .33 + 1.03 2,911 36,004 38,586 + .74 + .57 27. TABLE 4. Soli-Lunar-Nodical Cycles The following table was prepared i n much the same way as the table of soli-lunar-anomalistic cycles. Two separate tables were f i r s t made, the one of solar-synodic cycles, the other of solar-nodical cycles. A l l that then remained was to note what periods were common to both tables and therefore cyclic i n both respects. Soli-lunar-nodioal cycles are, of course, eclipse cycles. I f , for example, we take as our starting point a January 6th when the moon is f u l l and is suffering eclipse, any accurate soli-lunar cycle w i l l lead us to another January 6th when the moon w i l l be f u l l , but only a s o l i -lunar-nodioal cycle w i l l lead us to another January 6th when the moon w i l l be not only f u l l but also again suffering eclipse. The table displays a l l numbers whose soli-lunar error is not appreciably greater than a day and whose lunar-nodical error is less than two days. The practical effect of the lunar-nodical error is relatively small. An interval may have a lunar-nodical error approaching two days and yet be a true eclipse interval. The moon may s t i l l be sufficiently close to the plane in which the earth is revolving about the sun, to pass through the earth's shadow. As in the previous table, i n the soli-lunar error column, plus and minus signs indicate whether the lunar period is greater or less than the solar; and i n the lunar-nodical error column, plus and minus signs indicate whether the nodical period is greater or less than the lunar. TABLE 4. Soli-Lunar-Nodical Cycles 28. Solar Lunar Nodical Soli-Lunar Lunar-Nodical Years Months Months Error i n Days Error i n Days 19 235 255 + o09 mm .57 38 (19) 470 510 + .17 - 1.14 57 (19) 705 765 + .26 • - 1.72 334 4,131 4,483 .03 + 1.52 353 4,366 4,738 + .05 + .95 372 4,601 4,993 + .14 + .38 391 4,836 5,248 + .22 mm .19 410 5,071 5,503 + .31 - .77 429 5,306 5,758 + .40 - 1.34 448 5,541 6,013 + .48 - 1.91 706 (353) 8,732 9,476 + .10 + 1.90 725 8,967 9,731 + .19 + 1.33 744 (372) 9,202 9,986 + .28 + .76 763 9,437 10,241 + .36 + .18 782 (391) 9,672 10,496 + .45 - .39 801 9,907 10,751 + .54 - .96 820 (410) 10,142 11,006 + .62 - 1.53 ,097 13,568 14,724 + .33 + 1.71 ,116 (372) 13,803 14,979 + .41 + 1.13 ,135 14,038 15,234 + .50 + .56 TABLE 4. Soli-Lunar-Nodioal Cycles 29 Solar Lunar Nodical M Soli-Lunar Lunar-Nodical Years Months Months Error in Days Error i n Days 1,154 14,273 15,489 + .59 - .01 1,173 (391) 14,508 15,744 + .67 mm .58 1,192 14,743 15,999 + .76 - 1.15 1,211 14,978 16,254 + .85 mm 1.73 1,488 (372) 18,404 19,972 + .55 + 1.51 1,507 18,639 20,227 + .64 + .94 1,526 (763) 18,874 20,482 + .73 + .37 1,545 19,109 20,737 + .81 - .20 1,564 (391) 19,344 20,992 + .90 .78 1,583 19,579 21,247 + .99 - 1.35 1,602 19,814 21,502 + 1.07 - 1.92 1,860 (372) 23,005 24,965 + .69 + 1.89 1,879 23,240 25,220 + .78 + 1.32 1,898 23,475 25,475 + .86 + .75 1,917 23,710 25,730 + .95 + .17 1,936 23,945 25,985 + 1.04 - .40 1,955 (391) 24,180 26,240 + 1.12 - .97 2,251 27,841 30,213 + .92 + 1.69 2,270 28,076 30,468 + 1.00 + 1.12 2,289 (763) 28,311 30,723 + 1.09 + .54 30. TABLE 5. Soli-Lunar-Anomalistio-Nodical Cycles. There are a few periods oommori to Table 4 and Table 5 and, there-fore, embraoing the characteristics of both. The effect upon eolipses is that eolipses separated by such intervals w i l l be of similar charaoter: an annular eclipse w i l l be followed by an annular eclipse, a total eclipse by a total eclipse. TABLE 5. Soli-Lunar-Anomalistio-Nodical Cycles• Solar Lunar Anomalistic Nodical Soli-Lunar Lunar-Anom. Lunar-Years Months Months Months Error i n Error i n Nodical Days Days Error in Days 372 4,601 4,931 4,993 + • 14 + 1.25 + .38 725 8,967 9,610 9,731 + .19 - 1.56 + 1.33 1,097 13,568 14,541 14,724 + •33 - .31 + .1.71 1,955 24,180 25,914 26,240 + 1.12 - 1.01 .97 31 The above tables display a l l the more accurate lunar cycles embracing a whole number of years. We have refrained from making a com-plete table of cycles of the solar year and the sidereal month because such a table would be l i t t l e more than a duplicate of table No. 2. The length of the sidereal month i s such that solar-year synodic-month cycles are also solar-year sidereal-month cyoles, the main difference being that each year contains one more sidereal month than i t does synodic months. Thus i n 315 years there are 3,896 synodic month6, but 3,896 plus 315 or 4,211 sidereal months. Another difference is that the error of the side-real oyoles reaches i t s minimum somewhat earlier than the error of the synodic cycles. A glance at Table No. 2 w i l l show that after the 19 years' cycle the synodic oycles reach their f i r s t period of minimum error at the oycles of 334 and 353 years. The sidereal cycles, however, reach their f i r s t period of minimum error with the 277 years' cycle as the following brief table w i l l show. Solar Sidereal Days in the Sidereal Difference Years Months Solar Period i n Days 239 3,195 87,292.89 . - .18 258 3,449 94,232.49 . .08 277 3,703 101,172.09 + .02 296 3,957 108,111.69 + .12 32. MORAL CYCLES There now remains the interesting task of examining "the professed revelations of great moral cycle s " ^ ^ found i n the apooalyptio literature of the Old and New Testaments, and of tracing the history of exposition respecting them. We shall be oonoerned, therefore, with: (1) The "time and times and half, a time" of Daniel 7/25, 12/7, and Revelation 12/14, whioh period is unquestionably identical with the "forty and two months" of Revelation l l / 2 and 13/5, and with the 1,260 days of Revelation l l / 3 and 12/6;(-) (2) The 2,300 days of Daniel 8/l4; (3) The 70 weeks of Daniel 9/24; (4) The 1,290 days of Daniel 12/11; (5) . The 1,335 days of Daniel 12/12; (6) The 5 months of Revelation 9/5; (7) The "hour and day and month and year" of Revelation 9/l5; and (8) The "three days and a half" of Revelation l l / 9 . Of these periods the 70 weeks of Daniel 9/24 was the f i r s t to receive an interpretation whioh proved, to a considerable extent, stable. (1) See above, page 2. (2) Thus Augustine says., " i t is patent from the context that the time, times and half a.time means a year, and two years, and half a year; that is to say, three years and a half." City of God, chapter 23. Commenting on the passage i n his Chronographies (written about A.D. 221) Julius Africanus says: "This passage, therefore, as i t stands thus, touohes on many marvellous things. At present, however, I shall speak only of those things i n i t which bear upon chronology, and matters connected therewith. "That the passage speaks, then, of the advent of Christ who was to manifest Himself after seventy weeks, is evident. For i n the Saviour*s time, or from Him, are transgressions abrogated, and sins brought to an end. And through remission, moreover, are iniquities, along with offences blotted out by expiation; and an everlasting righteousness is preached, different from that whioh is by the law; and visions and prophecies (are) u n t i l John, and the Most Holy is anointed. For before the ad-vent of the Saviour these things were not yet, and were therefore only looked f o r . "And the beginning of the numbers, that i s , of the seventy weeks which make up the 490 years, the angel instructs us to take from the going forth of the commandment to answer and to build Jerusalem. And this happened i n the twentieth year of the reign of Artaxerxes "king of Persia. For Nehemiah his cupbearer be-sought him, and received the answer that Jerusalem should be b u i l t . And the word went forth commanding these things; for up to that time the c i t y was desolate. For when Cyrus, after the seventy years' oaptivity, gave free permission to a l l to return who desired i t , some of them under the leadership of Joshua the high priest and Zorobabel, and others after these under the leadership of Esdra, returned, but were prevented at f i r s t from building the temple and from surrounding the cit y with a wall, on the plea that that had not been commanded. It remained i n this position, accordingly, u n t i l Nehemiah and the reign of Artaxerxes, and the 115th year of the sovereignty of the Persians. And from the oapture of Jerusalem that makes 185 years. And at that time King Artaxerxes gave order that the c i t y should be built; and Nehemiah being despatched, superin-tended the work, and the street and the surrounding wall were b u i l t , as had been prophesied. And reckon-ing from that point, we make up seventy weeks to the time of Christ. "For i f we begin to reokon from any other point and not from this, the periods w i l l not correspond, and very many odd results w i l l meet us. For i f we begin the calculation of the seventy weeks from Cyrus "and the f i r s t restoration, there w i l l be upwards of one hundred years too many, and there w i l l he a larger number i f we begin from the day on whioh the angel gave the prophecy to Daniel, and a much larger number s t i l l i f we begin from the commencement of the captivity. For we find the sovereignty of the Persians comprising a period of 230 years, and that of the Macedonians ex-tending over 370 years, and from that to the 16th year of Tiberius Caesar is a period of about 60 ye ars. " i t is by calculating from Artaxerxes, therefore, up to the time of Christ that the seventy weeks are made up, acoording to the numeration of the Jews. For from Nehemiah, who was despatched by Artaxerxes to build Jerusalem i n the 115th year of the Persian Empire, and the fourth year of the 83rd Olympiad, and the 20th year of the reign of Artaxerxes himself, up to this date, which was the seoond year of the 202& Olympiad, and the sixteenth year of the reign of Tiberius Caesar, there are reckoned 475 years, which make 490 according to the Hebrew numeration, as they measure the years by the course of the moon; so that, as i s easy to show, their year consists of 354 days, while the solar year has 365 1/4 days. For the latter exceeds the period of twelve months, according to the 36. "moon's course by 11 l/4 days. Hence the Greeks and the Jews insert three intercalary months every eight years; for 8 times 11 1/4 days makes up three months. Therefore 475 years make 59 periods of 8 years each, and three months besides. But since thus there are three intercalary months every eight years, we get thus 15 years minus a -few days; and these being added to the 475 years, make up i n a l l the seventy weeks." '(•'•) Afrioanus'main calculation w i l l bear the test of the closest cri t i c i s m . His date for the starting point of the 70 weeks, the fourth year of the 83d Olympiad, which corresponds to B.C. 445, is the date assigned also by modern scholars to the 20th year of Artaxerxes. So, too, the second year of the 202d Olympiad (A.D.30) corresponds, as he says, to the 16th year of the sole rule of Tiberius, and was the 475th solar year or the 490th lunar year from B.C. 445. His view of the 70 weeks, which regards them as weeks of lunar years extending from the decree to Nehemiah (Nehemiah 2) to the time of Christ, has been adopted by a long line of expositors reaching down (2) to modern times. Zookler t e l l s us that i t was the view adopted by Chrysostom (d.A.D.407), favoured hy Jerome (d.A.D.420), adopted by (1) Robers and Donaldson's edition of the Ante-Nicene Fathers, v o l . 6, p.134, 135. (2) Zockler on Daniel, p.207-209 i n Schaff's edition of Lange's Commentary. Theodoret (d.A.D.429), Isidore of Pelusium (d.A.D.450), the Venerable Bede (d.A.D.735), Euthymius Zigahenus (early 12th century), hy a majority of the expositors i n the Oriental church generally, by Thomas Aquines (d.1274), by Hassenkemp (d.1777), by J.D. Michaelis (d.1791), and others. Bede's exposition of the passage which, we are told, was the basis of most of the mediaeval exegesis, i s so suggestive that we subjoin our translation of i t . Bede has been discussing hebdomads of various kinds. The f i r s t hebdomad, according to his enumeration, i s the Creation week (Gen.l); the second, the seven-day week of the fourth commandment (Ex. 20/9); the third, the seven weeks leading to the Feast of Pentaoost (Deut.16/9 f«)j the fourth, the seventh month of the Jewish year, almost a l l of which was given over to religious duties (Numbers 29)j the f i f t h , the seventh year, the year of rest for the land (Lev-iticus 25/3); the sixth, the Jubilee after seven weeks of years (Leviticus 25/8); the seventh he identifies with Daniel's "seventy weeks; and comments as follows: (2) "The seventh form of hebdomad is that which the prophet Daniel employs-1*. That he should regard each hebdomad as seven years is i n accordance with the oustom of the law, hut that he should cut s h o r t t h e years themselves is new. Thus each year i s composed of twelve lunar months; for he does not insert, every 2nd or 3rd year, the customary (1) C. W. Jones, Bedae Opera de Temporibus p.344. (2) De Tempore Ratione, cap.9, p.198-201 i n Jones Bedae Opera de Temporibus. (3) Latin, abbrevians. 