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 ASTBOIOMICAL AID HISTOEICAI 
 
 CHROlOIOai 
 
 W. LEIGHTON JOEBAN 
 
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ASTEONOMIOAL AND mSTOHlCAL 
 CHRONOLOGY 
 
 IN THE BATTLE OF THE CENTURIES 
 
 BY 
 
 WILLIAM LEIGHTON JOEDAN 
 
 FELLOW OP THE ROYAL INSTITUTION OP GREAT BRITAIN ; FELLOW OF THE 
 
 ROYAL STATISTICAL SOCIETY 
 
 ASSOCIATE OP THE INSTITUTION OP CIVIL ENGINEERS 
 
 FELLOW OP THE ROYAL METEOROLOGICAL SOCIETY 
 
 FELLOW OP THE ROYAL GEOGRAPHICAL SOCIETY ; FELLOW OP THK SOCIETY OP ARTS 
 
 PAST PRESIDENT OP THE ENGLISH LITERARY SOCIETY 
 
 OP BUENOS AYRES 
 
 ff ^ or THE ^'^P 
 
 '' UNIVER3/TY 
 
 LONGMANS, GKEEN, AND CO. 
 
 39 PATERNOSTER ROW, LONDON 
 
 NEW YORK AND BOMBAY 
 
 1904 
 
 All rights reserved 
 
c.^n\ 
 
 f^ ^J>^ 
 
 ^iisE 
 
'4L 
 
 I DEDICATE THIS LITTLE BOOK 
 
 TO ALL LIBRAEIANS 
 
 IN THE CITIES OP FLORENCE AND PISA 
 
 OP GLORIOUS RENOWN 
 
 IN THE HOPE THAT THROUGH SO DOING I MAY RECEIVE 
 
 PROM SOME AMONG THEM 
 
 FURTHER EVIDENCE FOR THE ELUCIDATION 
 
 OP THE SUBJECT 
 
PEEFAOE 
 
 The following Argument (excepting the references to 
 the State Library of Venice and to the 1875 edition 
 of Bond's ' Chronology ' ) was written in the year 1900, 
 when discussion was rife as to whether that year 
 properly belongs to the nineteenth or to the twentieth 
 century ; and I have retained it as a basis for argument, 
 as it sometimes simplifies references and discussion. 
 
 I have used the term historical rather than the 
 usual term vulgar chronology in the title because 
 the origin of the latter term makes it properly include 
 astronomical chronology, it having been intended to 
 signify that it does not give the true number of years 
 from the Annunciation or from the Nativity. And also 
 * historical chronology ' was a technical term for the 
 Christian era used with Julian years before the 
 Gregorian Keformation, which identified vulgar chro- 
 nology with it, so that my present use is, in fact, the 
 original use of the term. 
 
 Royal Institution, ALBE^LVRLE Street, London : 
 April 2, 1904. 
 
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ASTEONOMICAL 
 
 AND 
 
 HISTOEICAL GHEONOLOGY 
 
 Astronomers call the year which immediately pre- 
 ceded 1 A.D. the year ; but in historical chronology 
 that epoch year of the astronomical system is called 
 1 B.C. 
 
 The purpose I have before me is to show reason for 
 such a reformation of historical chronology as to bring 
 it into accordance with the method of numbering the 
 years B.C. which has been adopted by astronomers. 
 
 Besides the question as regards the method of 
 using figures for numbering the years, there is a minor 
 difference between astronomical and vulgar reckoning 
 due to the astronomical days commencing at noon 
 twelve hours after the commencement of the day by 
 vulgar reckoning. As regards that minor difference, 
 Sir John Herschel has advocated a reform of the 
 astronomical method for the purpose of making it 
 agree with the vulgar method ; and if the astronomical 
 world to whom he appealed should decide on that 
 reform jointly with the reform of historical chronology 
 which is the subject of this paper, then the two methods 
 
8 ASTRONOMICAL AND 
 
 of reckoning would agree as regards the enumeration 
 of both days and years. 
 
 Sir John Herschel, being himself an astronomer, 
 fully recognised the inconvenience which would be 
 caused by having to record astronomical observations 
 for the same night under two different dates, but he 
 nevertheless declared uniformity of nomenclature and 
 modes of reckoning to be of such vast and paramount 
 importance as to outweigh every consideration of 
 technical convenience or custom.^ 
 
 The impracticability of changing vulgar chronology 
 on that point makes a reformation of the astronomical 
 system, as regards it, the only way of arriving at 
 uniformity. 
 
 That reform, suggested by Sir John Herschel, is, 
 however, a distinct and subordinate question ; and that 
 which I advocate can be more easily effected, and is, in 
 fact, quite independent of the reform suggested by Sir 
 John Herschel. 
 
 My argument will be found to be to the effect that 
 the astronomical method of placing a zero year between 
 the B.C. and the a.d. years is intrinsically superior to 
 the historical system, which places 1 B.C. and 1 a.d. in 
 juxtaposition; and that, in fact, when the existing 
 enumeration of the years of the Christian era was 
 arranged the year which is now the zero year of 
 astronomers was regarded as the first or epoch year of 
 the era, and the enumeration of 1 a.d. was purposely 
 given to what was then recognised as the second year 
 of the era. And, therefore, when astronomers found it 
 expedient to push back the numbers of the B.C. years, by 
 
 ' Outlines of Astronomy, p. 87, 1849. (London : Longmans.) 
 
HISTOEICAL CHRONOLOGY 9 
 
 treating as zero what had become in historical chrono- 
 logy 1 B.C., they unconsciously re- adopted the enumera- 
 tion of years B.C. which was originally adopted tacitly, 
 if not explicitly, by the Benedictine monks who founded 
 the era. 
 
 My argument shows that through a misunder- 
 standing on the part of comparatively modern 
 historians they treated as 1 B.C. the year which when 
 the era was first established was called 1 a.d. by those 
 who used ordinal, and the year by those who used 
 cardinal, numbers ; and that the manner in which the 
 centuries are now generally considered to be divided is 
 therefore erroneous. 
 
 For an exposition of the questions involved histori- 
 cally and scientifically in this subject some brief 
 references to the writings of Sir John Herschel^ 
 Dr. Lardner, and some others, will suffice not only to 
 represent what have been prevalent ideas, but also to 
 create a basis for the establishment of some facts of 
 which they appear to have had no knowledge. 
 
 Herschel says that ' in the historical dating of events 
 there is no a.d. 0. The year immediately previous to 
 A.D. 1 is always called B.C. 1 ' ; and the years ' are 
 denominated as years current {not as years elapsed) 
 from the midnight between December 31 and Jami- 
 ary 1 immediately subsequent to the birth of Christ.' ^ 
 
 He further says that ' the designation of a year 
 by A.D. or B.C. is to be regarded as the name of that year, 
 and 7iot as a mere number uninterruptedly designating 
 the place of the year in the scale of time.' He says : * The 
 
 * Outlines of Astronomy, by Sir John Herschel, pp. 628, 629. 1849. 
 (London.) 
 
10 ASTRONOMICAL AND 
 
 scale of A.D. and B.C. is not continuous, the year in 
 both being wanting ; so that (supposing the vulgar 
 reckoning correct) our Saviour was born the year 
 B.C. i; • 
 
 Dr. Lardner says that 1 a.d. is the year of Kome 
 754 ; and that ' the first year of the Christian era is 
 not, as might be imagined, that of the birth of Christ, 
 but the following year. It is the year in which, 
 according to Dionysius Exiguus, Christ completed his 
 first year.' ^ 
 
 Though Dr. Lardner is correct in those statements, 
 they nevertheless show that he did not know that 
 before the Gregorian Reformation the ordinal numbers 
 applied to the years by Dionysius were discarded for 
 cardinal numbers, so that 1 a.d. became apphed to what 
 was recognised by the advocates of both systems to be 
 the second year of the era and had in fact been called 
 
 2 A.D. 
 
 ^According to the Benedictine records, Dionysius 
 did not make the mistake of calling the year of Rome 
 753 the year 1 B.C. That error has been introduced 
 subsequently by others not so conversant as he was 
 with what were then supposed to be, and were 
 accepted as, the facts of the case. What Dionysius 
 called 1 A.D. began on March 25, 753 of Rome, and 
 ended with March 24, 754 of Rome,^ and his method 
 was adopted in Pisa, while at Florence and by St. 
 
 ' Outlines of Astronomy, by Sir .John Herschel, p. 6o6. 1849. 
 (London.) 
 
 - Common Things Explained, by Dr. Dionysius Lardner. 1856. 
 (London.) TJie Almanack, p. 6. 
 
 ' L'Art de Verifier les Dates, par un Religieux Benedictin de la 
 Congregation de S. Maur ; vol. i. p. v., troisierue Edition. 1783. (Paris.) 
 
HISTORICAL CHRONOLOGY 11 
 
 Augustine in England the following year was called 
 1 A.D. The Benedictines record that position of the 
 question as indisputable, and it is confirmed by the 
 fact that in the twelfth century our present method of 
 calling the year of Rome 754 the year 1 a.d. did not 
 universally prevail even among those who used for 
 the new era the Julian year commencing on January 1, 
 in conformity with the year of Rome. By them the 
 years of our era were numbered so as to make the year 
 of Rome 753 identical with the year 1 of our era, so that 
 the same year which we call 1102 a.d. was by them called 
 1103 A.D.* They did not change the day for the com- 
 mencement of the year, but merely substituted 1 a.d. 
 for 753 A.u.c. It is not any dijfference of opinion as to 
 which is the epoch year of the era, but merely the 
 difference between using cardinal instead of ordinal 
 numbers that has changed the above-mentioned date 
 from A.D. 1103 to 1102 ; and a peculiarity of the 
 position is that in consequence of the epoch year 
 having become erroneously called 1 B.C. the cardinal 
 numbers used by the Florentines are now supposed to 
 be ordinal numbers, as stated by Sir John Herschel, 
 whereas in fact it was those who differed from the 
 Florentine method of applying figures to the years 
 who used ordinal numbers, while those who followed 
 the Florentine enumeration, which has become 
 universal, used the figures as cardinal numbers. If the 
 Dionysian enumeration had been maintained the present 
 year would have been a.d. 1901, but the substitution 
 of the Florentine method has made it a.d. 1900.- 
 
 * L'Art de Verifier les Dates, pp. iv, viii, and ix. 
 2 See Preface. 
 
12 ASTRONOMICAL AND 
 
 The records of which I shall now give some 
 examples place the historical accuracy of the fore- 
 going beyond the reach of dispute. 
 
 The two phrases Atmo ah Incarnatione Dom'uii and 
 Anno Incarnationis Dominlccc seem to have been used 
 at times promiscuously before the abbreviation a.d. 
 came into use ; but they clearly represented originally 
 the two different systems of numbering the years, the 
 former being used with the cardinal and the latter 
 with the ordinal numbers. 
 
 A charter signed by King Kobert II. of France, 
 dated ' Anno Dominicae Incarnationis Mxxviii,' is shown 
 to belong to the year 1027 a.d. according to the now 
 prevailing method of numbering the years. ^ 
 
 Another charter signed by the same king, dated 
 * Anno Incarnati Verbi millesimo,' is shown to belong to 
 the year 999 a.p.^ according to the Florentine system, 
 which has now completely displaced the ordinal enu- 
 meration used by Dionysius. 
 
 And the date of King Kobert's death, which 
 occurred on July 20, 1031 a.d., is recorded by the 
 historian Helgaud as ' Anno qui est Incarnationis 
 millesimus tricesimus secundus.' ^ That clearly declares 
 what we call 1031 a.d. to be the 1032nd year of the era. 
 
 A Strasbourg date is recorded as * Anno Incarna- 
 tionis Dominicae milesimo quinto,' and is shown to be 
 apphcable to the year 1004 according to our present 
 system ^ ; and it has been therefore inferred that the 
 document must have been signed between Christmas 
 Day and January 1, between which dates there was 
 
 ' UArt dc Verifier les Dates, p. v. - Ibid. 
 
 ^ Ibid. * Ibid. p. ix. 
 
HISTOEICAL CHEONOLOGY 13 
 
 often confusion as to which year was current. But, 
 whatever may have been the fact in that special case, 
 it seems clear that such a date as Anno Incarnationis 
 Dominicae quinto, used under the Pisan system, was 
 originally recognised as equivalent to Anno ab Incar- 
 natione Domini quatuor (not quinque) used under 
 the Florentine system ; the ordinal number quinto 
 designating the same year as the cardinal number 
 quatuor. 
 
 A charter signed in a monastery near Eeims, and 
 dated ' anno Domini, secundum cursum Ecclesiae 
 Eemensis Mcccxc, decima tertia die mensis Junii,' is 
 shown to belong to the year 1389 a.d. by our record. 
 
 King John's submission to Pope Innocent III. is 
 dated ' on the third day of October in the year from 
 the incarnation Mccxiii.,' ^ and the number of the 
 year accords with the Florentine system, which has 
 always prevailed in England. 
 
