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The Calendar: Its History, Structure And !!i\LENDAR jS, HISTORY, STRUCTURE 1 III i; Q^^feiTAA^gvyuLj^^ v^ i Jb^ n n !> f llfelftr I ^'^\C)SL<^ THE CALENDAR BY THE SAME AUTHOR THE IMPROVEMENT OF THE GREGORIAN CALENDAR, WITH NOTES OF AN ADDRESS ON CALENDAR REFORM AND SOCIAL PRO- GRESS DELIVERED TO THE ABERDEEN ROTARY CLUB. 32 pp. Crown 8vo. zs.dd. GEORGE ROUTLEDGE & SONS, Ltd. A PLEA FOR AN ORDERLY ALMANAC. 62 pp. Crown 8vo. Cloth zs. 6d. Stiff boards is. 6d. BRECHIN : D. H. EDWARDS. LONDON : GEORGE ROUTLEDGE & SONS, Ltd. THE CALENDAR ITS HISTORY, STRUCTURE AND IMPROVEMENT BY ALEXANDER PHILIP, LL.B., F.R.S. Edin. CAMBRIDGE AT THE UNIVERSITY PRESS I 9 2 I CAMBRIDGE UNIVERSITY PRESS C. F. Clay, Manager LONDON : FETTER LANE, E.C.4 fij n*'A NEW YORK : THE MACMILLAN CO. BOM HAY ) CALCUTTA I MACMILLAN AND CO., Ltd. MADRAS j TORONTO : THE MACMILLAN CO. OF CANADA, Ltd. TOKYO : MARUZEN-KABUSHIKI-KAISHA ALL RIGHTS RESERVED M u rO(Ku CE 73 f.HS PREFACE THE following essay is intended to serve as a text-book for those interested in current discussion concerning the Calendar. Its design is to exhibit a concise view of the origin and develop- ment of the Calendar now in use in Europe and America, to explain the principles and rules of its construction, to show the human purposes for which it is required and employed and to indicate how far it effectively serves these purposes, where it is deficient and how its deficiencies can be most simply and efficiently amended. After the reform of the Calendar initiated by Pope Gregory XIII there were published a number of exhaustive treatises on the subject—^voluminous tomes characterised by the prolix eru- dition of the seventeenth century. The chief authorities are enumerated in the annexed Ust. The works of Clavius, Scaliger, Petavius, UArt de verifier les dates, and Hales are very voluminous—their contents except in the case of Clavius being largely devoted to the elucidation of particular problems in chronology. The little works of Nicolas and Bond contain many useful and generally accurate calendrial tables and rules, but are both very badly arranged and their explanations often not clearly stated. The elucidation of chronological problems is one of the main uses of the Calendar and it is the one to which these writers have chiefly attended. This, however, is by no means the only and hardly even the principal purpose for which a Calendar is required. It is also used and required constantly and universally for the fixing of future dates of recurring events and appoint- ments and for measuring intervals of time. The merits and defects of our Calendar in these respects have recently attracted widespread attention and call for ad- justment. To enable this urgent problem to be studied with «3 VI PREFACE intelligence and a due regard to historical, scientific and ecclesi- astical requirements on the one hand, and practical uses on the other—such is the principal object of the following essay. With the exception of the dates of the Nativity and the Crucifixion particular chronological problems are not at all dealt with. Ancient Calendars, the Indian, Chinese and Mahometan Calendars are only referred to so far as necessary for illustrative purposes, and attention is concentrated on the existing Julian and Gregorian Calendars. The Calendar is based on certain elementary astronomical facts. The present writer is not an astronomer, but these facts have been derived from the commonly available sources. The intention is to state them with the degree of accuracy requisite for the subject in hand—disregarding qualifying refinements known to modern astronomy but irrelevant to a calendrial purpose. The most conspicuous, if not the most serious irregularity in our time-scheme is the fluctuation of the date of Easter. It is to be hoped that the courageous action of Lord Desborough in proposing to mitigate this irregularity may lead to the correction of the other defects of the Gregorian Calendar on scientific and conservative lines. Already a Bill to provide a fixed Easter date has been introduced into the House of Lords, and on the initiative of M. Armand Baar of Liege the International Chamber of Commerce has decided to ask the principal Governments to convene a conference on the whole subject. The writer owes an acknowledgement to his friends James Taggart, Esq., B.Sc, Brechin, and G. E. Allan, Esq., D.Sc. Glasgow, for kindly reading his MS. and making helpful suggestions. A. P. Oct. 1921. CONTENTS PAGE PREFACE V ASTRONOMICAL DATA IN MEAN SOLAR TIME IX A UNIVERSAL CALENDAR FOR THE TWENTIETH CENTURY ...... LIST OF AUTHORITIES ON THE GREGORIAN CALENDAR XI PART I I. THE MEASUREMENT OF TIME. NATURAL UNITS, DAY, YEAR, MONTH I II. THE THREE POSSIBLE FORMS OF CALENDAR 6 III. THE GREEK CALENDAR. METONIC CYCLE 7 IV. THE LATIN CALENDAR 9 V. THE JULIAN REFORM II VI. MONTH AND DAY IN THE ROMAN CALENDAR i6 VII. THE GREGORIAN CALENDAR 20 VIII. OTHER CALENDARS —JEWISH, MAHOMETAN FRENCH REPUBLICAN . 