38. "intercalary months which grow out of the annual 11 days' epact; but, on the contrary, when they have increased to twelve months, introduces another whole year. He has d o l ^ ^ h i s , not because he begrudges recognition of the truth to those who are i n quest of i t , but rather because (after the fashion of a prophet) he desires to exercise the s k i l l of the seekers. For he would prefer that his pearls should be hidden from his own sons and be sought for by f r u i t f u l sweat, than that they should be profusely poured forth and, with fastidious contempt, be trodden under foot by swine• "But, i n order that we might understand these things more clearly l e t us look at the very words of the angel to the prophet, 'Seventy hebdomads, he says, 'are cut o f f ^ ^ i n regard to your people and your holy ci t y , that transgression might be finished, sin be brought to an end, iniquity be destroyed, everlasting righteousness be brought i n , vision and prophecy be f u l f i l l e d , and the Holy of Holies be anointed.' No one doubts but that these words refer to the incarnation of Christ who bore the sins of the world, f u l f i l l e d the law and the prophets, and was anointed with (l) Latin, abbreviatae sunt. the o i l of gladness above his fellows; and that the seventy hebdomads, each defined as 7 years, amount to 490 years. But i t ought to be noted that i t is not said simply that these hebdomads are assigned or determined but that they are 'cut off.' (1) He thus darkly cautions the reader that he might know that shorter years than ordinary are intended. "•'Know therefore, 1 he says, 'and consider: from the going forth of the word that Jerusalem is to be built again up to Christ, the Leader, shall be 7 hebdomads and 62; and i t shall be built again with street and wall i n troublous times.' We know (from the pen of Ezra) (*-) that Nehemiah, when he was cupbearer of King Arta-xerxes, i n the 20th year of his reign, i n the month Nisan, secured permission from him to re-store the walls of Jerusalem (Cyrus having long before given permission to build the temple). This task, as we are told, he accomplished i n troublous times, and so much was he opposed by the neighbouring peoples that a l l the builders are said to have worn swords and to have fought with one hand and bu i l t the v/all with the other. (1) Latin, abbreviatae sunt. (2) Bede evidently believed Ezra wrote the book of Nehemiah. "From this time, therefore, to Christ, the Leader, the 70 hebdomads are to be computed; that i s , the 490 years of 12 lunar months, whioh amount to 475 solar years. From the 20th year of Artaxerxes (mentioned above) to the death of Darius, the Persians reigned 96 years. From that time to the death of Cleopatra, the Macedonians reigned 300 years. Thence to the 17th year of Tiberius Caesar the Romans held the monarchy for 59 years. A l l these periods added together give the number we mentioned, 475 years, and contain 25 nineteen years' cycles (for 19 times 25 amounts to 475). And, sinoe i n each cycle there are 7 interoalary months, i n the 25 cycles or 475 years there are a total of 25 times 7 or 175 intercalary months. I f , therefore , you wish to know how many lunar years they oan make, divide the 175 by 12 (12 times 14 amounts to 168). Accordingly, the result is 14 years and 7 months. Add these to the aforementioned 475 years and they become 489 years. Add, also, the seven months' excess and the part of the 18th year of Tiberius Caesar i n which our Lord suffered, and you w i l l find from the time before mentioned to His passion 70 weeks cut off, that is 490 lunar years. "But to His baptism when the Holy of Holies was anointed hy the Holy Spirit descending upon Him as a dove, not only had the 7 and 62 hebdomads been completed, but also part of the 70th hebdomad had already begun. 'After 62 hebdomads,' he says, •the Christ shall be slain, and the people who w i l l have denied Him shall cease to be.' Not immediately after the 62 hebdomads was Christ slain hut at the end of the 70th hebdomad. This hebdomad he has separated from the others because (so far as we can judge) he was going to relate more things i n regard to i t . For i n i t Christ was crucified, i n i t He was denied by the deceitful populaoe, not only at the time of His passion but from the moment His coming was heralded by John. "The next phrase, 'And the people with their leader who shall come shall destroy the c i t y and the sanctuary and i t s end w i l l be a ruin, and after the end of the war desolation i s determined,1 does not pertain to the 70 hebdomads, for i t was previous! predicted that the 70 .hebdomads themselves reached to the leadership of the Christ. This passage, therefore, since Christ's advent and passion had already been pre-dicted, shows us what would oome to pass even after these things i n regard to the people who had refused to receive Him. For i t speaks of the coming leader Titus, who i n the 40th 42. year after our Lord's passion, together with the Roman people, so demolished the city and the sanctuary that there was not l e f t one stone upon another. "But from these anticipatory foretastes he soon returns i n order to expound the things of the omitted hebdomad. 'He shall confirm the covenant with many for one hebdomad.' That i s , i n that last one i n which John the Baptist, the Lord, and His apostles, by their preaohing turned many to the f a i t h . 'And i n the midst of the hebdomad he shall cause the sacrifice and the oblation to cease.' The midst of this hebdomad coincides with the 15th year of Tiberius Caesar, the year of Christ's baptism. From this time on, purification by animal sacrifices was less and less esteemed by the believers. "The next phrase, 'And there w i l l be i n the temple the abomination of desolation, and right up to the consummation and the end desola-tion w i l l continue,' respects subsequent times. It is a prophecy, to the truth of whioh both the history of ancient times and the daily happenings of our own bear witness." Modern expositors^ 1) who follow Africanus and Bede differ from (1) e.g. Dr. H. Grattan Guinness. them only i n placing the death of Christ in the midst instead of at the end of the 70th week(^) and i n admitting a secondary fulfillment in solar years measured from the decree given to Ezra i n the seventh year of Artaxerxes (Ezra 7 ) . ^ The periods l i e thus: (l) This is by no means a recent refinement, Calvin i n commenting on the phrase, fIn the midst of the week he shall cause the sacrifice and the.oblation to cease," said "We ought to refer this to the time of the resurrection,. For while Christ passed through the period of His l i f e on earth, He did not put an end to the sacrifices; hut after He had offered Him-self up as a victim, then a l l the rites of the law came to a close." Calvin's Commentary on-Daniel, p.226. (2) This date as a terminus a quo for the 70 weeks also i s not new. It was held by Abraham Calovius (d,1686), Sir Isaac Newton (d,1727), G.S. Faber (d. ), E.B. Pusey (d.1882) and many others. The dates given above are those assigned to the events by competent chronologists. A.D. 29 is the date given for the death of Christ in the article "Jesus Christ" in the Encyclopaedia Britannioa (14th edition). B.C. 458 is the date assigned to the seventh year of Artaxerxes in a l l recent works on the chronology of the period. B.C. 444 corresponds to the 21st year of Artaxerxes (1) in the f irst month of which Nehemiah received his commission. From the month Nisen B.C. 458 when the decree was given to Ezra( 2) to the corresponding month Nisen A.D. 29 when Christ was (3) orucified is a period of 486 solar years. From the above tables^ ' i t wi l l be seen that this period is a soli-lunar-anomalistio cycle con-taining to within a fraction of a day a whole number of lunar months. From the month Nisan B.C. 444 when permission to return was granted to Nehemiah^4) to the month Nisan A.D. 29 when Christ was crucified is a period of 472 solar years. In 472 solar years there are, to the nearest month, 5,838 lunar months which is the number of lunar months in 486 1/2 lunar years .( 5 ) From the above i t wi l l be seen that the history of the exegesis of Daniel's seventy weeks has involved a considerable acquaintance with the time order of nature as well as with that of history, and that the (1) In Neh. 2/1 i t is called the 20th year of Artaxerxes, but this must be by the Jewish oivi l reckoning (beginning with the seventh month) for December of the previous year is also said to f a l l in the 20th of Artaxerxes (Neh.1/1). Cf. the review of Parker and Dubberstein's, Babylonian Chronology, in the Journal of Near Eastern Studies, vol.2, No.2, April 1943. (2) Ezra 7/9. (3) See tables 2 and 3 above. (4) Neh. 2/L. (5) 472 solar years s 172,394.32 days 486 l/2 lunar years = 172,399.57 days. 45. From the above i t w i l l be seen that the history of the exegesis of Daniel's seventy weeks has involved a considerable acquaintance with the time order of nature as well as with that of history, and that the f i n a l positions arrived at display an interesting relationship between the volumes of revelation, history, and nature: the interval of 69 l/2 weeks of years is significant i n a l l three. Before we proceed to examine the remaining ohronologio inter-vals we have mentioned, we propose to glance b r i e f l y at the history of the exposition of the passages which form their setting; i.e., of the 7th, 8th, 11th and 12th ohapters of Daniel, and of the book of the Revelation. DANIEL 7 The four empires of Daniel, represented in chapter 2 hy the four metals of the image, and i n chapter 7 by the four great beasts arising from the sea, have from very early times been identified with the Babylonian, Medo-Persian, Macedonian, and Roman Empires. Zookler t e l l s us that "The 'orthodox' view which refers the f i r s t three kingdoms to Babylon, Medo-Persia, and Greece, hut the fourth to Rome and the states which have sprung from i t since the empire" was held "by Josephus (Ant. IO /10/4), by a majority of church fathers - especially by Jerome, Orosius, and Theodoret; also by a l l the expositors of the Middle Ages after Walafrid Strabo (d.A.D.849), and hy a majority of moderns. (1) Zockler's Commentary on Daniel, Shaff's edition p.86. 46. Hippolytus, bishop of Rome (d.A.D. 235) expresses the view very succinctly. He says, "The 'golden head of the image' is identical with the •lioness' by which the Babylonians were represented. •The golden shoulders and the arms of silve r ' are the same with the 'bear* by which the Persians and Medes are meant. 'The belly and thighs of brass' are the 'leopard 1 by which the Greeks who ruled from Alexander onwards are intended. The 'legs of iron* are the 'dread-f u l and terrible beast' by whioh the Romans who hold the empire now are meant. The 'toes of clay and iron' are the 'ten horns' which are to be. The 'one other l i t t l e horn springing up i n the midst' is the 'anti-christ'. The stone that 'smites the image and breaks i t i n pieces* and that f i l l e d the whole earth, i s Christ who comes from heaven and brings judgment on the world. After the Roman Empire had broken up, the ten horns of Daniel 7/7, 24, gradually came to be interpreted of the invading barbarian tribes or of the kingdoms they established on the site of the former empire. Thus Berengaud, an Apocalyptic commentator of the 11th century, says: "The fourth beast, by which the Romans are designated, is described as having ten horns. (1) Roberts and Donaldson's Ante-Kicene Fathers, v o l . 5, p. 178, 9. By these horns are designated those kingdoms whioh ; „ ( 1 ) destroyed the Roman Empire." Finally, at the time of -the Reformation, the l i t t l e horn which arose among the ten horns, displaced three, had "eyes like the eyes of a (2) man and a mouth speaking great things," and "made war with the saints," oame to he interpreted hy almost a l l Protestants, of -the Roman Catholic Papacy. Thus Luther says that when Daniel "saw the terrible wild beast which had ten horns, which by the consent of a l l is -the Roman Empire, he also beheld another small horn come up in the middle of them. This is (3) the Papal power, which rose up i n the middle of "the Roman Empire." The three displaced horns were -variously interpreted: some considered them contemporary states out of which the Papal temporal (4) dominions were carved, others as three successive barbarian tribes up-rooted before the growing power of the Pope of Rome. The number ten was regarded as a round number unaffected, eventually, even hy the f a l l of the three horns before the rising l i t t l e horn. (1) "Quarta Bestia, per quam Romani designati sunt, decern cornua .habuisse describitur, per quae ea regna quae Romanum imperium destruxerunt designate sunt." Quoted in E l l i o t t ' s , Horae Apocalypticae, 5th edition, v o l . 