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

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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

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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 .

m e r o f ea e ars al re a asse (2 ) Nu b l p y dy p d . m e o f he da o f he mon (3 ) Nu b r t y t th .

e a o f mo n (4) S o lar R gul r th .

e v e em n e e ee Th n di id by 7 , r ai d r giv s day W k

ex Day Ind . LIST OF AUTHORITIES ON THE GREGORIAN CALENDAR

1 Christo er C avius . K a l enda ri um Gr e ori a num er etuum cum rivil e io . ph l g p p p g T i s a was mmi P onti cis et a l iara m P ri nci um Ro m e 1 8 2 . s e s sa fi p , , 5 h y

ann exe to th e P a a B u of th e ru ar 1 8 1 . d p l ll 24 F b y , 5

. M . R e tituti E x l ica tio o l o f o o XI II P s . V R oma ni Ca l enda rii a Gr eg ri p . V ’ wo rk is e in 1 6 1 Cl avius s co llecte d s publ h d 2 .

Gl and v s La Chia ve del Ca l enda ro In H o l i ni arte i Bis o o f e e . . 2 . u g M ll , h p 8 C ear con cis e an d in e res in one of th e est written and ione 1 . L , 5 3 l , t t g ; b he s c least read treatises o n t u bj e t .

D Doc na Tem orum ri b 1 6 and a ain a An er i . u . t tw P e avius . e tr . 2 t p O g p 7 , g p , — 0 Reco nis e as the s an ar re a is e on the C a en ar a s o r 1 7 5 . g d t d d t t l d h t abridgement entitled Ra tiona rium Temporum dea ls chi efly with chro l o no gy. I

i De E menda ione Tem oru P b at o l ni A S c a er t m. u . C o ae l o Joseph l g . p l 1 6 His rin ci a o ec was to in ro uc e the u s e of the bro gum in 29. p p l bj t t d —a i er cri i c of avi Jul ian perio d b tt t Cl u s .

i D D c a T m orum Antwe 1 6 C n ain Ae idiu s B u cher u s . e o trin e . r . o t s g p p , 34 a detailed acco unt o f the va rio u s cyc les emplo ye d f o r the computation o f Easter bas e d u pon the cyc le design e d by Victo rius (or Victorin us) of A ain q uit e .

T hronol o o A nci K n ms a mended. P 6 Sir saac ew on . he C ent i do ub . I N t gy f g . 1 8 His c n o o is i m an a n o s um ou s in 2 . ro n c ses ot a cce te p th ly 7 h l gy y p d , b o m a ers o f cal en drial rin ci e the e ssa is va a e ut n tt p pl y lu bl .

am r on Astronom . P b 1 0 1 h n 1 8 0 D es e us . u . t e itio in S l 2 . eal u J F g y 77 , d 9 f l y ca l endria ro m with l p ble s .

’ Art de veri er l es da tes 8 vo s P a ris 1 8 Th e s en o 8 L . . . tu us ch rono . fi l , 7 3 p d o ica rea ise o f th e B ene ictin es ea s u wi the Ca en ar l g l t t d d l f lly th l d .

m Ha e s A N ew A na l sis o Chronol o 1 8 0 A i ia . . ver so un an d W ll l y f gy , 9 y d re a is e able t t .

’ Sir Harris ico as . The Chronol o o Histor 1 8 o un e on L Ar t N l gy f y , 3 3 . F d d de ver er l es da tes ifi .

’ B Fra c T a l r n mu r . heorie da C end er 1 8 . . i L , 42 .

A D r The B ook o Al ma a cs . i 1 1 . e o an . n rst e i ion 8 t ir edi io n M g f F d t 5 , h d t 1 0 9 7 .

B n Ha nd B ook o R l es r . o . u Ta bl es o veri in da tes . a nd irs J J d y f f f y g . F t e ition 1 86 o urt 1 88 d 9, f h 9.

E nc cl o a edia B rita nnica 1 1 h Ed 1 1 0 a ic e Ca en ar b B t . rt S . . y p , 9 , l l d , y W . o o o Exc — ms a e raical use . e en trea s c al en drial ro e W lh ll t t p bl lg b ly .

PART I

I

THE MEASUREMENT OF TIME

UR knowledge of time is wholly dependent on measure t ment . Without the specification of magnitude or quanti y

. can i the idea of time is meaningless Now , we measure t me —in —b physically one way only y counting repeated motions .

Apart , therefore , from physical pulsations we should have no t u natural measure of time . In par ic lar the ope ration of the astronomical Law of Periodicity supplies us with the principal i t me units . The primary periodic movements to whi ch we owe our know ledge of time are the two movements of our own earth in which ‘ 1 we necessarily participate . These are ( ) the rotation of the — earth on its axis - which gives us day and night and (2) the — revolution of the earth rouhd the sun which gives us the year o and the seasons . A third uniquely imp rtant periodic motion is — the revolution of the moo n round the earth which gives us the month . THE DAY

’ The earth s rate of rotation on its axis is constant , and a day is the interval between two successive passages of a given celes tial object across the meridian . The sidereal day is the interval between two successive passages of a given star . The stars being at an infinite distance , the length of the sidereal day is exactly a the the s me as time taken by one complete rotation of the earth , and by reference to the record of ancient eclipses it is known that the length of the sidereal day has been invariable for at least two thousand ye ars . The solar day is the interval between e e a two successive passag s of the sun across the m ridi n . As the ’ the earth s rate of rotation is constant , it follows that length of t But the mean solar day is also a constant quanti y . as the sun

P . C . 2 THE MEASUREMENT OF TIME has an apparent motion in opposition to the revolution of the e starry sphere amounting to nearly one d gree per day , it follows that there is a corresponding diff erence between the length of the sidereal and the mean solar day .

It follows als o that in 365 solar days the earth has really rotated ou 66 m s e o o n he r ab t 3 ti e . If w g r u d t ea th from east to west we neu tral ise the effe of the m o o ove re e re to ose one ct ti n ab f r d and l day . ere s we o rom es to e s s e is s o e we Wh a , if g f w t a t , whil t ach day h rt r , the ourse of the ou r e gain a day in c j n y .

’ r Again , the sun s appa ent eastward motion is not a cons tant a t e qu nti y in ach successive day . This is owing to the facts , ’ (I ) that the rate Of the earth s motion in its elliptic orbit is not 2 the uniform , and ( ) that ecliptic is inclined at an angle to the

. e equator There is , ther fore , a variation in the actual length of x 0 the solar day amounting at its ma imum to about 3 seconds . This accumulating from day to day makes a variation in the time of apparent noon amounting to upwards of half an hour— being at a maximum of minutes before mean noon about 4th

I ~ 1 th Feb November , and of 4% minutes after mean noon about 2

ar . iz . th 1 th ru v . 2 . 1 th y Four times annually , on 4 Nov , Feb , s 2 th e May and 9 July , the actual length coincid s with the average

e 2 . l ngth of the solar day , which is exactly 4 hours Four times viz 1 th 1 1 st annually , . at or about s April , 5th June , September 2 th and 4 December , the time shown by an accurate clock and a true sundial would coincide . In almanacs the difference between the clock and the sun is usually noted at its maximum point ” a under the entry clock before or clock fter sun . It is usual to describe the W hole period of 24 hours as the — i hi t civil day distingu s ng it hus from the natural day , which is e ni the interval between sunrise and sunset . The b gin ng and end t of the civil day have been variously computed . In the earlies times it appears to have been usu ally held to commence with B e the evening . In the ook of Genesis the account of the cr ation refers to the evening and the morning as composing the day .

This method of computation was also observed by the Greeks , 1 z Ta citus and , according to Caesar and , the ancient Gauls and — Germans computed their times and seasons by the ni ght a

2 1 ma nia De B el l Ga l l I 1 8 Ger . . . V , . THE MEASUREMENT OF TIME 3

relic of which is found in our own expression a fortnight . Amongst the Jews it was also the custom to commence the day with the evening . With the Romans the day began at various 1 the hours . According to Macrobius civil day of the Romans

e . b gan from the sixth hour of the night , that is midnight At h e t e m . other tim s the Romans computed day from 6 a . The ’ be e hour of Christ s death was said to the ninth hour , qual to m the e 3 p . . The night amongst J ws and other early nations was Th divided into three watches . e Greeks and the Romans divide d e m it into four watches . In mod rn times it is usual to co pute the e e day comm ncing from midnight , but by astronom rs the day 1 is held to commence at noon . In 925 the civil reckoning is to be adopte d by them .

THE YEAR

e The true l ngth of the year is . also susceptible of various e : I interpretations . Astronom rs distinguish ( ) The sidereal year or length of the ye ar measured by reference to the fix ed stars ; — (2) the anomalistic year being the interval between two suc cessive returns of the earth to perihelion ; and (3) the tropical — year being the interval between two successive returns of the

the . sun to equinox It is on this latter that the seasons depend , and this year is the only one of the three with which we have e ff construc any conc rn in the ordering of human a airs , or in the tion of a Calendar . Arising out of a primitive seasonal or vegetational year the idea of a year astronomically determine d was developed amongst m E the ost ancient civilisations of the ast at a very early date . ee 60 At first its length seems to have b n taken at 3 days . In the z z E tian Greek earliest Chinese , Chaldean , gyp , , and , according to 3 Plutarch , also in the earliest Latin records , this was the assumed length of the year . e e e 60 Ind ed , all ov r the M diterranean area 3 days was the But length of the original astronomical year . long before the e Christian era its l ngth was known more accurately . Plutarch tells us that the fi ve odd days were discovered by the se cond e t Hermes in Egypt . H rodotus also ascribes the discovery o the

1 2 3 l ia I Hero o 1 . S a turna . us Li e o Numa 2 . , , 3 d t , , 3 f f

I —2 4 THE MEASUREMENT OF TIME

E and 11 gyptians , tells us ( , 4) that they added the five days at the end of the twelve months . According to Sir Isaac Newton the 360- day year was tia l l a l una r twel ve- month o 0 y , the m nth being taken to be 3 days e e in l ngth as the lunation was compl ted on the 3oth day , and the idea of the year being furnished by the seasons and by the H succession of the equinoxes and solstices . e suggests that the Egyptians by observing the heliacal risings of prominent stars 1 fi rst directed a ttention to the sol a r yea r which they computed to fi ' d comprise 365 days . Plutarch mentions that the ve od days added at the end of the year were named after five divinities of hi the the Osiris family . T s gives a clue to date when these days

. i n o were first added to the calendar The Ch ese also , fr m a very 6 ad early date , had reached the computation of 3 5 days . The dition of the odd five days at the end of the year was common to 2 hi E . gyptian , Chaldean , C nese and several other early calendars The Egyptians seem to be entitled to the further discovery of the other six hours required to complete the tropical year . Though the odd quarter of a day was not place d in the calendar till the time of Greek influence its recogni tion is involved in 3 the Sothiacal period , and must therefore draw back to a remote antiquity . A still closer approximation to the truth was reached by Hipparchus , the greatest of ancient and perhaps of all as tronomers ; most famous as the discovere r of the precession of a e the e quinoxes . He detected an excess of at le st five minut s in 4 the year length of 365% days . According to Mommsen the a 6 ex ct length determined by Hipparchus was 3 5 days , 5 hours , 1 E 2 2 . 5 minutes , seconds ssays by Hipparchus on the length of the year , on the length of the month and on the intercalary or embolismic month are referred to but are now lost . His estimates of the tropical year and of the lunation were adopted by Hillel II AD when he reorgani sed the Jewish Calendar in 3 58 . The exact length of the tropical year is now known to be

- 6 8 6 1 . 3 5 days , 5 hours , 4 minutes , 4 5 seconds

1 is view is su orte Hero otus 11 an d il s son o . cit. . 2 . Th pp d by d , 4 , N , p p 79 2 The 3 6 5 - day ye a r appeare d at B a bylon from Egypt afte r th e overthrow o f the Assyrian empire by Nabo nass ar but Chalde a su bse q uently develo pe d a un i - so ar E a so a r ca en ar l l , gyp t l l d . 3 4 6 See . 1 ostea Hist Rome vol . IV . 8 . p 4 , p . . , , p 5

6 THE MEASUREMENT OF TIME

f di ficult observation of equinoxes or solstices . According to Mommsen 1 the day and the month being determined by direct cal cul ation were observation , not by cyclical , therefore the earliest time units .

I I

THE THREE POSSIBLE FORMS OF CALENDAR It might be possible to preserve a record of the passage of time by enumerating days in constant succession from some ni real or imaginary starting point . This , though very inconve ent , might be sufficient for the registration of past events , but it would be useless for what is after all one main object of a e u re calendar , namely , to record beforehand the dat of fut re curring events . A calendar is an attempt to establish fix ed relations between the day , the month and the year . The variations in the forms whi ch calendars have taken are principally due to the fact that neither the month nor the year is an exact multiple of the day ; nor is the year an exact multiple of the month . As a result of this there are three possible forms of a calendar : (1 ) a solar

-“ calendar that is to say , one which adheres to the true length r irres ec of the year , but gives an arbitra y length to the month , p 2 tive of the length of the lunation ; ( ) a lunar calendar , in

- which lunar month lengths are adhered to , but the length of

- the year is arbitrary ; (3) a luni solar , in which an endeavour is made to observe the true length of both the month and the year , and to adjust their inequalities by means of what are called intercalations .

Notwithstanding its greater complexity , many important

- calendars of antiquity were of a luni solar character . In almost 2 every case they took the length of the lunation at 9% days , and 2 0 employed months of 9 and 3 days alternately , thus giving a

- hi lunar twelve month of 3 54 days , w ch they sought to harmonise with the solar year by the introduction at various intervals of

intercalary or additional months . A good example of such a l - uni solar calendar is the Jewish . Of a purely lunar calendar the

1 H R e ol 1 ch . xv . ist. om , v . , THE THREE POSSIBLE FORMS OF CALENDAR 7 outstanding example is the Mahometan ; and of a purely solar u calendar the capital instance is the J lian . The observation ’ e e the of the moon s phases b ing asier than that of stars , and m e e e e oonlight being sp cially s rvic able for religious f stivals , it is found that luni - solar calendars have a pre - eminently sacral 1 h h u . e t e t e or religio s origin On the oth r hand , observation of stars arose amidst sailors and travellers over plains . Hence a e or e e sider al solar cal ndar has a distinctiv ly secular , nautical and commercial reference .

I II THE GREEK CALENDAR

- date and The Greek Calendar was luni solar from a very early ,

e e e e sev ral att mptswer madeto establish a satisfactory concordanc . 2 According to Macrobius the normal Greek year was a lunar

- K twelve month of 3 54 days . nowing that the solar year com prises 3 651 days they adde d 1 1 1 x 8 90 days every eight e i years . This intercalation was divided into three mbolism c

The - e months of 30 days . eight y ar cycle was known as the

Octaeteris . e e There are trac s of sev ral variations in this cycle , but the great triumph of Greek chronometry was the discovery by

a 2 B . C . 1 e 2 Meton , in or bout 43 , that 9 solar years contain d 35 6 lunations . It is understood that Meton took 3 5% days as the

e . length of the y ar On that assumption , and taking the exact the e : astronomical length of the lunation , quation is as follows

r f 6 s 6 1 u e s o s 1 8 ou s . 9 J lian y a 3 51 day 939 day , h r 2 un ons of 2 d s 1 2 ou s 3 5 l ati 9 ay , h r , minu es 2 se o s 6 1 6 ou rs 1 m u e 44 t , c nd 939days , h , 3 in t s

1 - 228 As 9twelve months amount to months , Meton intercalated e e P t s ven mbolismic months in his cycle . According to e avius rd 6th 8th and most authorities , these were introduced in the 3 , , , 1 th r B 1 1 1 1 ea s . e th , 4th , 7th and 9 y ( ond gives the sev n years which Petavius immediately precede these , but no doubt is

1 P imi ive Time R eckon i sso n r t in . 2 1 8 etc . N l , g , pp 7 , 3 43 , 3 5 , 2 a turna l ia 1 1 S , , 3 . 3 a e f P r etua ar A S ee o e un l manac . 66 6 al so T bl p l L , pp , 7 ; p . 6 5 f o r the a n atu ral interv ls . 8 THE GREEK CALENDAR

i 1 a ni n A Meton c cycle , then , is a cycle of 9 solar years , cont i g 2nd th th th th l oth 1 2th 1 1 th 1 6th in the I st , , 4 , 5 , 7 , 9 , , , 3th , s , 1 8 1 2 2 0 and th years , lunar months of 9 and 3 days alternately , e 1 the and in the oth r seven years 3 months of similar length , odd or embolismic month having in the case of six years 30 days and in the case of the last year 29. Of the 228 normal months one - half or 1 1 4 were full months

0 1 1 o r 2 . of 3 days , and 4 short cave months of 9 days Of the embolismic months six were of 3 0 days and one of 29. Thus we have : 1 1 6 1 x 0 600 s 4 20 3 3 day . 1 1 4 + I 1 1 5 X 6935

6 0 i —a c showing a deficiency of five days from , wh ch cording — 94 to Censorinus was the length of the cycle . It is probable that these 43 o r 5 deficient days were made up by adding another — day to one o f the cave months every fourth year thus antici ffe a c pating , though for a di rent re son , the intercalary devi e of the Julian Calendar . According to Mr Woolhouse , the cycle in practice contained : 1 25 months of 30 days 3750 1 1 0 months of 29 days 3 1 90 6940 E High honours were conferred on Meton and uctemon , the hi cal endar and authors of t s , , their names are said to have been inscribed in letters of gold on the Temple of Minerva at Athens . At any rate the years of the cycle were numbered successively 1 1 d from to 9, and these numbers as employed to esignate in a series each p rticular year were , and have ever since been , k l mb s called and nown as the Go den Nu er . In the middle ages the number applicable to any one year was frequently called The the Prime . cycle was then sometimes called the cycle of 1 the Moon . The Metonic cycle is said to have b een enacted on 1 6th July

B C . . 433 . , and the first year of the first cycle ran from that date It has long been regarded as the masterpiece of Grecian chro

- nol o fl . gy, and has in uenced luni solar adjustments ever since

1 ’ L A r er r l es da t t de v ifi e es . THE GREEK CALENDAR 9

e e re Whether it was indep nd ntly discovered by Meton , or c eived by him from the east , cannot now be ascertained , but there is evidence that the value of a cycle of 1 9 years as a luni m a solar adjust ent was known to the Chinese . It is st ted by Dr 1 i o 226 B . C . Hales that in 9 two Ch nese astron mers , named Hi a nd the the Ho , reformed calendar , and adjusted solar year of

3 65 days to the lunar by intercalating seven months in 1 9years . A disturbing element in the cycle was the fact that the num b er a of leap years which it contained was not a const nt quantity . To obviate this inequality Cal ippus of Cyz icus in the following c e tu e e 1 x 6 hi n ry propos d a cycl of 9 4 7 years , in w ch period the e 1 numb r of leap years is always 9, and this improved cycle

a C . B t w s substituted in Gre ece for the Metonic about 330 B . u throughout the Christian Era the cycle of 1 9 years has remained

. e e the favourite There are trac s of other cycl s in early Greece , 2 sufli cient im notably one of 5 years , but none of these is of

portance to detain us . It should be noted here that the Greek month was divided into three decades of ten or nine days each .

