BY THE SAME AUTHOR THE IMPROVEMENT OF THE GRE GORIAN C E E E AL NDAR , WITH NOT S OF AN ADDR SS ON CALENDAR REFORM AND SOCIAL PRO GRESS DELIVERED TO THE ABERDEEN o . 6d B 2 . 8v 2s . ROTARY CLU . 3 pp Crown GE E E GE ° S LTD RG R 69 S . O OUTL D ON , E E A P L A F O R AN O RD RLY AL M A NA C . ff r 6 o . 6 1 s 6 . C w 8 o 3 d . d 2 pp . ro n v Cl th 2 . Sti boa ds B D . RE . E AR S CHIN D H . DW ’ GE RGE R E GE 69 S S LTD . LONDON O OUTL D ON , THE CA LE N DA R ITS H STORY STRUCTUR D I , E AN IMPROVEMENT D P H ILIP B AL X R LL . R S D N N F . E A E , , E I C A M B R I D G E AT THE UNIVERSITY PRESS 1 9 2 1 CAMB R IDGE UNIVE R S ITY P RE SS M N . CL Y GE R C F . A , A A TTE R A E NE E . LONDON F L , C 4 N E W Y O R K TH E MAC MILLA N CO . B OM BAY UTT N AND CO . LTD . CALC A MACMILLA , MADRAS T R F O ONTO THE MACMILLAN CO . O N D LTD CA A A, . TOKYO MARUZE N- KAB USH I KI -KAISHA A LL RIGHTS RES E RVE D l O fi b q q P RE FAC E HE following essay is intended to serve as a text - book for Tthose interested in current discussion concerning the e Cal ndar . Its design is to exhibit a concise View of the origin and develop e E m nt of the Calendar now in use in urope 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 f e indicate how far it e fectiv ly 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 . are The chief authorities enumerated in the annexed list . ’ ’ Petavius L Art de verz er The works of Clavius , Scaliger , , fi l es da tes — , 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 cal endrial and generally accurate 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 fl hi have chie y attended . T s , 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 defe cts 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 vi PREFACE hi eccl esi intelligence and a due regard to storical , scientific and l astica 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 . a hi e Ancient C lendars , the Indian , C nes 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 elementa ry astronomical e facts . The present writer is not an astronomer , but th se facts have been derived from the commonly available sources . The intention is to state them with the degree of accuracy re quisite for the subject in hand—disregardi ng qualifying refinements known to modern astr onomy but irrelevant to a cal endrial purpose . a t The most conspicuous , if not the most serious irregul ri y in - fl tuatl o E our time scheme is the uc n of the date of aster . It is to be hoped that the courageous action of Lord Desborough in proposing to mitigate thi s irregularity may lead to the correction of the other defects of the Gregorian Calendar on scientific and B e E conservative lines . Already a ill to provid a fixed aster date e n has b en introduced i to the House of Lords , and on the a B a e initiative of M . Arm nd a r of Li ge 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 E E B E Es D c s . Sc . S . Taggart , q , . , rechin , and G Allan , q , Glasgow , for kindly reading his MS . and making helpful suggestions . O ct 1 . 92 1 . C O NTE N TS PAGE P REFACE ASTRONOMI CAL DATA IN MEAN SOLAR TIME A UNIVERSAL CALENDAR FOR THE TWENTIE TH CENTURY LIST OF AUTHORITIES ON THE GREGORIAN CALENDAR PART I I THE EAS RE E OF E A RA S . M U M NT TIM . N TU L UNIT , DAY EAR H , Y , MONT TH H I I . E T REE P OSSIB LE FORMS OF CALENDAR I II . THE GREEK CA E AR E C C C E L ND . M TONI Y L I THE A A AR V. L TIN C LEND V THE . JULIAN REFORM VI H AND DAY IN THE R A CA EN AR . MONT OM N L D VI I THE RE R A A E AR . G GO I N C L ND — . HER CA E ARS EW SH AH E A VIII OT L ND J I , M OM T N , FRENCH REP UB LICAN THE WEEK IX . THE A OR S A E ER X . DOMINIC L UND Y L TT CONTENTS PART II P AGE C C ES . THE E C C C E . THE AR XI . Y L M TONI Y L SOL C C E C Y L . INDI TION . ERAS P A ERA R E ETC . XII . OLYM I D , OF OM , THE CHR S A ERA A ES A XIII . I TI N . D T OF N TIVITY AND CRUCIFIXION X THE A P E IV. JULI N RIOD PART III THE DATE OF EASTER PART IV THE SES THE CA E AR XVI . U OF L ND THE E EC S THE CA E AR XVII . D F T OF L ND HOW ITS E EC S M AY B E RE E E XVIII . D F T M DI D INDEX ASTRONOMICAL DATA IN MEAN SOLAR TIME en h a 6 h 8 m 6 t of t e tro ical e r . 3 . L g h p y 3 5 d 5 . 4 . 4 5 h a r 6 6 h en o f t e ian e . L gth Jul y 3 5 d . 6 (1 1 6 1 ro ica ars . m . s 9 t p l ye 93 9 4 h . 2 3 7 . 6 8 h 1 an ars . 1 9 Ju li ye 93 9 d . d 1 h m 8 3 en of a a ion : 1 . 2 . L gth lun t z o . 2 44 7 8 8 m d h . 3 54 . 4 . 6 d 1 6 1 m 1 s 93 9 . h . 3 . 4 . Diff eren ce between (1 6 h a Ju li an ye ar and 3 65 . d 8 h 8 m s 1 2 lun ation s 3 54 . 4 . 3 4 . d 1 1 1 o h . 1 m 6 s . z . 2 . Diff e ren c e b etwe en ro ic a ear and 6 h 8 m 6 a t . s p l y 3 5 d 5 4 4 . 1 n a i d 8 h 8 m u ons . s . 2 l t 3 S4 4 . 3 4 1 o d 1 m 1 2 . o . 2 s . h . Diff e ren c e be twe en 1 ul ian e ars an d 6 1 8 9 J y 93 9 d . h . a i n 6 d 6 1 m 1 2 un t o s . 1 3 3 5 l 93 9 h . 3 . 4 . I 8 m 2 . 6 3 h . 4 . Diff eren ce between 2 un a io ns an d 6 1 6 1 m 1 s 3 5 l t 93 9 d . h . 3 . 4 . 1 ro ica e ars 6 1 6 m s 9 t p l y 93 9 d . 4 h . 2 . 3 7 . h m . s 2 . 4 3 7 . A UNIVERSAL CALENDAR FOR THE TWENTIETH CENTURY Solar Regu lars Jan . 0 F b e . 3 M a r. 3 Week Day Index S unday 0 Mon d ay 1 T u es day 2 To determine week day add together 1 m er o f ea r in the XXth Cent ( ) Nu b y ur y .