 A charter granted by Athelberht, King of Kent, and 
 with the granting of which St. Augustine, then Arch- 
 bishop of Canterbury, appears to have been connected, 
 is dated ' in the City of Canterbury, anno ab Incarna- 
 tione Christi, DCV.^ In the absence of any suggestion 
 to the contrary, I presume that the enumeration of the 
 year 605 accords with our present usage. 
 
 The Benedictine work from which I have already 
 quoted does not mention any use of the Pisan enumera- 
 tion in England ; it says (p. x.) : ' Le calcul Pisan, 
 qui precede d'une annee entiere celui de Florence, a 
 
 ' Arbuthnot, Tlie Mysteries of Chronology, p. 49. 
 2 Rules for Verifying Dates, by John J. Bond, Assistant Keeper in 
 her Majesty's Record Office. 1875. (London.) 
 
14 ASTRONOMICAL AND 
 
 ete en usage, non seulement a Pise, mais a Lucques, a 
 Sienne, a Lodi ; plusieurs Papes s'y sont conformes 
 dans les dates de leurs Bulles, et plusieurs Erapereurs 
 d'Occident, des le IX'' siecle, dans celles de leurs 
 diplomes.* They have, however, as above shov^n, proved 
 its use in France. 
 
 Dr. Lardner says : ' Dionysius made historical re- 
 searches, the result of which assigned the birth of Christ 
 to the 25th day of December, in the 753rd year from 
 the foundation of Kome ' ; it appears to me, however, 
 quite clear that Dionysius deliberately preferred to 
 make the era commence with the first year of one of his 
 cycles of 582 years (consisting of twenty-eight lunar 
 cycles of nineteen years) rather than with the records 
 which he must have known make 4 B.C. of the vulgar 
 era the first year. Bond,^ after pointing out that the 
 Golden Number 1 of the Dionysian reckoning falls to 
 the year known as 1 B.C., says : ' But as that year 
 did not come within the range of the Roman reckon- 
 ing, the number 1 of the first cycle of 532 years 
 was represented by 0.' And then he adds : * Hence 
 arose a system by which the annus verus, or 4 B.C., 
 was called by ecclesiastical writers 8 B.C., by the 
 omission of 1 B.C. marked 0, and thus great confusion 
 has been caused when calculations have been made 
 subject to that erroneous system.' 
 
 I do not know what authority Bond has for the 
 fact of the zero year having been used as he states, but 
 I have no doubt as to the accuracy of any such state- 
 ments in his valuable work ; the tenour of my argument 
 is, however, all to the effect that he has not properly 
 
 • Rules for Verifying Dates, George Bell & Sons, 1875, p. 321. 
 
HISTORICAL CHRONOLOGY 15 
 
 appreciated the action of those who used it as he 
 states. His alhision to the comments on the absence 
 of a year which were made by Sir John Herschel 
 (who evidently did not know of such an enumeration 
 ever having been used) show that he considers the 
 method adopted by astronomers to be an erroneous 
 system of enumeration, and make it appear to me 
 that he misunderstood the object of Herschel's com- 
 ments. 
 
 In the article on Chronology in the ' Encyclopaedia 
 Britannica '^ W. L. K. Gates makes some contradic- 
 tory statements. He says the Christian era commenced 
 on January 1 in the 753rd year from the foundation of 
 Kome, meaning, I presume, 753 a.u.c, as, though 753rd 
 might be applied to 752, it cannot be applied to 754, 
 A.u.c, which corresponds with 1 a.d., and, so interpreted, 
 that statement agrees with the further statement he 
 makes (in direct contradiction to Herschel) to the 
 effect that the years of the Christian era are distin- 
 guished by the cardinal numbers. He, however, not 
 only does not comment on the fact that those state- 
 ments make the year 1 a.d. the second year of the era, 
 and are incompatible with the application of the name 
 1 B.C. to the year of Kome 753, but also he himself 
 further on treats 1 a.d. as the first of our era and the 
 preceding year as 1 B.C., regardless of the fact that 
 those statements directly contradict his previous state- 
 ments that the numbers are cardinal and that 1 a.d. 
 commenced with the 753rd year of Eome. His state- 
 ment that the era commenced on January 1 of the 
 4714th year of the Julian period also makes 1 a.d. the 
 
 * Ninth edition, vol. v. p. 712. 
 
16 ASTRONOMICAL AND 
 
 first of the era. The ' Encyclopaedia ' truly reflects 
 the confusion of ideas which has existed. 
 
 The fact is that the Gregorian Keformation has 
 virtually made the era commence with January 1, 
 753 of Home, reverting to the method of those who, 
 as already stated, applied the term ' year of the Incar- 
 nation ' to the years of Kome commencing on Janu- 
 ary 1, treating the first year of the Incarnation as the 
 year 753 of Eome, on the same principle as a year a.d. 
 might be referred to as the first of a king's reign and 
 the following year a.d. as the second of his reign, so 
 that he might be recorded as in the second j^ear of his 
 reign after reigning a few months, or even a few days.^ 
 By reverting to that principle the Gregorian Keforma- 
 tion got rid of the confusion created by the change 
 from the Julian to the Christian year. But that was 
 not the commencement of the year in the * year of the 
 Incarnation,' which was the original Christian era, and 
 was introduced into England by St. Augustine in the 
 sixth centmy, soon after its invention by Dionysius ^ ; 
 but St. Augustine appears to have used it with the 
 Florentine instead of the Dionysian enumeration. It 
 was, I understand, considered to commence with what 
 is now termed Lady Day, or the Feast of the Annun- 
 ciation, March 25 of the year of Eome 753. At 
 any rate, Dionysius called the year commencing on that 
 date the year 1, and St. Augustine's introduction of the 
 Florentine enumeration into this country resulted in the 
 
 ' ' Elagabalus reigned three years and nine months of solar years, and 
 yet we have coins dated in his fifth year.' Bond, Rules for Verifying 
 Dates, 1875, p. 23. 
 
 2 L*Art de Verifier les Dates, vol. i. p. iii. 
 
HISTOEICAL CHEONOLOGY 17 
 
 year 1 a.d. becoming recognised as commencing on March 
 25, 754 A.u.c. Statements by accurate authorities are 
 sometimes apparently contradictory merely in conse- 
 quence of two different years being used at the same 
 time in the same country, so that both may be true 
 though each ignores the existence of the system differ- 
 ing from that recorded by him. According to Bond's 
 1866 edition of the work quoted on page 14, the year 
 of the Nativity was in use in England at the time 
 of the Norman Conquest, and the Julian year was 
 then introduced by "William I. and continued to be 
 used for about 100 years, when Henry II. substituted 
 the year of the Incarnation. His 1875 edition, how- 
 ever, recognises the latter year as having been the 
 first used in England, and the French work I have 
 quoted is very explicit as to the years of the original 
 era of the Incarnation having commenced on March 
 25 .; and adds that after a.d. 744 and the time of 
 Charlemagne French historians who used the years 
 of Jesus Christ did not all agree as to the commence- 
 ment of the year. It is also pointed out that Gregory 
 of Tours confounded the era of the Incarnation with 
 that of the Passion, and that is perhaps the original 
 source of much subsequent confusion. The year of 
 the Nativity appears by the French work (p. x) to have 
 been first used in England in the seventh century. 
 And, in the thirteenth century, Gervais of Canterbury 
 asserted that it had been used by nearly all English 
 writers who had preceded him * pour la raison que ce 
 jour est comme le terme ou le soleil finit sa course et la 
 recommence.' The general tenour of the Benedictine 
 work shows them to have considered it clear that 
 
 B 
 
18 ASTRONOMICAL AND 
 
 (except some adherence to the Julian year) no year 
 but that of the Incarnation was used with the vulgar 
 Christian era until some time after the date of its 
 introduction into England. The question as to 
 whether St. Augustine used the year of the Nativity 
 or that of the Incarnation is not, however, material to 
 my main argument. St. Augustine was a Benedictine, 
 and was educated by Gregory I. before the latter 
 became Pope. Gregory, however, does not appear to 
 have used the Christian era at all, as the first recorded 
 use of it by any of the Popes is in 613 a.d. by 
 Boniface IV., fifteen years after St. Augustine's arrival 
 in England, and whatever may be proved to be the 
 method adopted by either will probably have been the 
 one used by the other. As St. Augustine was a Benedic- 
 tine, it seems natural that he should have used the year 
 of the Incarnation commencing on March 25, but it is 
 remarkable that the Pisan enumeration had apparently 
 been abandoned by him in favour of the Florentine. 
 
 In connection with the foregoing argument it is 
 expedient to record that the most recent of writers on 
 chronology, F. F. Arbuthnot,^ on the authority of 
 Father Hardouin, expresses doubts as to any such 
 person as Dionysius Exiguus having existed ; but 
 the fact of the invention of the Christian era remains 
 indisputable, and no reason is shown why the Bene- 
 dictine traditions should not have handed down the 
 name of the originator of the era. If the legend of 
 Dionysius is rejected, it can only be said that the 
 era was invented by some Benedictine monks whose 
 
 ' The Mysteries of Chronology, by F. F. Arbuthnot, pp. 18-22. 1900. 
 (London.) 
 
HISTOEICAL CHRONOLOGY 19 
 
 names have not been handed down to posterity, and the 
 foregoing argument remains unaffected ; for if Dionysius 
 is not the name of an individual who made a special 
 study of the subject, it serves the pm-pose of repre- 
 senting the group of Benedictines who originated the 
 era. 
 
 Arbuthnot, like Herschel, Lardner, Playfair, and 
 others, treats the year 1 a.d. as the first year of our 
 era ^ ; but the erroneous name, 1 B.C., given to the year 
 of Kome 753, which immediately precedes it, seems to 
 be the only reason for doing so. Having treated the 
 year 753 of Rome as 1 B.C., they could not logically 
 regard the year next following it as the second of the 
 Christian era, though the * Encyclopaedia Britannica,' 
 as above shown, disregards logic in the question ; for, 
 as already shown, it declares the figures we use to be 
 cardinal numbers, and that the year 753 A.u.c. is the 
 first of our era, directly contradicting Herschel on 
 those two points, but it immediately afterwards joins 
 with Herschel by treating 1 a.d. as the first of the era 
 and declaring the preceding year to be 1 B.C., thus 
 making both those figures ordinal numbers and 
 making 753 a.u.c. the same as 1 B.C. 
 
 In * Macmillan's Magazine ' for February, 1900, a 
 writer signing ' Dionysius Minimus ' says that he finds 
 it recorded, on the authority of the Astronomer Royal, 
 that it has been agreed in chronology to call the first 
 year of the Christian era 1 a.d. ; and that it also 
 appears that there are in existence two letters of Dio- 
 nysius which prove that arrangement to have been 
 his deliberate intention ; but the facts I have recorded 
 * The Mysteries of Chrofwlogy, p. 7 ; see also pp. 16, 17. 
 
 b2 
 
20 ASTEONOMICAL AND 
 
 above show that though it is true that Dionysius 
 called the first year of the era 1 a.d., the year so 
 named by him is that which became in vulgar 
 chronology called 1 B.C., and what the Florentines 
 called 1 A.D. was called by him 2 a.d. We apply to 
 the years of the era the same figures as the Florentines 
 applied to them respectively, but we erroneously treat 
 them as ordinal numbers, though the figures applied 
 by Dionysius, which really represented the ordinal 
 numbers, were always one figure in advance of the 
 Florentine figures, which latter are the figures of all 
 our now existing records of dates. 
 
 A question which must force itself upon the atten- 
 tion of anyone who considers the foregoing circum- 
 stances is as to why (excepting the minor difference as 
 to commencing at noon or at midnight) there should 
 be any difference between astronomers and other 
 chronologers in the system of recording historically 
 the dates of events. It certainly cannot be disputed that 
 the astronomical system is a reasonable and correct 
 method. If by that method an event occurred in the 
 year 100 B.C. and another event on the corresponding 
 day in the year ] 00 a.d., the lapse of time between them 
 is 200 years; whereas under the vulgar system one 
 year must be deducted after adding the dates together 
 to get the correct number of years between the two 
 events. So also for reckoning leap years the same 
 rules apply under the astronomical system for the 
 dates B.C. as for those A.D. ; whereas under the vulgar 
 system the rules which apply to the dates a.d. do not 
 apply to those B.C. On the other hand, the vulgar 
 method does not seem to have any advantage over the 
 
HISTOEICAL CHKONOLOGY 21 
 
 astronomical method. Why should that confusion of 
 systems be persisted in ? 
 
 The authorities who established the era treated it 
 as if they supposed Christ to have been born in the 
 year of Kome 753, and, therefore, in treating that as 
 the epoch year of the scale of time, and numbering it the 
 year 0, and the year preceding that 1 B.C., astronomers 
 merely comply with what were accepted as historical 
 facts when the era was adopted. 
 