IV THE LATIN CALENDAR

The calendars of modern Europe having descended from the R r e oman , it is necessa y to describ its origin and development . e According to Macrobius and C nsorinus , the original Roman

1 0 0 . : year contained months , and comprised 3 4 days Of these

6 viz e Sex s Se em r o m . u e ve e , April , J n , tili , pt b , N b r, ecem er e c 0 s 1 80 D b , a h 3 day iz r n v . c u s c o e e 1 1 2 4, Ma h , May , Q i tili , O t b r , ach 3 4 3 04

T 1 his original year began with st March , as is proved (says

M acrobius) by the names of the six last months . These writers say that Numa introduced January and Pebru 2 3 r a y. Scaliger and Hales dispute the above statement as to a

1 A N ew An l is o Chronol o l a s vo I . y f gy , . , p 3 7 . 2 3 De E menda tione Tem orum 1 . 2 . ci t p , p 7 Op . . p . 43 . 1 0 THE LATIN CALENDAR

- I o month year , and hold that the year always contained 1 2 1 - ffi b months . The original ten month year is repeatedly a rmed y

Fasti . r Ovi d in his The poet , with the cha acteristic obsession of i a decimal st , advances various fanciful reasons for its adoption . Li e o Numa Plutarch , however , in his f f , states that the Roman year during the reign of Romulus contained 360 days and that e 1 the lengths of the months , which he evidently b lieved to be 2 ma n s r e . hi s Ro ue tions he in number , were ve y irr gular In Q affi rms that some were of opinion that the Roman year at first 1 0 e consisted of months , some of which contained mor than E tro iu t 0 . u s o 3 days p , probably with truth , states that prior Numa the Roman year was confused and without regular E s di vision . ven Macrobius refers to two innominate month r mi hi atiebantu absu . w ch , he says , p According to both Macrobius and Censorinus the two addi tional months were formally incorporated in the calendar by 0 Numa . They state that he added 5 days to the year , raising m its length to 3 54 days , and that he then deducted one day fro

0 2 - da each of the six months of 3 days , reducing these to 9 y 6 di months . These 5 days thus made available he vided between e s January and February , but in d ference to the superstitiou hi dislike of even numbers w ch prevailed amongst the Romans , e the he added a day to January , thus raising the total l ngth of year to 3 55 days , and ensuring an odd number to each month r e — except Februa y , which was left with an even numb r partly

- because it was devoted to the Infernal Gods and partly because , the by so doing , Numa ensured that the number of days in year should be uneven . ea uma To equalise these twelve months with the tropical y r , N ni is said to have employed the Greek octen al intercalation , or , di t e eris . u r according to Plutarch , a or biennial cycle A f rthe ’ correction was rendered ne cessary in consequence of Numa s

- raising the lunar twelve month to 3 55 days . According to Livy I 1 e 2 ( , 9) a complete corr ction was provided for in a cycle of 4 z years . 1 ommsen re ers to th e ten - m ont e ar as the e ar iest but W it o ut a d M f h y l , h ducin roo He a mits a th e du o - e cim a ivision a o v g p f. d th t d l d was d pte d ery

2 O r ac cor in to som e m an s cri ts 0 e ars d g u p 2 y . THE LATIN CALENDAR 1 1

Notwithstanding the antiquity and authority of the writers e who furnish the foregoing account , it is probably very larg ly a conjectural . According to Ovid , the decemvirs , who were p h B . C th t e pointed about 452 . (shortly before e time when e e e Metonic cycle was introduc d) , mad certain corr ctions in the m e e the then existing calendar , and restored the co m nc ment of ’

1 st u se . year to March , the date in prior to Numa s reform It seems not improbable that they also introdu ced the other ad u the e ni e justments , partic larly the adoption of bi n al int rcalation dieteris the e e 2 2 or , consisting of ins rtion of an xtra month of

2 e . r and 3 days alt rnately This intercala y month , which Plutarch e the attributes to Numa , was w ll known to Romans under the e e name of Mercedonius . At any rate a somewhat irr gular sch me e of intercalation was still required , and b ing in the hands of the Pontifi ces e e , whose methods and reasons wer kept strictly secr t , e e — n gligence , ignorance , and still mor corruption , led to great irregularities and a resulting dislocation and uncertainty in the

Roman Calendar . e not It is to be noted , however , that these uncertainti s did e ext nd to the divisions of the months , and the enumeration of the days of each month . A highly practical scheme for the regu i e a lat on of th se det ils was early established , and survived , w ithout alteration , all subsequent reforms of the Roman Calen dar . Its principles will be described after the Julian reform has been explained .

V THE JULIAN REFORM Such was the state of matters when Julius Caesar with the l 1 help of Sosigenes , an A exandrian astronomer , undertook his

- fl the . immortal reform . We must bri e y recount oft told tale His proposals partake in a high degree of the comprehensive e en simplicity which is a usual f ature of works of g ius , and which often obscures to the common - place mind the real e greatness of the conception . The cardinal f ature of the Julian

1 H s x111 P in Na t i t 2 . l y, . . , 5 1 2 THE JULIAN REFORM

the 6 6 o reform was the adoption of solar year of 3 5 days , h urs ni as the fundamental u t , and the abandonment of all attempt to adapt either the months or the twelve - month to the length of the lunati on . It is now believed that the Julian re form was in principle a re production of a reform of the Egyptian Ca lendar B C enacted 238 . . ; possibly designed by the Greek as tronomer

Eudoxus . Many of the Roman festivals nece ssarily bore a relation to r a the seasons , and Caesar , therefo e , deemed it desir ble to a t e a roxi restore the dates of the dislocated calendar , l ast pp e t e e mat ly , to their original position wi h ref r nce to the tropical s year . The sin of the intercalators appea r to have been prin ci al l n o t p y si s of mission , with the result that calendar da es anticipated the natural events with which they were properly vice versa tu E o n associated ; or , , the na ral phemerides fell a later

c al endrial to . date than that properly appropriated them Thus , ’ e a re rd for example , we find Cic ro , four ye rs befo Caesar s thi o f M a a l thou h consulate , dating the vernal equinox on the ides y, g E e s r t e d that ph meri , if the inte cala ion had be n maintaine , should d have fallen on or about the 23 r of Ma rch . ’ e x Caesar s first step was to correct this disloc ation . He

08 6 B . C . to exce tended the then current year 7 4 , an p l n t r r a the tiona le gth . In hat year after Feb ua y he interc lated n usual Mercedonius of 2 3 days . The le gth of January being

2 2 8 80 d . 9 days and February , this gave a quarter of ays Then between November and December he intercalated two months of 34 and 3 3 days . This extraordinary year of 445 days ended just about where the Roman year would have done if the inter l i ns n ca at o had been regularly observed . This year was k own as fi ttin l the year of confusion , although Macrobius more g y called it the last year of confusion . The reformed year which followed

0 A U . C . B C . was of course 7 9 . or 45 . The above is the account of the year of conf usion given by 1 Censorinus , and confirmed by Macrobius . The account of

i . 0 Sueton us in his life of Julius Caesar , chap 4 , though very brief is quite consonant with these so far as it condescends on hi e 22 detail . Dion Cassius (XLIII) gives the length of t s y ar as 4

1 S a turna l ia I 1 1 acro iu s ives its en t as a s . , , 3 , 4 . M b g l g h 443 d y

1 4 THE JULIAN REFORM

This story is inconsistent with the definite statements of

Macrobius and Censorinus , but so far at least as regards the e transf r of a day from February to August , it is not improbable . e It se ms quite possible that those two writers , giving only a r e brief summa y of the r form , had not deemed it nece ssary to

refer specially to such a minor subsequent change , or that , di d writing as they after the lapse of a considerable time , they e had overlooked it . Macrobius ind ed hints that some change in The the Julian scheme was made by Augustus . rubric of chapter “ 1 I S a turna l ia : e 4, book of the is as follows Qu m in modum ” deinde Caesares correxerint primum Julius Augustus annum . In the text of the said chapter he says : Martio Maj o Qu intili Octobri servavit (Julius) pristinum statum ; quod satis pleno erant numero ; id est dierum singul orum tricenorum qu e ideo et septimanas habent nonas sicut Numa constitu it quia h his ul ius mutavit sed nu u s Sex s e em e u u ni il in j Ja ari tili D c b r , q ib s Caesa r binos dies addidit licet tricenos singul os habere post Caesarem oe erint c p .

La Chia ve del Ca l enda ro In , a rare and learned essay by Hu ol ini e B Gl andeves 1 8 con g Mart lli , ishop of , published in 5 3 l icentia de l i su eriori 1 0 g p , page 3 , a table of the Julian months is e r 2 0 1 8 given in which F b uary has 9 and Sextilis 3 , and on page 4 occurs the following sentence : Caesar Augustus diem unum ” d n t 1 detraxit Februario et suo Augusto o avi . Scaliger writes as follows : Cum autem Septem f uerint cavi menses in anno Roman o Janu arius Aprilis Juniu s Sextilis September November D ecember qu orum quinque singul i dies rel iquis autem duobus bini additi sunt a s e Cae ar . The twb months to whi ch Caesar added two days each he

states to have been January and December . It follows that the 0 other five were raised to 3 days only . 2 Scaliger also describes and reproduces a calendar in ” u saxu m incisum a Romae repertum . In this calendar Aug st XXI IX 28 has XXX days , February , which apparently meant , as to Novemb er are given XXXI . On the whole the probability seems to incline in favour of

1 2 . cit 0 . ci t. . 2 2 . Op . p . 44 . Op p 3 THE JULIAN REFORM 1 5 the View that Caesar would have been likely to maintain the lengths of the months as near as possibl e to the average or 0 standard of 3 days , and further would not have favoured a hi in monthly syllabus , w ch he could not have failed to notice v olved a serious and quite avoidable inequality in the length of

- e e e the two half years . For th s reasons we hav little hesitation in accepting the traditional story and in ascribing this obvious blot in the Jul ian Calendar to the selfish craft of Augustus . A singular mistake disturbed the first op eration of the Julian The Pontifi ces e Calendar . int rpreted the instruction to inter c alate one d ay eve ry fourth year in accordance with the usual hi enumer Roman method of enumeration , by w ch the number ated was inclusive both of the day from and the day to which h t e . computation extended They , therefore , intercalated a leap hi d a . 6 y every third year T s continued for 3 years , during which 1 2 in place of 9 days had been intercalated . This error was

c 1 B . C . A D . orrected by a provision that the 2 years from 9 to 3 . 1 s hould be common years . Thus after the expiry of 48 years from the original introduction of the Julian Calendar the normal

s e . be yst m was finally brought into operation It may noted , h e ow ver , that chronologers have not recorded this error but have treated the leap years as having succeeded one another r egularly from the start . Julius Caesar prescribed the intercalation of a 3 66th day to b e made after the feast of Terminalia on 23 rd February of every f th . 2 e ourth year The 4 F bruary was , by the Roman method , th th e sixth day before e Kalends of March . This day was to be d e e uplicate d . The int rcalated day was r garded as a part of the 2 th e e 4 , it was henc that it receiv d the name of bissextus or bis xt l i z s e i s . According to the theory of the Juli an Calendar there a re 6 e only 3 5 days in a l ap year , but one of them , namely the 2 th 4 February , comprises two natural days in one civil day . The e unctum tem oris int rcalated day was treated as a mere p p . A person born on that day had his birthday annually on 24th

February . Many subtle legal discussions took place under the

1 P in Na t His . t I I I 2 . l y , . X , 5 2 T is erm im ies a 28 - da e ru ar bu t was n o t coine e o re the h t pl y F b y , d b f Au u stan c o rrec i g t on . 1 6 THE JULIAN REFORM

E r the as ff mpi e and during middle ages to the e ect of these,

r i . e the s p ov sions V ry curious as are some of questions rai ed , it ee e sa t s ms unn ces ry to refer to hem here . t As the week was no part of the Roman Calendar , a h ast until n n e the reig of Co stantine , it s ems unlikely that these pro visions in any way interrupted the regul ar succession of week s r day where these were obse ved , although this is not quite so

certain as some suppos e . At any rate such an interruption does not seem to have be en the result of the important English t De Anna bissextil i 2 1 r 1 2 6 statu e , , passed in Hen y III , 3 , by which it was provided that the day of the leap year and the da h y before s ould be hol den for one day .

VI

MONTH AND DAY IN THE ROMAN CALENDAR

Suc he was s a of i h , t n , the imple fr mework the Jul an Calendar .

As an instrument of dating it required also. the use of some rule The for the enumeration of eac h single day . method already for a lo ng time in use for this purpos e was continued without disturbance . Three days in each month were taken as fi xed points f or — a . Th enumeration the K lends , the Nones and the Ides e r Kalends was in every case the fi st day of the month . In the o s hi th f ur month , March , May , July and October , w ch from e earl ies t times and throughout the whole length of Roman hi story l b eni i . e . u e 1 s had een p , f ll l ngth months of 3 days , the None were the 7th and the Ides the 1 5th of the month . In the cas e of the other eight months the Nones were the 5th 1 s and the Ides the 3th day reckoning from the first day onward . Dates were determined by enumerating from these days ba ck wa r t ds . The days of any mon h subsequent to the Ides were enumerated by computation backwards from the Kalends of - “ o tw Norl 3s e the f llowing month . Dates be een the Ides and wer e n similarly computed backwards from the Ides , and days betw e the Nones and Kalends backwards from the Nones . In every rom the case , following the Roman method , both the day f and MONTH AND DAY IN ROMAN CALENDAR 1 7 1 8 MONTH AND DAY IN ROMAN CALENDAR

to day which the computation was made were enumerated . The day immediately preceding any of these three fixed points was P ridie called , the day before that was the third day from the

fi x e d point and so on . The days of the month were also distinguished as fa sti and ne ast Dies asti i th f i . f were days on wh ch e courts were open Dies e . n asti e e business days as we should say f the r v rse . Any additional days added to the months by Caesar were declared dies ne asti d s m t l asti . ie co i ia es i e to be f No additional f nor ( . . days when public assemblies might be convened) were instituted by er a s s him . These must be distinguished from f i e or die fe ti religious festivals or holy days . Where the lengths of the months were altered Caesar pro vided that the additional days should be held to be added at 1 the the end of month , thus securing that no interruption should e e tak place in the dates of religious f stivals . Thus if the third day from the Ides of any month was one of the feria e or festi and if that day was the 1 6th before the Kalends of the following month , still the religious observance was preserved intact on the third from the Ides , although that day might now become t the 1 7th or 1 8 h before the following Kalends . The method of backward enumeration seems to us awkward simply because it is unfamiliar , and its use of course required that the exact number of days in each month should be con st l ant y memorised . This obstacle to slovenly thinking (which was always distasteful to the resolute intellect of the Roman) re being overcome , the Julian Calendar as an instrument for cording dates both past and future was the most nearly perfect —i which the world has ever seen ndeed , but for the one fact of its slow secular dislocation with reference to the tropical year , n it was practically perfect . It furnished the gover ment and the people of Rome with the immeasurable boon of a perpetual calendar . The programme of future work of each individual , of t each ci y , of each institution , of the army , of the law courts and of the whole State could be definitely fix ed and made available ;

e . could be at any moment inspected , ref rred to and understood These programmes under this calendar were ready for instant

1 acro ius S a turna l ia I 1 . M b , , , 4 MONTH AND DAY IN ROMAN CALENDAR 1 9

e use , remained unchanged until alt red , were capable at any e e e e mom nt of being alter d to meet altered r quirem nts , or to be more perfectly adapted to the exigencies which experience e e e discovere d . Without this simple and p rf ct instrum nt it would have been impossible to organise the widespread activitie s of the e e The Roman mpir . Julian Calendar made that organisation the m e possible , and enabled rulers of the e pire , without st am e e e e or lectricity , to arrange and administer the ord rly gov rnm nt of their many scattered provinces and dominions with a cer tainty and regularity which have never since been realised . Very diff erent is the state of matters under the modern E e uropean calendar . The observance of we k days and the occur rence of Sundays and other movable holidays without any fixed correspondence to the dates of the calendar absolutely E r e . prevents the adoption of any fix d working plans ve y year , the e e on I st January , whole sch me or syst m of engagements is ad overthrown . All gradual , steady improvement of social or e ministration commercial arrang ments is impossible , and the progress so constant and so remarkable in science and the mechanical arts finds no counterpart in the unprogressive confusion which characterises social and administrative ar rangements . The Julian Calendar was not so well suited to serve the other main purpose for which the calendar is required , namely , the e m asurement of equal intervals of time . The lengths of the months approximated suffi ciently to the standard length of 3 0

- days , but the sub divisions of the months were too unequal for e practical use . W are not well acquainted with the methods employed by the Romans for the measurement of intervals .

There are frequent references to a period of eight days , known as nundina e the , said to have been introduced by Servius Tullius , the eighth day having apparently been a market day without the religious significance . Probably , however , fact that the calendar was perpetual enabled equal intervals to be arranged without serious inconvenience .

2—2 20 THE GREGORIAN CALENDAR

THE GREGORIAN CALENDAR

1 1 1 We have seen that the Julian year is minutes , 4 seconds — longer than the tropical or natural year consequently the dates of natural periodic events , and in particular of the equinoxes t 1 1 l n and sols ices , fell annually minutes ear ier in the Julia

hi was . t Calendar . T s unsatisfactory In the course of cen uries the seasons would gradually have moved backwards to an earlier ff calendar date . The di erence , however , was so small and the change so very gradual that little practical inconvenience re l hi fl su ted . The discrepancy was c e y noticed in connection with a he E . t the observance of aster As will be expl ined later on , date E of aster , owing to its original derivation from the Passover d festival , depen ed upon the occurrence of the first full moon happeni ng after the vernal equinox . A In 3 25 D . the General Council of Nicea decreed that the celebration of Easter should be uni form throughout the Chris tian Church . The Decree does not appear to have contained ni i any defi te reference to the date of the vernal equ nox , but that date was certai nly assumed by the framers of the Easter Tables

1 st 2 AD . to have been the 2 of March , although in 3 5 the th equinox actually fell on the eveni ng of the 20 . It may be noted that apart from the excess of 1 1 minutes in the length of the Julian year there are other causes of variation in the date of the equinox . The fact that the assumed excess of six hours over the even period of 365 days is accumulated and added as one day every fourth year entails an oscillation of the date of the equinox , which might be avoided by an alteration in the years t when the intercalary day is in roduced .

As time went on , however , the calendar date of the vernal i f equinox fell constantly earlier . Th s led to much di fi culty and

' di spute as to the proper date for the observation of the great u 2 1 8 1: festival . If the first f ll moon after March was adhered to it gradually moved further away from the true date of the equinox . In course of ages , as one writer pointed out , the date

22 THE GREGORIAN CALENDAR

years , instead of leap years as under the Julian Calendar ; those centurial years only which were divisible by 400 without re mainder being retained as leap years . Further (3) the use of the Epacts designed by Lilius was also enjoined in place of the Tables of Golden Numbers , and (4) the r $ necessa y adjustment of the Dominica Letters was provided for . 1 82 The year 5 was the initial year of the Gregorian Calendar , which was at once adopted by the various countries whi ch recognised the spiritual authority of Rome . France adopted the

1 82 . z new style in December , 5 Swit erland , the Catholic Nether E 1 lands and the Catholic States of the mpire in 583 . The Pro

s . 1 6 testant State for a considerable time refused to follow In 99, fl ni z however , chie y at the instigation of the philosopher Leib , the Protestant States of Germany came into line . In Great Britain the new style was not adopted until the passing of the Calendar New Style Act under whi ch

Act it came into operation in 1 752 . In consequence of the fact 1 00 that the year 7 was a leap year under the Julian Calendar , but not under the Gregorian , the disparity by that time 1 1 r amounted to days , and it was accordingly found necessa y to 2nd 1 2 provide that the day following the of September , 75 , should be called the 1 4th of that month . Opportuni ty was taken at the same time to fi x the official date of the commencement E 1 of the year in ngland at st January , the date which had been taken as the commencement of the year under the Gregorian i Calendar , and wh ch had already by a Decree of the Privy 1 600 1 i Council been adopted in S cotland in . Up till 752 n England the ofli cial date of the new year had continued to be th the 25 of March . These facts must be kept in mind when dealing with English — dates prior to 1 752 dates between I st January and 2sth March being frequently referred to both of the alternative years although it should be noted that in intercalating the 3 66th day E 1 2 in the month of February , ngland , even before 75 , had — treated the year as commencing on I st January the February of the intercalation having been the February of the year e divisibl by 4, on the assumption that the years were reckoned

from I st January . THE GREGORIAN CALENDAR 23

For some time the change produced considerable discontent E the in ngland , and riotous crowds assembled to cry of Give ” e us back our el ven days . The countries which ofli cial l y profess allegiance to the Greek or Eastern Church have continue d to employ the Julian Calen dar up to the present day ; and have only recently adopte d the

Gregorian . However justifiable the correction of the Julian Calendar may have been , there is no doubt that the change was productive of e much confusion , which has p rsisted almost to our day . Customs dependent on the calendar become deeply embedded in the the the national life , and in Scotland , for example , adjustment of

- new half yearly terms to the dates was only partially effected . e e e em Termly paym nts of mon y gav little trouble , but termly a ements g g of servants , especially in the rural districts , and termly occupations of houses and farms continued to be regu late d by the old calendar dates almost up to the present day . e It is important , therefore , to ascertain the caus of this con fusion . Had the Gregorian reform been confined to ensuring that for the future the disparity between the tropical and the calendar years should be removed by the omission of leap day from three out of eve ry four centurial years no confusion could e have arisen . The troubl was entirely due to the fact that Pope Gregory XIII determined to make the correction draw back to A the date of the Nicene Council in 3 25 D . It was for that reason 1 0 1 82 only that the omission of the days in October , 5 , and of

1 1 1 2 . the days in September , 75 , was required Had the con there seems re sequences been foreseen , little doubt that the . d inconveni form would have been confine to the future . The e nces of a retrospective correction have long been recognised 1 by students of the calendar . e The Gr gorian adjustment is not absolutelycorrect . The error a 2 of the Gregorian Calend r in tropical years is days , 2 1 2 . 4 hours , 4 minutes Sir John Herschel suggested a further correction , to be effected by providing that the leap day should 000 be excluded from years divisible by 4 without remainder .