24 IX. THE WEEK . 28 X. THE DOMINICAL OR SUNDAY LETTER . 33 viii CONTENTS PART II PAGE XI. CYCLES. THE METONIC CYCLE. THE SOLAR CYCLE. INDICTION .... 41 XII. ERAS. OLYMPIAD, ERA OF ROME, ETC. 47 XIII. THE CHRISTIAN ERA. DATES OF NATIVITY AND CRUCIFIXION .... 50 XIV. THE JULIAN PERIOD .... 59 PART III XV. THE DATE OF EASTER . 6l PART IV XVI. THE USES OF THE CALENDAR . 83 XVII. THE DEFECTS OF THE CALENDAR . 85 XVIII. ITS HOW DEFECTS MAY BE REMEDIED . 93 INDEX 103 IX ASTRONOMICAL DATA IN MEAN SOLAR TIME Length of the tropical year 3656.. 5h. 48m. 46-158. Length of the Julian year 365d. 6h. 19 tropical years 6939d. I4h. 26m. 37s. 19 Julian years 6939d. i8h. Length of a lunation : i 29d. i2h. 44m, 2-87J 12 354d. 8h. 48m. 34*445 235 6939d. i6h. 31m. 14s. Difference between a Julian year and 365d. 6h. 12 lunations 354d. 8h. 48m. 34s, lod. 2ih. iim. 26s. Difference between a tropical year and 365d. 5h. 48m. 46s. 12 lunations 354d. 8h. 48m. 34s, lod. 2ih. cm. I2S. Difference between 19 Julian years and 6939d. i8h. 235 lunations 6939d. i6h. 31m. 14s. ih. 28m. 46s. Difference between 235 lunations and 6939d. i6h. 3ini. 14s. 19 tropical years 6939d. i4h. 26m. 37s. 2h. 4m. 37s. A UNIVERSAL CALENDAR FOR THE TWENTIETH CENTURY Solar Regulars: Jan. o April 6 July 6 Oct. o Feb. 3 May I Aug. 2 Nov. 3 Mar. 3 June 4 Sept. 5 Dec. 5 Week Day Index: Sunday o Wednesday 3 Friday 5 Monday i Thursday 4 Saturday 6 Tuesday 2 To determine week day add together (i) Number of year in the XXth Century. (2) Number of leap years already passed. (3) Number of the day of the month. (4) Solar Regular of month. Then divide by 7, remainder gives day of week as per Week Day Index. XI LIST OF AUTHORITIES ON THE GREGORIAN CALENDAR 1 Christopher Clavius. Kalendarium Gregorianum perpetuum cum privilegio summi Pontificis et aliorum Principum, Rome, 1582. This essay was annexed to the Papal Bull of 24th February, 1581. Romani Calendarii a Gregorio XIII P. M. Restituti Explicatio. Vol. v of Clavius 's collected works published in 1612. 2. Hugolini Martelli, Bishop of Glandeves. La Chiave del Calendaro. In Lione, 1583, Clear, concise and interesting; one of the best written and least read treatises on the subject. 3. Petavius. De Doctrina Temporum. Orig. pub. 1627, and again at Antwerp, 1705. Recognised as the standard treatise on the Calendar—a short abridgement entitled Rationarium Temporum deals chiefly with chro- nology. 4. Joseph Scaliger. De Emendatione Temporum. Pub. at Coloniae Allo- brogum in 1629. His principal object was to introduce the use of the Julian period—a bitter critic of Clavius. 5. Aegidius Bucherius. De Doctrina Temporum. Antwerp, 1634. Contains a detailed account of the various cycles employed for the computation of Easter based upon the cycle designed by Victorius (or Victorinus) of Aquitaine. 6. Sir Isaac Newton. The Chronology of Ancient Kingdoms amended. Pub. posthumously in 1728. His chronology is in many cases not accepted, but on matters of calendrial principle the essay is valuable. 7. James Ferguson. Astronomy. Pub. 1770, 12th edition in 1809. Deals fully with calendrial problems. 8. UArt de verifier les dates. 8 vols. Paris, 1783. The stupendous chrono- logical treatise of the Benedictines deals fully with the Calendar. 9. William Hales. A New Analysis of Chronology ^ 1809. A very sound and able treatise. 10. Sir Harris Nicolas. The Chronology of History, 1833. Founded on UArt de verifier les dates. 11. L. B. Francoeur. Theorie du Calendrier, 1842. 12. A. De Morgan. The Book of Almanacs. First edition 1851, third edition 1907. 13- ]' J- Bond. Handy Book of Rules and Tables for verifying dates. First edition 1869, fourth 1889. 14. Encyclopaedia Britannica, nth Ed. 1910, article " Calendar," by W. S. B. Woolhouse. Excellent—treats calendrial problems algebraically. — PART I THE MEASUREMENT OF TIME OUR knowledge of time is wholly dependent on measure- ment. Without the specification of magnitude or quantity the idea of time is meaningless. Now, we can measure time physically—in one way only—by counting repeated motions. Apart, therefore, from physical pulsations we should have no natural measure of time. In particular the operation of the astronomical Law of Periodicity supplies us with the principal time units. The primary periodic movements to which we owe our know- ledge of time are the two movements of our own earth in which we necessarily participate. These are (i) the rotation of the earth on its axis—which gives us day and night—and (2) the revolution of the earth round the sun—which gives us the year and the seasons.
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