3, p.141. (2) Dan. 7/8, 20, 21. (3) Luther's works vol. 2 p. 386, quoted in H.Grattan Guinness' Romanism and the Reformation, p.231, 2. (4) The Heruli, Ostrogoths and Lombards. 48. DANIEL 8. We now turn to the vision of the ram and the he-goat of the eighth chapter of Daniel. The f i r s t part of this vision i s so clearly explained in the chapter i t s e l f that i t has never occasioned any d i f f i c u l t y . The ram is the Medo-Persian empire; the he-goat, the Macedonian; the great horn of the he.-goat, Alexander; the four notable horns which arose after the great horn was broken, the four kingdoms into which Alexander's empire s p l i t after his death. On the other hand, tiie concluding part of the vision, the l i t t l e horn which waxed exceeding great toward the south, and toward the east, and toward the glorious land, has been variously interpreted. Josephus (Ant. 10/ll/7 and 12/7/6), followed hy hosts of others down to modern times, saw the fulfillment of this vision of the " l i t t l e (1) horn" in the career of Antiochus Epiphanes. The early church fathers, however, thought that the passage must (2) have at least a secondary reference to the 'Antichrist. 1 S i r Isaac Newton, followed by Bishop Newton, Cuninghame and others, interpreted the " l i t t l e horn" of the Romans. They maintained that when the Romans conquered Macedon they became in that capacity, and in that capacity alone, a horn of the Macedonian beast. Thenoe i t pushed (1) See 1 Maccabees l / l - l O f . (2) So Irenaeus, R. and D. Ante-Nicene Fathers, vol. 1, p. 554; and Origen, idem, vol. 4, p.594. By 'Antichrist' the fathers meant the power pre-figured i n 2 Thess. 2, Daniel 7/25, Rev. 13/6, etc. 49. i t s conquests in the precise directions prophesied of the l i t t l e horn, "became mighty as a horn of the he-goat, not by i t s own Greek power but by the strength of Italy and the West: and that i t notoriously stood up against the Prince of princes and took away the daily sacrifice, when i t crucified the Messiah and placed the abomination of desolation i n the temple of Jerusalem."^''") Faber and E l l i o t t , on the other hand, understood by the l i t t l e horn the Mohammedans; Faber interpreting i t of the Saracens, E l l i o t t of the Turks. A l l four of the above powers unquestionably did flourish i n the geographical theatre indicated by the prophecy; have had a part in giving "the sanctuary and the host to be trodden under foot;" and were, the f i r s t two to the Jews, the last two to both Jews and Christians, awesome and desolating judgments. It may be, then, that this prophecy is one of those "to be regarded as having many fulfillments by -springing and (2) germinal developments.'" DANIEL 11 and 12. Just as the predictions of the seventh chapter of Daniel are parallel and supplementary to those of the second, so the predictions of the eleventh chapter are parallel and supplementary to those of the eighth. After a brief mention of the coming Persian monarchs (v.2), and of the career of Alexander the Great (v.3), and of the divisions of his (1) I am following Faber*s summary of the view i n his Sacred Calendar of Prophecy vol. 2, p. 139, 140. (2) Farrar, The Book of Daniel, p. 286. empire (v.4), we enter upon the main theme of the ohapter, the struggle between the "king of the north" and the "king of the south. "^"^ A description of the i n i t i a l successes of the king of the south (v.5-9) is followed by an account of the oampaigns of three great kings of the north. That the f i r s t of these (v.10-20) corresponds to Antiochus the Great and the second (v.21-39) in i t s primary reference to Antiochus Epiphanes has been recognized since the days of Josephus. The third (v.40-45) has been variously interpreted of Antiochus, the Romans, the Mohammedans, or of some future king. The Christian fathers, moreover, regarded Antiochus as simply a type of Antichrist. Thus Jerome says in regard to this prophecy, "Our writers are of opinion that a l l these prophecies relate to A n t i c h r i s t . — And since many of the things which we are about to read and expound, do not agree with the person of Antiochus, they oonsider him a type of (2) Antichrist." ' Subsequently, i n line with this interpretation of the fathers, Mede, Isaac Newton, Bishop Newton, E l l i o t t , Guinness, and others applied these prophecies to the Roman desolation of Jerusalem^ the Roman Catholic Papacy, and the exploits of the Mohammedan powers. (1) The directions are i n relation to Palestine. (2) . Quoted from Bishop Newton's, Dissertations on the Prophecies, p.331 51. THE BOOK OF THE REVELATION In the course of the history of exegesis of the Revelation, Mie seven seals, the seven trumpets, and the seven vials (which constitute the framework of the hook) came to be applied with a considerable measure of agreement to historical events of -the Christian era. The seven seals (Rev. 6 f.) have been most commonly interpreted of the :events of -the f i r s t four centuries A.D., thus: The f i r s t seal - Of the period of victory, prosperity, and internal peace under the Antonines in the century immediately after the Revelation was given, i.e., A.D. 96 - 180, during which period the Roman empire attained i t s greatest extent. The second, third, and fourth seals - Of the c i v i l war, famine, and pestilence which subsequently prevailed in the empire until the time of Diocletian. The f i f t h seal - Of the persecution of Christians under Diocletian, the great "era of martyrs." The sixth seal - Of the end of the Pagan world brought about by the o f f i c i a l acceptance of Christianity by Constantino. The seventh seal - Regarded as embraoing the succeeding trumpets. The above interpretation of the seals i s that adopted, i n large measure, at any rate, by Brightman (1600), Mede (1632), Fleming (1700), Isaac Newton (1720), Bishop Newton (1754), E l l i o t t (1844), Guinness (1905), and many others. The seven trumpets (Rev. 8 f.) have been most commonly inter-52. preted of the f a l l of the Western and Eastern divisions of the Roman Empire, thus: The f i r s t trumpet - Of the invasion of Alaric the Goth, c. A.D. 395. The seoond trumpet - Of the invasion of Genseric the Vandal, c. A.D. 428. The third trumpet,,- Of the invasion of A t t i l a the Hun, c. A.D. 433. The fourth trumpet - Of the invasion of Odoacer the Heruli, the f a l l of the Western Empire, the beginning of the "Dark Ages," A.D. 476. The f i f t h trumpet - Of Mohammed and the Saracens, A.D. 610 f. The sixth trumpet - Of the invasions and conquests of the Turks, c. A.D. 1060 f . The seventh trumpet - Regarded as embracing the seven v i a l s . The above interpretation has been adopted i n i t s essentials by a large number of expositors including practically a l l those named above. Prior to the pouring forth of the seven vi a l s , which we are distinctly t o l d are the last (Rev. 15/l), there are four supplementary chapters (10-14) dealing largely, i n the view of a l l the expositors named above, with the rise of the Roman Catholic Papacy whioh is identified with the beast of Revelation 13. The seven vials (Rev. 15 and 16), having reference to judgments upon the beast (Rev, 16/2), whose rise and exploits have just been described (Rev, 13), have been interpreted generally of judgments leading to the weakening of the Papacy; so Brightman (1600), Parous (1615), Mede (1632), Jurieu (1685), and Fleming (1700); and more specifically, thus: 53.. The f i r s t v i a l - Of the outbreak of i n f i d e l i t y i n France prior to the French Revolution. The second, third, and fourth vials - Of the French Revolution and.the conquests of Napoleon which drenched Europe i n blood. The f i f t h v i a l - Of the serious weakening of the Papal power hy the loss of.the Papal States in 1870. The sixth v i a l -(1) The drying up of the Euphrates - Of the gradual diminution of Turkish power (because of the identification of the symbol with the Turks, Rev. 9/l4). (2) The coming of the kings of the East - Of the return of the jfews to Palestine consequent upon i t s being freed from Turkish control, A.D. 1917. (3) The frogs - Of unholy influences leading the nations of the world to war. The seventh vial - Of the great catastrophies of this present era of world wars and atomic power. The application of the f i r s t four vials to the French Revolution is common to Bicheno (1800), Galloway (1802), Frere (1826), Faber (1828), Cunninghame (1838), E l l i o t t (1844), Barnes (1851), Guinness (1905), and many others. This view was prepared for hy the prevalence before the Revolution of the conviction that a l l the vials were s t i l l future. So Bengel (1742), Bishop Newton (1754), and Dr. G i l l (1776). The exegesis of the Revelation had made sufficient progress prior to the historical fulfillment of the vials to enable a large amount 54. of correct anticipation. So might be regarded the anticipation from the f i f t h v i a l of some calamity affecting the City of Rome as the centre of Roman Catholic worship. So Brightman (1600), Pareus (1615), Mede (1632), Fleming (1700), G i l l (1776), and others. So also the anticipation from the sixth v i a l of the decline of the Turkish Empire and the return of the Jews to Palestine. So, Brightman (1600), Mede (1632) Bishop Newton (1754), Faber (1828), Cuninghame (1838), and others. Also, from the sixth and seventh vials, the anticipation of a world war i n which England as the favoured home of Protestantism would be involved, E l l i o t t (1844).^ CHRONOLOGIC PROPHECIES In the course of the history of the exegesis of the chronolo-gical element of the above predictions the "days" of prophecy have been quite variously interpreted. They have been taken l i t e r a l l y , or they have been regarded as mystical periods of indefinite length, or they have (2) been thought to symbolize months, or years, or even planetary periods. Thus the early Christian fathers regarded the time and times and / (3) / half a time of Daniel 7/25 etc., as a period of 3 1/2 l i t e r a l years during which, after the division of the Roman Empire into ten kingdoms, Antichrist would reign. (1) In this review of the exegesis of the Revelation, I am largely indeb-ted to the "sketch of the history of apocalyptic interpretation" found i n E l l i o t t ' s , Horae Apocalypticae, vol.4* as well as to the individual works of Fleming, Bengel, Bishop Newton, Faber, Barnes, and Guinness. (2) The non-Christian Greek world also was familiar with a symbolic i n -terpretation of prophetic periods; cf. Claudius Ptolemy, Tetrabiblos 2/6, Loeb edition p.167, where, for a lunar eclipse, 1 hour of ob-scuration r 1 month's duration of the predicted event, etc. (3) For the seven places in which the period occurs (in one form or another), see above p. 32. 55. In subsequent times, however, this same period, especially in i t s reference to the prophesying of the witnesses, Rev. l l / 3 , and to the woman's wilderness-dwelling, Rev. 12/14, (by whioh were understood the Churoh's witnessing and suffering respectively), came to he interpreted of the whole duration of the Churoh's existence. This was accomplished •ese: (2) hy considering a "time" to repr nt a hundred years, ^  or by under-standing the phrase mystically. Julius Afrioanus (A.D. 220), on the other hand, interpreted the 2,300 days of Daniel 8/l4 as 2,300 months. He says: "For i f we take the day as a month just as elsewhere in propheoy days are taken as years, and i n different plaoes are used i n different ways...we shall find the period f u l l y made out to the 20th year of the reign of Artaxerxes, from the capture of Jerusalem. For there are (3) thus given 185 years, ' and one year f a l l s to be added to these - the year i n whioh Nehomiah bu i l t the wall of the c i t y . In 186 years, (1) So Tichonius, in the 4th century A.D. (2) So Primasius (6th century), Andreas (6th oentury), the Venerable . _ Bede (8th oentury), Ambrose Ansbert (9th century), Berengaud (11th century), and Bruno Astensis (12th century). (3) Incidentally, Afrioanus is quite wrong in saying that 185 years elapsed from the capture of Jerusalem to the 20th year of Artaxerxes. He seems to be reckoning the .70 years' captivity back from Cyrus' aooession (559 B.C.) instead of from his oapture of Babylon and decree that the exiles oould return. See above p.34. 