1 ’ S e e B rink e s El emen ts o Astronom 6 l y f y , p . 2 2 . 2 Trea tise on Astronom ch XI I I 6 y , . , 3 2 . 24 THE GREGORIAN CALENDAR

A curious instance of the persistence of the old style is to be the fi B E found in date of the nancial year of the ritish xchequer . 1 ffi Prior to 752 that year o cially commence d on 2 5th March . In order to ensure that it should always comprise a complete year the commencement of the financial year was altered to the

th . 1 800 5 April In the year , owing to the omission of a leap r day obse ved by the Julian Calendar , the commencement of the rw 6th th financial year was moved fo ard one day to April , and 5

. 1 00 April became the last day of the preceding year In 9 , how ever , this pedantic correction was overlooked , and the financial th year is still held to terminate on 5 April , which is about the ni most inconve ent date imaginable , as it so often happens that the Easter celebration occurs just about that time—indeed one result is that about one - half of the British financial years include

E - E two asters and about one half contain no aster date . It would surely be a very simple matter to make the financial year com wi ~1 st hi C E mence th March , in w ch ase the aster interruption o would always ccur during the course of the first quarter , ni causing comparatively little inconve ence , whilst any dis turbance due to the incidence of the odd leap day at the end of r r every fou th Februa y would be entirely relieved .

OTHER CALENDARS

Many other calendars besides the Julian and the Gregorian have been , and some still are , employed in certain countries . We do not propose to give any account of these except in so cal ndrial far as they may illustrate some relevant e problem .

We therefore pass the Chinese Calendar , interesting though

m ni - it be , merely re arking that it is lu solar , containing months 2 0 not of 9 and 3 days alternately , balanced by an intercalation nl u ike the Jewish . We also make no further reference to the Chalde an and E hi gyptian Calendars , containing features w ch undoubtedly suggest a common origin and whi ch display a remarkable degree OTHER CALENDARS 2 5 o f accuracy in the knowledge whi ch their framers possessed of the astronomical data on which a calendar is based . Nor is it within the scope of our design to say anythi ng of the early Indian Calendars nor of the interesting Mexican Calendar with i ts 1 8 months of 20 days .

THE JEW ISH CALENDAR

Of calendars still operative the Jewish can claim the most e e ni a ncient unbroken lineage . It is an xcellent exampl of a lu

2 0 . s olar calendar . The months are of 9 and 3 days alternately The e qualising intercalary month is introdu ced usually every third year . Now and ever since the adjustments made by Rabbi rd 6th 8 AD . Hillel II in 3 5 the intercalations are made in the 3 , ,

8th 1 1 th 1 1 1 th . , , 4th , 7th and 9 years The intercalary month is introduced after the month Adar at the end of the ecclesiastical year and is called Veadar .

The original Jewish year commenced with the month Tisri , — a t the autumnal equinox a fact whi ch suggests an Egyptian hi e o rigin . T s is still the commenc ment of the civil year ; the e cclesias tical year begins with the month Nisan six months e arl ier at the vernal e quinox . Veader is intercalated immediately

- e before Nisan . Further , to enable the luni solar adjustm nt to be maintained as nearly accurate as possible the Jewish Calendar r ecognises three different lengths for the year whether normal r 8 o embolismic . There are common years of 3 54 or 3 4 days , perfe ct years of 3 55 or 3 85 days and imperfect years of 3 53 or

3 83 days as the case may be . It has been alleged that the use of the intercalary month can n ot be trace d earlier than the date of the establishment of the

M e ni e e . . to c cycl by the Gre ks This , however , is uncertain The u se of the 1 9- year cycle can be traced in various countries at a e e e e very early dat , and it is impossibl to say wh r it first origin e ee ee inde end ated , or wh ther , as s ms likely , it may have b n p ently discovered in more places than one . At any rate it is certai n that the Jewish months always com me nced with or very nearly with the new moon and the eff ect o f the intercalations is to ensure that the lunation corresponding 2 6 OTHER CALENDARS to the month Nisan is always that during which the vernal equinox occurs , although of course as the intercalation is not made annually it inevitably happens that the commencement n of Nisan does not coincide with the date of the vernal equi ox , only that the vernal equinox always falls sometime whilst that lunation is in progress .

THE MAHOM ETAN CALENDAR

A luni - solar calendar with lunar months and an intercalation somewhat similar to the Jewish was familiar to the Arabs in the time of Mahomet . That remarkable man was not a phi losopher he and certainly not what we should call a man of science , but seems to have been possessed by a singular intuition of reality which is reflected in many of hi s civil and ecclesiastical institu o t tions . Like s many other men of keen perceptions Mahome recognised the immense importance of the calendar in the work ing of the social machine , and the Mahometan Calendar which he introduced bears the impress of his extraordinary character . It seems probable that he found the established system of inter cal ations e disturbed by abuse and corruption , just as was the cas in Rome before the Julian reform . He therefore absolutely sup of e pressed the use the intercalary month , alleging that twelv was the number of months according to the ordinance of God , and that a thir teen- month year was contrary to the divine appoint 1 E ment . ver since its institution the Mahometan Calendar has been purely lunar -the one outstanding example of such a ’ d calendar in actual use . Under it the day and the moon s perio are the only natural units . The extreme simplicity of such a rule may largely compensate for its entire failure to maintain a fixed relation with the seasons of the year . Such a calendar is probably only possible in lands where the diff erence of the seasons is not so marked as it is in more temperate regions . The call it imposed on his followers to ignore the law of Nature in their regulation of their time - scheme may be regarded as an item in the ascetic a ppeal which Islam makes to its devotees .

1 ’ K c t a i . . . or n a . . S al e s transl 1 . S ee al so il sson o . c 2 2 , h p 9 . p . 53 N , p p 5 OTHER CALENDARS 2 7

THE FRENCH REP UB LICAN CALENDAR

The short - lived Revolutionary Calendar of the French Con venti on t 2 th e 1 was insti uted on 4 Nov mber , 793 , and only sur i d v ve 1 st 1 80 . until 3 December , 5 This calendar has little his torical or scientific importance , but the attempt is not without instruction . The Convention commenced their new era with the autumnal

viz . equinox of the year in which the republic was founded , nd tu 22 e 1 2 . e S ptember , 79 It was decid d that the au mnal equinox should thereafterbe the commencement of the civil year dividedinto 1 2 0 each with fi ve whichwas months of 3 days , super numerary days at the end of each year . The week was abolished and the month divided into three decades of 1 0 days each . This calendar claimed to be founded on a purely scientific u basis , but like most scientific reforms introd ced by politicians e unacquainted with sci nce and impatient of practical tests , it su erfi cial it bears marks of haste and p y , and also of a total dis of regard the advantages of continuity . Its chief features were The u strangely archaic . adoption of the aut mnal equinox as ff the commencing date of the year , though made for a di erent e E reason , was a reversion to the rul of the ancient gyptians who were influenced by the fact that the Nile flood was then at its height . The addition of five intercalary days at the end of the year was a reproduction of the ancient Chaldean plan and was the e detrimental to the value of cal ndar , both as an instrument of dating and as a means of measuring out equal intervals of time . The division of the month into three decades was also a e revival of a feature of the old Greek Calendar . No consid ration seems to have been given to the question of suitability for prac tical use , and even if the enemies of the Revolution had not been in any haste to abolish it we may doubt whether its use would have been permanently established after the revolution e ary fev r had abated . At any rate , for the purposes of historical study it would have been necessary to maintain the concurrent use of a dating system which maintaine d continuity with the — past to break with which was probably one of the main objects of the promoters of the Revolutionary Calendar . 28 THE WEEK

IX THE WEEK The legal isation of the weekly Sunday within the Roman empire eff ected a very serious dislocation of the Julian Calendar .

It deprived that calendar of the advantages of perp etuity . The week now occupies a position so important in the calendars of r the modern world that we must devote some space to its histo y . In the widespread Mongolian or Turanian race described by “ Isaac Taylor as the ethnological substratum of the whole 1 ” hi world , and with w ch we should probably associate the mega lithic remains so extensively distributed throughout the world ,

- there are evidenttraces of the early observance of a fi ve day week .

i . Such a week , for example , has long been known in Ch na A week of five days was also observed amongst what ethnol o gists now describe as the Nordic Race—the race which inhabited B the lands surrounding the altic , and by whom rather than by Teutonic inhabitants of central Europe it is now well establ ished that the British Isles were largely colonised . It seems probable that the blood of these Nordic races contained a Turanian

u . admixt re That , however interesting , does not directly concern us now , but their calendar does . ’ n Northm n s Our k owledge of the e Calendar is imperfect , but there is ample evidence that it contained 1 2 months of 3 0 du days , each containing six weeks of five days each . M . Paul 2 Chail l u gives us the names and etymology of the twelve months K h il l : a armal 6 . C a u taken from Skalds p , c . 3 Du adds

The m v e o six ee s e ee a e fi ve onth was di id d int w k , ach w k cont in d The e e e days . days w r call d Tysdag Tuesday Odirfsdag Wednesday Thorsdag Thursday Frj adag Friday 3 Lau arda - - g g (bath day) or Thvattdag (washing day) Saturday .

v The etymology of the first four is ob ious , they being named after the four principal deities of Northern Paganism . Whether

1 2 E trusca n R e h —8 sea rches Th n A e c IV . . e Viki . , p . 3 4 . g g , , pp 3 7 3 ’ r D S ee o uff e rin s Letters r Hi h La titudes . 6 . L d f om g , p 4

30 THE WEEK

According to Jewish tradition it was instituted at the creation , i the successive stages of wh ch it was believed to symbolise . Its observance , having been neglected , was revived whilst the chil dren of Israel were journeying through the wilderness . The daily supply of heavenly manna which was vouchsafed to them was e hi omitted on the seventh day , to compensat w ch a double 1 E e portion descended on the sixth . mbodi d in the Fourth Com mandment the observance of the week has ever since been re garded as of divine obligation upon Jew and Christian . It is to be noted , however , that its observance was enjoined upon the

Jews as a mark to distinguish them from the Gentile nations . Ez 1 2—20 are In ekiel xx , , we told that God gave the Israelites the Sabbath to be a sign between him and them . The usual gloss on thi s passage is that the observance of Sabbath was to serve as a distinction between them and other nations . Among the Jews the seventh day was named and observed as e e the Sabbath , the other six were merely id ntifi d by their number as First , Second , etc . , unless that latterly the sixth day was frequently called the preparation . The term Sabbath 2 was not confi ned by the Jews to the e seve nth day of the week . Various other holy days were call d

Sabbaths . On the weekly Sabbath all work was forbidden , on the othe r Sabbaths the prohibition generally was limited to “ ” the all servile work , but full prohibition applied to one of

viz . the . these special Sabbaths , Great Day of Atonement Besides the weekly Sabbath there were seven of these holy : days annually . These were Un 1 and 2 . The first and seventh days of the Feast of B leavened read .

3 . The day of Pentecost or First Fruits .

. e 1 . 4 The F ast of Trumpets , st of Tisri 6 5 and . The first and eighth days of the Feast of Taber l nac es .

7 . The Great Day of Atonement . It is generally understood that these special Sabbaths did not interfere in any way with the weekly succession , although

1 E - xo . . 0 d xvi 2 3 3 . 2 In B abylonia sha bba ttu meant o riginall y the day of full moon . THE WEEK 3 1

ta the practice in early times must be uncer in , especially in View of the fact that in several cases these days were ordered to be e duplicated and observed during two natural days , in ord r to e nsure an observance at least partially simultaneous throughout the Jewish world . The Jewish month being lunar and the first day of each month being ascertained by the actu al visibil ity of the e ai new crescent , unc rt nty might and sometimes did exist e a s to the true day on which the month began . H nce the dupli e e e cation abov referred to which appli d and still applies , at l ast to Pente cost and the I st of Tisri . It is thus evident that there is most ample ancient sanction the e for observance of two Sundays in immediat succession , and also that the ancient Jews either intercalated an additional Sabbath between two seven - day weeks or else that the inj unc ” tion of the Fourth Commandment , six days shalt thou labour , was not interpreted so literally as to exclude the occasional pro hibition of work on one of the six working days of certain seven day weeks . In commemoration of the fact that the Resurrection of our the Lord took place on the first day of the week , and also that foundation of the Christian Church at Pentecost took place on the same day , the early Christians commemorated the first day e e of the we k as the we kly day of rest and worship . For some time , indeed , they continued , in certain places at any rate , to

o . bserve the seventh day also Ultimately , however , this double

o 6 A.D . bservance was abolished by the Council of Laodicea in 3 4 , the reason for their decision being that the practice savoured of judaising , not at all that a departure from six continuous days of labour in each week was a contravention of the Fourth Com —a hi mandment View which , if sound , would pro bit all holidays o r l - e re week y half holidays , whether d voted to religion or to cre ation . To some extent the double observance continued to a

. a later date in outlying regions For ex mple , St Columba held

Saturday as the day of rest from work , whilst on Sunday he 1 commemorated the Resurrection by a religious service . t e ve There are , therefore , plen y of anci nt precedents for a fi da rk n we k y wo i g e .

1 ’ Ad mnan s Li e o S Col umba e d 1 8 6 a t . f f , 74 , p . 9 . 3 2 THE WEEK

The true View of the Christian duty in regard to the observ ance of Sunday is well stated by Dr Thomas Arnold in a letter 1 nd r 1 8 0 : dated 22 Feb uary , 4 , as follows

An ordinance of Constantine prohibits other work but leaves r o ee o e Leo Em ag icultural lab ur fr . An rdinanc of I ( peror of Con s r u u ou so t tantinopl e) fo bids agric lt ral lab r al . On he other han d ou r 2 own reformers required the Clergy to teach the people that they would grievou sly off end God if they abstained from working on u s es me the u e of E r VI th 6th S nday in harv t ti ; and Stat t dwa d , 5 and , 111 ex ess o s e so or r e or o o e r chap . , pr ly all w all p r ns to w k , id f ll w th i ma be s of the e calling whatever it y in ca e need . And pr amble of hi s e was u ou e r u the u o u t Statut , which nd bt dly d awn p with f ll c nc r e e the r e o mers not tu e em r nc of p incipal r f r if ac ally writt n by th , declares in the most expres s terms that the observance of all religiou s es v s is e the s re o of the C u r and e e o e ro f ti al l ft in di c ti n h ch , th r f r it p ceeds to order that al l Sundays with many other days named shall An d the e r e of the u e o e be e o . e h k pt h ly cl a languag Stat t , t g th r wit the total omission of the duty of keeping the Sabbath in the Cate sm ou o esses to e our u ow r s God om chi , alth gh it pr f coll ct d ty t a d fr the ou s Com me o es to m us the f r fir t mand nts , pr v y mind that in ing fourth Commandment in the Church Services the reformers meant it to be understood as enf orcing to u s simply the duty of worshipping God evo s ome o o of me to His o ou the u , and d ting p rti n ti h n r, partic lar portion so devoted and the manner of observing it being points to r be fixed by the Chu ch . After the legal establishment of Christianity in the Empire during the fourth century various enactments were passed f or ff the observance of Sunday , the indirect e ect of which was to put the seven- day week into an intimate relation with the other th elements of the calendar . Most of these are collected in e

I I I XII D Feriis . e . e : Cod (Justinian) , Lib , Title , They include hi 1 A 2 D . em Cap . 3 . A constitution by w ch Constantine in 3 joined the solemn observance of Sunday but permitted agri cul l dies so is . r tural work . His rescript makes use of the term In late

. m legislation , as Gibbon (ch XX , note g) points out , the ter ’ s do — die minions . usually employed is the Lord s Day Cap 2 . An enactment of Theodosius fixing various feria e and making

dies nicus . . t n the domi a legal blank day . Cap 7 A consti utio

Th i 8 A .D Val entinian eodos u s . ascribed to , and Arcadius , dated 3 9 ,

1 3 ’ l L e vol 11 . 1 6 See Cranmer s isitation Arti c es . if , . , p 7 . V THE WEEK 3 3

dies eria e by which various f were provided , including the birth e E days of Rome and Constantinopl , the fifteen days of aster ,

Christmas Day and Epiphany . With regard to Sunday it was d ecreed that :

In eadem observatione nu meramus et dies Solis (qu os D ominicos rite dixere majores) qui repetito in sese calcu lo revol vuntu r : in quibu s parem necesse est habere reverentiam : ut nec apud ipsos arbitros vel co nitio u r iorum a ju dicibus flagitatos vel sponte electos ulla sit g j g . Nostris etiam diebus qui vel lucis auspicia vel ortu s inperii pro

tul erunt .

A e e By constitutions of Leo in 469 D . furth r provision was mad for the observance of Easter and of Sunday . In particular by Ut dominicis dicha s omnes a b Constitution LIV , under the rubric o eribus va cent k p , provision is made for a suspension of all wor on Sunday inclusive of agricultural work .

