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ELEMENTS OF THE
JEWISH AND MUHAMMADAN CALENDARS
ELEMENTS OF
THE JEWISH AND
VIUHAMMADAN CALENDARS
RULES AND TABLES
EXPLANATORY NOTES ON
JULIAN AND GREGORIAN CALENDARS
BY THE REV.
M.A., F.R.A.S.
LONDON
GEORGE BELL & SONS, YORK STREET, COVENT GARDEN
MDCCCCI
HCKr
8<?tB
608356
LL
UNWIN BROTHERS, THE GRESHAM PRESS, WOKING AND LONDON.
PBEFACE
THE following treatises on the Jewish and Muhammadan Calendars
were not originally intended for separate publication. They were
first written as part of a more comprehensive book containing
an account of other Calendars and Eras to which reference was
frequently made. When, through the kindness of friends among
my parishioners at Hampstead, I found it possible to publish this
portion of the work, I gladly availed myself of the opportunity, and
rearranged the MS. in such a manner that it assumed its present
form. This, I thought, rendered it necessary to add some brief
explanatory notes on the Julian and Gregorian Calendars, such as
might take the place of references made to Articles in the larger
work.
A work of this kind must, of necessity, partake more or less of
the nature of a compilation. Without claim to originality, I have
endeavoured to bring to a focus materials gleaned from many
various sources, as indicated by the list of books which I have
consulted. There will, consequently, be found herein little, perhaps,
which may not be read elsewhere; but many of the books and
pamphlets which have been written on these Calendars are not easily
accessible to the general reader, and in many, though rules are given
and legal enactments respecting them are stated, the reasons for
these rules and enactments are not fully and clearly described. This
VI
PREFACE
is particularly the case with respect to the Jewish Calendar ; while,
with regard to the Muhammadan, the rules for the reduction of Hijra
dates to the Christian Era are generally of such a nature that implicit
reliance cannot be placed upon them.
I have endeavoured to simplify the rules for both Calendars, and
to explain the reasons for them in such a manner that a student who
will take the trouble to read this book may not have to encounter
the same difficulties which I myself experienced when I commenced
the study of the subject. I have perhaps used too much freedom
in my criticisms ; if that be the case, I can only express the hope that
others may be more lenient with respect to errors and imperfections
which they may detect in my own work.
I have spared no pains in trying to render the Chronological
Tables as accurate as possible by careful revision. The Christian
dates corresponding to Tishrl 1, Nlsan 15, and Muharram 1 are
not usually given beyond A.D. 2000 or thereabouts. I have computed
them for an additional thousand years.
I am much indebted to the Kev. Dr. Lowy and to the Very Kev.
Dr. Gaster for valuable assistance afforded me with respect to the
Jewish Calendar, and particularly to Mr. James Kennedy, of H.M.
Bengal Civil Service, in the first place for 'the suggestion by which
the publication of the work has been made possible, and, again, for
bringing to my notice many of the books which I have found useful.
I have also, through Mr. Kennedy, become indebted to Mr. A. G.
Ellis, Curator of Oriental MSS. in the British Museum, who was
good enough to correct my transliteration of Arabic words and names.
It must not, however, be supposed that any of these gentlemen is
answerable for errors or misprints, for none of them has seen either
my MS. or the proof sheets.
SHEKKAKD B. BUENABY,
_ Late of the Vicarage, Hampstead.
LONOFIELD,
GREAT MISSENDEN.
CONTENTS
PART I
THE JEWISH CALENDAR
CHAPTEE I.
PAGE
The Hebrews, when in Egypt, probably used the Egyptian Calendar. The " Beginning
of Months." The Abib. Names of months in Old Testament. Names of months
during and after the Captivity. Tammuz ; Ezekiel's vision. The Hebrew year is
Luni-Solar. The Passover to be celebrated at the Full Moon of the Vernal Equinox.
How did the ancient Hebrews find the time of New Moon ? In later tunes the New
Moon was found by actual observation. The Watchers. How intercalations were
determined. The sheaf of new barley. The Dispersion. Cycles employed, first of
ejghty-four, afterwards of nineteen years. Years of B. Adda and B. Samuel.