56. therefore, we find 2,300 Hebrew months,^ as eight years hare in addition three interoalary months. From Artaxerxes, again, i n whose time the command went forth that Jerusalem should be b u i l t there v « ( 2 ) are seventy weeks." Many expositors, furthermore, from early times interpreted the 3 l/2 days of Rev. l l / 9 , 11 as 3 l/2 years, adducing i n support of this view the B i b l i c a l precedents of Hie 40 years wandering i n the (4) wilderness (Numbers 14/34), and the 390 years punishment of Israel / (5) (Ezekiel 4/5), i n whioh passages a day unmistokeably symbolizes a year. Subsequently this year-day principle was applied also to ihe other prophetic periods. Thus Joaohim Abbas near the close of the 12th century applied i t to the five months or 150 days of Rev*. 9/5 and to the 42 months or 1,260 days of Rev. 13/5. The famous Jewish Rabbis, Saadia Goon and Solomon Jarohi of the 12th and 13th centuries, applied i t to the 1^290 and 1,335 days of Daniel 12/ll and 12/l2. R. Isaac, a Portugese Jew of tha 15th century applied i t to the 2,300 days of Daniel 8/l4, as did also (6) Abarbanel of the 17th century. (1) Practically true. In 186 years there are 2,300 lunar months and 15 days. (2) R. and D. Ante-Nioene Fathers, v o l . 6, p.137. The fragment of Julius Africanus from whioh this quotation oomes i s preserved i n tho Chronographia of George Syncellus, a Byzantine historian of the eighth century. . (3) So Tichonius (4th century), Prosper (5th century), Primasius (6th century), AmbroseAnsbert (9th century), Haymo (9th century), Borengaud (11th century), and Bruno of Asti (12th century). (4) So Primasius and Ambroso Ansberti (5) So Haymo and Bruno of A s t i . (6) Again I am indebted to E l l i o t t , Horao Apooalyptioae vol. 3, p. 279 f . 57. The earliest expositors who applied the year-day principle to the periods of 1260, 1290, and 1335 days dated their beginning either from Christ's b i r t h or from Titus' or Hadrian's destruction of Jerusalem. Subsequent to the Reformation, however, and the identification of the l i t t l e horn of Daniel's fourth beast with the spiritual Power whioh then dominated Europe, i t was thought that the terminus a quo of the three times and a half must be some epoch when, in aooordanoe with Daniel 7/25, the times and the laws and the saints of the Most High were given into the hand of this l i t t l e horn. This was thought enigmatically to relate to "a grant from the imperial head of the Roman World, by which the Latin Patriaroh was constituted the ruler of a l l the churohes, and hy whioh he was made a supreme judge in a l l s p i ritual cases." ^ Hence the year 606 A.D. when the Emperor Phocas declared the Roman church to be head of a l l (2) the churohes came to be the date most oommonly regarded as the probable point of commencement for the 1260 years of the l i t t l e horn's dominion. Thus David Chytraeus (A.D. 1571) says, "If the commencing date... be dated from Alario's taking of Rome, the ending date would he A.D.1672: (3) i f from Phocas' Deoree, i t s ending would be A.D. 1866." So also, "Pareus i a his commentary on the Apooalypse A.D. 1643 boldly reckons the 1,260 years of Papal dominion from the decree of Phooas ia 606.... (1) Faber, Sacred Calendar of Prophecy, vol. 1, p.136. (2) "Hio, rogante Papa Bonefaoio, statuit sedem Romanae et Apostolicae Eoolesiae caput esse omnium eoolesiarum" Paul.Diao. de gest* Longobard. l i b . 4 o.36. quoted i n Faber, Sacred Calendar of Prophecy, vol. 1, p.142. (3) Quoted i n E l l i o t t ' s Horae Apoc. vol. 3, p.303. Bonifaoe III he says was exalted by a deoree of Phocas 'to the ohaire of universal pestilence' i n 606. 'Prom the yeere of Christ therefore 606, until this time the holy o i t i e hathbeen trodden under foot by the Roman Gentiles, whioh i s the spaoo of 1,037 yeoros, and is yet to be trodden down 223 yeoros moro, to wit, unt i l the yeere of Christ 1866.'"^ ^  (2) Holland (A.D. 1650) said, "There romain 216 years more." Fleming (1700), Dr. G i l l (1746), Reader (1778), Galloway (1802), Frero (1816), Biokerstoth (1823), and E l l i o t t (1844) concurred in selecting A.D. 606 as tho commencing epoch of this period. Fleming, however, thought that special "prophetioal years" of 360 days each wore intended. Hence ho says (writing C.A.D. 1700), "If wo may suppose that Antichrist began his reign in the year 606, the additional twelve hundred and sixty years of his duration, were they Julian or ordinary years, would lead us down to the year 1866, as the last period of tho seven-headed monster; but soeing thoy are prophetioal years only, we must cast away eighteen years, i n order to bring them to tho exact measure of time that tho Sp i r i t of God designs in this book; and thus the f i n a l period of Papal usurpation (supposing that ho did indeed riso in tho year 606) must conclude with the year 1848. (1) Quoted in Dr. H. Grattan Guinness', History Unveiling Prophecy, p. 347, 348. (2) I&waf p. 348. (3) Fleming, The Rise and F a l l of tho Papaoy, p.16. E l l i o t t , again, i s careful to mention that the calculation i a approximate. He says, "Let me now, i n reference to this epoch, note a few important events whioh rendered not the one year only, hut the four that may he associated with i t , from 604 to 608, (like the four associated with the Justinian Decree from 529 to 5 3 3 ) , n o t a l i t t l e remarkable." Grattan Guinness writing i n 1878 after the f a l l of the Papal temporal power in A.D. 1870, would date the commencing epoch A.D. 606 to 610 (the latter being the date of Phocas* death) and the corresponding (3) terminal epoch A.D. 1866 to 1870. Respecting the 2,300 days of Daniel 8/l4, Bishop Newton quotes Jerome as saying, "This place most Christians refer to Antichrist; and affirm that what was transacted i n a type under Antiochus w i l l be f u l -f i l l e d i n truth under Antiohrist," and then oomments: "The days, without doubt, are to be taken, agreeably to the style of Daniel in other plaoes, not for natural, but for prophetic days or years; and as the question was asked, not only how long the daily sacrifice shall be taken away, and the transgression of desolation continue, but also how long the vision shall last; so the answer is to be understood, and (1) E l l i o t t with others noted that 1260 years from Justinian's Deoree terminated with the era of tJie Frenoh Revolution and regarded this as an i n i t i a l fulfillment of the prediction. (2} E l l i o t t , Hor. Apoc, v o l . 3, p.302. (3) Guinness, The Approaohing End of the Age, p. 426, Light f o r the Last Days, p.173. these two thousand and three hundred days denote the whole time from the beginning of the vision to the cleansing of the sanctuary. The sanotuary is not yet cleansed, and consequently these years are not yet expired. When these years shall be expired, then their end w i l l clearly show from whence their beginning i s to be dated, whether from the vision of the ram, or of the he-goat, or of the l i t t l e horn. It i s d i f f i o u l t to f i x the precise time, when the prophetio dates begin, and when they end, t i l l the propheoies are f u l f i l l e d , and the event declares the -(I) oertainty of them.,iv ' Of the three points of commencement suggested by Newton, Mr. Bioheno, writing i n 1797, ohose the f i r s t and accordingly dated the com-mencement of the 2,300 years from the beginning of Xerxes invasion of (2) (3) Greece B.C. 481, 480. Subsequent expositors saw confirmation of this i n the Greek War of Independence whioh began 2,300 years later i n A. D. 1821 and was an important epoch in the downfall of the Turkish Empire, and hence an i n i t i a l step toward the oleansing of the sanotuary, or freeing of Palestine from Mohammedan control. The 150 days of Rev. 9/5 (the f i f t h trumpet) have been oommonly applied to the 150 years A.D. 612 to 762 during whioh the Saracens made rapid advances. So, praotioally, said Brightraan (1600), and Fleming (1700); (1) Bishop Newton, Dissertations on the Propheoies p. 290 (2) E l l i o t t , Hor. Apoo., vol. 3, p.446. (3) E l l i o t t , Guinness, e t c 61. so exactly, Daubuz (1720), Bishop Newton (1754), Faber (1828), and E l l i o t t (1844). The hour and day and month and year of Rev. 9/l5 (the sixth trumpet) has been interpreted either as 3 9 1 ^ or 396^ 2)years depending on whether the expositor regarded the prophetical "year" of the expression as representing 360. or 365 true years. It has been applied, either to the period from the commencement of the Turkish invasions, o. A.D. 1057, to (s) the f a l l of Constantinople A.D. 1453,* ' or to the period from the Turkish revival under the" Othmans, c. A.D. 1300, to the peaoe of Karlowitz, A.D. (A.) 1699v ', which marked the end of Turmish aggression i n Europe. There is s t i l l one other prophetic period whioh must bo dis-cussed i n this skotoh, v i z . , tho period of seven times or 2,520 years. In the preface to Faber*s, Sacrod Calendar of Prophecy (1828) wo are informed that, "The present Treatise rests upon tho grand master number of seven times, produoed by tho duplication of the throo times and a half, and hithorto almost universally overlooked. Yet tho period, marked out by this palmary number, c omprehends what our Lord (1) So, Fleming (1700), Isaao Newton praotioally (1720), Bishop Newton (1754), and Guinness (1878). (2) So, Brightman (1600), Mode (1632), Whiston (1744), Faber (1828), Cuninghame (1838), and E l l i o t t (1844). (3) So Modo (1632), Fleming (1700), Isaao Newton (1720), and E l l i o t t (1844). (4) So Brightman, i n anticipation, (1600), Whiston (1744), Bishop Newton, roughly (1754), Faber (1828), Cuninghame (1838), and Guinness (1908).. styles the times of the Gentiles x ; . . . i t i s the chronological measure of Daniel*3 great compound metallic image." In the body of the work Faber j u s t i f i e s his regarding the seven times as a legitimate prophetic period, (1) By an appeal to the obviously imperfect oharacter of the three times and one half, (2) By noting that the usually assigned commencing epoch of the 3 l/2 times (7th century A.D.) i s removed, roughly at any rate, by a complementary period of 3 l/2 times from the era of Nebuchadnezzar, (3) By supposing that the "seven times" prophetically (2) -pronounced upon Nebuchadnezzarv 'was designed to have a double fulfillment; f i r s t , i n the personal l i f e of Nebuchadnezzar, and secondly, in the historical l i f e of the great image which also, i n a sense, was (3) Nebuchadnezzar, for he was i t s declared head and (4) i t s animating principle, Faber says, "Hence the seven times, during which the king was to be physically deranged, are the figure of seven prophetic times or 2520 natural years, during whioh the great compound Empire,,.should he subjeot to the moral madness (1) Luke 21/24. (2) "Let seven times pass over him" Dan. 4/ 1 6»23,25. (3) Daniel 2/38. (4) In the book of Revelation the 4th Empire i s s t i l l mystically oalled "Babylon" Rev. 17. 63. of Paganism or Popery or Mohanmedism or Infidelity." Subsequent expositors ^ f o l l o w Faber i n this interpretation of the seven times, but, as we shall see later, i t was l e f t to Guinness to adequately apply the prediction. Faber attempts to date the period from the birth of Nebuchadnezzar, but this date has not been recorded by history and can only be fixed by oonjeoture. Cuninghame, more satisfactorily, makes the period oommence at the time when the ten tribes were made tribu-tary to Shalmanezer, and thus terminate at the French Revolution. E l l i o t t simply says that a certain measure of dubiousness attends i t s terminating epoch, "For, according as i t is measured from the oognate Assyrian king's f i r s t invasion of the sacred land of Judea, or from the rise of the independent Babylonian empire 100 years later, the terminating epoch w i l l either f a l l about the time of -the French Revolution A.D. 1791, or somewhat later than the close of the present century." v ' (1) Notably, Cuninghame, E l l i o t t , and Guinness (2) E l l i o t t , Hor. Apoc. vol. 4, p. 239. 