THE DOMINICAL OR SUNDAY LETTER

In consequence of these various enactments and of the

e e e - e gen ral practic of the Church , the sev n day w ek , or more e e e corr ctly the various w ek days , acquired a definite r lation to e e the oth r lements of the calendar , which became more strin gent through the need which arose for a cal endrial rule to E e e determine the aster date . It th refore b came necessary to devise a method for ascertaining for any given year the con s tantl fl e e ee y uctuating r lation b tw n the week and the month , and in particular f or readily ascertaining the cal endrial dates o f the Sundays in any particular year . This device known as the Dominical or Sunday Letter must now be described . The table of the Week Day Letters in no way depends upon e the e or ref rs to lunar calendar , but is employed sol ly for the purpose of indicating the relations between the day of the month e the one and year in the civil cal ndar on hand , and the day of th the week on e other . To every day of the year there is attached 34 THE DOMINICAL OR SUNDAY LETTER one t e or o her of the first seven letters of the alphab t , thus I A 23 C D E 6F G 8 A . January , , 3 , 4 , 5 , , 7 , , and so on In lea p years the 29th February has no letter It is obvious that under thi s arrangement the same day of the week will always hav e the same letter of the alphabet throughout any given year except where the introduction of leap day oc curs . Whatever letter coincides with the first Sunday of the a wi a to ye r ll , therefore , necessarily be the letter att ched every hi subsequent Sunday . T s letter is called the Dominical or Sun day Letter of that year . It follows that if we know the Dominical Letter of any given year we can tell the whole order of the days f o the week within that year . To ascertain the order of week days in each year we require 1 ni ( ) A table showing the Domi cal Letter for each year , and (2) A table of the seven different almanacs varying in accord ance with the different week days with which the year may begin . We append (I ) A table of the Dominical Letter of every year of the

r Era 1 00 000 A .D . Ch istian from 7 to 4 (Fig . (2) A table showing the almanac for every year after the

Dominical Letter is known (Fig . It will be seen that the possible almanacs of monthly and Ea s are weekly correspondence , leaving out the ster adjustment , only seven in number for common years , and seven for leap years .

di . 2 n Accor ngly , if from Table Fig or otherwise the Domi i of cal Letter any given year is known , the almanac for that year i can be found immediately in Table Fig . 3 . It is also obv ously s i ni a po sible , w thout any second table , on being told the Domi c l Letter to ascertain what day of the week falls on I st January of the year in question . In order to become thoroughly familiar with the use of the Dominical Letter it isimportant constantly to keep in mind the distinction between fi r 1 i . e . ( ) A table of Week Day Letters , the st seven days of — the the year , and every succeeding seven days indicated by fi rs se t t ven let ers of the alphabet , thus THE DOMINICAL OR SUNDAY LETTER 35

January I st A 2nd B 3 rd C 4th D 5th E 6th F 7th G and so on to 3 1 st December . 2 hi ( ) And a table which , from the day of week on w ch I st

January falls , indicates the Sunday Letter for the year , thus A 1 . If st January is Sunday , Sunday Letter is G Monday , . F Tuesday , .

E . Wednesday , D Thursday , . C Friday , . B Saturday , .

These tables are the counterparts of each other , but at the same time one is very apt to confuse them unless care is taken to distinguish them . If these distinctions are kept in View they enable us to under stand the use of the solar cycle . In consequence of the unf ortunate fact that leap day inter t venes in the course of every fourth year , two Dominical Let ers are required to indicate correctly the calendar for any leap year , and as leap year occurs once in four years , it follows that in place of seven almanacs being suffi cient and repeating 28 re themselves in a constant succession , a cycle of years is quired to reproduce the various possible almanacs in the same order .

The operation of this cycle is well seen from the table (p . 91 ) giving the years with identical calendars during the first half tu of the twentieth cen ry . e The cycle is som what inaptly called The Solar Cycle , simply because it deals with the succession of the week days the within solar or tropical year , and without any reference to e the phases of the moon . In this r spect it is distinguishable — 3 2 3 6 THE DOMINICAL OR SUNDAY LETTER

E from the other cycles employed in the determination of aster , i and th s is the only reason for its name . The solar cycles are held by convention to have commenced B C a 1 AD 1 0 with the year 9 . . and the ye r . was No . of a cycle . To find the number of this cycle applicable to any given year — the rule is therefore simple add 9 to the date and divide by 28 . The remainder is the number required ; if no remainder the number is 28 . According to the foregoing rule the year 1 896 was the first year of a new cycle . A continuous sequence of these cycles from B C B t e 9 . . is assumed in most almanacs . u such a sequ nce is only valid for the Julian Calendar . The change over to Gregorian broke the then current cycle . Moreover the intervention of a centurial common year dislocates the cycle in which it, occurs , although the 2 8 - year period applies whenever it is not thus in

terru ted . n . 2 p In the a nexed Tables , Figs and 4 , this dislocation is provided for , the Dominical Letters for centurial years being ’ i n B Hand B ook first placed by themselves . The Tables ond s y , — . 8 2 pp 3 5 , may be usefully consulted ; also an interesting essay B E 1 on the Irregularities of the Calendar by Mr F . A . lack , F . R . S . . 1 — A—G 1 — If 7 January are represented by , it follows that 7

D F G A B C . March are represented by , , , , , It is therefore quite easy to construct a table of the Domini cal Letters and a table of the almanacs for a year commencing I st March . Such z hereto tables are annexed . They have this great advantage that they serve without alteration either for common or leap years , 3 an d are simpler and equally serviceable .

1 P robl ms n T e i ime a nd S a ce . etc . p , p 3 4 , 2 i and . F gs . 4 5 3 Fi wo e r on if th e al e ars were al an ce b g . 4 ul d s rve witho u t a lte ati h f y b d y ar tran sferrin g a day from Au gust to the fol l owin g Fe bru y .

38 THE DO MINICAL OR SUNDAY LETTER ‘ THE DOMINICAL OR SUNDAY LETTER 39

F ig . 4 . The CA E ERS for e ars rom 1 00 to 000 D DOMINI L L TT y f 7 4 A. .

New St e . 1 st arc to 28 2 th e ru a yl M h / 9 F b ry .

PA RT 1 1

XI CYCLES

UR investigations must by this time have made it evident O to the reader that the framers of calendars have a strong the im liking for cycles . The use of cycle indeed plays a very The e portant part in calendar construction . month is a cycl of m days , the year a cycle of days and also of onths , and the week , s tanding apart from the other elements of the calendar , is itself

a . cycle of days The week , however , is not itself a component o f i ff any larger cycle , and a very curious result of th s di erence be must pointed out . To be a component of a cycle confers th E identity on e component member . very day is identified by enumeration of its position in the month ; every month acquires an identity , or , if we might use the term metaphorically , a per l i s ona t . y, in virtue of its position in the year Similarly every day has an identity in respect of its position in the week . The w e eek , on the oth r hand , not being a component of any larger 0 cycle has no identity . N week is distinguished from another e e ither by number or by name . Th y follow on in endless suc

c s . ession , each one passing nameless into the abyss of the pa t a Not content , however , with these primary and fundament l c - we ycles , calendar makers , as have already had occasion to e l note , have be n largely occupied in designing onger cycles with s e years as their component . One of the earliest of thes is that known in ancient times both in Chaldea and in Egypt—called E e in gypt the Sothiacal or Canicular Period . It is vaguely ref rred to in a reported conversation between Herodotus and the priests E 1 of gypt . It comprised 1 46 1 years of 3 65 days and consisted o f an equation recording that these 1 46 1 Egyptian years 1 460 The e . solar , or as we should say , tropical y ars name is said to b e E a derivative from Sothis , the gyptian name of Sirius , the ' Th c l dog star . e yc e began at a year when the heliacal rising of

He ro otu s I I d , , 42 CYCLES

1 that star coincided with the summer solstice . A cycle at

1 2 B . C . any rate was held to have begun with 3 2 , because Cen sorinus—De Die Na ta l i— 8 AD h mentions 23 . as the hundredt year of the next cycle . In Chaldea thi s cycle was known as the Nabonassarean 2 e 6 B . C . Period , one of which was held to have comm nced in 8 7 The Chaldean astronomers also thought of a cycle of 2 1 60 x 1 8 hi e years 4 , w ch suggests that they were acquaint d with the cycle of lunar eclipses commonly calle d the Saros . Owing to its freedom from intercalation the Nabonassarean r year was a favourite with Hipparchus , Ptolemy and othe ancient astronomers . n r a a A other ve y import nt cycle was the Greek Olympiad , f ni of cycle of our years , suggested by the quadren al celebration E i e the Olympic Games at Olympia , a city of l s . The Games wer c 1 elebrated in July and the first Olympiad runs from 7th July ,

C . im 776 B . The Games were held at the t e of the first full moon fall ing after the summer solstice and the Olympiads were there m r fore co puted from that date . The Greek months were luna and were kept in relation with the s olar year by the Metonic n t intercalations , the first month being that of the lunation ex h t after the lunation in which the summer solstice occurred . T a s being so , the first month corre ponded approximately with ff e July . The marked di erence of almost six months in the tim of th e commencement of the Olympiad year and the Julian year requires to be carefully attended to in dealing with chro l i l x e no o c ff . g a problems a ected by the Olympiad For e ampl , when it is said that the first yea r o f the Christian Era agrees with the first year of the 1 95 Olympiad it must be understood

B 1 AD . (as J . J . ond points out) that the first six months of s h 1 1 corre pond with the last six mont s of Olympiad 95 , , and A the six that the last six months of 1 D . correspond to first

1 2 . months of Olympiad 95 , s ti The Olympiad cycle is much used by historian of the me ,

but seldom or never in documents of state or inscriptions . fli i l l 1 A D . m o c a s e In 3 2 . the Oly piads were y upers ded by the I Roman Indiction of 5 years .

1 2 Hal e s o A n e i was com ute rom B . C . . cit. vol . I . 0 . s a ra t , p , p 4 p d f 747 CYCLES 43

THE METONIC CY CLE

E en qual in fame , more widely distributed and of far more e we during value was the Metonic cycl , which have already e the e describ d , and which , being xpression of an important tu e e na ral ratio betwe n the lunation and the solar y ar , has been put in requisition from the earliest times up to the present day . u se Its can be traced to an early date in China , and it constituted the ee Cal endar as the basis both of the Jewish and of Gr k , well as of the Ecclesiastical Calendar of the Christian states of Europ e . “ ” The term Metonic Cycle is properly applied to the cycle

1 - e of 9 twelve months reinforced by sev n intercalary months ,

B C . and is said to have been inaugurated by Meton in 43 2 . 1 2 e e n As 3th July , 43 , was the comm ncem nt of the first Meto ic

e 1 I B . C . 1 cycle , it follows that the y ar from 3th July of to 3th

1 AD XIVth e e . July of . was the year of a M tonic cycl A new A Metonic cycle therefore began on 1 3th July of 6 D . The

- 1 2 AD . 1 0 AD . twelve month from 3th July , 9 to 3th July , 3 e ni was thus number V of a M to c cycle .

THE PASCHAL CY CLE

The cycle of (1 9 x 28) 532 years said to have been de 1 vised by Victorius (or Victorinus) of Aquitaine was understood

A . to have been published in 463 D . by Pope Hilarius It is said that the year 463 was treated as the Vth year of a hi l 1nd cycle , w lst the second half of that year began the year ni c cl H n of a Meto c y unfortunate discrepancy which , how e ever , need not d tain us , as the lunar cycle which has been observed throughout the greate r part of the Christian Era is that usually associated with the name of Dionysius Exiguus A and said to have been introduced at his instance in 53 2 D . Under the rule of Dionysius a lunar cycle commence d with the

- the 1 B .C . last mentioned year , which implies that year was the

- 1 1 AD . . first of a 9 year cycle , the second , and so on The cycle of 53 2 years was devised as the multiple of a lunar 1 e 28 cycle of 9 years , and a solar cycl of years , and was rightly

1 B u cheriu s w o se wo rk was a c omm en ar o n is c c l e ca s him , h t y th y , ll Victo rius b t men io n m ic o rin s u t s 0 t at o ers ca hi u . , (p . 9 ) h th ll V t CYCLES

— Wa m/ cr s r AA AA. em y fi t? fi

46 CYCLES

The use of the Dominical Letter table has already been ex plained .

INDICTION

The Indiction was a cycle of 1 5 years introduced by the E 1 A D — mperor Constantine in 3 2 . . originally intended to be employed in connection with the public accounts and the col lection of the imperial taxes . Some years after its introduction the Nicene Council ordered it to be employed generally for purposes of chronology in place of the Olympiads . This enactment was conceived as an item in the general policy of christianising the order of civil society which naturally led the Council to substitute the period insti tuted by their patron Constantine for the earlier pagan style of reckoning by Olympiads .

o s The me use of the o . : i Gibb n , ch XIII , ays na and Indicti ns wh ch se rve to ascertain the chronology of the middle ages were derived e o om t u The Em o from the r gular practice f the R an rib te . per r sub scribed with his own hand and in purple ink the solemn edict or indiction whi ch was fixed up in the principal city of each diocese during two months previ ou s to the 1 st day of September ; and by a ” very easy connection of ideas the word Indicti on was transferred to the measure of the tribute which it presented and to the annual o f or h me term whi ch it all wed t e pay nt . The Indi ction as thus settled was computed to commence

1 A .D . Or with I st January , 3 3 , and is usually called the Roman

Imperial Indiction . The Indiction has been long employed as the instrument of dating by the Papal Court . Under the Eastern Empire the principal taxation appears to have taken the form of an assessment on property based on an ofli cial valuation w 1 hich was made at intervals of 5 years , and held good during im the ensuing indictional period , subject , however , to the

- position of a super indiction when deemed necessary . It follows that if the reckoning be carried back to the commencement of A the Christian Era the year 1 D . would have been the year 4 of the current Indiction . Therefore , to find the position of a year i 1 n in the ind ctional cycle , add 3 to the date and divide by 5 , whe the remai nder will be the indictional number of the year . ERAS 47

' A69 71 06 o n e rea l xa pw r iwm Tau ryci v x tvrjo-w wei d un was the f - amous postulate of Archimedes , and the calendar maker , no — l n ot) c ib ess than the mathematician , requires a r some sort

o f e . tu starting point or fix d datum Na rally for a long time , a nd whi lst the creation of the world was beli eved to have been a n almost instantaneous act , the date of that event would be regarded as the proper and obvious point of departure . The fli u l t a di c y was to scertain when the creation took place . So s ffi erious was this di culty that , with the exception of the Jews , no other people seem to have adopted that event as the ofli cial o rigin of their chronology . E e e ni be vid ntly , howev r , some u que physical event would hi — the most satisfactory datum . An event of t s description even — i f subject to a periodic recurrence provided only that its fli i ntl su c e . periodicity were y ample , would be ideal A conscious n ess of thi s fact appears to have pervaded the minds of the early c e hronolog rs , and there are indications that the heliacal rising o f e A some promin nt star , such as Sirius or rcturus , was at an e e E arly dat , both in Chaldea and in gypt , employed to supply the desideratum . By the heliacal rising of a star is meant the date when after h aving been obscured by the light of the sun it first becomes E v isible in the ast before sunrise . Some other astronomical event might have served the same purpose but none such has proved suitable . l m ia d e O y p . Recourse has gen rally therefore been had to the d ate of some civil historical occurrence conventionally selected . Era e . Thus we have the of the Olympiads , already r ferred to That era began with the victory of Coraebus in the foot race at — the Olympic Games an event which occurred on 1 7th July in

B C . 1 1 the year 776 . The Games lasted five days from the th to the 1 Hecatombeon a 5th days of the Attic lunar month , which p e proximately corresponded to July . The Olympiads w re form a lly superseded in the reign of Constantine and the Olympic 48 ERAS

AD B Games were abolished by Theodosius in 394 . ut in ebro nol ogy the Era of the Olympiads is so frequently referred to that

a knowledge of its limits is indispensable to historical students . Throughout the greater portion of the time during whi ch the Olympiads were in use the calendar was controlled by the rules

of the Metonic cycle . The arrangement apparently worked smoothl but e y, the Olympiads onlywere mployed in chronology . T r m he E a of Ro e . Another important era was that by which

the Romans reckoned , namely from the date of the supposed hi foundation of Rome . The dates of events in Roman story are usually indicated by reference to thi s starting point—the letters a nno urbis condita e to an abbreviation of , being employed i denotethe reference . Notwithstanding the un versal use of thi s datum by the Romans they differed as to the precise relation ni in which their i tial date stood to the Olympiads . Accordi ng wi VI I hi to Polybius it corresponded th Olympiad , 3 , w ch would

0 B . C . w identify it with 75 , but the more generally accepted vie T r nti . e e u s identi is that ascribed to the erudite M Varro , who

fi ed i VI B . C . e it w th Olympiad , 4 753 This date is support d 1 is by Cicero and Plutarch and is adopted by Censorinus . It now generally taken as the proper conventional commencement

of the Era of Rome . V his According to arro and as confirmed by. Plutarch in Lives o Romul us a nd Numa e f , the foundation of Rom took place 2 1 st on April , which date was also the birthday of Numa , the

the reatest . second and . g of Roman kings This therefore was the date from which the Era of Rome was B ai computed . Mr ond makes the curious mistake , again and ag n e hi repeated , of confounding the dat from w ch the era was com hi puted with the date from w ch the calendar year was reckoned . r b ass r i e w E a of Na on a . Th s early Chald an era began ith 2 i B . C V111 2 . e e 747 . Olympiad , A knowl dg of this era s now of no value unless to those specialists who study the chronology

of antiquity . It was of high importance in an age and to a civili sation once great and powerful though now remote and little known . It need not therefore further detain us . 1 De die a ta l i c 2 1 N , . . 2 In this yea r Nabona ss ar ove rthr ew the Assyrian Em pire and fo un de d B a l onian th e by . ERAS 49

In early times various other eras enjoye d a short and partial er e the Era e e Era obs vanc , such as of Al xander the Gr at , the of

e etc . e e be . Tyr , Thes n ed not described The J ulian Era or date of the institution of the Julian Calendar r e might ve y fairly have be n adopted as a starting point , but e e e e m e the Era of th r is but scant evid nc of its e ploym nt , Rome having retaine d its ofli ce as the initial date for some consider E i able time after the e stablishment of the Julian Calendar . v dentl u e y Caesar , with his us al sagacity , discourag d any change f not require d to make his great reform complete and ef ective . Another n ot inappropriate date was afforde d by the Battle of v i Actium , which signalised the irtual establ shment of the

Roman empire . There are traces of the use of this date under e Era the nam of the of Augustus , but its adoption was never

complete or widespread . For a short time the Christian Church treated the memorable p ersecu tion under Diocletian as an era date from which events A were reckoned and which corresponded to 284 D . Prior to the short - live d use of this era the early Christians sometimes em e Era u ploy d the Alexandrian , which drew back to a s pposed e e E Creation dat , though it cannot claim a truly anci nt gyptian usage . The ewish E ra Th m j . e co mencing era employe d when the e Jewish Calendar was in use , was the suppos d date of the

Creation . This event in the Jewish calendar is assumed to have happ ened 376 1 years or 3760 years and three months before the 1 AD e I st January of . The J wish civil year began with the month e e e Tisri , the comm nc m nt of which coincided as nearly as possible with the autumnal equinox .

Kal i u ee In India an era known as the y g has b n employed , u e e e e 1 0 B its ass m d comm ncement b ing the y ar 3 2 . C . to 2 B C In China the commencing date seems have been 397 . . of B e In the chronology ishop Usher , which has b en widely e E e e popular in modern tim s in ngland , the Cr ation dat is taken

00 B . C . thi e e e i e as 4 4 , but s dat has nev r be n util s d as an era to reckon from . Perhaps the curious student may be able to discover some general principle to account for so widespread a disposition to

P . C . 50 ERAS refer the Creation to a date some 3 000- 4000 years prior to the commencement of our era . S everal eras seem to draw back to the — date of the Deluge the traditional bel ief inwhi ch waswidely dis E tributed in the countries adjacent to the astern Mediterranean . The Christ a Er hi i n a . T s era will be dealt with in the following section . Era o r Era the e f the Hegi a . The of H gira is the only other era which we require to mention . The Mahometan Lunar Calendar e 1 6 6 A D th 22 . . e is computed to have comm nced with th July , , ’ fli i ni Prophet s ght hav ng taken place on the preceding eve ng .

XIII THE CHRI STIAN ERA

The custom of computl ng dates from the Incarnation did not come into use until a considerable time after the foundation of the Christian Church . Its introduction is usually attributed to Dionysius Exiguus ni l e (De s Petit) , said to have been a Scythian monk and Abbot of Rome early in the sixth century , who was also credited with E the establishment of the aster cycle of 53 2 years . The generally accepted account of Dionysius is taken from ’ B e e e L Art de the great chronological work of the n dictin s ,

’ eri er l es da tes v fi , from which it is copied without comment into cyclopaedias and books of reference . Mr F . A . Arbuthnott , in M steries o Chronol o y f gy , states that it was seriously questioned by a Jesuit Father Hardouin in a work on the chronology of the e Old Testament about two hundr d years ago , and may probably be to some extent fictitious . It seems doubtful if there was in ffi the sixth century any such o ce as Abbot of Rome , but Mr Arbuthnott was not fully informed as to Dionysius and seemed 1 ignorant of the account given by Petaviu s .