Hillel II. reforms the Calendar ... ... ... ... ... ... 3
Note to Chapter I. The Sojourn of the Israelites in Egypt ... ... 18
CHAPTEB II.
Divisions of the Hour, Chalakim and Begaim. Tribe of Isachar. Divisions of the
Day. Commencement of the Day. Correspondence and Coincidence. Synopsis
of coincident Jewish and Christian hours. Meaning of such an expression aa
" 7d. 3h. 540ch." Computation of Calendar time is for the Meridian of Jerusalem.
Astronomical and Civil months. Metonic Cycle is the basis of the Jewish Calendar.
The year of Hipparehus adopted by Hillel II. Common and Embolismic years. Bule
CONTENTS
PAGE
for (hiding position of any year in a Cycle. System of Embolismic years not arbi-
trary. Coincidence of 235 Jewish Lunations with 10 Jewish Astronomical years.
Jewish computation of the Metonic Cycle differs from the Christian. Six forms of the
Jewish year. Intercalated month is always the sixth in the Civil year, and the last
but one in the Ceremonial year. Erroneous statements on this point. Number of
days in the months according to the six forms of the year. Gregorian dates for the
months of eight Jewish years. Leading elements of the Calendar tabulated. Eetro-
gression of the Jewish from the Julian Calendar. Duration of time in a given
number of Jewish Astronomical years and Cycles 21
CHAPTER III.
The Jewish Mundane Era. Molads, definition. Computed time of Calendar New Moon
is not that of the actual Conjunction of Sun and Moon. Why the present, or
reformed, Calendar is called permanent. Commencement of the Mundane Era.
Molad ToHU ; BeHaRD. De Veil on Molad BeHaRD. Scaliger and Petavius on
Xovilunium ToHU. Folk-lore concerning rivalry between Sun and Moon.
Different views of Jewish chronologers as to the commencement of the Era.
Method of finding the Christian year corresponding to a given Jewish year ; and
the reverse. Era of Contracts. Confusion of ideas with respect to the true meaning
of Molad. Method of finding Molads for successive months. For successive years.
Molads for Cycles. General formula for Molad for any Cycle, C + n, when that for
Cycle C is known. Molad for year H 1 found from Molad for H. Computed
time of New Moon, or Molad, does not always indicate the first day of the year.
Isidore Loeb's short method of computing Molads for successive Cycles. Recur-
rence of Molads for Cycles after 689472 years 40
CHAPTER IV.
Uules of the Jewish Calendar as now established. The question of local time with
respect to commencement of Jewish days. Calendar arranged for Meridian of
Jerusalem. Regulations as to the hour at which any given day will commence.
Difference between the old and the reformed Calendar. The latter was an innova-
tion. Leading rules of the reformed Calendar. Rule with respect to Nisan 15, and
the reason ; BaDU. Feria for Tishri 1 in year H + 1 found from feria of Nisan 15
in year H. Rule with respect to Tishri 1 ; ADU. Two days of rest not to come
together. Days upon which Schabuoth, or Feast of Weeks ; Purim, or Feast of Lots ;
Kippur, or Day of Atonement, cannot occur. Forms of the Jewish year, In + x.
Postponement of Tishri 1 may be for two days, but never for more than two.
CONTENTS ix
PA.QE
Rules respecting the Astronomical postponement of Tishri 1, YaCH, OaTRaD,
BaTU-ThaKPhaT, and the reasons. Dechiyy6th. Rules for determining the
feria with which any given year can commence. Error in Lacoine's Tables. Error
in " The Perpetual Calendar " of Lazarus Bendayid. Table showing feriee with
which years, according to their form, can commence. Proofs of the statements in
the Table. Neglect of Regaim in the Molads. Table of Day-limits. Further
regulations with respect to commencement and form of year. Laylanot, or First
day of year of trees. Rule for finding the length of any given Cycle, which may
consist of 6939, 6940, 6941, or 6942 days. The last is of rare occurrence.
Examples of finding feriae with which Cycles commence, and the lengths of the
Cycles 63
CHAPTER V.