64. ADJUSTMENT OF THE PHYSICAL CYCLES TO THE MORAL Now that we have traced both the gradual approach of careful students of the time order of nature to an appreciation of the true oharaoter of that time order, and the gradual approach of careful students of the time order of Revelation to an appreciation of what they have be-lieved to be the true character of i t s time order, there remains but to recount the disoovery of the remarkable relationships nfchat exist between these two time orders of the physical and moral worlds, relationships whioh throw s t i l l further l i g h t upon the correct interpretation and appli-cation of the time periods and confirm our conviction in the r e a l i t y of Divine revelation. The i n i t i a l discoveries i n this regard were made about the middle of the 18th century by a Swiss astronomer M. de Cheseaux who i s otherwise known for having observed and described the six-tailed comet of the year 1744. The account of De Cheseaux's discoveries i s preserved i n the "Memoires Posthumes de M. de Cheseaux" edited and published hy his sons in 1754. In this work De Cheseaux, after explaining how by calcu-lation he came upon the faot that 315 years i s a soli-lunar oyole, says: "The oycle of 315 years thus found, I forthwith observed that i t was the quarter of the 1,260 years' period, or the 3 l/2 'times' of Daniel... and consequently that this prophetic period was i t s e l f a lunar oyole.... "The agreement of this period, destined by the Holy S p i r i t to designate o i v i l periods, with 65. the length of most remarkable periods of cele s t i a l movements, led me to conjecture that i t might also be thus with the period of 2,300 years. I examined then this last period by astronomic tables and I found that...the prophetic period of 2,300 years... i s also a oyclical period.... "The equality of the errors of this cycle of 2,300 years with those of the preceding led me to oonolude -that their difference, that i s , 1,040 years ought to be entirely exempt from error, and one a l l the more remarkable heoause i t unites at the same time the three kinds of cycles, and forms consequently t h i s famous cycle of the fourth kind -vainly sought so long, and ultimately believed to be chimerio or impossible.... This period of 1,040 years or solar revolutions, indicated i n a certain way hy the Holy Spirit, i s a cycle at once solar, lunar, and diurnal, perfectly exaot... ...May I be permitted...to give to this oyole the name of THE DANIEL CYCLE? "^^ These discoveries of De Cheseaux "seem to have almost completely (2) dropped out of sight" v ' for some f i f t y years, hut interest i n them was revived i n the nineteenth century, f i r s t by Mr. William Cuninghame and (1) Quoted in H. Grattan Guinness, Creation Centred in Christ, vol. 1, p.329, 330. (2) I6*d, vol.1, p.327. later by Professor Birks of Cambridge i n his Elements of Propheoy (1843). Dr. H. Grattan Guinness t e l l s us that: "It was when reading tiiis work of Professor Birks just after the f a l l of the Papal temporal power i n 1870 that my attention -was arrested by that portion of i t referring to these remarkable oycles, and I was consequently led to investigate their character with considerable care, and i n doing so made a number of chronological discoveries, some of which I have since published i n my writings on the fulfillment of propheoy."^1) The most remarkable of Dr. Guinness' discoveries relating to the c y c l i c a l charaoter of the prophetic times were: (1) That 2,300 years is not simply a soli-lunar cycle but a soli-lunar-anomalistio cycle. (2) That astronomy as well as Scripture knows of a 75 year period supplementary to 2,520 years. "In the last ohapter of Daniel the angel intimates to the prophet in answer to his chronological inquiries, that while the scattering of the power of the holy people should terminate at the end of the second half of the 2,520 years, yet that there should be additions of thirty and forty-five years before the era of f u l l blessedness would arrive (Dan. 12/11-13). In other (1) Grattan Guinness, Creation Centred in Christ, vol. 1, p.328. 67. words, to the long period of 2,520 years Scripture adds a brief period of seventy-five years, and as we have just seen, astronomy does the same. The d i f f e r -ence between 2,520 true lunar and the same number of true solar years i s seventy-five years. In other words, the seventy-five years added i n the prophecy is exaotly equal to the epact of the whole 'seven times.' If 2,520 lunar, and the Same number of solar years begin together, the former w i l l run out seventy-five years before the l a t t e r . " ^ (3) That the period of 391 years, the hour, day, month and year of Rev. 9/l5, is a soli-lunar-nodioal cycle. This last is perhaps tho most important of Guinnoss' cyolioal disooveries and yet one that, strangely enough, he did not emphasize. It i s simply alluded to i n his Creation Centred i n Christ. Ho speaks there of "the prophetic 391 years' lunar and oclipse cycle."( 2) Tho Canadian scientist Dr. W. B o l l Dawson (d.1944)^ made a s t i l l further important disoovery linking tho prophetio numbers not simply with solar year, lunar month cycles, but with a very accurate solar year, lunar year cycle. In his papor, Prophetical Numbers i n Daniel, i n Relation to Celostial Cycles, ho t o l l s us: (1) G. Guinnoss, The Approaching End of the Ago, thirteenth edition, p.442. (2) G. Guinness, Creation centred in Christ, v o l . 1, appendix 6, p. 520. (3) Son of tho lato Sir John William Dawson who f o r many years was principal and ohanoollor of MoGill University. 68. "It ocourrod to the writer that instead of the method adopted by De Cheseaux, this higher result could he obtained by taking the numbers 2,300 and 1,260 in the prophecies to represent lunar years; and i t was then discovered that i n the correspond-ing number of solar years there were fractional remainders which, i f added together would be almost exaotly unity. By taking the half-sum, therefore, (instead of the difference as De Cheseaux did) an equivalent i n whole numbers would be found between lunar years and solar years.,., 2300 lunar years - 2,231.517159 solar years 1260 lunar years = 1,222.483513 solar years Half the sum = 1780 lunar years = 1,727.000236 solar years This cycle f a l l s short of perfect exaotitude hy only two hours in i t s whole period, as shown hy the above decimal of a year (.000236)."^ The tables which appear i n the f i r s t part of this present treatise enable us to evaluate accurately the cyclical oharacter of these Bi b l i c a l numbers. From the f i r s t table, for example, we see that 391 years i s a solar year, lunar year cycle; and that of the five cycles of that nature shorter than 1,000 years the 391 years* cycle i s the most accurate. Also (1) Journal of the Transactions of the Victoria Institute for 1935, p.142 . . The f i r s t announcement of this discovery appeared t h i r t y years before i n the Transactions of the Royal Society of Canada for 1905. 69. from this table we see that of the 16 cycles shorter than 3,000 years the 1,727 years' cycle is the most accurate. From the second table we see that the B i b l i c a l periods of 391, 486,^1260, 2300, and 2520 years are a l l soli-lunar cycles with an error of less than a day. We note, however, that numbers whioh are soli-lunar cycles of this accuracy are not extremely rare. There are 202 such cycles in 3,000 years or about one i n every 15 years. If one were to choose a number at random the chance of i t s being a soli-lunar cycle with an error of less than a day is about one i n f i f t e e n . From this second table we note also that the cycles of 1,040 and 1,727 years are both at points of minimum, error, and that such points of minimum error reour about every 360 years. W© not© further from this second table that 1,040 years is very nearly a true cycle of tho solar year, the lunar month, and the day, as Do Cheseaux claimed, i t s greatest error being .11 of a day. We note also that no other cycle shorter than 1,040 years so nearly approaches being a year-month-day oycle except only th© cycle of 706 years whose greatest error i s .10 of a day. We note further that 706 is tho sum of 391 and 315, tho latter being the primary cycle at the base of the 1,260 and 2,520 years' cycles. In regard to tho third table wo notioe that, on the average, only one number in 100 years is a soli-lunar-anomalistic cycle, yet of tho four B i b l i c a l oycles, 315, 391, 486,t 1) and 2,300, two are anomalistic in their primary form , viz., 486 and 2,300, while the remaining two are (1) See above, p.44 70. anomalistic in their f i f t h multiples. Prom the fourth table we see that of the forty soli-lunar-nodioal cycles shorter than 3,000 years the 391 years* cyole is the most accurate. We may practically say that 391 years i s the most accurate eolipse oyole, embracing a whole number of years, in, existence. When i t i s recalled that 391 years i s also the most accurate cycle of the solar year and the lunar year.shorter than 1,000 years the truly phenomenal character of this cycle w i l l begin to appear. A further comparison of this fourth table with the f i r s t w i l l reveal that 391 is the only number common to both tables. It is not simply the most accurate but the only solar year, lunar year, eclipse year cycle i . e r i s W e . ( 1 ) Of the four numbers in the f i f t h table, one, viz., 1,955, the f i f t h multiple of 391, is also a solar year lunar year cycle, and hence is the most remarkable of the four. The solar eclipse of Jan.26, A.D. 1153, and that of January 24, (2) A.D. 1544, are historical illustrations of eclipses separated by the 391 years' cycle. The apparent two-day error i s the error of the Julian oalendar not of the cycle. In the 391 Julian years there are 97 leap years and therefore 391 times 365 plus 97 days or 142,812 days, but there are only 142,810 days i n 391 true tropical years. The total eclipse of (3) November 24, A.D. 29 'and the yet future total eclipse of November 22, (4) A.D. 1984, i s an i l l u s t r a t i o n of an eclipse recurring even after the (1) 391 solar years = 403 lunar years e 412 eclipse years. A l l of the soli-lunar-nodical cycles of Table 4 could he expressed in terms of eclipse years. The eclipse year is simply the time occupied by the sun i n passing from one of the nodes of the moon's orbit to the same node again. Russell, Dugan, Stewart, "Astronomy" vol. 1, p.226. (2) Referred to i n G.F. Chambers, "Story of Eclipses" p.149, 152. (5) Referred to in Chambers. (4) Listed i n the Encyclopaedia Britannioa, a r t . Eclipse. 71. f i f t h multiple of this 391 years' cyole. Again the apparent error i s mainly of the oalendar not of the cycle. In regard to the fulfillment of this prophetic cyole in the history of th© Turks, we not© that, "In 1308 a hand of Turks and of Turoopuli, or Turks who wore in the regular employ of the Empire, was induced to cross into Europe and join with the Catalan Grand Company to attack the Emperor Andronicus. This entry of the Turks into Europe, though not of the Ottoman Turks is i t s e l f an epoch-making event. and that, "The peace of Earlowitz (January 2 6, 1699) marks the definite termination of Turkey's power of (2) offence in Europe." (S) The now moons and eclipses of A.D. 1699 must have occurred, of course, on tho same days of the year as those of 1308 for those years are separated by the 391 years' ©clips© o y c l e . ^ (1) Th© Cambridge Medieval History, v o l . 4, p.658. (2) The Encyclopaedia Britannica, 11th Edition, art. Turkey. (3) In ©very year there are, at least, two solar eclipses. (4) Compare above, p.61. 72. DAWSON'S CYCLE Dr. W. Bell Dawson's discovery, which we have mentioned above, may he regarded as the discovery that the sum of the Bi b l i c a l cycles  1,260 and 2,300, i. e . 5,560, is cy c l i c a l when regarded either as solar  or as lunar y e a r s . ^ This i s an extremely rare phenomenon. There are only four other numbers smaller than 10,000 that are of this character, v i z . 1,545, 5,105, 8,665, and 9,303. A legitimate theological inference from Dawson's discovery is that the 2,300 and 1,260 year periods may be expected to he f u l f i l l e d on either a lunar or a solar soale and perhaps on both. GUINNESS' ANTICIPATIONS Of equal interest and importance to Guinness' discoveries concerning the relationships between the prophetic time order and the time order of nature, were his discoveries concerning the relationship of that prophetic time order to i t s fulfillment i n the time order of history. Guinness' researches along this line were far more comprehensive and exhaustive than those of any previous expositor. Perhaps the most signi-ficant of a l l were his measurements of the period of "seven times" from the o r i t i c a l epochs i n the downfall of Judah, and his measurements of the period of three and one-half times from the Nabonassar era. We shall examine f i r s t Guinness' measurements of the "seven times" from the f a l l of Judah. And, i n order to avoid giving any false (1) 3560 solar years s 44,031 lunar months. Error - .90 days 3560 Lunar years s 3,454 solar years. Error + .17 days impression respecting his anticipations of events and times future to his own day, wo subjoin a rather extended quotation from his work, Light for the Last Days (1887). "The firBt nineteen or twenty years of Nebuchadnezzar, whioh witnessed a l l the stages of the f a l l of Judah before Babylon, were the main and terminal years of the oaptivity  era. A l l that had gone before -was only preparatory. The Tail of the ten tribes before the Assyrian conquerors, and ©von the brief captivity of Manasseh, did not permanently shake the throne of Judah, or compromise the independent sovereignty of th© house of David. Tho penumbra of the ©olipse had indeed f a l l e n on th© moon, but not as yet th© dark shadow. A l l through these years Babylon was steadily rising, and with the accession of Nebuchadnezzar, and his f i r s t campaign against Judah, reached i t s climax. In the eighth year of Nebuohadnezzar th© throne of David f e l l , and the indepen-dent national existence of Judah oeased u n t i l the "times of the Gentiles'1 should be f u l f i l l e d . Hence those nineteen years especially form the important c r i t i c a l era; the rubicon of history was crossed at one or other of the crises in i t s course. It extended from B.C. 605 to B.C. 587, and th© principal c r i s i s in i t was the f a l l of Johoiachin in the eighth year of Nebuchadnezzar, B.C. 598. "The corresponding terminal years after the lapse of •seven times 1 i n f u l l solar measure, extend from A.D. 1915 to A.D. 1934. During these years then we may expect to se© th© f u l l and f i n a l f a l l of th© anti-typical 'Babylon th© Great;• and i f that ©vent i s to answer chronologically to th© culminating point of tho typioal Babylon, i t seems probable that i t w i l l occur at one of the central dates A.D. 1917 or 1923. This Gentile age closes, as w© have seen, with an era, and not witii a date. Most of th© c r i t i c a l years i n that era are already passed; the f i r s t four or five of the s t i l l future dates seem to be connected with Eastern and not Western chronology, and are consequently scarcely l i k e l y to indicate anything oonneoted with 'Babylon th© Groat.