1 P etavius re co rds th e text o f a le tte r by Dionysiu s to a bis ho p n am ed Petro nius a s fo ll ows : Q ui a ve ro S an c tu s Cyrill us p rimum cycl um ab an no Dio cl etiani 1 53 co epit et ul tirn um in 247 termin avit N05 a 248 anno ej us dem tyranni po tius q u am p rincipis inc ho antes n o l uimu s circ ul is no stris m emo riam irnpii et p ers e cu to ris inn e cte re ; s e d m a gis e l egirnu s ab in cam ati on e Domini Nos tri Je s u Chr isti annorum tempo ra p rae no ta re : q u atenu s exo rdium S p e i i xis eret et c au s a re ara tionis h um anae id e st as s io no strae n otius nob s e t , p , p ” P av 11 A 8 c e r et . . . . Redempto ris nostri evidentiu s e l u et . pp p 49 THE CHRISTIAN ERA 5 1

There is no harm in assuming that someone named Dionysius early in the sixth century took in hand the adjustment of the E s e e 2 e e Victorius a t r cycl of 53 y ars , already invent d by of

Aqu itaine . His object seems to have been to make the first e t e the u e cycl star from the dat of Incarnation , and th s incid nt he e the of ally was cr dited with introduction Incarnation datings . No otherwise can we justify his alteration of the chronological position of the lunar cycle which had hitherto been treate d as

e e the e e . e a cons cutiv continuation of M tonic cycl At any rat , if be e e e the common story is to accept d , som thing lik this was h e . e D what did He mad the year we now call 53 2 A . . the first of n e h i h ew I B . C h be t e e . e a cycl , t us making (wh ch took to y ar of the Incarnation) to be the commencing year of the first E e e of ast r cycl 53 2 years . In arriving at the date of the Incarnation Dionysius is under stood to have accepted the widespread tradition that Christ was the 28th y e the e of hi born in ar of r ign Augustus . T s is the state 1 e ment of Cl ment of Alexandria .

e e e com Dionysius , howev r , f ll into rror in computing the m encement of that reign which he assumed to be 727 the e the e e y ar inwhich Octavius adopted nam or titl of Augustus , whereas in point of fact his reign was always computed from th B e e z u d e 2 A . U . C . dat of the attle of Actium , Septemb r , 7 3 3 1 The position can be best understood by reference to a tabular statement of corresponding date s commencing with B e m the attl of Actiu and which we here subjoin .

2nd Se A d e of h of c m . 2 . U . t e B e u . pt 7 3 C . at attl A ti Se —Se . 2 . 2 I st e r of u s u s pt 7 3 pt 7 4 y a A gu t .

Se - Se . 0 1 8th e r of s s . pt 75 pt . 75 2 y a Au gu tu th D 2 ec 0 B of r s B . C . 5 . 75 irth Ch i t 4 I st an 1 — l s Dec 1 1 nno r s B . t C .C . J 75 3 . 75 A h i ti 3 I st an —I Dec n o 1 A . st n r s D . J 754 3 . 754 4 A Ch i ti

DATE OF NATIVITY

Valuable assistance in ascertaining the probable date of the

e ve the o of e the Incarnation is d ri d from chron logy H rod Great , a s e e r cord d by Josephus .

1 S tr oma ta 1 1 , , 2 . 52 THE CHRISTIAN ERA The cardinal data are b the (1 ) That Christ was orn during reign of Herod . e f (2) That H rod died during the in ancy of Christ . 1 Now Josephus state s that Herod die d in the 34th year of his reign , counting from the death of his rival , Antigonus , and the 37th year counting from his nomination as king by the Roman

Senate . 2 Agai n Josephus states that the Battle of Actium was fought ’ in the seventh year of Herod s reign . Commentators are agree d ’ that in reckoning the dates of events during Herod s reign e the Josephus always comput d these from death of Antigonus , h e e 2 e i . e . and cons quently died 34 7 7 y ars after Actium , ’

A U . C . B . C . he died 750 . 4 Christ s birth was therefore shortly before that date . Josephus also tells us that Herod die d shortly after a lunar hi 1 0 eclipse , presumably that w ch occurred on 3th March , 75 e and that he di d before the following Passover , and

e a 0 A .U . C . therefor in the latter half of M rch , 75 (Care must be taken to distinguish between Herod the Great r e e who reigned at Je usalem over an xt nsive area , and Herod e Antipas , who after his death was tetrarch of Galile and was e present at Jerusal m at the time of the Crucifixion . ) e hi It is point d out by Hales that the chronology of P lip , who e e ffi e Iturea succeed d H rod the Great in the o ce of t trarch of , confirms the date of the death of Herod the Great as having been 750 because Josephus states that Philip died in the h ni 20t . year of Tiberius , after gover ng Trachonitis 37 years i 0 A 3 n U . C This brings the begin ng of his reign to 75 . . Further light as to the date of the Nativity is sought for from the e e 1 2 passag in Luk ii , and

And c me to ss in ose s ere e out ecree it a pa th day , that th w nt a d r m es r u s u s the wor s ou be xe s o C . f a a A gu t , that all ld h ld ta d (And thi x n was s m de e C ren us was over or of S r And ta i g fir t a wh n y i g n y ia . ) be xe e er one o hi s o en to v wn t . all w t ta d , y int ci y

4 Josephus informs us that a taxing by Cyrenius was fini shed ’ th e e in the 37 y ar of Ca sar s victory over Antony at Actium .

1 2 A I I 8 e l n i . . B l d . 1 8 Anti xv nt . 2 . . 2 . q XV , 7 , 3 , q , 5 , 3 4 A n I I I o s i . I 6 Anti I I . s e u t . . 2 J ph , q XV , 4 , q XV ,

54 THE CHRISTIAN ERA

e e e Arch laus Cyrenius came at that tim to Syria , b ing sent by

Caesar to be a Judge of that Nation , and to take an account of ” e e Co onius th eir su bstanc . Aft r mentioning that p was sent hi m to e the e on with have supr me power over Jews , he go s , “ e en u e hi now Mor over Cyr i s cam himself into Judea , w ch was e e add d to the provinc of Syria , to take an account of their the e substance , etc . On whol it looks as if Luke had in his 6 A D mi e . . nd the c nsus made or at least finished in , and that his parenthetical sentence was intended to connect the taxation completed then with an e arlier enrolment . Luke certainly does not say that Cyrenius was Governor of Syria when Joseph and B e the Mary went to ethleh m , and question cannot be regarded as settled without definite evidence as to the date of the Decree e e e r of Augustus and the subs qu nt n olment in Judea . It can hardly be affirmed with confide nce that the evidence of these inscriptions is sufficient to upset the defini te statement of Matthew that the massacre of the innocents took place during the infancy of Christ . It seems as likely that Luke writes loosely

the . e as to census , or that his text is in some word corrupt Mor e over the traditional view , as we may call it , is support d by early extant writings of the fathers and the fact of the massacre innocents thou h r of the , g not referred to by Josephus , is confi med 1 ni Tol doth eshu by Macrobius , and also by a rabbi cal work , j ; 2 e although the latter is admittedly not a reliabl authority . These computations cannot be exact to a year without more precise kn owle dge than we possess as to the day and month from which the commencement of the year was reckoned by different e — writers , and the exact dat of the death of Antigonus but they obviously confirm the Vi ew that Dionysius made a mistake of — at least 3 4 years . According to the chronology now f or so many centuries e adopted by historians and chronolog rs , Christ was born on h 2 th e e 1 B . C . t e 1 5 D c mber of , and following (Saturday) st 3 r 1 AD . e e Janua y was the first day of Astronomers , how v r , are

1 S a tu a l ia I I 0 . rn , , 4 2 ’ Th e w o e su e ct is ul is cu s se in P ro e s so r Ram s a s wo rk The h l bj f ly d d f y , ' on the Trus twor thiness o the New Tes ta ment B ea ring of R ecent Discov ery f . 3 B t i s re ckonin th e in e rval etwe en an ate in s a 1 00 B .C . an d the y h g — t b y d , y, e in 00 is not I o o but e ars . s ame dat 9 AD . p 999 y THE CHRISTIAN ERA 55

’ in the habit of treating the actu al year of Christ s birth as a i A D . 1 B . C . e . z ero year or 0 . and calling the year pr vious Th s difference of reckoning has given rise to considerable trouble e bu t the m e e e and som confusion , in antime both parti s adher D m . e e to their own method of co putation Prof ssor Morgan , ’ e the e B ook o for exampl , adopts astronomers r ckoning in his f Al ma na s em c . As a math atician he naturally inclined to the ’ o e e astronomers meth d . In certain cas s chronological probl ms ’ of nicety are fu rther complicated by the astronomers rule of

e e e comm ncing th ir day with noon , whilst chronolog rs , his torians and the civil population generally begin it at midnight . The diff erence of method in re ckoning the year of the Nativity gave rise or at least gave colour and encouragement to the dis putes which in 1 800 and again in 1 900 took place as to whether these years were the last of the old or the first of the new cen ’ r the e e the en tu y . Under astronom rs rul latter View seemed titled to more support than it received .

DATE OF THE CRUCIFIXION

Indirectly the settlement of the date of the Crucifixion has e of the e also a b aring on that Nativity . It has a mor important bearing on some of the questions which have been agitate d as the E to date of aster . The problem may be best presented under successive stages .

I . It must be accepte d as beyond all question that Christ f The e a e su fered under Pontius Pilate . Gosp l narr tives by th m f or e are the selves leave no room doubt , and th y supported by 1 absolu tely indep endent statem ent of Tacitus that Jesus suffere d death in the reign of Tib eriu s under the procurator Pontius 2 e e Pilat , and also by Jos phus 2 II . Now we have it on the au thority of Josephus that Pontius ’ Pilate s tenu re of the ofli ce of procurator of Judea corresponded ’ the 1 f — 0 o e u i . e . 2 A . D . with last years Tib ri s s reign , from 7 37 These then are the limits within which the year of the Cruci fi xi on must be found .

III . We have the fact that Christ was crucified on the day e e after he had eat n the Passov r with his disciples . The state

1 2 3 Anna l s . Anti I I A i I . I . nt . I I 2 , XV q XV , 3 q XV , 4 , . 56 THE CHRISTIAN ERA

v 1 1 1 2 xxu ments of Matthew xx i , 7 , 9; Mark xiv , ; Luke , 7 , I i and John xiii , , are on this point unan mous . The suggestion a that they are all wrong , and that the L st Supper was not the e Passover Feast , seems to be too far fetched to be t nable .

IV . The Paschal Lamb was eaten in the first month on the E 1 . 6 4th day of the month at even ( xod xii , ; Leviticus xxiii , 6 5 ,

V . The Jewish months were lunar and commenced with the

first visibility of the new moon , probably a day after the actual 1 conjunction . The 4th day of the moon was therefore generally l l moon the day offu .

The Jewish day ran from sunset to sunset , and it might therefore be supposed that on a strict interpretation of the text the Paschal Lamb was eaten on what we should call the eveni ng 1 1 ni of the 3th day or just after the 4th day , by Jewish recko ng , had begun . In point of fact , however , the evening of the I 4th day meant the afternoon of that day— the interval from about — m . . 3 p . to sunset just before the close of that day

Levit. xxiii 2 That this is the true interpretation is shown by , 7 Al so on the tenth day of this seventh month there shall be a day o eme of at n nt . 1 0th as The of Tisri is observed the great day of atonement . Now verse 3 2 is as follows : ‘ be u o ou of es e s afll ict o It shall nt y a Sabbath r t , and y hall y u r s ou s : the of the mo eve rom eve un o eve l in ninth day nth at n , f n t n , o r shall ye celebrate y u Sabbath . h hi l ot . T s Sabbath was the of Tisri It would seem , therefore , that the expression by which they referred to the evening with B which the l oth day began was the ninth day at even . y analogy ” the 1 da e words On the 4th y of the month at ven , would 1 mean the evening at the close of the 4th day .

n Exo us xii 1 8 re s : In the rs mo on the ou ee Agai d , ad fi t nth , f rt nth da of the mo eve e s eat u e ve e re u the one y nth at n , y hall nl a n d b ad , ntil ” mo eve and twentieth day of the nth at n . Now if in thi s verse it were meant the even with which the

di e one and twentieth day began , that rea ng would exclud the whole of that day . Such a result would be directly contrary to x 6 hi a Levit . x iii , , in terms of w ch the fe st of unleavened bread THE CHRISTIAN ERA 57

e 1 b gan on the 5th and continued seven days , thus including 1 2 e e h I st . t e the z Moreover , Jos phus xpressly states that second h 1 day of unleavene d bread was t e 6th of the month . The the e VI . day of Crucifixion is stat d by all the four 3 to e n a a a /c evi Gospels have been the pr paration , p j , the common h e t e e . nam for Friday , the day before J wish Sabbath It is true “ t the the hat St John calls it preparation of Passover . Some commentators have suppose d that that expression means a day But e e precedent or preparatory to the Passover . th r is no trace 4 o f su ch a day in the Jewish ritual . The preparation of the Passover was simply a familiar description of the particu lar hi e e e e Friday w ch chanc d to fall at the c l bration of the Passov r , E E th pretty much as we speak of aster Monday . ach of e s ynoptic Gosp els sp eaks simply of the preparation of the Sab e e be bath . Moreover th r can hardly any doubt that the day fol a the lowing was Sabbath , and that next day , being the third a ni ccording to the ancient inclusive recko ng , was the first day

of the following week . There can therefore be no reasonable doubt that the Crucifixion took place on a Friday . Great diffi culty has b een found in the statement in John 2 8 xviii ,

Then l ed they Jesu s from Caiaphas unto the hall of Judgment : and was e r and e emse ves wen not n o the u d me it a ly ; th y th l t i t j g nt hall , l es e s ou be defi l e d but e m eat the sso e t th y h ld ; that th y ight Pa v r .

Thi s verse has led to an immense amount of dispute and dis c us i n s o . It apparently implies that the High Pri ests ate the

e e Passover a day later than J sus and his disciples . Innum rable

e ff e . h e . a t e e xplanations hav been o ered , g ( ) that Last Supp r e we e was not a Passov r , a view which set asid as quite unten able ; (b) that there was at Je rusalem a stricter sect who com u te d t m e of p the new moon as at the ac ual ti conjunction , to w i e e who h ch s ct Christ adh red , and a popular sect computed the e e to be it as at the first visibility of cr sc nt , which Caiphas

1 This a rgum ent is fre q u ently a dvance d by B ede in his E ccl esias tical His tor y . 2 Anti 111 1 0 q . , , 5 . 2 a xxvii 6 2 a rk xv 2 uke I II o n Xix 1 M tt . , ; M , 4 ; L XX , 54 ; J h , 3 . 4 ark xv 2 ex re ss e ne s the re ara io n as th e da e o re the M , 4 p ly d fi p p t y b f S a a bb th . 58 THE CHRISTIAN ERA longed ; (c) that owing to weather conditions the re was on that — occasion doubt as to the exact day of first visibility a thing which actually happened so often that s pecial provision was e mad for it in the Jewish Calendar . This view seems to be more likely . The ff e e e e di erence may have b en , to some xt nt , responsibl for the feud between the Qu artadecimans and the Quintadeci e and mans which convulsed the Church in the fourth c ntury , which possibly arose out of the discrepancy in question , though e its entire complexion soon und rwent a change . The difli cu l ty of course may be due to some mere clerical t n t error or obscuri y in the Gospel MSS . At any rate it need o detain us for it cannot be allowed to disturb the clear and con e e e n sist nt evidence of all the oth r authorities as to $ th day whe

Christ ate the Passover and the day which he died . With ‘ on these data the question resolves itself into the astronomical : e e AD the problem To find in which year b tw en 27 and 37 . e first full moon after the vernal equinox f ll on a Thursday . i e . With th s problem the astronomers have wr stled long Hales , hi m 1 A with the astronomical evidence before , favoured 3 and James Ferguson , a very sound and careful astronomer 1 A D But chronologer , selected 33 . . . the bulk of astronomical i 0 AD a opin on most strongly favours 3 . In that year it is said new moon would probably have been visible on the evening of r we th 23 d March . The day call 24 March would therefore be Th 1 6th 1 . e the st of Nisan 4th Nisan would be Thursday , h A D 2 t e th 0 . April , and Crucifixion , Friday , 7 April , 3 . . m e he in This would ak the age of Jesus , assuming was born i B C . tw e n 4 . , be een 33 and 34 years , which entir ly harmo ses with the statement of Luke that at his baptism by John he began to 0 e e the e be about 3 years old , suppl m nted by generally accept d view that his public ministry thereafter laste d rather over 3 or 3 31 years .

1 An an c ient ra ition t at C rist was cru ci e on 2 th a rc 2 h as o n t d h h fi d s M h , 9, l g re c eive cre en c e b ut In 2 .D . is an I e o n Sun a 1 th A ri the d d ; 9 A N 4 f ll d y, 7 p l , revio p u s fu ll m oon b ein g prio r to the e q uinox . 2 i n vo l I . 6 0 a so S e e ourna l of B riti s Astronomica Asso c atio . XX j h l , , p 3 ; l ’ H B on s a nd B ook . xxxvi 2 2 2 2 2 . d y , pp , , 2 Luke sta tes that the baptism o f Je s us to ok plac e in th e fifteenth ye ar o f THE CHRISTIAN ERA 59

Although there seems reason to accept the View that the idea of the Christian Era was first suggeste d in connection with the

me E e 2 A . D . readjust nt of the aster cycl by Dionysius in 53 , it was several centuries later before the u se of Incarnation datings m The e e beca e at all general . arliest or one of the arliest to e the Be of employ th m was Venerable de Jarrow , a man whose influence on the Continent was far greater than is usu ally sup who em e em Histor o En l and posed , and ploy d th in his y f g , written in the first qu arter of the eighth century . It is to hi m f I A D the that we owe the actual date o . . Assuming that Nativity e on 2 th e em e he e the e took plac 5 D c b r , 753 treat d y ar h th A U . C . 1 AD . t e e e e e 754 . as This is accept d rul , assumed dat

the e 2 th of e be ore 1 A . D . of Nativity b ing 5 December the y ar f ,

C . e 0 A .D . . called by chronologers 1 B . and by astronom rs

XIV THE JULIAN PERIOD

Amidst the varieties of cycles and eras it occurred to the celebrated Joseph Scaliger to devise a period sufficiently com prehensive to fu rnish a general standard of reference for one and all of them . e the e e He might hav taken p riod of y ars , which covers one complete revolu tion of the equinoctial points . He e e he e proposed , how v r , what call d the Julian Period 80 e (P . J . ) of 79 y ars . e of 1 the e e 2 8 This figure is the multipl 9 ( M tonic cycl ) , (the

- so called solar cycle) and 1 5 (the Indictional cycle) . He fou nd that by carrying each of these cycles back a com mencement of each of them would coincide with the year 47 1 3 h 1 . m . T e B C . This happy coincidence deter ine d him st January th m f e hi e e 1 B . C . e e o of y ar 47 3 he ad the b ginning his p riod , w ch not be u A D will complete ntil 3 267 . . ’ Scal i er s e De Emenda tione Tem orum ee g gr at work , p , s ms to have been written mainly with the design of introducing this

bu t be A .D Ti ri s Re ckon in rom h e a f A s s a wou 2 . e u . t e o u u tu b g f d th g , th t ld 9 , Luke p ro ba bly c ompu te d th e ye a rs o f Tiberius from the date of his a sso cia ' A tion with Au gustu s in the impe rial o fli c e s in 1 2 D . 60 THE JULIAN PERIOD

universal period to chronology , and the highest praise has been awarded to the utility of the idea by subsequent chronologers and astronomers . The period was fixed to commence at I st

January , and the rule of the Julian Period thus furnishes us with reason for re sisting any proposal to change the date of ru commencement of the year as an inst ment of dating . Few things have more perplexed chronologers and interfere d with the simplicity of calendars than the endless variations in the date of commencement of the dating year . This in no way , how u s ever , obliges to employ I st January as the beginning of the year in reckoni ng legal or commercial intervals of time or in adjusting the tables of the solar or Metonic cycles .