 Admitting that the year of Kome 753 is not really 
 the year in which Christ was born, but that it is 
 expedient to adhere to the date which was accepted for 
 the establishment of the epoch based on that event 
 when the era was invented, the year of Eome 752, 
 which is in vulgar chronology called the year 2 B.C., is 
 correctly called by astronomers 1 B.C. ; and the year of 
 Kome 753, which in vulgar chronology is called 1 B.C., 
 is the epoch year of the Christian era, and is correctly 
 called by astronomers the year 0. 
 
 A misconception of the principles on which an 
 epoch for the record of events ought to be based seems 
 to be the only explanation for the epoch year having 
 been omitted when historians first numbered the B.C. 
 years in vulgar chronology ; and its omission creates 
 an error in the record of time identical with that which 
 would be created by the omission of the unit cipher 
 between the teens and the twenties or between the 
 twenties and the thirties. By passing from 29 to 31, 
 ignoring the cipher of the thirties, a correction, by 
 deducting one year from every date, would for ever 
 afterwards be necessary to get a true record of years 
 elapsed ; and the cipher year of the forties would have 
 
22 ASTRONOMICAL AND 
 
 to be reckoned as belonging to the thirties in order to 
 keep the ten-year periods equal, though in the absence 
 of the erroneous omission of the year 30 the year 40 
 would arithmetically belong to the series of the forties, 
 because it would signify that forty years of the era had 
 elapsed, not that the 40th year was current. The 
 error appears to be due to the consecutive framers of 
 the vulgar era, as now constituted, not having always 
 recognised that a zero year is requisite for its com- 
 mencement, to divide the a.d. from the B.C. years, just 
 as a zero is arithmetically requisite between each 
 separate group of integral units. That error is avoided 
 by astronomers and was not made by those who 
 gave to the a.d. years the numbers now^ in use, but 
 was made subsequently by those who numl^ered the 
 B.C. years. To use Sir John Herschel's phrase, 
 chronologers have been driven to the expedient of 
 'calHng the years names,' instead of counting them 
 mathematically, in consequence of the erroneous 
 omission of the zero year between the B.C. and the 
 A.D. years. 
 
 Sir John Herschel says, in one of the above extracts, 
 that the year is wanting in the a.d. as well as in the 
 B.C. part of the scale of years. The fact, however, is 
 that it is because we do not know where the true 
 origin is that we have to create a fictitious origin ; and 
 it would be as great a mistake to constitute two zero 
 years, one for the B.C. scale and another for the a.d. 
 scale, as that made by the total omission of the zero 
 year in vulgar chronology. The astronomical scale as 
 at present constituted is all one scale with a perfect 
 arithmetical sequence throughout ; the years in one 
 
HISTORICAL CHRONOLOGY 23 
 
 direction from zero being virtually ^j/?/.s, and those in 
 the other direction minus quantities ; and the arithme- 
 tical sequence is not affected by the position selected 
 for the zero. The zero of astronomers is in fact the 
 zero year of time transferred to an artificial position 
 arbitrarily determined ; and wherever placed it is the 
 zero of all years, whether B.C. or a.d. The year of 
 Rome 753 was the chosen epoch year when our era 
 was founded, and it properly belongs to the first 
 century of the era based upon it wherever that century 
 may be in the absolute scale of time ; so that the year 
 of Rome 853 was the first year of the second century 
 of our era, not the last of the first century. The 
 calling of the year of Rome 753 the year 1 B.C. after 
 having made 1 a.d. represent the year of Rome 754 
 is an error to which astronomers cannot reasonably 
 conform, as that number arithmetically belongs to 
 the year of Rome 752, and is correctly appHed to it by 
 astronomers ; and as we are now (November 1900) in 
 the year of Rome 2653, we are therefore in the first 
 year of the twentieth century of years in the Christian 
 era. If the year of Rome 753 really were the year 
 1 B.C., as in vulgar chronology it is now erro- 
 neously called, then we should not be in the twentieth 
 century of the Christian era until next year (a.d. 1901) 
 commences. 
 
 It is because Sir John Herschel makes the Chris- 
 tian era commence with the year following what 
 historians call the year 1 B.C. that he says, as above 
 stated, that the dates represent years current, not years 
 elapsed. But as that year is properly treated by 
 astronomers as the year 0, and is in fact the epoch 
 
24 ASTEONOMICAL AND 
 
 year of the Christian era, the numbers as at present 
 appHed to the years A.D. do in fact represent years 
 elapsed in the Christian era, not years current, as 
 declared by Herschel on the supposition that the 
 erroneous name 1 B.C. given by modern historians to 
 the epoch year puts that year out of the era. 
 
 Avowedly knowing the year of Kome 753 to be 
 determined on for the epoch year of the vulgar era, in 
 contradistinction to what must have been known to be 
 the true era, the Florentines seem to have delibe- 
 rately rejected the enumeration of 1 a.d. which had 
 been appHed to it under the Pisan system, and to have 
 termed the year of Kome 754 the year 1 a.d., because 
 in cardinal enumeration the first year of the era is the 
 zero of years, and the second 5^ear is the first in which 
 a complete unit of years can be counted. At any rate, 
 the adoption of their method by modern astronomers 
 shows that they took the correct course in fixing 1 a.d., 
 and the further evidence I have cited shows that 
 though Dionysius used ordinal numbers to represent 
 the years of the era, that method was gradually 
 rejected in favour of cardinal numbers, making what 
 was recognised as the second year of the era 1 a.d. 
 
 It is mere matter of fact that the ordinal enumera- 
 tion, first, second, third, &c., does not correspond with 
 the common arithmetical (or cardinal) enumeration, 
 one, tw^o, three, &c., respectively, but with the arith- 
 metical index figures, 0, 1, 2, &c., respectively. The 
 arithmetical index figure 1 cannot appear in the scale 
 of time in which years are the units, until what is in 
 ordinal enumeration the first year is passed. 
 
 Though the idea of treating zero as a number does 
 
HISTOEICAL CHEONOLOGY 25 
 
 not appear to have been entertained by ancient mathe- 
 maticians,^ is now acknowledged to be the first 
 number, and is, therefore, also the first figure in 
 arithmetic, and 9 is the 10th. 
 
 Confusion has been created by the imperfect or 
 contradictory ideas of enumeration which formerly 
 prevailed. Archimedes represents the numbers 1 to 9 by 
 letters of the Greek alphabet, but does not give a letter 
 to represent zero. It is only more recently that the 
 cipher was brought into arithmetic as a tenth figure ; 
 and still more recently mathematicians have realised 
 the fact that zero must be regarded as a 7iumher ; and 
 its acceptance as such gives the cipher, which was 
 previously treated as the tenth figure, the position of 
 the first number, and, therefore, that of the first figure, 
 and makes the position of tenth figure still given to it 
 in text-books a survival from the erroneous theory 
 which formerly excluded zero from the category of 
 numbers. 
 
 Sir John Herschel's remarks show that he recog- 
 nised that in vulgar chronology the years are now 
 considered to be reckoned by ordinal numbers, both 
 B.C. and A.D., and that such a system is unsuitable for 
 the measurement of time. But his comment as to the 
 absence of a year in the A.D. scale shows that he 
 supposed that though the years B.C. are reckoned in the 
 astronomical scale by cardinal numbers representing 
 years elapsed (counting backwards), those of the a.d. 
 scale are reckoned in ordinal numbers representing 
 years current. He evidently regarded the a.d, and the 
 B.C. years as belonging to two separate scales. But 
 ' Century Dictionary. 
 
26 ASTRONOMICAL AND 
 
 the astronomical scale of time is in fact all one 
 continuous scale, and as such cannot have more than 
 one zero year upon it. It would, as above said, be as 
 great a mistake to put in two zero years as to leave the 
 zero out altogether. 
 
 A foot rule measures the same distance whether it 
 is turned with the enumeration of the inches running 
 from left to right or from right to left. Suppose, for 
 the sake of illustration (the epoch inch, like the epoch 
 year in the astronomical scale, being treated as zero), 
 the beginning of time to be found at any point of time 
 —say, exactly at 4713 B.C. (the moment that figure 
 leaves the vulgar scale as an ordinal number and ap- 
 pears on the astronomical scale as a cardinal number). 
 Then the B.C. part of the scale might be inverted; 
 and the zero year of the Christian era w^ould take its 
 proper place as the zero year of the complete scale of 
 time, the number 4713 being substituted in its place so 
 that 4714 would remain identical with 1 a.d., and, as 
 at present numbered, the a.d. years, at any date, added 
 to the B.C. period of 4713 years would give the correct 
 measure on the scale of time ; but to do so the numbers, 
 both A.D. and B.C., must of necessity represent cardinal 
 numbers recording years elapsed, not years current. 
 The year 0, which was the enumeration of the first 
 year of the old era, continues to be that of the first 
 year of the new era. It is the zero of all years 
 wherever it may be placed. If a second zero year had 
 been added specially for the a.d. part of the scale then 
 the present numbers would be pushed forwards, 1 a.d. 
 taking the place of 2 a.d., and the mistake made by 
 the insertion of the second zero year w^ould have to be 
 
HISTOKICAL CHRONOLOGY 27 
 
 corrected by always adding one year to the date to get 
 the true position on the scale of time. 
 
 The admission of a single zero year makes the 
 figures in both directions from it cardinal numbers and 
 the absence of a zero year, as in the vulgar scale, makes 
 them ordinal numbers in both directions. Those 
 ordinal numbers were rejected by the Florentines ; and 
 not only have modern astronomers re-adopted the 
 Florentine system, but also Sir John Herschel ex- 
 pressly declares ordinal numbers to be unsuitable for 
 the scale of time. 
 
 As a question of pure theory the astronomical 
 system is the only correct method of recording time on 
 a single scale. One zero year only can appear on the 
 scale, and that must of necessity be the first year of 
 the era ; the years which follow it being plus quantities 
 and those which precede it minus quantities. The 
 difference between plus one year and minus one 
 year is two years, which is correctly shown in the 
 astronomical scale ; but the vulgar scale makes the 
 difference only one year instead of two years, and 
 the suggested additional zero year for the a.d. years 
 would make such a scale show^ a difference of three 
 years instead of two years. I must repeat that not 
 only does theory require the first year of any era to be 
 enumerated by the index figure 0, but also the year 
 of astronomers is in fact the original epoch year of our 
 era, and as such was numbered by Dionysius the year 
 1 as he used ordinal enumeration, and the figures as 
 now applied in the subsequent cardinal enumeration of 
 the years a.d. do in fact represent years elapsed, not 
 years current. 
 
28 ASTRONOMICAL AND 
 
 Though not material to the main purpose of my 
 argument, it is nevertheless of interest to record the 
 opinions of leading authorities as to what was the 
 date of the birth of Christ. 
 
 Some students of the question argue that a con- 
 junction of the planets Jupiter and Saturn which 
 occurred in the year of Kome 747 (the vulgar 7 B.C., 
 or astronomical 6 B.C.) formed the Star of Bethlehem, 
 and thus make that the true epoch year ; while others 
 suggest that the first of two comets recorded by 
 Chinese astronomers in the years of Kome 749 and 750 
 respectively makes the first of those two years the true 
 date, which by the astronomical record would be 4 B.C. 
 or by the vulgar record 5 B.C. This latter is the date 
 accepted by James Play f air. ^ He, however, alludes 
 to it as ' about four years prior to the date of the 
 vulgar Christian era,' - professing himself unable to 
 decide as to whether the event occurred towards the 
 end of 748 or in the middle of 749 of the years of 
 Rome. His argument is to the effect that an eclipse 
 of the moon which occurred on March 13, 4 B.C. (astro- 
 nomical 3 B.C.) fixes that year, which is 750 a.u.c, as 
 the date of the death of King Herod the Great ; and 
 that ' it is highly probable ' that Christ was born ' not 
 much more than a year before Herod's death.' 
 
 Playfair incidentally refers to Dionysius as having 
 ' adjusted ' the first year of the Christian era to the 
 
 ' A System of Chrcynologij, by James Playfair, D.D. Edinburgh, p. 2G0. 
 1784. 
 
 - Ibid. p. 50. The ' era of Jesus Christ ' was at one time used with 
 the numeration commencing with 4 b.c. of the Vulgar era, thus agreeing 
 with Playfair's argument. 
 
HISTOKICAL CHEONOLOGY 29 
 
 4714th of the Julian period/ though the fact is that 
 the so-called Julian period or cycle was invented by 
 Scaliger (as Playfair of course knew) only in the year 
 1582 A.D. (the year of the Gregorian Keformation) for 
 the concordance of various cycles of which it is a 
 common measure, and March 25, 4713 (not 4714) of 
 the Julian period corresponds with the commencement 
 of the year 1 as fixed by Dionysius. If, as stated by 
 Playfair, Dionysius invented the Christian era about 
 the year 527 a.d., his so-called adjustment was with 
 the years of Kome ; and March 25, 527 a.d. (termed 
 by him the 528th year of the era) was March 25, 
 1280 of Kome ; but his work was not one of adjust- 
 ment, but of disturbance, for he took the above date 
 instead of January 1 as the commencement of the 
 year. The adjustment was effected by the Gregorian 
 Reformation (in 1582 a.d.), which made the year 1280 
 of the Roman era (A.u.c, or Anno Urbis Conditae) 
 identical with 527 a.d. by making the Christian years 
 commence, like the Julian years (which were the years 
 of the Roman era) on January 1. 
 