The possible and impossible sequence of years. Proofs of the ten rules with respect to
the sequence of years. Table of collected results showing how the years can follow
each other. Correspondence between Jewish and Christian dates, obtained by
actual interval of time elapsed ; with examples. Date of Nisan 15 in year H found
from that of Tishri 1 in year H + 1. Table of correspondence between the
Christian dates of Tishri 1 and Nisan 15. If D be the day of September for
Tishri 1, D + 21 is the day of March for Nisan 15. Computation for a series of
three Cycles, namely, 296, 297, and 298. Corresponding Christian dates for these
Cycles. Full particulars of the three Cycles in tabulated form. Checks upon
results obtained. The week-day for every day of every possible year. Method of
finding the week-day corresponding to any Jewish date : description of Table XI.
Week-day of any day in a Jewish month occurring in a given Christian year, with
description of Table XVI 10$
CHAPTER VI.
Kebioth ; explanation of the term. Error respecting the Iggul, or Cycle of 247 years.
Perpetual Calendars. Errors of Scaliger, and of Lazarus Bendavid. Proof of the
error. Scheme for showing when the changes in the (so called) Perpetual Calendar
take place ; providing also the means of finding the feria for Tishri 1 in the first year
of any Cycle. The only way of approaching the formation of a Perpetual Calendar
is by considering the Molads. Computation for Types of the Cycle. There are
sixty-one Types. Professor Nesselmann's method of arriving at the Types. Com-
putation according to this method. Check upon results obtained, with explanation
of Tables XIV. and XV. 146
x CONTENTS
CHAPTER VII.
PAGE
Fasts and Festivals. The Sabbath, its institution, provisions, and penalties ; announced
in later times by sound of trumpets. Sabbath is a term employed for all days of
rest. Feasts of the New Moons. Observance of two Rosh Chodesh. Detailed
account of days observed in each month of the year. Calendar of months, with
numerical order of days according to each of the six forms of the year. Explana-
tion of Tables of feriae for Hosh Chodesh, and chief Fasts and Festivals 175
CHAPTER VHI.
Formula of Dr. Gauss for finding the Christian date of Tishri 1 and of Nisan 15 ... 219
CHAPTER IX.
Megillath Ta'anith, or Scroll of Fasting. Description of the book. Title should be
"List of Festivals." List of the thirty-five commemorative days. The same
arranged chronologically in six divisions, with commentary and historical notices.
Division A : Mosaical Ordinance. B : Anterior to the time of the Hasmonaeans. C : In
the time of the Hasmoneeans. D : Disputes between the Pharisees and Sadducees.
E : In the time of the Roman Domination. F : After the destruction of the Temple.
List of twenty-five days of mourning '240
GENERAL TABLES.
I. Equivalents in minutes and seconds of Chalakim and Regai'm 278
II. Equivalents in Chalakim and Regai'm of minutes and seconds 278
III. Duration of Jewish Astronomical Common and Embolismic years ... ... 279
IV. Time elapsed at close of each year of an Astronomical Cycle 280
V. Astronomical duration of Jewish Cycles 280
VI. Additions to be made to Molad for Tishrt to obtain the Molad for any other
month in the year 281
VII. Additions to be made to Molad for first year in a Cycle to obtain that of any
other year in the same Cycle 282
VIII. Additions to be made to the Molad for any Cycle to obtain that for any
succeeding Cycle ... 283
CONTENTS xi
PAGE
IX. Molads for the Cycles 1 to 258, A.M. 1 to 10014 284
X. Day-limits, and Form of the year, according to the Molads ... ... ... 290
XI. For finding feria of any day in Jewish year ... ... ... ... ... ... 291
XII. For finding feria with which any Cycle commences... ... ... ... ... 293
XIII. The sixty-one Cyclical Types > 294
XIV. XV. For finding the feria with which any year commences ; the Molad for the
year; and Type of the Cycle ... ... ... ... ... ... ... 296
XVI. Calendar showing the feria for any date by means of day-letters... . ... ... 297
XVII. Christian dates for chief holy days according to that of Nisan 15 300
XVIII. Chronological Table of corresponding Jewish and Christian dates for Tishri 1
and Nisan 15. A.M. 4371 to 6764. A.D. 610 to 3003 .. . 301
PART II
THE MUHAMMADAN CALENDAR
CHAPTER I."