62 THE DATE OF EASTER

third day thereafter which , according to the ancient rule of in cl usive computation , was the first day of the following week . The three synoptic Gosp els are most explicit in their state ment that Christ ate the Passover on the day prior to his Cruci h fi xion . t e 2 8 A passage in Gospel of John , xviii , , suggests that e the High Priests were to celebrat the Passover on the Friday . No generally accepted explanation is available to account for ff the the di erence of date , and discordance led to an incredible amount of discussion and dispute in the early centuries of our era . u artadecimans Two parties , named respectively Q and Quinta

decimans . ff , divided the ecclesiastical arena It would be di icult , and is happily unnecessary , to follow the controversy in detail . Originally it perhaps arose out of the difference above referred to between the day observed by Christ and that said to have But been observed by Cai aphas . to judge from the terms of ’ Abbot Ceol f rid s letter on the rules for the ke eping of Easter 1 Be e B quoted by d , as well as from several remarks by ede him it ni self, hinged upon the question whether the eve ng of the fourteenth day meant the afternoon of that day or the previous i — ni even ng , when according to the Jewish custom of recko ng 2 e — from sunset to suns t the fourteenth day had begun . The uintadeciman uart d i former was the Q , the latter the Q a ec man e View . The l tter in question is an interesting statement of the i n e E Quintadec ma case . The Gre k or astern Church supported u artadecimans e the Q , who wer represented by Polycrates , B E B ishop of phesus ; whilst Victor , ishop of Rome , supported the Quintadecimans . Latterly the controversy al tered to a dis pute as to whether the Easter festival should be celebrated on the actual anniversary of the Passover or as a Memorial of the B Resurrection on the following Sunday . y supporting this latter uintadecimans e View the Q r taliated on the charge of judaising, e originally brought against th m by their opponents . The ques tion was finally de cide d by the Nicene Council in favour of the n revise d Quintadecima doctrine . The Christian Church in

B u artadeciman e of ritain , which was originally Q , was th n out

1 E ccl esi a stica l Histor oo k c a XXI y , b V , h p . . 2 6 S e e S e ct . I I I a nte X , , p . 5 . THE DATE OF EASTER 63

the e e re touch with Contin nt , and when Roman missionari s appeare d in the sixth century it was not without controversy and bloodshed that the Celtic Churches were ultimately per uartad im s uaded or compelled to abandon the Q ec an rule . The h istor e y of the disput has some chronological value , but l nee d not occupy more space in a survey of ca endrial problems . e e e e ee e The t rms of the Nic n D cr were long suppos d to be lost , but the purpose and eff ect of the decision have b een traditionally the e e e transmitted , and r c nt r covery of the text has not thrown a ny substantial doubt on the accuracy of the accepte d interpre u e e tation of the Nicene r le of practice . The all g d text of the 1 ee e e e E e Decr do s not expr ssly sp cify the date of ast r , but simply e njoins the brethren of the Eastern Church to conform to the e rule observ d by Rome and Alexandria . The practice of these u e Ch rch s was well known , so that there can be little doubt as to the purpose of the Council . Although this may not have been expressly defined in the the text of decree , it is admitted that the date of the Resurrection w as the first day of the week which immediately followed that u i n which the Passover was celebrated . To avoid the s spicion o f judaising it was agreed that Easter should never coincide w bu t e the subse ith the Passover date , should be observ d on the q uent Sunday . Thus rule was adopted that Easter should b e the first Sunday after the first fourteenth day of the moon e falling on or aft r the vernal equinox . It was generally assumed by the e cclesiastical authorities for AD the m any centuries after 3 2 5 . that date of the vernal e quinox f th o that year was 2 Ist March . It was said (by e late Professor M il l osevitch) that the fathers of Nicea ascertaine d the true date

e e . e of the occurr nc by means of gnomons This is quite probabl , a lthough , in point of fact , the actual hour of its occurrence in A t e 3 25 D . appears o have b en some time in the evening of the

2 0th . e to the the Owing , howev r , fact that Julian Calendar m the e of the e to 6 6 assu ed l ngth y ar be 3 5 days hours , which exceeded the tru e length of the tropical year by 1 1 minute s

1 e the u e u e 4 s conds , eq inox f ll ann ally by that amount earli r

- in the calendar . As time passed an ever widening interval

1 S ee Pi ra S icil e ium S a l esmense ome IV 1 t , p g , t , p . 54 . 64 THE DATE OF EASTER

tu 2 1 st th separated the ac al date from the March , and e object of the Gregorian reform was to provide a solution of the difli di hi cu l ties and sputes w ch thence arose . Meantime we have to explain how the date of this movable festival is ascertained in practice . The leaders of the early Church manifested a strong desire to di scover a cycle of years within the limits of whi ch the dates of E aster would repeat themselves in the same order . It is probable that their kn ow — ledge of the Metonic cycle in which the dates of new and full — moons repeated themselves in 1 9 years fi rst suggested to their E minds the desirability of seeking a cycle of aster dates . The establishment of such a cycle would also facilitate the deter E as mination of aster , and might ensure a general agreement B e to its proper date . that as it may , there is no doubt that the search for a cycle was prosecuted with vigour for several cen

tu ries . e It is unnecessary to d scribe the several very inaccurate , imperfect and purely empirical cycles whi ch were from time to e time proposed . Most of th se were multiples of the lunar cycle

1 e . 1 x 2 of 9 y ars Such , for example , as a cycle of 9 3 437 years e 1 x proposed by Theophilus of Al xandria , and the cycle of 9 5

1 2 A .D . h 95 years proposed by Cyril of Alexandria in 4 , and whic appears to have been much admired . In outlyi ng portions of the Western Church duringthe earl ypart of the fi fth centurya Quarta 8 1 x 6 8 e deciman cycle of 4 years ( 9 4 7 ) was employ d . The date of the vernal equinox having bee n assumed fixed 1 st two E on 2 March , the variables on which aster must de 1 1 2 s o pend were ( ) the lunar cycle of 9 years , and ( ) the m called solar or do inical cycle of 2 8 years . It follows that the x proper cycle is one of 1 9 28 53 2 years . Such a cycle is said to have been constructed by an ecclesiastic named Victoriu s or Victorinus of Aquitaine and to have been adopted by Pope e Hilarius in 463 . A subsequent change in the date of commenc e Exi uus m nt of the cycle , attributed to Dionysius g , was made 2 e about 53 , and the cycle thus adjusted was thereafter employ d for the determination of the Easter date up to the time of the 1 Gregorian reform .

1 The first year o f the Dionysi an c yc le co rre spo n ds to th e fo ur tee n th o f h r H ri the Meton ic an d the s even teenth o f t e cycle o f Victo in us o r il a us . THE DATE OF EASTER 65

The Easter dates f or this period of 53 2 years were compute d

1 B . C . e from , and these having been ascertained and r corded , any one in possession of such a record was equipped with a

table vali d for an indefinite period . W e must now explain how the dates to be so recorded were

ascertained . In the first place it is necessary to prepare a Perpetual Lunar e e Calendar , that is to say to tak a sk leton almanac of monthly dates on which are note d at their respective days the 2 3 5 days 1 on which a new moon would fall during the cycle of 9 years . Starting with the ascertaine d date of the new moon of January in the first year of the Metonic cycle the subsequent moons are

e ntered at intervals of 29 and 3 0 days alternately . These being the moons of the fi rst year of the cycle the number I is entered

against the days on which they occur . The moons of the next 1 1 i 1 1 . e e year occur days earlier Th r fore , days earl er the num ber e e II is ntered at the respectiv dates , and so on until the whole 2 35 new moons of the cycle have been recorded in their ” e u appropriat positions , nder the heading Golden Numbers . This being done it will be found that those years of the cycle in d viz . r which Meton introduced an embolismic month ( the 3 , th 8 I I th 1 1 6 1 th 1 5 , th , , 3th , th and 9 ) contain 3 new moons . ’ In the annexed Lunar Al manac (adapte d from that in L Art de ’ verifi er l es da tes) the first new moon of the first year falls on 23 rd 1 January and the first of the third year on the 1 st January ; and the seven thirteenth or intercalary new moons and the seven embolismic months of 3 0 days which start from them are identi fi ed with the following :

d e — — I IIr r 1 De . 1 I I Ith e r 2 c . X D 1 ec . 2 an y a 9 Jan y a 3 9 J .

- — Vrh 29 27 XVIth 28 25 — VI I Ith 2 6 2 XIXth 2 —22 —4 4 XIth 23 2 1

The annexe d table of a Perpetual Lunar Almanac shows the e positions of the new moons in each y ar of a cycle , and during

1 N a a The G . tes re o se in the . d th Julian calen dar ; the Epact date s a re e a Gr go ri n . 2 Thi s lun ation in the Me to nic c ycle wa s 2 9 days and woul d thus end o n z l st an uar but the n ext l una io n o f N I mm c G . . co en es on rd a J y ; t 23 J nuary .

P . c . 5

68 THE DATE OF EASTER the Middle Ages it was taken for grante d that these were the new only days on which a moon could occur . In order to ascertain the date of Easter for any particular year , it was only necessary to find the Golden Number of the

i . e . year in question ( its position in the lunar cycle) . This gave the dates of all the new moons of that year , from which it was a simple matter to find the first fourteenth day of the moon 1 occurring on or after 2 st March . Having ascertained that date the next step was by reference to a table to ascertain the domi ni

. n cal letter for the year in question That k own , it was easy to

find the first Sunday after that date . The day thus ascertained was Easter Sunday . The movable feasts were deducible there from in accordance with the ecclesiastical rule . W e have seen that 23 5 lunations fell short of 1 9 Julian years 1 h r ff e by oiI 29 minutes . That di er nce amounts to a day in 08 about 3 years , at the expiry of which time the new moons u wo ld fall one day earlier than was noted in the Lunar Almanac . It wo uld have been an extremely simple matter once in 308 years to prepare and publish a new table of Golden Numbers B ff . ut giving e ect to this simple correction that was not done . The dread of innovatio n or some sort of superstitious regard the e c for stablished table apparently prevented any hange , and the original scheme of Golden Numbers continued in use up to e the date of the Gr gorian reform , although by that time the new moons actually occurred about four days earlier than the dates indicate d In the table . The table of Golden Numbers could easily have been adjusted to the new Calendar . The omission of ten days in the year 1 582 required that the dates of the new moons should be shi fte d to But w dates ten days later . o ing to the accumulated error already referred to they ought to have been moved to dates four days B i earlier . y sh fting them six days later they would have been in hi e their correct places in the Gregorian Calendar . T s , howev r , — ff was not done at least not o icially . The use of the Golden ofli cial l ff Numbers was y abandoned , and a slightly di erent e dient e p was adopted by Clavius , the priest employ d by Gregory XIII to prepare the necessary tables for operating the reformed Calendar .

THE DATE OF EASTER THE DATE OF EASTER 7 1

h i at the end of the next year t e Epact will be 22 . In the th rd year it will be 3 3 but that of course means that another lunation would have been completed and that there were 1 3 new moons the 1 in the third year . The age of the moon on st January fol th lowing would therefore be 33 3 0 3 . Thus e rule for con

s tru ctin e E u e viz . 1 1 g a cycl of pacts is q ite simpl , to add to the Epact of the year preceding and deduct 3 0 when the sum ex E f or c eeds that figure . Thus the pacts the cycle in question are

If the same rule were continue d in the year whi ch follows e the e the last of this cycle (i . . first y ar of the next cycle) the following Epact would be 29 1 1 40 3 0 1 0 . The cycle But would not therefore be rep eated . it would not be correct so e : The to continue the series according to rule , for this r ason nu mbers 1 1 and 3 0 which are added and subtracted as above E described are approximations only . The exact pact or the difference between the length of the Julian year and the length of twelve lunations is not I 1 days but 1 0 days 2 1 hours 1 1 minutes and the exact length of the lunation is not 30 days but 29 days the ff e e 1 2 hours 44 minutes . To show e ct of using the xact figures we give in paral lel columns a table in which these are used (seconds excepted) and a table in whi ch the conventional figures

1 1 and 3 0 are employed . Now in this table the Epact (1 1 ) is added 1 9 times and the 0 The di 1 1 lunation (3 ) is deducted 6 times . fference between and the exact Epact of 1 0 days 2 1 hours 1 1 minutes is 2 hours m r 49 minutes , which is the a ount in excess of the t ue figures 1 — to which has been added 9 times that is say , the addition is e 1 u 0 e exc ssive by 53 hours 3 min tes . Again 3 has b en deducted 6 times in place of 29 days 1 2 hours 44 minutes ; therefore 1 1 hours 1 6 minutes too much has been subtracted 6 times ; that 6 6 too is to say , 7 hours 3 minutes much is subtracted , from

1 m e - added l eaves 1 which deducting 53 hours 3 inut s over , 4hours h t e . 5 minutes , which exactly corresponds with table But 2 1 e i 9 days 4 hours 5 minut s is more than a lunat on . e the 2 From this d duct therefore length of a lunation , 9 days 1 2 m 1 2 1 hours 44 inutes , leaving hour minutes , to which adding 8 minutes for seconds omitted gives 1 hour 29 minutes as the M ’ fi : fi h ’ r : g i ‘ u 1 c C cl a cts 21 3 Deta il of a M etoni y e of Ep z 1x3 24

Years times THE DATE OF EASTER 73 e rror at the end of the cycle , which exactly corresponds to the th error as derived from e total number of days in the cycle . e e It follows , th refore , that inst ad of counting from the last Epact of 29 it i s more correct to count from it as 3 0 and start new z e r the cycle from ro , and thus carry fo ward , to the next e e 1 2 cycl , only the true r sidual error of hour 9 minutes . Such was the principle upon which the pre - Gregorian Epact cycle was constructed . E e the e The pact was known befor Gr gorian reform , although f not used o ficially . The cycle given above commencing with E 1 1 e h t e e 1 B . pact was suppos d to have commenced in y ar C . e e e 1 2 Th re was still , how ver , the residual rror of hour 9 e e 08 minutes in ach lunar cycl , and , therefore , in the course of 3 e E y ars the pacts if originally correct would all be one day wrong . To correct the eff ect of this accumulating error in the cycle of Epacts all that is necessary is to increase each Epact by one at 0 the end of 3 8 years or thereby . This was not attended to in

re - e p Gregorian times , but it is what Clavius d cided to do . In point of fact for the sake of simplicity he proposed to increase the cycle by unity at certain centurial years only and to make the — change eight times in 2 500 years seven times at the end of 3 00 the th years and eighth time at e end of 400 years . The average interval between a shift of Epacts was thus a little over 3 1 2 ffi e e years which he considered a su ci ntly clos approximation . The readjustment of the Epacts by increasing them by unity e e e e the on th s dates has , by some writ rs , been call d lunar cor rection . Bu t there was another correction necessary In order to keep the E pacts in harmony with the new Calendar . In the Metoni c cycle the length of the year was taken to be 6 6 th h 3 5 days hours exactly . That is e assume d length under t e

u e e we . J lian Calendar , h nc have called it the Julian year Now thi s length as we know was 1 1 minu tes 1 4 s econds in excess of the e to e e true tropical y ar , corr ct which Pop Gregory XIII decided to delete the intercalary or leap day in three out of e r a f ve y four centurial years . It follows th t when the cycle o E e e e was e pacts arriv d at a c nturial y ar , which a common y ar e under the Gr gorian Calendar , the order of the cycle would be 74 THE DATE OF EASTER dislocated and the new moons would not arrive until one day later in the Calendar than the day on which they would have e arrived if the Julian Calendar had r mained unreformed . To corre ct this dislocation it was necessary that when the cycle of Epacts re ached such a centurial year the Epact should thereafter

t . be reduced by uni y This then is what Clavius resolved , and this correction has received the name of the solar correction . It will be observed that the solar correction is made in the reverse order to the lunar . The latter requires the Epacts to be one e u m d increased by , the former r q ires them to be di inishe e by one . When , therefore , as will frequently happen , we arriv at e a centurial y ar in which both corrections are required , it the e follows that at that time no change is necessary , and cycl E of pacts is continued without alteration . Clavius started with a cycle which he assu med to be operative at the beginning

t i . e . 1 00 AD . He e of the current cen ury , 5 therefore r quired a 1 00 AD e lunar correction in 8 . and thereafter he proposed to mak 00 s them at seven intervals of 3 years and one of 400 . The date when the solar correction fell due were fix ed by the Gregorian to Calendar . In the annexed table we show for the pe riod up 0 AD i are 600 . the years in wh ch each of the two corrections

e e e . respectiv ly r quired , and when they canc l each other It will be seen that in 4000 years from 1 900 there are 1 3 lunar corrections required of which 1 0 are cancelled leaving e 3 operative . On the other hand , in the same period , th re are 0 1 0 e 3 solar corrections of which of course are cancelled , l aving 20 the E s operative , the result being that successive cycles of pact

are subject to a slow nett retrogradation , each cycle being dimin — ished by uni ty as compared with its predecessor until the E e e the series of possible pacts is xhaust d , limit being determined E a can 0 e e by the fact that no p ct exceed 3 , the assum d full l ngth ar of the lunation . Of course in the rare occasions when the lun correction stands uncancelled the line of Epacts is moved in

the reverse direction . The complete table of Epacts already referred to exhibits all E possible pact cycles , and it will be observed that these are xh 000 to e austed in a period of 7 years , the cycle which applies 8 00 A 0 A 1 0 D . 5 D . being the same cycle as that whi ch applies to 5 THE DATE OF EASTER 75

Years in whic h Ye ars in whi c h o c cu rs th e Occu rs th e so lar co rre ctio n Un can c e lle d lunar co rre c tion Un c an cell e d

2 1 00

2400

3 000 3 1 00

3 3 00

43 00

4900 76 THE DATE OF EASTER

Such is the complete scheme of Gregorian Epacts laboriously b constructed y Lilius and reproduced by Clavius , but still far a from astronomically pe rfect . It has app rently served its pur o pose , and was at any rate involved by its author in such a cl ud of erudite detail that few have ventured to master its really f ew e simple rules , and , ther fore , have dared to criticise it .