 Playfair also refers to the Incarnation as if repre- 
 senting our Christmas Day instead of our Lady Day, 
 and that confusion of the origin of the era of the 
 Incarnation seems to have become general. The Bene- 
 dictines say of the year : 
 
 * Plusieurs la commen9oient sept jours plutot que 
 nous, et donnoient pour le premier jour de I'annee le 
 25 Decembre, qui est celui de la naissance du Sauveur. 
 D'autres remontoient jusqu'au 25 Mars, jour de la 
 Conception, ou de son Incarnation dans le sein de 
 
 ' A System of Chronology y p. 50. 
 
30 ASTRONOMICAL AND 
 
 la Yierge, coinmuncment appele le jour de TAnnoii- 
 ciation.' ^ 
 
 The year 4 B.C. of vulgar reckoning is now 
 generally accepted as the date of the birth of Christ, 
 though according to the researches of Playfair just 
 mentioned it may have been 5 B.C., or perhaps 6 B.C. 
 The framers of the vulgar era must (as I have 
 already stated) have knov^n at least as well as we now 
 do what was the true era if commenced from the birth of 
 Christ. That generally accepted date, 4 B.C. vulgar or 
 3 B.C. astronomical, makes the year 1900 the fourth year 
 of the twentieth century of years from the date of that 
 event ; for if we counted from that year, treating it as 
 the epoch year, and the year which follows it as 1 a.d., 
 the year 1900 would be counted as 1903, or the 1904th 
 year of the era. And if the Dionysian estimate, 
 which brings the event nearer than any other to our 
 time and forms the basis on which the era was 
 founded, be accepted subject to the Gregorian Eeforma- 
 tion, nineteen complete centuries of years had elapsed 
 in the era when the year 1900 commenced, making 
 that year therefore the first in the twentieth century. 
 
 It must of course be borne in mind that every new 
 era which has been invented has given to all preceding 
 events dates which were unknown when the events 
 occurred. An eclipse of the moon which occurred in 
 the year of Rome w^hich Dionysius supposed to be 
 that of the Incarnation and of the birth of Christ is now 
 recorded as having ocdirred on January 11 of the year 
 of the astronomical scale, which is identical with the 
 year of Rome 753 excepting the difference of six hours 
 
 ' L\irt dc Verifier les Dates, p. iv. 
 
HISTOKICAL CHRONOLOGY 31 
 
 which Herschel has suggested ought to be reformed in 
 the astronomical scale. Since the commencement of 
 that year a complete cycle of the seasons, winter, 
 spring, summer, and autumn, had occurred 1900 
 times when the month of January 1900 commenced ; 
 and we therefore, on January 1, 1900, entered on the 
 twentieth century of cycles of the seasons in the 
 Christian era according to both the Florentine (or St. 
 Augustine) and the Pisan (or Dionysian) methods of 
 counting combined with the Gregorian Reformation, 
 which made the Pisan year 1 and the Florentine 
 identical with the year 753 A.u.c. 
 
 Twice since the foundation of the Second Baby- 
 lonian Empire by Nabonassar, who reformed the 
 previous chronological system with the assistance 
 of Egyptian astronomers, the vulgar record of years 
 has been subjected to further reformation for the pur- 
 pose of correcting its divergence from the true record 
 of the seasons. The year of Nabonassar, consisting of 
 exactly 365 days, was used in the era of the Eomans 
 until the time of Julius Caesar, when, in order to 
 correct an accumulated error due to the vulgar years 
 being shorter than true years, Caesar ordered that the 
 year of Rome 708 should last for 445 days, making the 
 year 709 commence with the first new moon which 
 occurred after the winter solstice of the previous year ; 
 and the intercalation of days was so arranged as to 
 make January 1, 709 A.u.c, coincide with that new 
 moon.^ At the same time, to prevent a recurrence of 
 
 * Bond, on pp. 322-323 of his 1875 edition already quoted from, 
 gives a table of corresponding years of the Julian era and the years of 
 Borne. His table, however, ignores the years of the Roman era as 
 
32 ASTRONOMICAL AND 
 
 the error which was corrected as above shown, Caesar, 
 under the guidance of Sosigenes of Alexandria, ordered 
 that every fourth year should consist of 366 days, so as 
 to make the average length of the year 365^ days ; but 
 whereas the year of Nabonassar is nearly a quarter of 
 a day shorter than a true year, the Julian year of 365 
 days and 6 hours is slightly longer than a true year, the 
 length of the astronomical year on which the seasons 
 depend being 365 days 5 hours 48 minutes and 46 
 seconds approximately. Caesar and Sosigenes doubtless 
 knew their year to be inexact, but considered that the 
 necessary correction might be trusted to the intelli- 
 gence of future statesmen who might be in possession 
 of more accurate knowledge for their guidance ; and 
 that expectation was somewhat tardily justified by the 
 action of Pope Gregory XIII., who in the year 1582 a.d. 
 ordered that October 5 should be treated as the 15th, 
 thus shortening that year ten days to correct the 
 amount by which the years since the Julian Eeforma- 
 tion had been too long to keep time exactly with the 
 earth's revolution round the sun. That reformation, 
 then effected wherever the authority of the Pope pre- 
 vailed, was not effected in England until the year 
 1752 A.D., by which time the error had increased to 
 eleven days, to remedy which September 3 was 
 
 reformed by Csesar ; and it therefore shows that after the Julian Reforma- 
 tion three systems were used by Rome — namely, the old style of the 
 era of Rome, the reformed era of Rome, and the Julian era dating 
 from the Julian Reformation. It is immaterial to my argument whether 
 it be based on the eras with their years coinciding, as arranged by the 
 Julian and Gregorian Reformations, or on the old style Roman years, 
 commencing on April 21, and the Julian years of the Christian era, 
 commencing on January ] allowance being made for the overlapping of 
 the years of the two eras. 
 
HISTORICAL CHRONOLOGY 33 
 
 ordered to be called the 14th. To prevent a recurrence 
 of the error then corrected it was ordered that three 
 times in each 400 years a year which, under the unre- 
 formed Julian Calendar, would be a leap year of 366 
 days should be a common year of 365 days ; but the 
 rigid working of the Julian Calendar in accordance 
 with the Gregorian Keformation still creates an error 
 of one day in about 3,000 years, for the correction of 
 which one of the years which under the Gregorian rule 
 would be a leap year will doubtless be ordered by the 
 authorities of the time to be treated as a common year. 
 The excess in the length of the reformed Julian year, 
 which is now the vulgar or civil year, amounts to 
 about 2 days 14 hours and 24 minutes in 10,000 years. 
 In a paper on ' The Secular Acceleration of the 
 Moon's Motion ' which I pubHshed in the year 1879 
 I alluded to the absence of any common measure be- 
 tween days and years as being due to the fact that 
 the motions which they respectively measure are due 
 to the interaction of two independent forces — the sun's 
 and the earth's revolving force — whose relative quan- 
 tities not only have no necessary mathematical pro- 
 portion, but have a ratio which is subject to a slowly 
 progressive change which is at present beyond the 
 grasp of mathematical knowledge. 
 
 As a matter of detail, it must be observed that between 
 the introduction of the era of the Incarnation into 
 England by St. Augustine and the final restoration of 
 the Julian year, many changes occurred in England. Not 
 only did usage change between the use of the years of the 
 three eras — the Incarnation, the Nativity, and the Julian 
 — but civil and ecclesiastical courts used different 
 
 c 
 
34 ASTRONOMICAL AND 
 
 eras at the same time. The change from March 25 to 
 January 1 for the commencement of the year, effected 
 by the Gregorian Keformation, merely corrected the 
 distm'bance caused by the temporary adoption of the 
 years specially adapted, sometimes to one and at other 
 times to the other of the two above-mentioned Christian 
 eras, and restored the general use of the Julian year, 
 which does not appear ever to have gone completely 
 out of use. 
 
 It must also be observed that the error by which 
 the Christian era has been made to commence with the 
 beginning of the year 1 a.d., instead of treating 
 the first day of that year as the first anniversary of the 
 commencement of the era, is also made in naming the 
 years of the ScaHger cycle, commonly called the Julian 
 Period, of 7980 years (in which the year 4718 of the 
 current cycle corresponds with the year of the 
 astronomical scale), the enumeration of the years in 
 that cycle being made in ordinal numbers because the 
 error seems to have been made in every then existing 
 era except the original Florentine, and when the 
 Scaliger cycle was invented the Florentine figures 
 were erroneously supposed to represent ordinal numbers. 
 The original Florentine system is in fact the present 
 astronomical system of treating the Christian era as 
 above interpreted, and is the only scale of time that 
 has ever been clearly organised on a correct mathema- 
 tical basis. 
 
 The disturbance of the Julian years, sometimes by 
 those of the era of the Incarnation and at other times 
 by those of the era of the Nativity, was due to narrow- 
 minded views of the subject which created confusion 
 
HISTORICAL CHRONOLOGY 35 
 
 throughout our historical records for more than a 
 thousand years until corrected by our adoption of the 
 Gregorian Eeformation. 
 
 The Julian year, then legaHsed, does not appear 
 ever to have been completely out of use. It was used 
 by the kings of England in the eleventh and twelfth 
 centuries ; and was afterwards used as the ' historical 
 year ' to distinguish it from the year of the Incar- 
 nation re-introduced by Henry II ; and the documents 
 of the Venetian State Library copied by Kawdon 
 Brown show that in the fifteen century, more than 
 a hundred years before the Gregorian Eeformation, the 
 Popes of Rome were, in the months of January and 
 February, one year in advance of the kings of 
 England in dating their letters, as would be the case if, 
 while the kings of England were using the years of 
 the Incarnation, the Popes of Rome were using the 
 Julian years. ^ Bond, however (in agreement with 
 other chronologers) , states that the year of the Nativity 
 was at that time used in Rome, and in that case 
 (which also accords with the recorded letters) then the 
 Popes must have been using the year of the Nativity 
 with the Pisan enumeration while the kings of 
 England were using the years of the Incarnation with 
 the Florentine. Among numerous protests in London 
 of bills of exchange drawn in Venice there is one 
 dated *on the 31st of December, 1442 (Anglican 
 Style), " secundum cursum et computacionem Ecclesiae 
 
 ' Calendar of State Papers and Manuscripts relating to English 
 affairs existing in the Archives and Collectio^is of Venice, and in other 
 Libraries of Northern Italy. Edited by Rawdon Brown, published by 
 the Lords Commissioners of the Treasury. Vol. i. pp. 134, 135, &c. 
 1864. 
 
 c 2 
 
36 ASTEONOMICAL AND 
 
 Anglicanae " ' : i and I see no reasonable explanation 
 for such a specification of the date except on the suppo- 
 sition that the year 1443 a.d. (not 1442) was then the 
 legal enumeration of the year, which had to be distin- 
 guished from that legally current in England. That 
 accords with the idea of the English enumeration 
 having originally been cardinal and that used in some 
 parts of Italy ordinal. The general tenour of the 
 admitted historical facts bearing on the question seems 
 to allow of no other explanation for the enumeration 
 of the years of the Nativity (commencing on December 
 25) having been such as to make them precede that 
 of the years of the Aimunciation (commencing on 
 March 25). And the evidence is, therefore, to the 
 effect that the difference of one complete year in the 
 enumeration of the Christian era which at one time 
 existed, as pointed out in ' L'Art de Verifier les Dates,' 
 was in the first instance reduced to a difference of three 
 months by the years of the Nativity being used with 
 the Pisan enumeration while the years of the Incar- 
 nation were used with the Florentine enumeration ; 
 that a second approximation was made, reducing 
 the difference seven days further, by changing the 
 Pisan method in Eome from the years of the Nativity 
 to the Julian years ; and that the third, and final, step 
 was made by those who used the Florentine enumera- 
 tion changing from the years of the Incarnation to 
 the Julian years. That seems to me to be clearly 
 the course through which the discrepancy of one 
 year disappeared, and to leave no doubt as to the Pisan 
 
 ' Calendar of State Papers and Mami scripts, dx. Vol. ii. p. 568. 
 1807. 
 
HISTOEICAL CHKONOLOGY 37 
 
 enumeration having originally been ordinal and the 
 Florentine enumeration cardinal. 
 