Arabian Calendar in ancient times was purely Lunar. Pilgrimage to the Ka'ba made
in the twelfth month. Inconvenience caused by the Lunar year being shorter than
the Solar. The remedy effected by addition of a thirteenth Lunar month called
Nasi. Different opinions as to when the month was added. The custom dates from
A.D. 412 ; it was abolished by Muhammad. The sacred months. Declaration of
Muhammad as to the Nasi. He sustains the character of the sacred months to
some extent. Era of the Hijra. Meaning of the word. Errors connected with its
commencement as related to the Flight of Muhammad. Date of Flight to be dis-
tinguished from date of commencement of the Era. M. Caussin de Perceval
objects to the generally received date. Special names given to the first years of
the Era . 367
CHAPTER II.
Computation of time as established by Muhammad. Calendar is based on a Cycle
of thirty years. Civil and practical reckoning. Years of Cycle which receive an
xii CONTENTS
PAGE
additional day. Computation for the system of Kabisah years. The Muhammadan
day commences at Sunset. Hours. Muhammadan and Christian time compared.
Tables of Muhammadan years, beyond A.D. 1900, condemned erroneously by
Woolhouse. His Table is the same as that in " L'Art de Verifier les Dates," which he
condemns. Errors do exist in certain Tables. The Muhammadan week. Fortunate
and unfortunate days. The months. Etymology of their names 377
CHAPTER III.
The Muhammadan Cycle of thirty years. It contains 10631 days. Great Cycle of
210 years. Sign of a Cycle. Formula for the Sign of a Cycle is 6 +
oU
Sign of a year. Formula for the Sign of any year, H, is 6 + 5N -|- 4 (R 1) + B,
where N = |sx[ an d B = -, . - j- . Method of determining the value
of B. Why Table II., which shows the Sign for each year in a Great Cycle, differs
from that of Uluigh Beigh. Method of finding the Sign of any month in a given
year ... ... ... ... ... ... ... ... ... ... ... ... 393
CHAPTER IV.
Correspondence between Julian and Muhammadan dates for initial days of successive
years. Julian dates for Muharram 1 in first thirty years of the Hijra. Method of
checking results obtained for a Chronological Table. Recurrence of Julian dates
for Muharram 1 cannot take place before 43830 years of the Hijra have elapsed.
Muhammadan dates for January 1 in A.D. 623 to A.D. 656. Results checked by
Julian dates for initial days of successive Cycles. General rules for reduction of
Muhammadan to Christian dates are frequently inaccurate. Reduction of dates by
method of Days Elapsed ... 402
CHAPTER V.
Examination of rules given for reduction of dates by various authors. That of
M. Francffiur for finding the Julian date of Muharram 1. His reverse method,
for finding the Muhammadan date of January 1. Methods are inaccurate when
CONTENTS xiii
PAGE
they are made to depend upon the ratio between a mean Julian and a mean Muham-
madan year. This ratio is expressed by H = J x -970203, and J = H x 1-103071.
Method adopted by Ciccolini. That of Le Boyer and his alternative method.
Rule given by Sir Harris Nicolas, which is also found in the " Companion to the
British Almanac," and is given by Bond in a more definite form. Examination
of the rule as given by Bond. Three rules given by Professor Wilson, of which
the third is adopted by T. P. Hughes in "A Dictionary of Islam." Method of
Woolhouse, and the "Encyclopaedia Britannica." How to reduce nominal
Gregorian dates, before the Change of Style, to the actual Julian dates. The
reverse rule of Nicolas, which is also given by Crichton in his " History of Arabia."
The reverse rule as given by Bond ... ... ... ... ... 413
CHAPTEB VI.