* For i t s f a l l w© should consequently look to on® of the four f i n a l dates, and for the reasons above stated apparently not to the last. Which of the remaining three stands pre-eminent above i t s fellows? It is impossible to say. One of them, A.D. 1923, has a distinct historical I 74. pre-eminence as corresponding chronologically to the Jehoiachin overthrow of B.C. 598. Of the four cam-paigns of Nebuchadnezzar against Judah this was hy far the most fa t a l ; indeed, we may say i t was not an overthrow, hut the overthrow of the kingdom of Judah; i t was emphatically the breaking up of the nation and the f a l l of the independent sovereignty. It was more-over the date of the captivity of the prophet Ezekiel, the date from whioh he uniformly reckons the visions of the remarkable series that were granted to him i n Babylon and hy the river of Chebar, visions of the de-parting and returning glory; and the question naturally occurs whether i t s answering year i n this 'time of the end' i s not destined to witness the return of the glory and_the re-establishment of the throne of Judah. "On the other hand, the astronomical features of this measurement of the 'seven times* are not as re-markable as are those of two other measurements; that from the f i r s t of Nebuchadnezzar, and that from his f i n a l overthrow of Zedekiah. It was in the year B.C. 606 that Nebuohadnezzar f i r s t came against Judah, and carried Daniel and the Hebrew children among others captive. At this time he was acting on behalf of his father, and i t was not u n t i l nearly two years later, B.C. 604, that he himself acceded to the throne. That year i s consequently, properly speaking, the f i r s t of Nebuchadnezzar; and i t was probably also the year i n which he saw the vision of the great image, in con-nection with which i t was said to him, ''Thou art this head of gold.'* This year has therefore. some special claims to he considered as a very principal starting  point of the 'times of the Gentiles.• Measured from i t the period runs out in A.D. 1917,.and i t i s a very notable fact that a second most remarkable period also expires then. The 1,335 years of Daniel x i i . 12, the ne plus ultra of prophetic chronology, whioh i s e v i -dently Eastern i n character, and consequently lunar in soale, measured hack from this year 1917, lead up to the great Hegira era, the starting-point of the Mohammedan calendar, the birthday of the power whioh has for more than twelve centuries desolated Palestine and trodden down Jerusalem. The two periods l i e thus: B.C. 604 2520 solar years A.D. 1917 A.D. 622 1335 A.D. 1917 75. "The year 1917 is consequently doubly indicated as a f i n a l c r i s i s date, i n which the -seven times- run out, as measured from two opening events, both of which are clearly most c r i t i c a l i n connexion with Israel, and whose dates are both absolutely certain and unquestionable. The 1,335 years' measure i s , as we before pointed out, the half--week or 1,260 years, plus the additional seventy-t h i r t y and forty-five years. Th© passage i n whioh these periods are announced gives no. distinct indication of the ©vent6 to which they lead, nor does i t state whether lunar or solar years are intended. Prophecy indeed never does this; but the astronomic features of this period seem to indicate distinctly that lunar years are intended, for seventy-five years i s exactly the difference between  seven times lunar and seven times solar, and hence the addition of seventy-five years to the lunar measurement of the period makes i t equal to the solar measurement. We have before stated that both Jewish and Mohammedan chronology are s t r i c t l y lunar, and that chronological periods connected with Eastern ©vents seem to be always calculated on this soale, while those connected with Wes-tern or Papal events are measured by the solar year. "The coincidence of the close of these two periods seems.to answer a question whioh w i l l occur to ©very re-flective mind,-the question, Are the supplementary seventy-five years of the last verses of Daniel to be added to the latest solar terminus of the seven times? The answer i s , They may be; i t is possible: but i t seems extremely unlikely, because of the astronomic fact just indicated. "The year in which these two periods—-the one of over twenty-five centuries, and th© other of over thirteen centuries—run out together is astronomically a notable one. We have before met, i n th© course of our investiga-tion, years such as 1848, i n whioh several prophetic periods meet; but they were only those from more incipient starting-points, and minus the seventy-five terminal years. Here, on -the contrary, w© have a main starting-point, the f i r s t of Nebuchadnezzar, as our terminus a quo for th© one period, and the acknowledged commencing date of the groat Eastern apostasy, Mohammedanism , as that of the other; and we see that the latter in i t s extended form meets the former, and expires with i t i n the future year A.D. 1917. "Thoughtful readers w i l l weigh the facts and draw their.own conclusions, asking themselves, in the light of a l l the chronologioal facts mentioned i n this work, i f the year B.C. 604 witnessed the rise of the typical five, which i n the prophecy 76. Babylon, and i t s supremacy over the typioal Israel, what event i s the corresponding year in this time of the end l i k e l y to witness? The f a l l of the an t i -typical Babylon—the extinction of Gentile supremacy on earth, and the restoration of Judah's throne i n the person of Christ? The secret things belong to God. It is not for us to say. But there can he no question that those who live to see this year 1917 w i l l have reached one of the most important, perhaps the most momentous, of these terminal years of c r i s i s . "Yet we must also c a l l attention to a further interesting fact connected with the last possible measure of this comprehensive and wonderful 'seven times,' that starting from the capture of Zedekiah and the burning of the temple i n the nineteenth year of Nebuchadnezzar, and terminating i n A.D. 1934. The termination of the 'times of the Gentiles' meets at tiiis point the 1,335.lunar years, dated from the Omar capture of Jerusalem— an event more momentous in i t s effects on Palestine and Jerusalem than the Hegira era of the commencement of Mohammedanism. No chronologic prophecy of Scripture indicates any date whatever beyond this year, as astronomic considera-tions forbid the thought that the supplementary » seventy-five ie to be added to these solar measures."^ ' From our vantage point of A.D. 1946 the errors of Guinness' anticipations are quite apparent. The great culminating c r i s i s of the ages has not yet occurred. Christ has not yet come. Whether or not chronologic prophecy indicates any date beyond the year 1934, there have been dates, extremely o r i t i c a l dates, beyond that year. Nevertheless, even i f we were to oonoede more than we have a right to concede respecting Guinness' premature anticipation of the end of the age, ' there yet remains a remarkable residuum of correct anticipation. The years 1917, (1) Grattan GuinneBS, Light f o r the Last Days, p.220-224. (2) We should note carefully that Guinnees himself distinguishes between his own "wishful thinking" and what could he certainly inferred from the predictions. That 1917 would he c r i t i c a l he f e l t was certain, hut exactly what would constitute i t s o r i t i c a l character he f e l t was quite uncertain: "The secret things belong unto God. It is not for us to say." 77. 1923, and 1934 have been c r i t i c a l and c r i t i c a l i n the very connection in which the nature of the prophecies would lead us to suppose. The year of the Hegira 1335 came to an end on Tuesday,. October 16, 1917. Two weeks later (October 31) Beersheba f e l l to the B r i t i s h forces under Allenby. On November 2 Lord Balfour issued -the famous declaration whioh proclaimed that, "His Majesty's Government view with favour the establishment in Palestine of a national home for the Jewish people, and w i l l use their best en-deavours to f a c i l i t a t e the achievement of that object, i t being clearly understood "that nothing shall be done which may prejudice the c i v i l and religious rights of existing non-Jewish communi-ties in Palestine, or the rights and p o l i t i c a l status enjoyed by Jews in any other country." On December 11th Allenby entered Jerusalem. Since 1917 the Jewish population i n Palestine has risen from 50,000 to 550,000. In regard to 1923 we would quote from the a r t i c l e "Zionism" i n the Encyclopaedia Britannica (14th editioni): "In December 1920 the proposed terms of the Palestine mandate were submitted by the B r i t i s h Government to the League of Nations for con-firmation by the counoil....The mandate came into f u l l operation on September 29, 1923. In i t s f i n a l form i t recites the Balfour Declara-tion in the preamble, and includes among i t s 78. provisions various articles dealing with Jewish immigration." The years 1933 and 1934 saw the rise of Hitler and the commence-ment of his persecution of the Jews which resulted i n a large exodus of Jews from Europe to Palestine as the following s t a t i s t i c s o f Jewish immigration from 1917 to 1939 w i l l show: 1917 - 1921 18, 885 1922 7, 844 1923 7, 421 1924 12, 856 1925 33, 801 1926 13, 081 1927 2, 713 1928 2, 178 1929 5, 249 1930 4, 944 1931 4, 075 1932 9, 553 1933 30, 327 1934 42, 359 1935 61, 854 1936 29, 727 1937 10, 536 1938 12, 868 1939 16, 405 It w i l l he seen that more Jews returned to Palestine i n the three years 1933 to 1935 than in the sixteen previous years, 1917 to 1932 Dr. Guinness* measurements from the so-oalled Nabonassar era may he summarized graphically thus: (1) Based on the American Jewish Year Book for 1940-41, and quoted i n _ . Conrad Hoffman, The Jews Today, p. 76. (2) In another work, Guinness, said that 1934 was "a date in the future which promises to he of importance in connection with the f u l l restoration of the Jewish people." Guinness, On this Rock, p. 135. 7 9 . of Atomic Age 1 80. Guinness noticed also that seven times lunar or 2,520 lunar years from the Nabonassar era terminate exactly to the very day with the Peace of Karlowitz, January 26, 1699. ^ Justification for choosing the Nabonassar era as a starting point for the prophetic times may be found i n the following considerations: (1) The striking parallel between Daniel's prophecies and the astronomical canon of Ptolemy which begins with the f i r s t year of Nabonassar. This parallel has been recognized and commented upon for some time. Thus Faber (1828) says: "That the four great kingdoms, which form the sub-ject of Nebuchadnezzar's v i s i o n of the image and of Daniel's vision of the four beasts, are those four great kingdoms which are equally employed as the basis of Ptolemy's Astronomical Canon; namely, the Babylonian, the Medo-Persian, the Macedonian, and the Roman: is a matter so clear and self-evident, that i t is well denominated by Mr. Mede the A B C of prophecy."