 As a matter of detail it is, however, appropriate to 
 point out that the despatches of the Venetian am- 
 bassadors to foreign Courts show that at the time of 
 the Gregorian Keformation (1582) they were using a 
 year commencing on March 1 (not 25), so that in 
 the months of January and February they dated one 
 year less than the date of the Julian year established 
 by the reformation, but all through March their dating 
 corresponded with the established JuHan year.^ They 
 were perhaps also distinguishing their dates from those 
 of the years of the Nativity, but the dates of some of 
 the letters are at variance with the extension of the 
 difference over the intervening seven days. There is a 
 letter from Lorenzo Priuli, Venetian Ambassador in 
 France, which he dates : ' Paris, 11th January 1581 
 (m.v.),' to distinguish the year from 1582, then presum- 
 ably current in Eome. But there is another letter 
 of his, preceding the above, dated : ' Paris, 28th De- 
 cember 1581,' as if the year 1582 had commenced 
 in the rival enumeration (not on December 25) but 
 between the dates of the two letters. The evidence 
 is to the effect that the Julian year had been 
 substituted for that of the Nativity before the Gre- 
 gorian Keformation was decreed, the Bull being dated 
 February 24, 1582, which was then 1581 by the English 
 reckoning. 
 
 The relation which I have described between the 
 Pisan and Florentine systems makes it of interest to 
 
 ' Caleiidar of State Papers and Maiiuscripts dx. Edited by Horatio 
 F. Brown, vol. viii. p. 27, &c. 1894. 
 
38 ASTEONOMICAL AND 
 
 notice that Bond, under the heading ' The Era of Pisa,' 
 says : * This era differed from our common Christian 
 era only by preceding it by one year ; probably the 
 first year of the Christian era was made to correspond 
 to 753 A.u.c. instead of 754 a.u.c, the Dionysian 
 date.' ' 
 
 The fact certainly is that it was by the Gregorian 
 Keformation that the year 1 of the original * era of 
 Pisa ' was made to correspond with 753 A.u.c, while at 
 the same time the year 1 of the era of Florence was 
 made to correspond with 754 a.u.c, as (subject to 
 various changes in both ' eras ' between years of the 
 Nativity, years of the Incarnation, and Julian years) 
 the ' era of Pisa ' was used in Kome and the era of 
 Florence in England and Venice until the adoption of 
 the Gregorian Keformation in all three places merged 
 the two ' eras ' into one. There is certainly no more 
 reason for treating the era of Pisa independently than 
 for dealing in the same manner with the era of 
 Florence. The Pisan appears to have been the 
 original, and to have always been used in Kome ; and 
 the Florentine, which became adopted in England and 
 Venice, was merely an attempt to change the Pisan 
 method of enumerating the years without any inten- 
 tion of changing the epoch, or date for the origin of 
 the era. The Florentines, in fact, anticipated the course 
 which has since virtually been adopted by astronomers ; 
 but the Pisan and Florentine systems were merely 
 different methods of enumerating the years of the 
 same era. 
 
 To account for the discrepancy between the vulgar 
 
 ' p. 225, 1875 edition. 
 
HISTORICAL CHRONOLOGY 39 
 
 Christian era and the true era Bond ^ supposes Dionysius 
 to have been misled through treating the ' era of 
 Augustus ' as commencing four years later than its true 
 date ; but the object of Dionysius is said to have been 
 to substitute for the era of Diocletian (or the era of 
 martyrs), then chiefly used among Christians, an era 
 dating ' ab Incarnatione D. N. Jesu Christi ' ^ ; and, in 
 the absence of any definite proof of his having made 
 the mistake with which he is commonly discredited, 
 it appears to me incredible that he was not fully 
 acquainted, not only with the era of mart3TS, but also 
 with the * era of Christ,' which was then a well-known 
 era also used among Christians ; and, if so, he must 
 have discarded what was accepted as the true era, not 
 for the sake of correcting any historical error, but for 
 what he considered the advantage of making it com- 
 mence with some period in the lunar cycle which 
 regulated the Church festivals, in the organisation of 
 which he was an expert. 
 
 Bond treats as the true date of the birth of Christ 
 December 25, 750 a.u.c, which was the first day of the 
 first year in the ' era of Christ ' ; and Dionysius appears 
 to have substituted March 25 of the year 753 A.u.c. 
 (not 754, as supposed by Bond). March 25, which my 
 argument makes the epoch fixed on by Dionysius, 
 belongs to 753 a.u.c. Jahan style ; to 752 A.u.c. old 
 style ; to 45 of the JuHan era ; and to 4713 of the 
 Scaliger cycle, commonly called the Julian period. 
 The question, therefore, is as to whether the lunar 
 
 1 p. X of his 1875 edition. 
 
 2 Dictionary of Christian Biography, edited by William Smith and 
 Henry Wace. 
 
40 
 
 ASTKONOMICAL AND 
 
 
 •S +> '^ aJ 
 
 C tic CO 9} 
 
 •2 = ?^ 
 
 S 5 as 
 12; 
 
 X bo 
 
 Oi C r/3 O 
 
 u £ 2 
 
 ^ cJ « C 
 
 ^ «» be"© 
 ^ §,■§§ 
 
 o 01 j: 
 
 \c 
 
 S St S d 
 
 I 1^ 
 
 ! O 
 
 
 be 
 i ^ 
 
 
 
 S2SS^Si2"=S5S^g^S^^S;^'^ 
 
 as 
 
 COfNCOOOOOt-OWS'^JOfMi-iOCftXt-OiO 
 
 Cycle 
 used 
 in , 
 Saxon 
 Charters 
 accord- 
 ing to • 
 Bond 
 
 XVII. 
 XVIII. 
 XIX. 
 
 I. 
 
 11. 
 
 III. 1 
 
 IV. ; 
 V. i 
 
 VI. 1 
 
 VII. i 
 
 VIII. 
 
 IX. 
 
 X. 
 
 XI. 
 
 XII. i 
 
 XIII. 1 
 
 XIV. 1 
 XV. 
 
 XVI. 
 
 , Meton's 
 i Cycle 
 '■ accord- 
 ing to 
 ! Bond 
 
 • 
 
 
 a.c >.ia a o » o 
 I •''.2-^sg'tg? 
 
 ..S 85 
 
 w m a^ -^ a » C 
 
 
 X 
 
 
HISTORICAL CHBONOLOGY 41 
 
 cycle shows any reason for the selection of that dale 
 (not for any date in the year 754 A.u.c). 
 
 Bond says : ' To find the number of the Dionysian 
 cycle of 19 years, add I to the given year of the 
 Christian era (because number II belongs to 1 a.d. 
 according to the Dionysian system) ; then divide the 
 sum by 19, the quotient will show the number of cycles 
 elapsed since the year 1 B.C., and the remainder will 
 represent the year of the cycle.' ^ 
 
 As the enumeration of the years of the Metonic 
 cycle which was in use at the time of the Dionysian 
 Reformation was then altered for the special purpose of 
 adjusting them to the new era, it seems natural that 
 number 1 should be applied to the first year of the era ; 
 and, therefore, the above statement by Bond is a 
 confirmation of my argument to the effect that 1 a.d. 
 represents the second (not the first) year of the era as 
 originally organised. And as the enumeration of the 
 years of the Metonic cycle which had been in use ever 
 since the year 432 B.C. had been changed for use in the 
 Christian Church in such a manner that Number I of 
 the cycle corresponded with the year 1 of the ' era of 
 Christ,' the question is as to whether the organisation 
 of the calendar shows any reason for combining with 
 a change from the years of the Nativity to those of the 
 Annunciation a change of three years in the * golden 
 numbers ' of the lunar cycle as then used in all 
 Christian Churches. The facts of the case appear to 
 me to make it evident that for the commencement of 
 the year the date of the Annunciation was preferred to 
 that of the Nativity on account of the dates of the 
 
 ' P. 253, 1875 edition. 
 
42 ASTEONOMICAL AND 
 
 Church festivals being determined by the new moon 
 of the vernal equinox ; and that the year 753 A.u.c, 
 Julian style, was preferred to any other in the same 
 lunar cycle because the calendar new moon next 
 preceding that equinox occurs closer to the equinox 
 than in any other year of the cycle. That appears to 
 afford a still further confirmation of my argument to 
 the effect that Dionysius considered what is now 
 1 A.D. to be the 2nd year of the era. The calendar 
 shows no reason for taking anj^ year marked by the 
 golden number II as the first year of the era. 
 
 The Dionysian Eeformation not only abandoned 
 the then existing era of Christ commencing on 
 December 25, 750 a.u.c, but also abandoned the 
 numbering of the Metonic cycle based on that era, 
 and applied number I of the cycle to what is now 
 erroneously called 1 B.C. instead of to 4 B.C., as then 
 numbered for the original * era of Christ,' which com- 
 menced on Christmas Day of the year 4 B.C. of our 
 vulgar era. 
 
 As the original numbering of the Metonic cycle as 
 arranged in 432 B.C. had in fact been changed in such 
 a manner that Number I corresponded with the year 1 
 of the era of Christ, Dionysius and those who acted 
 with him must have had a thorough practical know- 
 ledge of it, and cannot have been influenced by any 
 historical mistake in the matter. 
 
 It is important to observe that the golden number I 
 of the Metonic cycle which Dionysius discarded did 
 not agree with the year 1 of the era of martyrs, but 
 with the year 1 of the era of Christ, so that if he had 
 merely wished to change from the era of martyrs to 
 
HISTOEICAL CHEONOLOGY 43 
 
 the era of Christ all that was requisite was to change 
 the enumeration of the years of the era by adding 287 
 years so as to make the era commence in the year of 
 the golden number I as then applied to the Metonic 
 cycle used with the era of Christ ; and he would then 
 have had for the epoch of the era what he must have 
 well known to be a closer approximation to the true date 
 of the birth of Christ than that which he adopted. 
 That is so because, as the year 288 of the era of 
 Christ commenced in the year 1 of the era of martyrs, 
 the addition of 287 years to the latter era would have 
 made the enumeration of years of the era of martyrs 
 and the Golden Number I of the era of Christ coincide 
 at the epoch of the latter era, which became known 
 as the annus venis in contradistinction to the vulgar 
 epoch} 
 
 ' Bond (p. X, 1875) says : ' The first year of the first Dionysian 
 Pascal Cycle of 532 years ' was ' 1 Anno Domini with golden number II 
 of the Dionysian Cycle.' 
 
 That statement, however, tends to create confusion in three distinct 
 ways. 
 
 First, because it is only by applying the Gregorian reform to our 
 golden numbers and not to the Pascal Cycle that golden number I and 
 year 1 of the Pascal Cycle are made to differ at all. They certainly 
 coincided when Dionysius framed the cycle and adopted the golden 
 numbers. 
 
 Secondly, because it is only the last three months (less seven days) of 
 the year 1 of the Pascal Cycle to which golden number II can in any 
 sense be applied. 
 
 And, thirdly, because the enumeration of the years of the first 
 Dionysian Pascal Cycle of 532 years is in fact the original Dionysian 
 enumeration of the years of our era, being identical with the era of Pisa, 
 which, as I have already shown, was used in Kome, while the era of 
 Florence was used in England. 
 
 I do not point out the above for the sake of being hypercritical regard- 
 ing statements which suited Bond's immediate purpose in verifying dates, 
 
44 ASTRONOMICAL AND 
 
 It must also be observed that a full moon more 
 closely precedes December 25 in the golden number I 
 of the Metonic cycle which agreed with the year 1 in 
 the era of Christ than in any other year of the cycle, 
 whereas August 29, which was the epoch in the era of 
 martyrs, has no definite connection with the lunar 
 cycle. The evidence is, therefore, to the effect that 
 the true era of Christ (as well as the era of martyrs) 
 was deliberately rejected in the Dionysian Eeformation 
 for the sake of adopting the first epoch in the life of 
 Christ which best suited as a basis for the regulation 
 of Church festivals as then organised. And it seems 
 also probable that the epoch Christmas Day of the * true 
 era of Christ ' was determined as much by the dates of 
 calendar full moons ^ in the Metonic cycle as by any 
 accurate knowledge of the true date of the birth of 
 Christ. It can only be said to be more nearly true 
 than the date according with the Dionysian epoch. 
 
 A peculiarity of the calendar which I have not seen 
 anywhere mentioned, is that the approximate dates of 
 the new moons have long been, and will for many 
 years continue to be, two years in advance of the 
 golden number to which the present dates were ad- 
 justed in the Dionysian cycle. That is to say, the 
 year 1900 is quite correctly designated in the almanac 
 
 but in order to clear apparent clashing between some of his statements 
 and my arguments. 
 
 ' Playfair, in his table of eclipses in the work I have already quoted 
 on p. 28, records an eclipse of the moon as having occurred on March 
 13, 4 B.C., and full moon would therefore occur on December 3 of that 
 year and again on January 2, 3 b.c. ; so thai the calendar full moon of 
 the epoch Christmas Day of the original era of Christ appears to have 
 occurred about eight days before the real full moon. 
 
HISTORICAL CHRONOLOGY 45 
 
 as being golden number I. of the cycle ; but the new 
 moons are not those which belong to number I., but 
 are those which belong to number III. For seven 
 of the moons the calendar date is the same as that 
 of the almanac ; and for the other five moons the 
 greatest discrepancy is less than twelve hours, which is 
 a discrepancy which must of necessity arise in the 
 calendar in consequence of the lunations being reckoned 
 sometimes as twenty-nine and sometimes thirty days 
 instead of in accordance w^ith the actual change in the 
 moon's position. The table which I have given on 
 page 40 can easily be compared with the almanac 
 for many years to come for verification of the position 
 of the real moon in relation to that of the calendar. 
 That table gives the dates of calendar new moons in 
 the line of the golden number for the year, and the 
 dates of real new moons for the same year are those of 
 the calendar new moons two years in advance. 
 