- fi sh e n Clavius , like the cuttle , protected his schem by the ocea of ink with which he surrounde d it . e When , however , the full series com to be written down in their places in the Perpetual Lunar Almanac there are one or two adjustments prescribed by Clavius in order to obviate the most apparent defects of his scheme . These are : (1 ) The Epacts are entered in the almanac from 1 st Januar y e e i 0 onwards in the rev rse order , b ginn ng with 3 , which is the age of the moon when a new moon occurs just after the year a the opens . If this were continued without a bre k series would u 60 — 1 1u nati n occ py 3 days in place of 354 the true length of 2 o s . Accordingly at every second lunation the Epacts 24 and 2 5 are writte n opposite the same date . These occur in the months of 2 th February , April , June , August (I st) , September ( 9 ) and

November . The reason is obvious ; but an equally obvious con in E 2 sequence is that , a lunar cycle which contains both pact 4 E 2 the and pact 5 , a new moon would be made to fall on same day twice within a single cycle of 1 9 years . This as a physical fact does not happe n . To prevent an error so glaring an alter atE 2 6 E 2 hi native date ( pact ) is assigned to pact 5 , w ch is entered on that other date in a di stinctive character of type . This is in tende d to intimate that the date on whi ch it is so placed is to be taken and employed as the correct date when such a step is rendered necessary to avoid the dating of two new moons on the same day within one lunar cycle . An examination of the complete table of Epacts reveals the fact that in no one of the

E 2 2 26 . e series do the three pacts 4 , 5 and all occur Cons quently Epact 2 5 is quite sure to find a safe place in one or other of the two days to whi ch it is allotted . An examination of the table further shows that in eve ry series on which both 24 and 2 5 occur (that is in the se ries de b e k n r B E N 2 noted by the index letters , , , , , , , ) the 5 is found

78 THE DATE OF EASTER

D a 1 6 The cycle , however , ceased to operate with the ye r 99 notme 8 00 and will again in use until the year 5 , so that we need

not worry over this dilemma . Notwithstanding these adjustments the elaborate tables of

Clavius are by no means perfect . They deviate more or less by the E e a day or two from astronomical ph meris , and they are not even completely successful from the ecclesiastical stand

point . In the earlier days of the Church a great desire existed to ensure that the Easter date should always happen after and

should never coincide with the date of the Jewish Passover . hi s Clavius specially intimated intention to secure this result . E ven in that however he was not always successful , for in the years 1 805 and 1 825 E aster Sunday under his tables fell on the very same day as that on whi ch the Passover was

observe d . a 1 82 1 0 When the Gregorian Calend r was introduced in 5 , days were omitted from that year but no alteration was made in 1 the constant succession of years in the lunar cycle of 9 years , hence the reform involved no change in the order of the Golden

Numbers . A lunar cycle was assumed to have commenced in the year

1 A . D . r 0 A D before , called by astronomers the yea . . , and by

h 1 B .C . c ronologers the year , and the Golden Numbers have run 1 on continuously since then in successive cycles of 9, so that to find the Golden Number of any year it is only necessary to a 1 add 1 to its date in the Gregorian C lendar and divide by 9. This eliminates the complete cycles which have elapsed since

C . e I B . and the remainder giv s the Golden Number of the year

in question . If there is no remainder it is the last year of a cycle 1 and the Golden Number is 9. Dates for the new and hence for the full moons were assigned to each of the 1 9 years of ' the cycle and these were repeated

for centuries , cycle after cycle , with the result already indicated that in the course of time they had moved away several days from the astronomical date . In the sixteenth century the astronomical moons happened about four days earlier than their assumed

date in the lunar cycle . We have already shown how , at the the time of reform , if the new moons had been moved six days THE DATE OF EASTER 79 l ater they would have regaine d an approximately true position i n the Calendar . This in effect is what Clavius did only (1 ) in order to avoid collision with the Passover he assume d the error of four days which had grown up to be only three ; and (2) in place of the h E Golden Number he inserte d t e pact . The cycle of Epacts applicable b efore the reform was that Th E indicated by line C . e line of pacts brought into operation D a fter the reform was that indicate d by . The Golden Number of the year 1 582 being 6 its Epact was e e 1 00 e C e e 2 6 . This line continu d in forc until 7 , when lin b cam

e em e 1 00 e o perativ , and so r ain d until 9 , wh n a transfer took 1 00 e place to line B . The year 9 b ing the first of a lunar cycle E i e 1 2 . ts Golden Numb r was , its pact was 9 In reference to the Epacts line D a rather misleading state ment is made by Professor De Morgan in the B ook of l ma na cs : A (p . xiv) h The year 1 577 was t e first of a lunar cycle . A cycle of line D

t e . E 1 1 2 2 herefor started with that year These pacts are , , 3 , 4,

1 26 1 8 2 1 0 2 1 2 1 2 1 6 2 8 1 . But 5 , , 7 , , 9, , , , 3 , 4 , 5 , , 7 , , 9 this series was e 1 82 not really put into op ration until 5 , which being the E s ixth year of the cycle had for its pact 26 . De Morgan prints the cycle commencing with this number “ He 1 8 1 a nd 1 . 2 6 1 ending with 5 says from 5 to 99, 9 is used

0 E 26 . a s 2 and the cycle of pacts is , 7 , etc This reads as if an unexplained saltus took place in the middle o f the cycle whereas in fact 1 9 was the Epact of the last year of the the e the cycle , and saltus is usual and r cognised saltus a lready explained as made at the end of each cycle to enable the c ycle to be again repeate d . 1 6 e E Again 99 was the ninth y ar of a lunar cycle with pact 29. the e According to rule cycl was not completed , but a shift was m e C 1 00 a the E ad to line in 7 and of that ye r pact was 9, being the Epact of the tenth year of that cycle . De Morgan tells us that for the passage from 1 699 to 1 700 o 1 0 e e to 1 8 1 8 1 nly is add d , and from th nce 99, is used as 9 and E 20 1 1 2 2 1 2 6 1 8 0 1 1 the cycle of pacts is 9, , , , 3 , 4 , 5 , , 7 , , 3 , ,

2 2 1 2 6 1 28 . e , 3 , 4, 5 , , 7 , The xplanation is of course that in 80 THE DATE OF EASTER passing from 1 699 to 1 700 a shift is made to a new line of ” E t 1 8 1 pacts diminished by uni y , and that is used as 9 for

e e e viz . xactly the sam reason as alr ady indicated , to comply the e with rule which was appli d to the last year of each cycle . B De Morgan then gives the cycle correctly , but without

a nte . 6 finding room for the explanation already given ( , pp 7 , 77) 2 e 2 6 for 5 b ing treated as in the course of this particular cycle . A D We have already explai ned that since 3 25 . . the accepted date of Easter Sunday has been the Sunday after the first 1 4th day of the moon falling on or after the vernal equinox . As it 1 5 1 was the Sunday after that moon it could not fall on 2 March . The earliest possible date for Easte r was therefore the 22nd 20th e 1 March . If a full moon fell on March the n xt 4th moon would not occur until 1 8th April . These dates are known as e E the Paschal Term . The latest possibl date for aster Sunday 1 th viz th h 8 . 2 . t e would be seven days after April , 5 April Thus festival oscillates with an amplitude of 3 5 days . Various ingeni ous tables have been prepared for enabling

Easter to be ascertained over a longer or shorter period . Prob ably the best of these is that printed in the Church of England — B B e . Prayer ook said to have b en constructed by Rev Dr radley , 1 2 was the Astronomer Royal in 75 , when the Gregorian reform f of legalised in England . The whole of the thirty di ferent lines Epact cycles which compose the Calendar Table of Epacts are covered by thi s table whi ch is valid for the whole period of But f are s 7000 years . these di ferent lines not identified by letter th E of e alphabet as in the Table of pacts , but are numbered B ’ i successively from 0 to 29. At the left of radley s table s a column containi ng the possible dates of the Paschal Full ar Moon from 2 1 st March to 1 8th April . In the next column e recorded the week day letters applicable to each of these dates . To the right are placed 1 9 columns numbered successively e 1 one being appropriated to each year of a lunar cycle . Th se 9 columns are fille d as follows 1 82 E e 0 Starting with 5 , when the cycle of pacts numb red e 0 cam into operation , the figure is placed opposite the Paschal

Moon of that ye ar . The full moon of each following year would hi e of course always fall 1 1 days earlier . In t s way the dat s of the THE DATE OF EASTER 8 1 82 THE DATE OF EASTER

E first cycle of pacts are filled in . The next cycle , which in this 1 table is numbered , would fall one day later , and so on with each successive cycle . In this very simple way a reliable table 000 of the Paschal Full Moons for 7 years is completed . Having ascertained the date of the full moon all that is necessary is to refer to the year letter and find by the Table of Dominical hi B Letters , w ch in the Prayer ook is printed alongside of the

the table under description , on what day of the week Paschal Moon occurred and what therefore was the date of the next

Sunday . Many other tables have been devised with more or less in i r enu t . g y, but it seems unnecessa y to describe them , If the reader has succeeded in following our explanations of the simple principles on which they must all be based he should have no ffi di culty either in using or understanding them . We may in conclusion point out that in a Perpetual Lunar Calendar a given Epact may occur much more frequently on certain days than another does on other days . Thus for the hi 22nd year in w ch the almanac gives a Sunday on March , E there can only be one pact , for those in which Sunday falls on

2 3 rd March two and so on up to seven . ni E viz One conve ent use of the pact may be noted , . to find the age of the moon on any given date of any month of any year E E . of which the pact is known Take the pact , add to it the number of the month counting from March and the day of the ’ 0 month . If the sum be less than 3 it equals the moon s age , if ’ more than 3 0 divide by 3 0 and the remainder is the moon s age . This rule only applies to the 1 2 months counting from 1 3 1

March . PA RT I V

XVI THE U SES OF THE CALENDAR

HE CALENDAR is require d for two mai n purposes T : to x da tes I , and primarily fi ; that is , to supply a continuous register of days , months and years on which we can record in their prop er place and order the dates of past and future events and engagements . measure II . To furnish an instrument whereby we may out s t m equal interva l of i e . (I) The dates to be recorde d are either

1 . e Physical or natural ev nts or phenomena .

i s . 2 . Civ l events or appointment E e 3 . cclesiastical vents or appointments . In each of these cases we should distinguish between past and future events . E 1 Physical events . These include the phemerides : the regu eriodic henomena o lar astronomical p p , the equin xes , solstices , eclipses , transits , appearances of comets , etc . ; and terrestrial

e e : . ph nom na tides , seasonal changes , harvests and so forth It e ast the e will be not d that , as regards the p , in addition to r gular ephemerides we also require to re cord exceptional cataclysmic non - periodic events both celestial and terrestrial (including such the as earthquakes , storms , volcanic eruptions , tidal waves and

i e . uture e l k ) As regards the f , the r cord of periodic events is still — more important indeed the recording of these by anticipation

. e e is one of the main objects of a Calendar Irr gular , xceptional , non - periodic events cannot of course be predicted and the ture a Calendar of the fu cannot cont in any such . A class of almanac has been continuously published for many years professing to foretell the occurrence of future non - p eriodic e events , both physical and civil , but these if they are now s riously

6—2 84 THE USES OF THE CALENDAR intended have no scientific value and need not be further re ferre d to . hi a 2 . Civil or storical events . ( ) As regards such events oc curring in the course of human history the record ofpast events of this class is one of the principal uses of a Calendar . A proper record of dates is the true framework of civil history , without whi ch no clear and adequate kn owle dge of human hi story is possible . To record these events at their proper dates is the object of chronology . (b) As regards thefuture what we require to record are chi efly cyclical or periodic events and appointments . The terms of the an possession of houses and l ds , the terms of payment of rents s and interests , salaries and wages , the recurring dates of market , authori fairs , sessions of law courts , of Parliament and of local

e ties , the terms of schools and universities , the dates wh n names must be enrolled , returns lodged , claims intimated , the close i times for game , publ c holidays and festivals , birthdays and commemorative anniversaries , etc . With few exceptions these r futu e civil events are recurrent and periodic .

3 . A third class of dates is composed of the dates of the ast ecclesiastical Calendar . These also may be divided into p and uture recurrin f g events , on a principle similar to that applicable the E — to civil dates . The ascertainment of date of aster the — principal future date of the ecclesiastical Calendar has domi m the r ated whole histo y of Calendar construction , and involve s a l l a curious composition of physic and civi cycles .

(II) The Calendar as a measure of intervals of time . The second and hardly less importa nt use and purpose of the

Calendar is to provide a means of measuring intervals of time . hi Contracts of ring , whether of lands , houses , shops or of the loan of money , or of labour or services , are usually made for a fixed interval of time and the remuneration is estimated by reference thereto . A uniform or standard interval is required for these purposes . Accounts of monetary transactions are , or a nd e should be , closed balanced at fix d intervals , and these if possible should have a simple and definite correspondence with th ni e periodic times of payment . Recurring intervals of u form or standard length are desiderated also for the efli cient use and

86 THE DEFECTS OF THE CALENDAR

— th times not to the Gregorian . The only part of e trouble for which it can be held responsible is the confusion whi ch has — arisen between the use of the old and new style a confusion due exclusively to the unfortunate circumstance that the Gregorian Calendar at its introduction was made to take effect retro l e the A spective y as if it had start d with year 3 25 D . Had it been introduced to operate for the future only and commencing with the date of its introduction no such confusion would have arisen . The different dates of commencement of the year and the diff erent date s at which the Gregorian Calendar was adopted by diff erent countri es have also been responsible for certain complications , but these are not in any way attributable to the construction of the Gregorian Calendar itse lf . With the addi ’ tional assistance derivable from Scal iger s comprehensive device of the Julian Period no more conveni ent system of date record ing can be imagined ; and any change calculated to disturb the t e continui y of our dating system is to be d precated .

F t re . 2 (b) . u u civil events and appointments In the case of certain dates of this class the existing Calendar is satisfactory . l i E This app ies to dates wh ch , like the phemerides , are recorded r u e without variation on the t e day of real or assum d occurrence .

e - to Such dates have been call d dates absolute , or , borrow a

- e . e term from the Roman Cal ndar , dates stative They includ ni most commemorative an versaries , birthdays , death days , e e dates of gr at actions , discoveri s , reforms or other political or hi as storical occurrences , also such fixtures the close times of hi e game w ch are directly based on an assumed s asonal necessity . The great majority of future civil dates however involve a — double reference i . e . both to the Calendar date and the occur e fl rence of the week day . In these cas s the constant uctuation in the relation between month day and week day seriously dis

tu rbs the operation of our present dating system . Such dates may be divided into two classes Cl ass A 1 e , including ( ) l gal terms , dates of sitting and rising

e . of law courts , schools , universiti s 2 tu e ( ) Sta tory dat s for meetings of magistrates , town and

county councils and other local authorities , dates for making t statutory re urns and lodging claims . THE DEFECTS OF THE CALENDAR 87

e e e m (3) Quarterly t rm days , mon y payment and removal t r s ,

maturities of bills . e i e e l a i (4) C rtain civ l f t days , national ho id ys and ann versary

celebrations . Cl a ss B 1 the e , including ( ) movabl feasts of the Church , E aster and its consequents .

2 etc . when xed ( ) Meetings of magistrates , local authorities , , fi r r r d s f o pa ticul a week ay .

(3) Local markets and fairs .

e e . (4) Local f stivals , holidays and cel brations These all depend upon a joint adjustment of month day and the A the e e fi x week day . In case of Class v nts are ed for a particular Calendar date or f or the first lawfu l day next ensuing

or next preceding . The month day alone does not determine the

- r e . c o e e obse vanc It is the primary ordinat , but the obs rvance e must also avoid a Sunday or other legal blank day . Wh n the e e e Cal ndar dat in such cases coincid s with a Sunday , it is usual to provide that the actual observance shall take place on the

first lawfu l day before or after .

- In the case , for example , of the Scotch half yearly term days , it is provided that if these fall on a Sunday the term is observed th on e day following . e e 1 2 th In lik mann r , if st January or 5 December falls on a the B k Sunday , Scotch an Holiday which is enacted for these th days is observed on e Monday following . The Cou rt of S ession in Scotland commences its Winter S ession on the 1 5th of October or the first sederunt day there

e . u u e aft r The sederunt days of that co rt are T sday , Wednesday , 1 Thursday , Friday and Saturday . It follows that if 5th October falls either on a Sunday or a Monday the opening is postponed to the Tuesday following . e the E r Convers ly , in nglish cou ts , if Call Day falls on a

or e . Saturday a Sunday , it is obs rved on the Monday following B e e e In Class , how v r , we have a larg class of cases in which it has b een found necessary or expedient to provide that the u e e e th occ rr nc shall always tak place on e same day of the week .

e e the e the c - In th se cas s w ek day is primary o ordinate .

E e e aster , for example , by the decr e of the Nic ne Council , 88 THE DEFECTS OF THE CALENDAR

ni must always be observed on a Sunday , and the an versary of the Crucifix ion must therefore necessarily always fall on a

Friday . hi There are many other cases of t s rule . It is found con veni ent in most places that markets should be held weekly at are suitable centres , and these almost invariably observed always

e . on the sam day of the week When , therefore , in certain cases once or twice a year a market of special importance is to be observed , it is natural that it should be attached also to a special week day . To determine the recurrence of the date in such cases the usual expedient adopted is to fix the event in question for the i first , second , th rd , fourth , or last Monday , Tuesday , or as the case may be of a particular month . s Thus , in Scotland the licensing magistrates meet for burgh on the second , and for counties on the third Tuesday of April , the and for burghs on the third , and for counties on last Tuesday

B 1 66 1 . 8 of October . y the Act , , ch 3 , Quarter Sessions were appointed to be held on the first Tuesdays of March , May and

August , and the last Tuesday of October . e to Sometimes , to end avour prevent a particular clashing hi refi ne w ch such dating has been found to involve , a further E ment is resorted to . Thus the annual meeting of the ducational Institute of Scotland takes place on the Saturday after the third Fr iday of September . Thi s discord between month day and week day is the most serious defect connected with the Calendar .

Every year on 1 st January the almanac is completely changed . We are so a ccustomed to this defect that we do not realise its But hi gravity . what would we t nk if the same thing happened with the weights and measures P—if the pound which is this year 1 6 ounces became 1 5 ounces next year and 1 4 ounces the following year , and so on , returning to its original value only at dista nt and irregular intervals ; or if the yard whi ch this year 6 is 3 inches became next year 3 5 and the next year 34, and so on ; or what would we thi nk if the letters of the alphab et or the nine numerals underwent a similar annual dislocation ?Would we not be di sposed to say that the whole fabric of society was

90 THE DEFECTS OF THE CALENDAR

1 01 1 2 ing in successive columns the years between 9 and 95 , whi ch have identical Calendars . An absence of progress is a feature of all the arrangements provided for the regulation of human action . If we compare a Statute or Act of Parliament of a hundred years ago with one passed last session , not only do we find no improvement in hi its conception and draughtsmans p , but the comparison is , Th . e if anything , unfavourable to the more recent production

ni ffi a e orga sation of labour , or of the tra c of our streets , the arr ng ment of business in Parliament , in the Law Courts , or in the E e Stock xchang , reveal no evident signs of steady and constant improvement . No doubt there are many changes , and more than enough of novelties and alterations , but of a general orderly continuous progress there is really no appearance . Let us contrast this state of affairs with the remarkable and continuous progress which , for more than a century , has been k of taking place in scientific nowledge , and in the application science to the arts . The constant improvement in the conditions of civilised life in modern times bears unceasing testimony to the reality of this progress . We visit an engineering museum , ’ and we see there a model of Stephenson s first locomotive along ma nifi with a succession of subsequent designs , down to the g

- hi cent engines of to day . The same t ng occurs if we examine hi e an ex bition of el ctrical apparatus , of ships , of motor cars , or indeed of any sort of scie ntific or mechanical contrivance designed for the service of mankind . It is to the advance of scientific knowledge and its appli cations that the remarkable amelioration of the conditions of civilised life during the last century or so is due . And the very vastness and universality of this improvement usually blinds us to the fact that it has not exte nde d itself to the regulation and organisa Y t tion of human activity . e the ever growing unrest and dis i e contentment , wh ch are seething in all ranks of society , b ar conclusive testimony to the fact that there is something sadly the unsatisfying and far amiss in the social condition , even of most civilised states . Now what is the cause of this strange contrast ?The answer is that progress is only possible where improvement is cumu THE DEFECTS OF THE CALENDAR 91

Fig . 1 1 92 THE DEFE CTS OF THE CALENDAR

The the lative . modern locomotive , modern Cunarder , the e mod rn motor car , or telephone exchange have not leaped fully

e e . r quipp d from the brain of the inventor On the contra y , their improvement has been a gradual and continuous process . ’ l n the case of the locomotive , starting with Stephenson s “ ” s m Rocket , its defect were noticed , improve ents one by one e e ai e were tried and t st d , the good were ret ned , the defectiv the were discarded , and in this way the engineer has arrived at

- locomotive of to day . And only because he could proceed thus was the improvement possible .