^ Again Faber says that the mode of reckoning the four kingdoms that i s found i n the prophecy of the great image (Daniel 2), whereby each successive kingdom is recognized only from the time when i t replaces the kingdom which precedes i t , "exactly corresponds with, and is admirably illustrated by, the famous Astronomical Canon (1) Guinness, On This Rock, p. 126. (2) Sacred Calendar of Prophecy, v o l . 1, p. 62. 81. of Ptolemy. As the good Spirit of God employs the four successive Empires of Babylon and Persia and Greece and Rome, i n the capacity of the grand calendar of prophecy: so Ptolemy has employed the very same rour Empires, i n the construction of his invaluable Canon .... In short, the Canon of Ptolemy may well be deemed a running comment upon the altitudinal line of the great metallic image. As the parts of the image melt into eaoh other, forming jointly one grand suc-cession of supreme imperial domination: so the Canon of Ptolemy exhibits what may be called a picture of unbroken imperial rule, though ad-ministered by four successive dynasties, from Nabonassar to Augustus and his successors ."^^ From this position i t was no great step to the dating of pro-phetic times from the date with which the Ptolemaic Canon began, especially i n view of -(2) The c r i t i c a l character of the epooh i n relation to Hebrew history. The Assyrian monarch who was the contemporary of the Babylonian king Nabonassar (B.C. 747-733), and who completely dominated him, was Tiglath-Pileser III (B.C. 745-728). He inaugurated a new policy of conquering small states, deporting their populations, and turning them into Assyrian p r o v i n c e s . H e i t was who f i r s t attacked the kingdom of (1) Faber, Sacred Calendar of Prophecy, v o l . 2, p-. 9,10. (2) The Westminster Historical Atlas to the Bible, p. 49. 82. Israel and carried some of the inhabitants captive (2 Kings 15/29). Hence the Hebrew people reckoned the beginning of their t r i a l s to date from the Assyrian kings (Kehemiah 9/32), whose invasions they considered to he Divinely ordained (1 Chronicles 5/26). Justification for the employment of apocalyptic numbers of planetary periods i n this particular oase may he found i n the astron-omical character of the e p o c h . U n d e r the providence of God this epoch came to he employed, f i r s t of a l l perhaps, by. the Babylonian astronomers, and then hy the Greeks, as an astronomical epoch, that i s , as an astron-omical point of reference. To this epoch, the noon of February 26, B.C. 747, Ptolemy reduces solar, lunar, and planetary positions. Throughout his great work, the Syntaxis Mathematica, or Almagest, there are constant references to this epooh. First of a l l Ptolemy calculates the position of the sun at this epoch (Syn. Math. 3/7), then the position of the moon at this epoch (Syn. Math. 4/8), then the position of the planet Mercury at this epoch (Syn. Math. 9/Ll), then the position of the planet Venus at this epooh (Syn. Math. 10/5), then the position of the planet Mars at this epoch (Syn. Math. 10/LO), then the position of the planet Jupiter at this epoch (Syn. Math. 11/4), and f i n a l l y the position of the planet Saturn at this same epoch of the noon of February 26, B.C. 747, the f i r s t o f f i c i a l year of Habonasser, king of Babylon (Syn. Math. l l / 8 ) . In other (1) In fact, i t is questionable whether the f i r s t year of Nabonassar was ever used as an historical era u n t i l after i t had become famous as an astronomical epoch. Though i t is true that one Babylonian chronicle does begin, like Ptolemy's Canon to which i t may hear some relationship, with the reign of Nabonassar, this is not considered sufficient evidence to prove "that the Babylonians employed an o f f i c a l or unofficial era beginning with Nabu-naMr." I am greatly indebted to Dr. Arno Poehel of the Oriental Instutute, the University of Chicago,.for very carefully outlining for me the facts hearing upon this question. 83. words, Ptolemy, at the conclusion of eaoh of the several parts of his work dealing with the sun and the moon and the five planets then known, has a section relating their positions to this epoch of the f i r s t year of Nabonassar. It must have been this fact which prompted Guinness to measure apocalyptic numbers of planetary revolutions, as well as of solar and lunar years, from this epoch, with the astonishing results we have out-lined above. That God has raised up historians for the purpose of recording, though unwittingly, the fulfillment of Bibl i c a l predictions is a con-viction often expressed. Josephus' history of the f a l l of Jerusalem has been viei*/ed i n that li g h t , Gibbon's Decline and F a l l of the Roman Empire and (as we have seen) Claudius' Ptolemy's Canon of the Kings. This last named writer may be viewed, i n particular, as having been providentially raised up to enable the ohronology of ancient times to be established, and hence to enable the fulfillment of the chronological predictions to be exhibited. The astronomical character of Ptolemy's chronology i s likewise remarkably appropriate to the astronomical character of Daniel's prophetic times. It might be said of Ptolemy as was said of Pharaoh of old, "For this very purpose did I raise thee up, that I might show i n thee my power and that my name might be published abroad i n a l l the earth." The fundamental motions of the moon, - the synodic, anomalistic, and nodical, - and their primary cycles as set forth i n Ptolemy's Syntaxis are basic to an understanding of the cyclic character of the numbers of Jewish apocalyptic. The epoch, also, with which Ptolemy's Canon commences seems to be a fundamental epoch of commencement for the prophetic periods. (1) Romans 9/l7. 84. And as that epoch of Ptolemy's Canon is astronomical as well as h i s t o r i c a l , and the planets Mercury, Venus, and Mars, as well as the earth and the moon, are i n Ptolemy's Syntaxis related to i t ; so also, when measured from this epoch, apocalyptic numbers of revolutions of Mercury, Venus, and Mars, as well as of the earth and the moon terminate at epochs of momentous sig-nificance i n regard to the relationship between the four great kingdoms of this world (which are the theme alike of Daniel's predictions and of Ptolemy's Canon), and the everlasting Kingdom of God. The variety of matters to which the 1260 year period i s applied i n prophecy, and the very general way i n which i t is used on at least one occasion (Dan. 12/7), as well as the fact of i t s frequent occurrence making i t the prophetic number, perhaps j u s t i f y the extended application made of i t above. It w i l l be noticed that i n measuring 1260 synodic periods of Mars from the Nabonassar era to A.D. 1945 Guinness breaks away from the limitation he had previously set upon the prophetic times (A.D. 1934). In so doing he is more i n line with what other expositors before him had said. E l l i o t t had written: "At the same time some signs are s t i l l wanting, even as I revise this a f i f t h time i n 1861:-especially the non-gathering as yet of the Jews to Palestine; and predicted troubles consequent:-whenee a further presumption i n favour of the later allocation of Daniel's concluding seventy-five years.^ 1- -(1) E l l i o t t , Hor. Apoc. vol. 4, p. 242. 85. By the "later allocation of Daniel's seventy-five years, " E l l i o t t meant that "the additional seventy-five years may be measured from the f u l l completion of the 1260 years i n 1866 or 1867. The f i r s t indication that Guinness was reconsidering his statement that "no chronologic prophecy of Scripture indicates any date whatever beyond this year (A»D. 1934)" appears i n an appendix to his work, Creation Centred i n Christ (1896), i n which, i n question and answer form the following information is given: Q. Have the Prophetic Times any later termination than you have already indicated? A. If the 1260, 1290, and 1335 years of Daniel 12 be reckoned i n solar measure from A.D. 610, the year of the death of Phooas, they terminate i n the years 1870, 1900, and 1945; and i t i s remarkable that 2,300 solar years from the birth of Alexander the Great, and 2,300 calendar years^ ^  from his death, both ter-minate i n A.D. 1945; and also 1, 260 synodic periods of Mars reckoned from the Nabonassar era. The 2,300 years of prophecy commenoe with the times of Xerxes and Alexander the Great, Dan. 8/2, 5, 13. (1) Ibid, P»1H and 112. (2) By "Calendar Years" Guinness meant years of 360 days each. Cf. Fleming above, p. 58. 86. Q. Why have you not given prominence to the date A. D. 1945? A. Because i t l i e s beyond the termination of "seven times" (or 2,520 years) reckoned from the destruction of the Temple hy Nebuchadnezzar, B. C. 587, which seems the proper f u l l commence-ment of the 'Times of the Gentiles.' A* D. 1945 may possibly prove to he the date of some important event connected with the returning glory of Israel (Ezekiel 43/4, 5), though A.D. 1923-4, or "seven times" from the Ezekiel starting point (Jehoiachin's captivity) seems to me a more probable Jewish c r i s i s date. While stating the facts as to the course of Prophetic, Historic, and Astronomic Times, I have carefully avoided attempting to anticipate or predict the "day or hour" of the Coming of Christ, which I hold to he purposely concealed. Subsequently Guinness broke away completely from this limitation of prophetic chronology to A.D. 1934, and wrote as follows: "One thousand two hundred and sixty synodic (2} revolutions of Mars occupy 2691 years, v ' the (1) Guinness, Creation Centred i n Christ, vol.1,p.521,522. (2) It is of interest to. note that 2691 years, which is to the nearest year 1260 synodic revolutions of Mars, i s a soli-lunar cycle, the sum of the two B i b l i c a l cycles 2300 and 391. See above Table 2, p.22. 87. period which extends from the Nabonassar Era to A. D. 1945. Remembering that to the seoond half of 'seven times' Daniel adds 75 years i n the last chapter of his prophecy, we note that A.D. 1945 is 75 years later than A.D. 1870, the date of the downfall of Papal Temporal Power at the culmination of Papal exaltation by the decree of Papal I n f a l l i b i l i t y . We further notice that 2,300 solar years from the birth of Alexander the Great, and 2,300 calendar years from his death, terminate i n A.D. 1945. While regard-ing this date as probably one of great im-portance i n relation to the duration of the four Empires, and the downtreading of the Jewish people and 'Sanctuary,' we avoid the  attempt to predict the time of the second  advent of Christ. As a 'thief i n the night' w i l l he the coming of that great event - an occurrence for which we should always he prepared."(*) So wrote Guinness i n 1908. Toward the close of 1945 the editor of the modern Jewish periodical, "Commentary", wrote: "Every schoolboy who listens to the radio knows that 1945 marks an epoch i n world history. • ( 2 ) (1) Guinness, On This Rock, p.178 (written A.D. 1908. Guiness' dates are 1834 - 1910) (2) Commentary, for November 1945 p. 1. 88. We are, of course, s t i l l (1946) too close to the epooh to estimate i t s f u l l significance. But that Europe's "ten kingdoms" have received a tremendous blow, and that the Jewish question has once again oome to the fore, no one can deny. Ten million of the world's pre-war Jewish population of sixteen million lived i n Europe. Of these ten million, "six million ... were ruthlessly slaughtered i n the Nazi campaign of e x t e r m i n a t i o n " H i t l e r i s said to have been told by an astrologer, "You w i l l die on a Jewish Holiday." Much perturbed, Hitler demanded, 'Which one?' 'I do not know,' replied the astrologer. Hitler became very angry, 'You must know,' he shouted, *I ins i s t upon the truth.' •I do not know,' persisted the astrologer, •because any day you die w i l l be a Jewish Holiday.'"( 2) CONCLUSION Our main thesis, v i z . , that the time order of the Bible, the time order of nature, and the time order of history bear marks of a common Authorship might conceivably be c r i t i c i z e d from7 l i t e r a r y , s c i e n t i f i c , and historical standpoints: An attempt ..could be made to c a l l i n question the genuineness of the. book of Daniel, and to minimize the significance of the oyclic and historical phenomena we have adduced. Associated Press dispatch from Nuernberg, Germany, Dec- 14, 1945. (2) Edmund Fuller, Thesaurus of Anecdotes (1942), p. 353. Needless to say the point of the anecdote by no means depends upon i t s l i t e r a l truth. 