 For about twelve moons following any 29th day of 
 February, the almanac date will usually be one or two 
 days less than the present amount of eight days in advance 
 of the calendar ; and then the discrepancy will again 
 gradually increase until another leap year stops the moon's 
 advance in the almanac by pushing the enumeration 
 of days forward to keep pace with the moon. The 
 mean advance between two successive leap years does 
 not make the almanac correctly measure astronomical 
 time, because an allowance for further correction must 
 be made at the rate of 2d. 14h. 24m. in 10,000 5^ears 
 (see p. 33). The mean difference between our almanac 
 measure and astronomical measure since a.d. now 
 amounts to twelve hours ; and that difference will go on 
 
46 ASTRONOMICAL AND 
 
 increasing until one of the years which the calendar 
 as now arranged makes a leap j'ear is treated as a 
 common year. By skipping a leap year now the dis- 
 crepancy between true measure and almanac measure 
 since the epoch of our era would not be corrected, 
 but approximately reversed. The almanac was ad- 
 justed to the moon in 1582 A.D., but the above cor- 
 rection is required in both directions from that date. 
 It ought not, however, to be made until the discre- 
 pancy exceeds half a day in relation to that adjust- 
 ment. 
 
 The reason for the existing position of the moon in 
 relation to the calendar is that it loses 2 hours 5 
 minutes, about, in each cycle, making rather more than 
 8 days in the 1900 years ; ^ and that difference chances 
 to bring it into agreement with the calendar moons of 
 golden number III. The fact that the discrepancy of 
 8 days is the actual difference between years I. and III. 
 of the cycle appears to make the calendar in the first 
 year of the era agree with the moon ; but a closer in- 
 spection shows 8 daj^s to be the maximum and 5 days 
 
 ' Playfair (on page 16) makes : 
 
 19 years = 6939d. 14h. 26m. 24^8., and 
 235 months = 6939 16 31 o" 
 
 difference 2 4 35i 
 
 And the relative lengths of the year and the astronomical month now 
 accepted make the figures : 
 
 19 years of 365d. 5h. 48m. 46s. and 235 months of 29-53059 days 
 equal respectively : 
 
 6939d. 14h. 26m. 34s., and 
 6939 16 31 3H 
 
 difference 2 4 56| ; and the secular accelera- 
 tion of the moon makes 2h. 5m. a closer approximation ; making the 
 difference in 1900 years = 8d. 16h. 20m., or about 8"^ days. 
 
HISTORICAL CHRONOLOGY 47 
 
 the minimum advance of our almanac dates on those 
 of the calendar of Table II. The average advance on 
 the dates as they stand in that table is only 6 days 
 17 hours, vi^hich does not agree with the idea of its 
 having been adjusted to the moon, either at the com- 
 mencement of the Christian era or at the time it v^as 
 brought into use. The moon of the Church calendar 
 appears to have become quite independent of the real 
 moon before Dionysius reorganised the calendar, and 
 he evidently did not base his reform on what was then 
 the true position of the moon. 
 
 The evidence is to the effect that the positions of 
 the calendar moons as they stand in Table II. in rela- 
 tion to the golden numbers now in use were adjusted 
 to the moon about three centuries after the com- 
 mencement of the Christian era ; and that Dionysius, 
 therefore, must have brought back into use an old 
 calendar without attempting to make it conform with 
 the changed position of the real moon in relation to it. 
 
 To make the basis of argument quite clear, I may 
 point out that Sir Harris Nicolas extracts from ' L'Art 
 de Verifier les Dates ' a * Perpetual Lunar Calendar ' 
 in which the moons placed against the golden numbers 
 now in use accord with what I have given on page 40, 
 but he says : ' To the golden number which was used 
 for ascertaining when the new moons occurred for the 
 old style, epacts have succeeded for the neiv.' The 
 dates given in that calendar are, however, the Dionysian 
 calendar moons of those respective golden numbers in 
 the new style ; and the discrepancy I deal with is the 
 same whether the argument be based on the dates of 
 the new or the old style almanac, correctly extended 
 
48 ASTEONOMICAL AND 
 
 back to Meton's time, or on the almanac dates of Meton's 
 time correctly extended forwards to oar time. My 
 argument deals only with the dates indicated by the 
 * Perpetual Lunar Calendar ' based on the golden 
 numbers of the Metonic cycle and the natural dis- 
 crepancies between those calendar moons and the real 
 moon. I am not concerned with the artificial arrange- 
 ments for corrections organised either in the Dionysian 
 or in the Gregorian calendar. At the time of the 
 Gregorian Keformation the date of the moon indi- 
 cated by the golden number was about seven days 
 before that of the real moon, but the corrections in 
 the calendar as it had been organised had actually 
 made the calendar moon five days later than the real 
 moon. The extreme discrepancy that can arise under 
 the new style is, according to Nicolas,^ three days ; 
 and De Morgan considers part of that discrepancy to 
 have been purposelj^ organised in order to keep Easter 
 Day from coinciding with the Passover. - 
 
 Another peculiarity which I have not seen alluded 
 to appears only when it is recognised that before 
 Dionysius changed the positions of the golden numbers 
 
 ' The Chrmwlogy of History, by Sir Harris Nicolas, K.C.M.G., p. 80. 
 1833 (London : Longmans). 
 
 - ' On the P^cclesiastical Calendar,' pp. 18, 19, &c., The British 
 Almanac, 1845. De Morgan gives the following quotation from Clavius, 
 who organised the new calendar : ' If the moon of the cycle fell on the 
 same day as the mean new moon of the astronomers, it might chance 
 that we should celebrate Easter on the same day as the Jews or the 
 Quartodeciman heretics, which would be absurd, or else before them, 
 which would be still more absurd.' Clavius seems to me to have been 
 in advance of the calendar in referring to the time the Jews ' celebrate 
 Easter ' ; but the extract makes it clear that a discrepancy between the 
 calendar and the moon was purposely created. The calendar of the Metonic 
 cycle is independent of any such arrangement of the ecclesiastical calendar. 
 
HISTOEICAL CHKONOLOGY 49 
 
 in the Metonic cycle they stood as they had been 
 arranged to suit the era of Christ. And the point 
 is that, as that era commenced three years before the 
 era Dionysius was substituting for it, he would of 
 necessity, on deciding to change the golden numbers, 
 have made his number I take the place of number IV 
 of the era of Christ, if the calendar moon then agreed 
 with the real moon and if he wished it to continue to 
 do so. If he had made that change, he would simply 
 have reverted to the original numbering of the Metonic 
 cycle. ^ But, instead of moving his numbers three years 
 forward, he moved them three years hack, making his 
 number I take the place of number XVII ; - so that the 
 golden numbers of the existing era must be considered 
 to commence either three years before or else sixteen 
 years after those of the era of Christ, though the era 
 itself undoubtedly began three years after the era of 
 Christ. That seems to confirm the view I have already 
 expressed to the effect that he selected for the golden 
 number of his epoch year the March new moon of the 
 calendar, which best suited as a starting point for the 
 era ; and it makes him appear to have cared as little 
 for the relative positions of the new and the old golden 
 numbers as for the relative phases of the real moon 
 and those of the moon of the calendar. 
 
 A third peculiarity which I have not seen alluded to, 
 and which seems worthy of special attention as throwing 
 
 ' That which (as shown in Table II.) Bond treats as the original cycle, 
 but which appears to me to have been framed more recently. 
 
 - Supposing the relative positions of the numbers in Bond's table to 
 be correct ; but I have (in connection with Table V.) shown that Meton's 
 number XVII, to which number I of the era of Christ was applied, is 
 that now in use. 
 
 D 
 
50 ASTRONOMICAL AND 
 
 a new light through the confusion, is that Bond gives 
 July 13, 432 B.C. as the epoch of Meton's cycle without 
 specifying any authority for that date (which has in 
 fact become generally accepted) ; whereas Playfair gives 
 July 16, 433 B.C. and states that a new moon which 
 occurred at 7.43 p.m. on that day fixed Meton's 
 epoch. 
 
 The point is that, if Playfair is right as regards the 
 day of the month, then the new moons of golden 
 number I in Meton's original calendar have been made 
 to correspond with golden number I of the cycle which 
 Bond gives as that of the Saxon Charters, but the 
 golden numbers themselves as we now use them stand 
 just as originally arranged by Meton, forming the only 
 unbroken record of years which has existed from so 
 early a date in Europe ; and his cycle must have com- 
 menced in 437 B.C. (astronomical = vulgar 438 B.C.), 
 which is 23 cycles before the year (vulgar 1 B.C.). 
 
 The evidence in support of the above view is as 
 follows : 
 
 According to both Playfair and Bond, the 123rd of the 
 Metonic cycles is now current and not far from ended ; 
 and in that time the moon must have advanced in rela- 
 tion to the calendar moon rather more than 10^ days 
 (122x2" 5™ = 10'' 14" 10"^ and 123x2" 5"^=10'^ 16" 
 15"). 
 
 That makes Playfair' s new moon of July 16 corre- 
 spond with the new moon of July 26, 1881, as ending 
 the 122nd cycle, and the new moon of July 26, 1900, 
 as ending the 123rd cj^cle. And, as 123 cycles are 
 2337 years, Playfair's new moon of July 16 must 
 have been July 16, 437 B.C. astronomical, which is 
 
HISTOEICAL CHRONOLOGY ol 
 
 438 B.C. of vulgar reckoning (not 433, as recorded by 
 him).i 
 
 ' An exact verification of the advance of the moon from the almanac 
 dates of Meton's time cannot be made without having the liour, as well 
 as the day, of each new moon of his calendar. For an approximation, 
 the days of new moons in his calendar must be set against the days of 
 the corresponding moons in our almanac, disregarding the additional 
 hours of each moon. Tested in that manner, the average advance of 
 the dates of the moons in our almanac from the corresponding dates of 
 the calendar in Table III. is 9 days 20 hours, instead of 10 days 16 hours, 
 making an apparent discrepancy of 20 hours. The greater part of that 
 discrepancy is, however, accounted for by 13^ hours included in the 
 2 days 14 hours 24 minutes which the calendar gains in 10,000 years, 
 as explained on page 33 (10,000 years : 2 days 14 hours 24 minutes 
 :: 2,337 years : 13| hours). And that the remaining difference (6| hours) 
 is due to the allowance of leap years having given a correction in excess 
 of what had been immediately requisite when the last February 29 had 
 been inserted, is shown by the fact that the omission of February 29 in 
 the year 1900 has made the average amount by which the moons from 
 July 1900 to December 1904 are in advance of Meton's calendar 10 days 
 21 hours, thus approximately reversing the discrepancy. 
 
 Another test is obtained by deducting Meton's epoch from the conclu- 
 sion of his 123rd cycle, as follows : 
 
 437 B.C. July 16 
 from 1900 a.d. July 26 
 
 difference 2337 years 
 
 2h. 5m. X 123 cycles = 
 
 difference 22 15 
 
 By making the year 1900 a leap year, the date of the above new moon 
 would have been July 25, Ih. 43m. p.m., making the difference Id. 22h. 
 15m. ; so that the omission of February 29 in the year 1900 appears by 
 this test also to leave more than half a day accumulated towards another 
 omission not yet fixed in the almanac. 
 
 As a basis for the discussion of this subject it is necessary to recognise 
 that though, by a discrepancy in one direction chancing to counterbalance 
 another discrepancy due to some other cause, the almanac might possibly 
 coincide with the moon at different dates, and show the same period for 
 separate lunations, the existence of secular acceleration makes it impos- 
 sible for such a coincidence to be effected by a recurrence of the same 
 causes in any cycle. 
 
 
 7h 
 
 . 43m. 
 
 
 1 
 
 43 
 
 9 
 
 18 
 
 
 
 10 
 
 16 
 
 15 
 
62 ASTHONOMICAL AND 
 
 As William Smith, after saying that ' the acknow- 
 ledged epoch of commencement of the period has been 
 placed B.C. 482,' further says, ' but we are far from 
 seeing how it has been made out,' ' it seems to me that 
 the argument I have given probably establishes the 
 true epoch. 
 
 That makes it appear that Dionysius must have 
 found Meton's original cycle with the calendar moons 
 readjusted to an early period of the Christian era, and 
 brought it back into use as he found it ; and also that 
 the cycle which Bond gives as Meton's must have been 
 framed for some subsequent purpose. 
 