The remark is of universal application . In short , the course of scientific progress resembles the erection of a building . Just as St Paul ’s Cathedral rose surely and gradually as one row of ni stones were laid upon another , so has the course of mecha cal improvement gone on its way . But such gradual building is only possible upon a fixe d and steady foundation . If an earthquake were annually to shake to y the ground all the work of the preceding ear , obviously ’ neither St Paul s Cathedral n or any other similar edi fice could eve r have been reared . And in like manner a basis of fixed data is the essential pre - requisite of all social and admi ni strative im im e . we provem nt In short , may say that all such progress is possible , that all efforts towards its attainment are futile , until ‘ r l l r we establish as its basis a pe petu a ca enda . e II . When w consider the Calendar as an instrument for measuring inte rvals of time we find it also deficient in the follow ing respects : 1 f ( ) The hal years and quarters are unequal . It is true that as the 6 e l e year consists of 3 5 day s absolute qua ity is impossibl , but an e qual division of 3 64 days leaving only one day over in common and two days in leap years would be perfectly prac tica bl e ; would greatly facilitate the calculation of apportionable w 1 payments , and ould ensure that each trimestre contained 3 complete weeks . 2 ar abso ( ) The month lengths e une qual . In this case again u t ffi l te equali y is impracticable , but there would be no di culty in arranging that no month should diff er by more than one day e 0 from the standard l ngth of 3 days . The wages of sailors are

E E BE E E 94. HOW ITS D F CTS MAY R M DIED

it was to fix this date that the Gregorian reform was introduced .

It is important , therefore , to note that the inequality of the hal f years can be corrected much more simply . All that is necessary is to subtract a day from August and ~add — it to February thus undoing the transfer from February to a August alleged to have been perpetrated by Augustus C esar . It will be found that this simple change provides us with two equal half years and four equal quarters , subject always of 6 th 66th hi course to the exclusion of the 3 5 and 3 days . It does t s ' not only in the case of the Calendar year commencing on I st

- b January , but also if we take the ecclesiastical twelve month e

on - 1 st ginning I st December , or the twelve month from March — the latter being for many purposes an extremely useful period . It is further to be noted that if the day taken from August be a dded to the Februa ry of the fol l owing yea r the change eff ected in this way leaves the date of the vernal equinox and all its con sequentsfl indeed all dates from 1 st March to 3oth August ff absolutely una ected . It is indeed remarkable how much the Gregorian Calendar is simplified and improved by this one altogether harmless change 1 i ( ) It provides a scheme of months , of which n common w exce years all except February , and in leap years all ithout p e 0 1 tion , are ither of 3 or 3 days in length , and in no case does any f month di fer by more than one day from the standard length . (2) Subject only to the sequestrati on of the 3 65th day it r p ovides us with two equal half years and four equal quarters . 0 Under the present Calendar one quarter contains 9 days , one 1 t 9 and two 92 days each . Under these condi ions the employ di i ment of equal quarterly v sions is impracticable , but there is nothing impracticable in setting aside the one extra day and thus providing ourselves with the four equal quarters for the calculation of apportionable payments . (3) Each quarter would then contain exactly three months 1 and 3 complete weeks . It would thus furnish us with the much needed common measure for the comparison of monthly and e we kly apportionments . Although the quarter or trimestre is not usually regarde d as one of the elements of the Calendar it has a true natural position 9 . . . “ u J b 5 ? F A Q 4 . . 8 a ' w . < a o mmz s ge mmmE fi 3 § m£ m2 9 3 E mwm 5 Z mm4 Q [L . . fi v— v m w h m v m w h w 03 o m m m m m m m o w 5 m m m m m m u m

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fi N CO fl ‘IO Ct O) o N m m m O N m « m w m m m o “ g E fi g 2 2 : 2 N a N m N u w m m m n 96 HOW ITS DEFECTS MAY BE REMEDIED — in the Calendar a fact to which attention was directed by l l in e P y . His point is that the quinoxe s and solstices naturally divide the year into four parts . The conventional quarters of the Calendar do not of course exactly correspond to the astro nomical intervals ; but being adjusted to an equal length of 91 days they furnish the needed common measure between month e and week . Independ ntly of these physical facts the quarter or trimestre has b een proved by experience to be in many cases i e the most conven ent interval for s ttling periodical accounts , — payments and engagements . Its use for these purposes a lready — extensive would be facilitated were the equality of the four working quarters established . Keeping these considerations in view we must next point out that the day to be excluded from computation in order to e 1 t If furnish the four equal quarters is vidently the 3 s May . that day be se questrated we at once arrive at the four equal e quarters , and it is important to note that this result is attain d whether we commence with the ecclesiastical year on 1 st Decem

wi 1 a . e n ber or th the st M rch Moreover , if we commenc to recko 1 1 st h our year either from st December or from March , bot i the 3 oth February , wh ch would be the odd leap day , and the l st hi the 3 May , w ch we are suggesting for annual sequestration , a t t e d o a ua rt of would fall h en f q er . In either of these periods a comput tion , therefore , the four quarters would be compact and continuous and would never suff e r any interruption as a result of these days being so excluded from enumeration . It ought to be pointed out here that whilst it would be inad vi sable and undesirable to make any alteration in the com mencement of the Calendar year f or purposes of da ting it is quite unnecessary , and is not even desirable , to adhere to that t starting point in computing intervals of time . In point of fac we seldom do so at present . In the engagements of servants or s the letting of hou es or lands , in fixing the terms and sessions of law courts , schools and universities , in settling the financial m ni year of public authorities , co mercial compa es and private business firms we seldom adhere to the Calendar year , and no ni inconve ence results . Indeed it is for many reasons undesirable

1 Hist Na t Lib xv111 c a . . . , p . 2 5 .

98 HOW ITS DEFECTS MAY BE REMEDIED of additional Sabbaths was recogni sed and strictly enjoined amongst the Jews , and indeed certain Sabbaths such as Pente — cost and the Feast of Trumpets were offi cially duplicated a rule still observed . The injunction Six days shalt thou labour is as much a part of the Fourth Commandment as the injunction ” the et he ' to Remember Sabbath Day , y no one supposes that is thereby prevented from observing a holiday or a half holiday ,

e . not only occasionally , but every w ek The spirit and purpose of the Fourth Commandment is to ensure the devotion of one - seventh of our time to rest and hi worship . T s object would not only be still secured but would be much more eff ectively secured if the week were placed in a e p rpetual relation to the other elements of the Calendar . Its S ni be ig ficance and importance would increased , its preservation would be assured and the whole scheme of the Christian year would be rendere d practicable to an extent hi therto u n realised . The Christian Church has not hesitated to transfer the ob servance of the weekly rest day from the seventh to the first day — of the week a fact whi ch proves conclusively that it is the spirit and not the letter of the commandment to which we owe — wa s re allegiance . And it may be incidentally noticed as well — marked recently by Pere Bertrand that the oretically at any rate such a shift could not have taken place without the inter vention either of two Sabbaths in immediate succession or of u one week of eight days . If s ch an interruption in the unbroken succession of seven - day weeks was permissible once it is vain to suggest that its regular observance annually would involve any disregard of the Divine Command . On the whole matter it may safely be said that the objection is based on an ill - informed i literalism , and displays a real ignorance of the h story of the

Sabbath . It has been suggested that to avoid thi s obj e ction it might be arranged to reduce the normal length of the year under the 6 ac Gregorian Calendar to 3 4 days , allowing the overplus to cumulate till it amounted to a week and intercalating an addi ti onal week every seventh and an addi tional fortnight every

- hi twenty eighth year . If t s were done there is no doubt but that HOW ITS DEFECTS MAY BE REMEDIED a Perpetual Calendar would be established without any inter d l ruption in the succession of week ays . The change would involve a serious interruption in the con tinuity of the Gregorian Calendar . It would be a departure from was i e v z . the principl on which the Julian Calendar based , the e re du ction of intercalations to a minimum . A larg and distu rbing e E e e oscillation would tak place in the dates of the ph m rides , and the practical u se of the Calendar for scientific purposes e wou ld be impaired . Its value also for statistical purpos s would e be adversely aff ected . It s ems incredible that science would submi t to such inconveniences and disturbance for no other reason than to pay deference to a fancifu l prejudice begotten of unhistorical conceptions of the origin and use of the seven - day week . e We now return to the qu stion , What day is most suitable ” to be excluded from the weekly series ? It is obviously expedient that each of the four quarters should 1 e comprise 3 complet weeks , beginning with a Sunday and ending with a Saturday . Now that result is at once attained if we select for exclusion from the weekly series the very same e oth r 1 st days , nam ly 3 Februa y in leap years , and 3 May annu hi e e ally , w ch we hav alr ady found it desirable to set apart in h th arranging t e fou r equal quarters of e year . If these days are selected then the 29th of February and the

3 oth of May should be Saturdays , and the I st of March and the

I st of June should be Sundays . Now this result can be at once secured by commencing the e cclesiastical year with a Sunday on I st D ecember . In that case each of the four quarters starting from that date will commence with a Sunday and end with a

Saturday and will comprise 1 3 complete weeks . In the proposals which have been recently published for re arranging the month lengths in symmetrical quarters either of 0 0 1 1 0 0 e the 3 , 3 , 3 days or 3 , 3 , 3 days , the reason for sugg sting latter alternative has been to secure that each month should the i comprise same number of work ng days , and at the same time each quarter should commence with a Sunday . The mis

1 Su ch a ye ar o f 3 64 da ys with an in tercalary we ek has actually been i m o e n c e an . ee a s o M . 1 0 . e S r . A . B a ck o . ci t. pl y d I l d l F l , p p 5 1 00 HOW ITS DEFECTS MAY BE REMEDIED take has been in supposing that the year from thi s point of view 1 st must commence with a Sunday on January . That , as we The . e have seen , is unnecessary prop r course is to commence so the ecclesiastical year with a Sunday on I st December . In far as the Calendar is employed as an instrument of dating , it is r altogether immaterial with what week day I st Janua y coincides . Under the proposed Perpetual Calendar 1 st January would be 0 0 a Wednesday , and the months , if arranged in a series of 3 , 3 , 1 6 3 , commencing with January , would each contain 2 working days . It is interesting to note that in that Calendar 1 st March

. E would also be a Sunday Under the line of pacts now in force , hi 2 1 E and w ch holds good until 99, aster Sunday would fall on one or other of the five Sundays which in the proposed Perpetual 22nd 2 th th 1 2th Calendar would be the March , 9 March , 5 April , l th E April and g April . Now as aster neve r falls on 22nd March E whilst the present line of pacts is in force , it follows that until 2 1 99 Easter would always fall on one or other of the four other

Sundays , and the amplitude of the oscillation would be reduce d

22 . e the existin B e from 35 to days Mor over , , g Prayer ook tabl E e for the determination of aster , which we print d in Section XV , would still be available Without correction for the ascertainment E r of the aster date , although it would be unnecessa y to refer to r e the supplementa y table for the Dominical Lett r , which would D always be . Under this simplified arrangement Easter Sunday th would still always fall during e period of evening moonlight , a circumstance to whi ch much importance was at one time attached by the ecclesiastical authorities .

E a Were aster to be absolutely fixed to one p rticular Sunday , e e e that last condition could no long r be fulfill d , but in the ev nt x e e of such fi ture being det rmined , it se ms obvious that the h 1 2t . proper date to select would be Sunday , April This date approximates very nearly to the most probable date of the i Resurrection , and it has this mmense advantage that an interval therefrom of 50 days takes us exactly to 3 l st May as the proper date for Pentecost . Thus the festival of Pentecost , the only one hi w ch has passed on unaltered from the earliest Jewish times , and which is now recogni sed throughout the Christi an Church as r the anniversa y of its foundation , would exactly , and most

1 02 HOW ITS DEFECTS MAY BE REMEDIED

business will be imperilled . Now if that correspondence is established there Will inevitably follow an increasingly urgent 1 demand for four quarters each containing 3 complete weeks . We have already pointed out that such a change would be in — in several other respects highly advantageous for example , connection with the calculation of apportionable payments .

That simple reform should , therefore , be taken in hand with It a out delay . can , as we have seen , be most easily ccomplished by the transfer of one day from August to February , and if desired the transfer can be so effected as to leave the date of ff the vernal equinox una ected . i im Th s change , though so small and simple , is in itself n portant , and it is really the o ly change of the Calendar which

ff . directly a ects its use in scientific work Men of science , there fore , so far as this change is concerned , should not merely look on but should take active measures for its adoption . It would remove the one serious and outstanding defect in the Gregorian

Calendar properly so called . Admitting that it is desirable that any reform should be com prehensive and complete we sti ll maintain that simplicity and effi ciency would be best secured by the adoption of this one change as a first preliminary step . Thereafter , the whole position could be reviewed with a clearer understanding of what as i t be w st ll required and hat , we are satisfied , would found not to involve any further interference with the Calendar as used by science . It is indeed possible that by the adoption of‘ tables of week day periods 1 all further legislative interference might be rendered unnecessary .

1 ’ i ion o f t es e s ee the aut o r s ess a A P l ea or a n rderl Fo r a de scr pt h h y , f O y

Al ma na c . INDEX

Ac ium att e o f Da c ivi 2 t , b l , 57 y , l , A manac e r e u a unar 66 6 si e rea 2 l , p p t l l , , 7 d l , A l ma na cs B ook o so ar 2 , f , 79 l , Atonem en Grea Da of 0 o f week 2 8 t , t y , 3 ,

Au u s us C aesar 1 1 De o r an P ro . on th e E ac g t , 3 , 4 M g , f , p t , 79 . B e e in tro u c es n carn ation a in s Dzes a stz 1 8 d , d I d t g , f , eri a e 1 8 5 9 f , uo e as to E as e r a e 6 2 ne a sti 1 8 q t d t d t , f , B issex i e o ri in o f te rm 1 Dieteris 1 0 t l , g , 5 , B u P a a of 1 8 2 2 1 io n s iu s Exi uu s 0 ll , p l 5 , D y g , 5 Dominica e e rs 22 2 l L tt , , 3 C aesar Au u stu s 1 1 a e o f , g , 3 , 4 t bl , 3 7 , 3 9 u iu s his re o rm o f the Ca en J l , f l dar 1 1 E as e r a x e ate f o r 1 00 , t , fi d d , Ca en ar C a ean ate o f 2 0 6 1 l d , h ld , 3 d , , C in es e ta e to fi nd 8 1 h , 4 , 9 bl , E ian E ac s a e o f 0 gypt , 4 p t , t bl , 7 Gre ek u se o f 6 , 7 , 2 2 , 9 ewis 2 E em e ri e s 8 J h , 5 ph d , 3 a in a e o f 1 E u inox e rn a 2 1 6 L t , 9 ; t bl , 7 q , V l , , 3 , 93 a om e an 2 6 E ra C ris ian 0 M h t , , h t , 5 Re u ic an 2 o f io c e ian p bl , 7 D l t , 49 Ca en a r un ar 6 o f He ira 0 l d , l , g , 5 a er e tua o f abo n a ss ar 8 p p l , 95 N , 4 e e c s o f 8 o f Rom e 8 d f t , 5 , 4 Gre o rian 20 Eu oxu s 1 2 g , d , im rovem e n o f p t , 93 u ian 1 1 a van a e s o f 1 8 eas o f Te rmin a ia 1 J l , ; d t g , F t l , 5 uni - so ar 6 o f Trum e s 0 l l , p t , 3 so ar 6 o f n eaven e B rea 0 l , U l d d , 3 se s o f 8 r a n f 1 u , 3 Fe u r e o , — b y , l gth 4 1 - m0nth rem ark on 0 1 3 s , 1 C en so rir us uote 1 0 1 2 1 2 Go en um e rs 8 ta e o f , q d , 9, , , 4 , 4 , ld N b , ; bl , 44 g Gre o r P o e 2 1 4 g y XIII , p , C aviu s C risto er 68 l . h ph , , 74 C ou nc i s Gen era of icea 20 6 Ha e s u o e 2 2 l , l , N , , 3 l , q t d , 9, 4 , 5 o f ao icea 1 He i ra E ra o f 0 L d , 3 g , , 5 o f ren 2 1 He iac a Risin o f a S tar T t , l l g , 47 C ru c i xio n a e o f 6 Hero c ro n o o o f 1 fi , d t , 5 d , h l gy , 5 C c e Ca i ic H e ro o u s u o e 1 y l , l pp , 9 d t , q t d , 4 , 5 , 4 Dion sian 1 Hi arc s e s im ate o f e ar y , 5 pp hu , t y , 4 e o nic 8 M t , 7 , , 43 abo n ass are an 2 e s ex ain e 1 6 N , 4 Id , pl d , m ia 2 n carn a ion a in s 8 Oly p d , 4 I t d t g , 5 P as c a n ic ion 2 6 h l , 43 I d t , 4 . 4 So ar l . 3 5 , 45 S o iaca o r C anicu ar 1 ose u s u o e 2 6 th l l , 4 J ph , q t d , 5 , 53 , 5 5 , 5 1 04 INDEX

Ka en s ex l ain e 1 6 uintadeciman s 6 2 l d , p d , Q , Kal i u uintil is n ame of c an e 1 y g , 49 Q , h g d , 3

i iu s A o sius 2 1 6 Rom e ate of oun ation 8 L l , l y , , 9 , d f d , 4 ’ un ar co rrection Ro ation E art s e rio o f 2 L , 73 t , h p d , un a io n L t , 5 S a at th e ewis 0 bb h , J h , 3 acro iu s uo te 1 2 1 1 8 S atur a et mo o of 2 M b , q d ,.3 , 9, , 4 , , d y , y l gy , 9 arte i Hu ol ini 1 S ca i er o se uo te 1 M ll , g , 4 l g , J ph , q d , 9, 4 , erce onius 1 1 M d , S9 e ton S extil is n am e of c an e 1 M , 7 , h g d , 3 omm sen u o te 6 1 0 S o ar co rre c i on M , q d , 4 , , l t , 73 ont th e S o si en es 1 1 M h , , 5 g , the em ol ismic 8 S ot iaca Pe rio 1 b , h l d , 4 , 4 ’ oon s P e rio St e New Act 1 22 w en M d , 5 yl , , ( 7 ; h intro u c e 2 2 d d , N ab o n assa rean e rio 2 8 S un a enactment f o r o servance of p d , 4 , 4 d y, b , ativit ate o f 1 2 N y, d , 5 3 , 3 3 , ’ ewton Sir saac uote 6 1 S no di c a P eri o mo on s N , I , q d , 4 , y l d , , 5 ic e a Co un c i o f 2 0 6 N , l , , 3 o ne s ex ain e 1 6 ac itu s uo e 2 N , pl d , T , q t d , , 5 5 um a his su ose re o rm 1 0 ermin a ia a e o f 1 N , pp d f , T l , d t , 5 Nun dina e 1 im e m easurement of 1 e atio n , 9 T , , ; q u of , 2 ctae eris th e Greek rum ets east o f 0 O t , , 7 T p , F , 3 l iad 2 O m p . 4 . 47 arro uo te 8 V , q d , 4 P asc a e rm 8 0 Victoriu s o f A uitain e 6 h l T , q , 43 , 4 e 1 P a ssover , th , 5 5 , 6 P ente co s 0 1 0 1 e ek th e 2 8 t , 3 , W , , P e rio u ian eek Da P erio s 1 02 d , J l , 5 9 W y d , P e rio ici Law of 1 hi s un a 1 0 1 d ty , , W t d y , P etaviu s uote 0 , q d , 7 , 5 P in uo e 1 1 1 6 ear comm en cement of l y , q t d , , 5 , 9 Y , , 9 P utarc uote 1 0 uh an l h , q d , 3 , J . 73 P re ara ion da of 6 1 e a 1 p t , y , 5 5 , l p , 3 th e 8 of Con u sion 1 Prim e , , f , 2 s i erea d l , 3 d cim an s 6 ro ical Quarta e , 2 t p , 4

P RI NTED IN EN GL D B Y B P E CE M . A . AN J A , AT THE CAM B RI DGE UN IVERS ITY P RESS