89. We cannot here enter upon the complex c r i t i c a l questions relating to the authorship and date of the hook of Daniel; hut we would point out that the "traditional" view which regards the work as genuine hats been strengthened rather than weakened by modern archeological dis-coveries. Thus Montgomery, though himself rejecting the traditional view, admits that, "Archaeology has ••• inspired a considerable revival of the defence of the authenticity of the hook, with many extensive monographs, e.g., n(l) those of Wright, Wilson and Boutflower. In regard to the cyclic phenomena i t ought to be remembered ;that though the chance of lighting upon a single number which i s a soli-lunar cycle with an error of less than half a day, is one i n thirt y , the chance of lighting upon two such numbers consecutively is hut one i n nine hundred (30 times 30), and the chance of lighting upon three such numbers i s hut one i n 27,000 (30 times 30 times 30). Further we must remember that the B i b l i c a l cycles are related not only to simple synodic cycles but also to anomalistic and nodical cycles. In faot a l l of the most accurate lunar cycles w i l l he found to bear some simple relationship to the Biblical numbers. We have already seen this to he true of the most accurate solar year, lunar year cycles, v i z . , 391, and 1727, and the most accurate nodical cycle v i z . , 391. It is also true of the most accurate anomalistic cycle v i z . , 1336, which is the difference between 1727 and 391. We note, too, that among the shorter synodic, (1) Montgomery's Daniel p. 109, i n the International C r i t i c a l Commentary series. (2) The prophetic numbers 391, 1260, and 2300 are a l l s o l i -lunar cycles with errors less than half a day. 9G. anomalistic, nodical, and sidereal cycles the numbers 353, 239, 391, and 277, are the most accurate^^ and that the sum of these numbers is 1260. Respecting the fulfillment of the predictions i n the course of history as we have outlined i t above, exception might he taken to the admission of multiple fulfillments of the chronologic periods. It must be remembered, however, that there is a difference between the finding of a single fulfillment when one has the choice of several scales and several starting points, and the finding of many fulfillments hy the employment of several scales and several starting points. The former case i s com-parable to a blindfolded person after many tries at length choosing the one black head from amongst nine white ones; the latter case, however, i s as i f he were to choose immediately the one black head from the nine white ones and then one red head from nine green ones, and then one blue head from nine yellow ones. In the f i r s t oase the likelihood of his choosing the different coloured head increases with every t r i a l ; hut i n the second case the likelihood of his s t i l l continuing to choose the different coloured bead decreases rapidly with every t r i a l . The rather general manner i n v/hich some of the prophetic periods are mentioned i n the Bible leaves the way open for such a comprehensive treatment of them. That profoundly solemn declaration i n Daniel 12/7 (for example) i s not exhausted by any one period of 1260 l i t e r a l days i n the time of Antiochus Epiphanes, nor hy any one period of 1260 solar years or lunar years or periods of Mercury, Venus, or Mars, hut includes and . transcends them a l l . There is a grandeur about the historical fulfillment (1) At the present epoch 334 i s slightly more accurate (about half an hour) than 353, but i n past centuries, because of the effect of secular acceleration, 353 was the more accurate cycle. 91. of th© prophetic times i n keeping with the grandeur of the predictions themselves and the majesty of their Author. "For wisdom and might are His. And He changeth the times and the seasons; H© removeth kings and setteth up kings; He giveth wisdom unto the wise and knowledge to them that have understanding; He revealeth the deep and secret things; He knoweth \vhat i s i n the darkness, and the light dwelleth with Him." ^ (1) Daniel 2/20-22. 92. APPENDIX A - THE PROPHETIC MONTH REGARDED AS AN ASTRONOMICAL CYCLE The prophetic month may be considered as the unit at the base of the main chronological predictions of the book of the Revelation, the five months (Rev. 9/5), the hour, day, month, and year (Rev. 9/L5), and the forty-two months (Rev. 11/2). Interpreted on the year-day scale this prophetic unit becomes an astronomical unit, the thirty years* soli-lunar c y c l e . T h e error of this cycle, however, is nearly one and one-half days, and hence the cycle rapidly deteriorates and requires correction. A modern student setting out to devise means of correcting a cycle would doubtless proceed, as the Greeks of old did, by tracing the growth of the error of the cycle u n t i l i t reached proportions such as could be corrected by intercalation. Two types of intercalation are possible, the intercalation of a year, or the intercalation or dropping ( i f the cycle has a lunar-greater- than-solar error) of a month. The eight years* cycle, for example, may be corrected either by the intercalation of a year at the end of seven cycles ( i . e . intercalating the 57th year), or by the dropping of a month after 19 cycles ( i . e . making the 152 year intercalary). I t is remarkable that the two periods naturally adapted to correct the thirty years* cycle are the periods of 391 and 630 years.( 3) (1) A cycle somewhat more accurate than the famous octaeteris. See above p. 5 and table 2, p. 14. (2) See above p. 6. (3) 630 is one-half of 1260. After thirteen 30 years' cycles (390 years) the lunar months have fal l e n short of the solar years by -18 days. Hence the eleven days' epact of the 591st year combined with these eighteen days make a f u l l lunar month which corrects the cycle. In other words, i f after thirteen 30 years' cycles we intercalate 13 lunar months we w i l l have compensated for the accumulated errors of the 30 years' cycle. On the other hand after twenty-one 30 years' cycles (630 years), the lunar months have fallen short of the solar years by one complete lunar month, thus making this period the period naturally adapted to correct the 30 years' cycle by the intercalation of a month. These phenomena w i l l be made clearer by the accompanying charts. Chart 1 traces the growth of the error of the 30 years' cycle. It should be noticed not only that the error increases to about 30 days after 21 cycles and to about 18 days (the complement of the 11 days' epact of a single year) after 13 cycles but also that i t increases to 7 days or one week after 5 cycles (the 5 months of Rev. 9/5). Chart 2 illustrates how the prophetic hour, day, month, and year of Rev. 9/15 i s equated with exactly 391 years. (l) After 1260 years, by two complete lunar months. Cf. Chambers, Handbook of Astronomy, v o l . 2, p. I' <e ST <— a »-* o H 'B' I P o O -> H re B D WW " " T !' 1 1 1 1 I 1 1 ! 1 — T i l l c 3HART _ PT a GROWTH OF 1 HE I :RROR ( TH s YRARS' CYCLE . • 1J 30 y e a r s ' c y c l e s J "l i . 3 * ? i t *< i f 10 11 2V- 1 Jf i J- U J7 y T f ) f t ? / *-\-J / j u f —1— a 1 f v / ff — I ~ 5 • . i — — i \ s '—1— 1 1 \ i — — N — — / / ./MP N I 1 '3 t 0 S — T / 7 N ~jr L_ i _ 10 \ T i f i i. * \ ( 2 > i • N s r * 1 X _ i — \ J * \ \ 7,' }7 i* i r *>J i y \ . tf N - Sra >v \ SI * ?9 In - - - — - L ± - - .X. — X. ~ ~ • • • -— _L_ - — I zb_ - • r - * j CHART 2 The hour and day and month and year expanded on the day-year scale* The hour The day The montji s one SG years' cycle The year s twelve 30 years' cycles The hour, day, month, and year = 4836 lunar months B 403 lunar years ( • 391 solar years s 1 lunar month r 12 lunar months e 371 lunar months^^ - 4452 lunar months (1) See above table 2, p. 14. (2) See above tables 1 (p. 12) and 2 (p. 15) 96. BIBLIOGRAPHY Ante-nicene Father^ The Translations of the writings of the Fathers down to A.D. 325, edited by the Rev. Alexander Roberts, D.D., and James Donaldson, LL.D., American reprint of the Edinburgh edition. 8 vols. Buffalo, The Christian Literature Publishing Company, 1885. Barnes, Albert (1) Notes on the hook of Daniel c r i t i c a l , explanatory, and practical. Edinburgh, Gall and Inglis, 1853. (2) Notes on the hook of Revelation explanatory, and practical. Edinburgh, Gall and Inglis, 1852. Bede, The Venerable Bedae Opera de temporibus, edited hy Charles W. Jones, Cambridge, Mass., The mediaeval aoademy of America, 1943. Bengel, J. A» Gnomon novi testament!. F i r s t edition 1742. Edition consulted, London, David Nutt,, 1855. Calvin, John Commentaries on the hook of the prophet Daniel, translated into English hy Thomas Myers, M.A», 2 vols. Edinburgh: printed for the Calvin Translation Society, 1852. Cambridge Medieval History Vol. IV The Eastern Roman Empire. New York, The Macmillan Co., 1923. Censorinus De die natali, recensuit Fridericus Hultsch. Lipsiae, i n aedibus B. G. Teuhneri, 1867. Chambers, George F. (1) A handbook of descriptive and practical astronomy, 4th ed., 3 vols. Oxford, Clarendon press, 1889. (2) The story of eclipses. London, Newnes, 1899. Commentary A Jewish periodical incorporating Contemporary Jewish Record, published monthly by the American Jewish Committee, 425 Fourth Avenue, New York. E l l i o t t , E. B. Horae apocalypticae; or a commentary on the Apocalypse, c r i t i c a l and hist o r i c a l ; including also an examination of the ohief prophecies of Daniel. 4 vols. Fi r s t ed., 1844. Final edition (the 5th) 1862. London: Seeley, Jackson, and Halliday. Encyclopaedia Britannica, 11th and 14th editions. 97. Faber, George Stanley The sacred calendar of prophecy, or a dissertation on the prophecies which treat of the grand period of seven times and especially of i t s second moiety or the latter three times and a half. 3 vols. London, C. and J . Rivington, 1828. Farrar, F. W» The book of Daniel. Contained i n the 'Expositor's Bible' series. London, Hodder and Stoughton, 1895. Fleming, Robert The rise and f a l l of the Papacy. Written o. 1700; edition consulted: Ingram Cobbins. London, printed by Knight and son, 1849. Fuller, Edmund Thesaurus of anecdotes. New York, Crown Publishers, 1942. Geminus Gemini elementa astronomiae...recensuit...Carolus Manitius. Lipsiae, i n aedibus B. G. Teubneri, 1898. Guinness, H. Grattan (1) The approaching end of the age viewed i n the light of history, prophecy, and science. F i r s t edition 1878, f i n a l edition (the 13th) 1897. London, Hodder and Stoughton. (2) Light for the last days, a study historic and prophetic. F i r s t edition 1887, f i n a l edition (the 7th) 1893. London, Hodder and Stoughton. (3) Romanism and the reformation from the standpoint of prophecy. London, Hodder and Stoughton, 1887. (4) Creation centred i n Christ. 2 vols. London, Hodder and Stoughton, 1896. (5) History unveiling prophecy. New York, Chicago, etc., Fleming H. Revell Co., 1905. (6) On this rock, or the certainties of f a i t h . Kilmarnock, Scotland, John Ritchie, 1908. Heath, Sir Thomas L i t t l e Aristarchus of Samos, the ancient Copernicus; a history of Greek astronomy to Aristarchus....Oxford, Clarendon press, 1913. Hoffmann, Conrad, Jnr. The Jews today; a c a l l to Christian action. New York, Friendship press, 1941. Montgomery, James Alan A c r i t i c a l and exegetical commentary on the book of Daniel. The 'International C r i t i c a l Commentary' series. New York, C. Scribner's sons, 1927. 98. Newton, Thomas Dissertations on the prophecies which have remarkably been f u l f i l l e d and at this time are f u l f i l l i n g i n the world. Written 1754; edition consulted: London, B. Blake, 1840. Ptolemy, Claudius (1) Claudii Ptolemaei Opera quae extant omnia...Lipsiae, i n aedihus B. G. Teubneri, 1898 - 19. v o l . I, Syntaxis mathematica, ed. J. L. Eeiberg. (2) Canon of Kings, ed. Halma, Paris, 1819. (5) . Tetrahihlos; edited and translated into English hy F. E. Robbins. Cambridge, Mass., Harvard University press, 1940. Pusey, E. B. Daniel the prophet: nine lectures delivered i n the divinity school of the University of Oxford. New York, Funk and Wagnalls, 1885. Royal Society of Canada, Transactions, 1905. Article hy W. Bell Dawson, Solar and lunar cycles i n the prophetic numbers i n the hook of Daniel. Russell, H. N.; Dugan, R. S.; Stewart, J. Q. Astronomy: a revision of "S>ung*s manual of astronomy. Vol. 1, the solar system. Revised edition. Boston, New York, etc., Ginn and Company, 1945. Victoria Institute or Philosophical Society of Great Britain. Journal of transactions v o l . LX7II (1935). Article by W. Bell Dawson, Prophetic numbers i n Daniel i n relation to cele s t i a l cycles. London, published hy the Institute, 1 Central Buildings, Westminster S.W.I, 1935. Wright, G. E., and Filson, F. V. The Westminster historical atlas to the Bible. Philadelphia, the Westminster press, 1945. Zockler, Otto The hook of the prophet Daniel theologically and homiletically expounded, translated hy James Strong, S.T.D., appearing i n Lange's, Commentary on the Holy Scriptures as edited by Philip Schaff. New York: Scribner, Armstrong and Co., 1876. 

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