 It is easy to be misled in the confusion which has 
 been created in connection with the calendar ; but it 
 appears nevertheless not out of place, in connection 
 
 If there were stability of action in the forces by which the solar 
 system is controlled, then (except slight differences in the effects of per- 
 turbations by the planets) there would be equal intervals of time between 
 each recurrence of a new moon at (1) the same distance from the earth, 
 (2) the same distance from the sun, (8) the same distance from the plane 
 of the earth's equator, (4) the same distance from the plane of the sun's 
 equator, and (5) with the earth in the same position in relation to the 
 sun and moon ; but a changing ratio of forces prevents a recurrence of 
 all those conditions in combination, as certainly as the course of evolu- 
 tion prevents any man from being twenty-one years old twice in his 
 life. A verification, subject to a small discrepancy which would represent 
 the secular acceleration combined with a slight difference in planetary 
 action in each cycle, which latter is on the average a retarding action, 
 but greater in some cycles than in others, could be arrived at by calculating 
 the position of Meton's epoch new moon in all the five above specified 
 respects, to make the requisite allowance for divergence of the new moon 
 of July 26, 1900, from each position. That elaborate analysis is not, how- 
 ever, I think, required for my purpose, as the rough approximations 
 I have given appear sufiicient to establish my argument. 
 
 ' Dictionary of Greek and Eonian Biography, edited by William 
 {Smith, vol. ii. p. 1009. (John Murray, 1840.) 
 
HISTOEICAL CHRONOLOGY 53 
 
 ( 
 
 with my argument, to give the foregoing indication re- 
 garding Meton's epoch quantum valeat. 
 
 If the cycle of golden numbers now in use really is, 
 as I have suggested, Meton's original cycle, the question 
 arises as to w^hat is the origin of that v^hich Bond has 
 considered to be Meton's original cycle. That cycle 
 seems to me to have been framed after the commence- 
 ment of our era with the year of the Crucifixion for its 
 epoch. 
 
 The evidence bearing on that point is the fact that 
 in the year 1896 the moon had gained eight days 
 on the calendar which Bond treats as being the one 
 originally created by Meton in 432 B.C. ; and, therefore, 
 instead of corresponding with the calendar in Meton's 
 time, it conformed with it at or after, rather than 
 before, the Christian epoch ; so that it is probably a 
 reorganisation of Meton's calendar created for some era 
 brought into use about that date. And as the golden 
 number I of that calendar corresponds with 33 A.D., 
 which is the generally accepted date of the Crucifixion, 
 the two coincidences justify its being regarded as the 
 cycle which was used with the * Era of the Crucifixion ' 
 in the absence of definite evidence to the contrary.^ All 
 
 ' Taking the full moon which occurred between the new moons of 
 March 6 and April 5, 33 A.D.,as the epoch of the era, the average advance 
 of the moons of the first five years of the calendar given in Table IV. is 
 8 days 6 hours ; which, with 12 hours accumulated towards the correction 
 of tlie almanac independently of the organised leap years (as explained 
 on page 33), makes the average advance shown by those five years 8 days 
 18 hours ; which shows the calendar to have been correctly adjusted to 
 the moon in 33 a.d. The evidence is to the effect that golden number I 
 was applied to the calendar moons of March 6 and April 5, because 
 those were the dates of the real new moons at the time of the Crucifixion ; 
 and subsequent arrangements have chanced to make 33 a.d. correspond 
 with them. 
 
54 ASTRONOMICAL AND 
 
 tlmt concerns my argument, liowever, is that it certainly 
 is not Meton's original cycle. The evidence based on 
 that calendar is that the full moon of the Crucifixion 
 occurred between real new moons of March 6 and 
 April 5 ; and also that golden number I was therefore 
 applied to those moons, and was, together with them, 
 given the position properly belonging to Meton's golden 
 number XV, which is the number belonging to 33 a.d. 
 in both those months. The moons of Meton's 
 number XV are March 5 and April 4, and had 
 advanced a full day when the Era of the Crucifixion 
 w^as framed.^ Table IV. serves to elucidate that point. 
 The invalidation of the claim of that cycle to be 
 considered Meton's is a further argument for con- 
 sideration of that which I have given in Table III. 
 
 It appears to be mere matter of fact (be the ex- 
 planation what it may) that the calendar moons of the 
 cycle now in use were moved to their present positions 
 4 golden numbers in advance of those against which 
 
 ' In Table IV. I have altered the relative positions given by Bond to 
 the golden numbers of the two cycles, but in doing so I keep in accord 
 with an argument alluded to by him to the effect that the Crucifixion 
 occurred in a year of Meton's cycle number XV (see p. 233 of his 1875 
 edition), together with my argument to the effect that he has mistaken 
 the golden numbers of the Era of the Crucifixion (instead of our present 
 numbers) for Meton's original numbers. 
 
 It therefore appears that the generally accepted date of the Cruci- 
 fixion, and my argument regarding the relation of those calendars, 
 mutually confirm each other; whereas Bond's argument leads him to 
 make the date of the Crucifixion 30 a.d. ; and his divergence from the 
 accepted opinion seems to be explained by the facts that his arguments 
 are based to some extent on what he supposes to be Meton's cycle, but 
 which he treats as commencing its golden number I in what is really 
 Meton's number IV ; so that the true date is three years in advance of 
 that supposed by Bond, 
 
HISTORICAL CHRONOLOGY 65 
 
 they stood in the calendar used with the era of Christ, 
 and that the change brought them approximately into 
 accordance with the real moon, not at the time of the 
 Dionysian Keformation, nor at the epoch of the Christian 
 era, but at that of the era of Diocletian, 284 a.d. ; so 
 that as Dionysius, while discarding the era of Christ, 
 discarded also the calendar framed for that era, he may 
 probably, while also discarding the era of martjTS, 
 have either kept in use, or else brought back into use, 
 the calendar which had been specially framed for that 
 era; for the era of martyrs was merely the name 
 applied by Christians to the era of Diocletian, which 
 was for a long time the prevalent and official era in 
 Eome.^ 
 
 And it also appears to be mere matter of fact that 
 the calendar used with the era of Christ, which 
 
 ' The era of martyrs is referred to by some writers as if it were a 
 Christian era estabHshed to commemorate the multitude who were 
 cruelly slaughtered in the reign of Diocletian, and Bond says nothing in 
 definite refutation of that erroneous idea. In his Preface he says ' the 
 early Christians adopted an era which they called the Era of Martyrs.' 
 And when stating that the era is ' also called the Era of Diocletian,' he 
 says it dates from the reign of Diocletian ' in consequence of the persecu- 
 tions of the Christians by that emperor.' The fact is that the era was 
 not in any sense a consequence of those persecutions ; and when it was 
 established in 284 a.d. Diocletian was quite the reverse of a persecutor. 
 The cruelties which led the early Christians to abhor the use of his 
 name occurred in 303 a.d., and are considered by Gibbon to have been 
 the cause of Diocletian's abdication. The action of Pope Hilarius in 
 substituting the era of Christ for the era of martyrs seems to have been 
 influenced by the same feeling as that which had led Christians to sub- 
 stitute the term Era of Martyrs for Era of Diocletian. 
 
 In establishing an era dating from his own reign, Diocletian followed 
 the example set by Caesar ; but if Casar had been satisfied with reform- 
 ing the era of Eome without introducing a new era, it seems unlikely 
 that any emperor could have ventured to displace it, and the reason 
 which led the Christian world to do so would not have existed. 
 
56 ASTRONOMICAL AND 
 
 Dionysius discarded, is Meton's original calendar 
 moved bodily — that is to say, the golden numbers 
 moved together v^ith their corresponding moons — three 
 years back from their original position in time ; that 
 is to say, from the positions in which the calendar 
 moons and the respective golden numbers would have 
 stood if Meton's calendar had been undisturbed. That 
 is made clear by comparison of Tables III and V.^ 
 
 The cycle of golden numbers which Bond gives as 
 those used in Saxon Charters, and as having been intro- 
 duced in 463 A.D., must therefore, if that is the true 
 date of its origin, have been expressly arranged by 
 Pope Hilarius to suit the era of Christ ; and his re- 
 organisation consisted merely of a change in the 
 position of Meton's calendar by pushing it back so 
 
 • The golden numbers may have been continued to be applied to all 
 the same calendar moons as in Meton's calendar ; but I have made 
 number I in Table V. begin with the December new moon preceding the 
 lull moon of the first Christmas Day, because the coincidence of Meton's 
 original number I with the full moon of the first Christmas Day is all 
 that concerns my argument. The new moon of December 23, 1897, 
 completed 100 cycles from the epoch of the era of Christ, showing an 
 advance of 13 days on the calendar moon of December 10 ; which makes 
 it evident that there was never any pretence of adjusting the moons 
 of that calendar with the real moon. That calendar accords with the 
 moon nearly 1,000 years before Meton's time. 
 
 I take it for granted that Bond has given correctly the calendar moons 
 for the respective cycles ; and the evidence I have adduced seems to me 
 to justify the change I have made in the relative positions of the golden 
 numbers themselves. I have (on page 48) commented on the peculiarity 
 of the relative positions of the numbers in Bond's table ; and the 
 admitted fact that the era of Christ began three years before our era fixes 
 its epoch to our golden number XVII, so that if golden number I was 
 applied to the epoch of the era of Christ-it must of necessity correspond 
 with our number XVII, And, also, as Bond makes the era of Christ 
 begin with what he calls Meton^s number XVII, the question is as to 
 which of the two cycles really is Meton's. 
 
HISTORICAL CHRONOLOGY 67 
 
 as to make the full moon which occurs on Christmas 
 Day in his calendar coincide with December 25, 750 
 A.U.C., which he had fixed on as the epoch for the com- 
 mencement of the era of Christ, though the change did 
 not bring the calendar moon into conformity with the 
 real moon. That calendar must have been created in 
 that manner whether it originated at the time of Pope 
 Hilarius or at any other time. Neither Playfair nor 
 the author of ' L'Art de Verifier les Dates ' appears to 
 have had knowledge of the calendar of the era of 
 Christ ; but it seems probable that evidence may be 
 found of it having been used in many parts of Europe 
 before the era of the Incarnation was invented by 
 Dionysius. If it is the calendar used in Saxon 
 Charters in England, it must have been brought into 
 this country before the time of St. Augustine, as he 
 would not have introduced it after the Christian era 
 organised by Dionysius had been adopted in Kome. 
 In the printed list of old documents in the British 
 Museum there is not, however, anything in confirma- 
 tion of this suggestion. 
 
 There probably exist in some old libraries records 
 regarding the relative ages of these calendars. The 
 evidence I find available is to the effect that the calendar 
 which Bond gives as Meton's was in fact created after 
 the epoch of the Christian era. That evidence is 
 given by the position of the moon of that calendar in 
 relation to the real moon, and by the coincidence of 
 its golden number I with the accepted date of the 
 Crucifixion. And the evidence as regards the calendar 
 used with the era of Christ is that it was created by 
 Pope Hilarius to be used in substitution of that specially 
 
58 ASTRONOMICAL AND 
 
 created for the era of Diocletian ; ]mt the calenclar 
 itself gives no clue as to the date of its creation. Its 
 golden number I is, however, so displaced from its 
 position in Meton's calendar as to show that, what- 
 ever may have been the date of its origin, it was 
 created specially for the era of the Nativity. Whatever 
 may have been the case as regards the calendar of the 
 era of the Crucifixion, it is evident that the calendar of 
 the era of Christ must at one time have been used in 
 Rome in substitution of that of the era of Diocletian ; 
 and, in the absence of evidence of the latter having been 
 reverted to before the time of Dionysius, it appears 
 that he discarded not only the era of Christ, but also 
 the calendar which had been framed for it, and re- 
 adopted the calendar of Diocletian for use with the 
 vulgar Christian era. It is quite possible, or indeed 
 most probable, that Dionysius and those acting with 
 him were influenced by the fact that the course they 
 were taking replaced Meton's golden numbers in their 
 true positions, making them a correct record of years 
 from Meton's epoch ; at any rate, it appears that they 
 effected that useful reform, whether by deliberation or 
 accident. 
 
 If Dionysius did not knowingly revert to Meton's 
 cycle when discarding that of the era of Christ, as I 
 have suggested, the alternative explanation is that the 
 calendar of Diocletian, which must have been then 
 well known, had been framed on Meton's original 
 cycle with the calendar moons adjusted to the true 
 moon at the Diocletian epoch without disturbing the 
 golden numbers, and as Dionysius did not adjust the 
 calendar to the moon in 532 a.d., the probability 
 
HISTORICAL CHRONOLOGY 59 
 
 seems to be that he merely re-adopted the use of the 
 calendar of Diocletian as it stood. 
 
 De Morgan says : ' Dionysius Exiguus seems to have 
 done no more than accommodate the cycle of Vic- 
 torinus to his new mode of reckoning ; he being the 
 person who first abandoned the era of Diocletian, and 
 reckoned from the supposed year of the birth of 
 Christ; ' 
 
 As * the cycle of Victorinus ' is that of Pope Hilarius, 
 De Morgan's statement confirms the view I have given 
 as to the era of Christ having been substituted in 
 Kome for that of Diocletian ; but the tables I have 
 appended and the arguments referred to in them show 
 that, if that was so, Dionysius deliberately abandoned 
 the cycle and calendar moons framed for the era of 
 Christ together with the era. 
 
 The acceptance of the argument to the effect that 
 the golden numbers as now used stand as placed in 
 Meton's original cycle vitiates arguments Bond has 
 based on the supposition of Meton's cycle having been 
 that which appears to me to have been created for the 
 era of the Crucifixion ; ^ but I cannot point that out 
 without expressing an opinion to the effect that Bond's 
 work is the most valuable contribution to chronology 
 since the publication of ' L'Art de Verifier les Dates.' 
 
 ' Article, ' On the Ecclesiastical Calendar,' p. 9, by A. De Morgan, 
 The British Almanac, 1845. 
 
 - Bond does not state his authority for what he supposes to be 
 Meton's cycle. But he seems to have accepted its identity as an 
 established fact, and to have based arguments confidently upon it without 
 any thought of questioning the historical accuracy of that supposed 
 origin. It seems to me that he is certainly mistaken where (on page xxxii 
 of his Preface) he supposes it to be the one which was in use by the Jews 
 in the time of Christ. 
 
60 ASTRONOMICAL AND 
 
 De Morgan's interesting contributions ' do not pre- 
 tend to a position of such practical utility ; and he 
 appears to have misappreciated the importance of a 
 correct record of time, as he alludes to the Gregorian 
 Eeformation as ' the stupid expedient of destroying 
 ten nominal days, which has created more con- 
 fusion and more chronological error than all the 
 anomalies of the old calendars put together. . . . 
 The Gregorian Eeformation has done much in this way ; 
 another attempt would go near to render the chronology 
 of the country in which it was made an unfathomable 
 mystery.' ^ Most practical men will, I think, agree 
 that the mischief was created by those w^ho failed 
 throughout the ' Dark Ages ' to act on the principles 
 on which the Julian Eeformation had been based, and 
 that the Gregorian Eeformation merely grappled with 
 that mischief and prevented the years from ceasing more 
 and more to constitute a true record of time. The 
 plea oi factum valet superimposed vo^on fieri non dehuit 
 is too often urged against the revision of such mis- 
 takes as that for which the Gregorian Eeformation 
 contrived a practical correction ; and any confusion 
 now connected with it may be considered as of a 
 trifling character in comparison with that of the con- 
 fusion which it averted. 
 
 A more practical view of the question is expressed 
 by Sir Harris Nicolas, who says : ' The absurdity of 
 retaining the 25th of March as the beginning of the year, 
 not because it was the 25th of March, but because it 
 was the time of the vernal equinox, which, in the 
 
 ' Tlie British Almanac, 1845, 1840. 
 
 - Ihid. ' On the Ecclesiastical Calendar,' pp. 12-36. 
 
HISTORICAL CHRONOLOGY • 61 
 
 eighteenth century, had receded so far back as from 
 the 25th to about the 10th of March, was forcibly 
 urged by Wilson in 1735. . . . These anomalies, 
 nevertheless, continued for seventeen years longer ; and 
 the reformation of the calendar, when it did take place, 
 was offensive in the highest degree to a large part of 
 the kingdom.' ^ 
 
 De Morgan alludes to the illness and death of the 
 Astronomer Royal, James Bradley, having been ' attri- 
 buted to a judgment from Heaven,' as if he intended 
 the animosity aroused against Bradley to serve as a 
 warning to all men in positions of authority to leave 
 established errors uncorrected ; - but, I think, most men 
 will now consider Bradley's action in the matter to 
 have been more worthy of his position in the scientific 
 world than De Morgan's policy of inaction. 
 
 The confusion has been a necessary consequence of 
 applying Meton's cycle to a purpose for which it is 
 not suitable. To get a really perpetual calendar the 
 ecclesiastical authorities ought to have used thirty 
 ' golden numbers ' instead of nineteen ; making the 
 number of the first day on which a new moon occurred 
 in any year the golden number for that year. 
 
 Under such an arrangement the moon could never 
 escape more than a fraction of a day from the calendar 
 moon, and the latter would automatically readjust itself 
 to the moon instead of allowing the discrepancy to 
 accumulate as it does in Meton's cycle. 
 
 The above arrangement would not have suited 
 
 ' The Chronology of History, by 8ir Harris Nicolas, K.C.M.G., 183.3 
 (London : Longman, Kees, Orme, Brown, Green, & Longman). 
 - ' On the Ecclesiastical Calendar,' p. 131. 
 
62 ASTBONOMICAL AND 
 
 Meton, because he required numbers to use in arith- 
 metical sequence ; but it appears to me that for the 
 purposes of the calendar the sequence of the golden 
 numbers is as immaterial as that of the Dominical 
 Letters. 
 
 Si quid novisti rectius istis, 
 Candidus imperti ; si non, his uteie mecum. 
 
 As the Koman era prevailed in Europe at the time 
 of the introduction of our present era, it is of interest 
 to record that it is now certain that the year 1 of 
 Kome does not correctly represent the year of the 
 foundation of that city, regarding which there are wide 
 discrepancies of opinion, whereas as regards the year 
 1 of Nabonassar the only doubt is as to whether it 
 represents the year of the foundation of the Second 
 Babylonian Empire or the second year of that empire. 
 It is a point of interest, because the year of Eome, 
 framed by Julius Caesar, and the year of Nabonassar, 
 framed by that king at the commencement of the 
 Second Babylonian Empire, are the two antecedent 
 phases through which our present system has been 
 evolved from a chaos of lunar, luni-solar, and solar 
 measures of time, which appears to have been some- 
 times made to run fast by counting lunations as 
 years. 
 
 The solar year seems to have been undoubtedly 
 invented in Egypt, whether by Edomite invaders, 
 Jewish conquerors of the latter, or by native Egyptians. 
 It was never officially adopted by the Jews, but became 
 important in chronology through its adoption by 
 Nabonassar in Babylon in displacement of the year 
 of twelve lunations, with occasional intercalary months 
 
HISTOEICAL CIIEONOLOGY 63 
 
 as still used by the Chinese ; and it became firmly 
 established in Europe by the Julian and Gregorian 
 Reformations. It is well to recognise that the Gre- 
 gorian Reformation was necessitated only because up 
 to the time of Gregory XIII. the successors of Julius 
 Caesar failed to act on the principles on which the 
 Julian Reformation was based. 
 
 The immediate origin of the solar year as the unit 
 of measure in the scale of time is narrated by Sir 
 Isaac Newton, who says ^ that King David's conquest 
 of the Edomites gave him possession of ports on the 
 Red Sea, and at the same time the Edomites, driven by 
 him into Egypt, became the first inventors of the use of 
 sailing ships by availing of the art of making linen cloth 
 already known in Egypt, and thus created an extension 
 of commercial enterprise which ' gave a beginning to 
 astronomy and navigation.' The navigators were 
 obliged to observe the positions of the stars to enable 
 them to know their course when out of sight of land, 
 and were thus led to the invention of the solar year of 
 365 days, which, 300 years after David's extension of his 
 kingdom to the Red Sea, was adopted in Babylon as the 
 year of Nabonassar. The merits of that system were 
 doubtless well known in Jerusalem long before they 
 became known in Babylon, though the vast importance 
 attached to ritual in the religious ceremonies of the 
 Jews made the official recognition of the system in use 
 among the Jewish traders impossible in their own 
 country. The rapid development of trade and com- 
 merce which followed the appearance of the Jews on 
 the Red Sea as a powerful nation rendered the reign of 
 
 ' Horsley's edition of Newton's Woiks, vol. v. pp. 13-5 &c. 
 
64 ASTRONOMICAL AND 
 
 King Solomon one of the most important epochs in 
 the world's history ; and the astronomy of Egypt was 
 carried to Babylon by the extension of ocean commerce 
 inaugurated by the Jews through the Bed Sea and the 
 Persian Gulf. The extension of trade and commerce 
 which was inaugurated by King David may well be 
 regarded as of not less epoch-making importance in 
 the history of the world than that which followed the 
 discovery of the western hemisphere in the reign of 
 Ferdinand and Isabella. 
 
 In his chapter on the 'Chronology of the Greeks,' 
 Sir Isaac Newton makes some remarks which may well 
 be recapitulated for the purpose of eliminating sectarian 
 spirit from the merits of the question as to the 
 improvement of the existing system of chronology. 
 
 Newton concludes that chapter by saying that 
 ' the morality and religion of the first ages still called 
 by the Jews *' The precepts of the sons of Noah" is 
 the primitive religion of both Jews and Christians, and 
 ought to be the standing religion of all nations, it 
 being for the honour of God and good of mankind. 
 .... The believing that the world was framed by one 
 supreme God, and is governed by him ; and the loving 
 and worshipping him, and honouring our parents, and 
 loving our neighbour as ourselves ; and being merciful 
 even to brute beasts, is the oldest of all religions.' 
 
 Those words of Sir Isaac Newton seem appropriate 
 and worthy of consideration in connection with any 
 attempt to strengthen the foundations of the Christian 
 era. 
 
 What is, however, immediately practical in the 
 subject is the fact that there has never existed any 
 
HISTORICAL CHEONOLOGY 65 
 
 system of chronology which, whether considered on 
 its theoretical merits or as regards its extensive practical 
 use in scientific records, can be placed in rivalry with 
 the present astronomical system ; and the arguments 
 I have adduced show, I think, its point of variance as 
 regards our vulgar system to be due to an error in the 
 latter which admits of easy reformation so as to 
 identify vulgar with astronomical reckoning. 
 
 The most important reform ever effected in 
 chronology is that by which the practical system 
 invented by the necessities of commerce was officially 
 substituted in the Babylonian Empire for what had 
 previously been their vulgar system ; and a further 
 development is now called for to bring the system 
 practically forced on astronomical science officially into 
 our vulgar chronology. 
 
 Many eras have been used for chronological records, 
 and until one has been established on a correct basis 
 rival eras will doubtless continue to compete in the 
 struggle, in which the fittest will survive. 
 
 The tangled confusion of records, even since the 
 establishment of the Christian era, leads Mr. Arbuthnot, 
 to whose work I have above referred, to propose that 
 we should inaugurate a new era dating from the com- 
 mencement of the reign of Queen Victoria ; but such 
 a course would, like the similar action of the first 
 French Eepublic, make confusion worse confounded 
 \\dthout any compensating advantage to be gained by 
 attempting, like the first French republicans, to displace 
 an era which has become accepted wherever European 
 civilisation has established itself. The more natural 
 and expedient course appears rather to be to disentangle 
 
 E 
 
66 ASTRONOMICAL AND 
 
 as far as possible those records and establish their 
 true positions in the existing era. 
 
 In ' Macmillan's Magazine ' for February 1900 a 
 writer under the initials A. G. comments on the con- 
 fused position of the subject in the words : 
 
 On algebraic tokens weird, 
 
 On decimals I daily pore ; 
 By these my mind is nowise cleared ; 
 
 They leave me where I was before. 
 By decimals correctly done 
 
 Can Speculation e'er be taught 
 To learn if time begins at one 
 
 Or naught ? 
 
 The discussions of to-day in the Battle of the 
 Centuries have the same raison d'etre as those which 
 must have been rife more than a thousand years ago in 
 the battle between the ordinal and cardinal enumera- 
 tion of the years of what was then the newly invented 
 era. But the present position has been further com- 
 plicated by what I trust I have clearly shown to have 
 been a mistaken numbering of the B.C. years. 
 
 But for that mistake the Florentine enumeration, 
 after it had displaced the Pisan, must have continued 
 to be treated as cardinal, and astronomers would have 
 had no reason for inventing a special system for their 
 own use, as their system is in fact an independent 
 re-invention of the original Florentine system. 
 
 If 1 B.C. is to be allowed to continue to immediately 
 precede 1 a.d., as it does in our existing vulgar system, 
 the twentieth century cannot commence until 1900 a.d. 
 has ended; and the German Emperor's celebration of 
 the commencement of the twentieth century on January 
 1 of this year (1900) therefore virtually constitutes a 
 
HISTORICAL CHRONOLOGY 67 
 
 step toward bringing vulgar reckoning into accord- 
 ance with that of astronomers. That celebration also 
 accords with the words of the English Prayer Book 
 which declare the nineteenth century to be ' from the 
 year 1800 till the year 1899 inclusive.' 
 
 The Prayer Book and the German Emperor are, 
 however, virtually in accordance with the astronomical 
 system, and their position in the question cannot 
 logically be maintained without a reformation as 
 regards the vulgar numbering of the B.C. years. 
 
 What is wanted now to give practical effect to the 
 reform which has been virtually decreed by the German 
 Emperor is that some leading historical society should 
 compile and publish a Chronological Table conforming 
 with the astronomical method of numbering the years 
 in both directions from the present zero year of 
 astronomers ; and that the above statement promulgated 
 when the English Prayer Book was first published should 
 be officially re-affirmed ; for the position, according to 
 the foregoing argument, is such as to make it as 
 imperative on all nations who use the era to clear away 
 the error which has crept into it, as it was for all who 
 aspire to the front rank in civilisation to adopt the 
 Gregorian Keformation. 
 
68 
 
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\. 
 
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