M. Caussin de Perceval on the Arabian year before Islam. Arabian writers not in
accord as to the system of Embolism. Arabs adopted a system of intercalation from
the Jews, but not the nineteen years' Cycle. They probably intercalated a month
at the end of every third year. The names of five months had reference to the
season of the year, and the names of four to their sacred character. The Pil-
grimage continued to be in the Autumn for half a century after the institution of the
Nasi. In A.D. 541 it occurred at the time of the Summer Solstice. It gradually
retrogressed until in A.D. 631 it took place in the beginning of March. In this
year, the tenth of the Hijra, the institution of the Nasi was abolished by
Muhammad. Arguments in support of April 19, A.D. 622, as the initial day of
the Era of the Hijra. Table showing the Julian dates for the first days of the
years of the Nasi, and for the tenth day of the Pilgrimage. Views of de Perceval
with respect to the Nasa'a 447
CHAPTEB VII.
Mahmud Effendi on the Arabian Calendar before Islam. His object is to show that a
purely Lunar year was employed without any intercalation. The word Nasi only to
be understood with reference to the occasional postponement of the sacred month.
He endeavours to fix three days: that of the death of Ibrahim, the infant son
of Muhammad, by an Eclipse of the Sun ; that of the Prophet's arrival at Medina
after the flight from Mecca ; and that of the birth of the Prophet. Five different
systems for the Calendar (before Islam) have been suggested. The result obtained
by each system. All rejected except the last, namely, that the year was purely
Lunar. The same conclusion reached by a comparison of the dates previously
established. Examination of the passage from Procopius quoted by M. de Perceval. 4(50
xiv CONTENTS
CHAPTER VIII.
THE OTTOMAN FINANCIAL CALENDAK.
PAGE
This Calendar is Solar, based upon Julian years. Introduced in Turkey A.D. 1676.
Year commences with March 1, Julian. Inconvenience of this Calendar. Modifi-
cation effected in A.D. 1840 471
GENERAL TABLES.
I. Serial enumeration of days' in the Muhamraadan year 475
II. Signs of the years for the Great Cycle of 210 years 476
III. Signs of the months, showing feria with which each commences according to that
of Muharram 1 478
IV. Days elapsed at the close of each year of a Cycle 480
V. Chronological Table 481
PART III
BRIEF NOTES ON THE JULIAN AND
GREGORIAN CALENDARS
The ancient Roman Calendar. Years of Romulus, Numa, and Decemviri. Confusion
in Roman Calendar. Correction by Sosigenes under Julius Caesar. The Julian
year. Bissextus. Alteration of months to present form by Augustus. The Gregorian
correction. Scheme for a new Calendar prepared by Aloysius Lilius. How carried
into effect by Pope Gregory. Rules of the new Calendar. Formula for number of
days nominally dropped. The artificial Moon of the Calendar. The Dominical
Letters. How employed to find the Week-day for any given date. The Golden
Numbers. Why so called. Earliest and latest dates for Easter. Paschal Terms.
Thirty-five possible forms for an Almanac. Paschal Cycle. Shifting the places
of Golden Numbers in the Calendar. Prayer-Book Tables for finding date of Easter.
The Julian period. Meaning of the initials B.C. There is no Chronological year
B.C. 0, or A.D. 0. Difference between Chronological and Astronomical reckoning of
the years. Days elapsed from commencement of Julian Period to close of year
B.C. 2. Commencement and termination of a "Completed Century." 511
CONTENTS xv
INDICES.
I'AOE
THI: JEWISH CALENDAR 533
THE MUHAMMADAN CALENDAR ... ... ... ... 545
THE JULIAN AND GREGORIAN CALENDARS ... 549
*
LIST OF AUTHORS CONSULTED 551
LIST OF SUBSCRIBERS 553
If
PART I
THE JEWISH CALENDAR
ERRATA.
Page 23, line 16, insert and after months.
29, ,, 6, for on read in the evening of.
7 , for 27 read 26.
,, 31, ,, 5, for Koenick read Kornick.
45, 8, after September 26 insert that is, for Id. 23h.
12, for which read and Gd. 14h. Och. 4d. 8h. 87Geh.
or 2d. 5h. 204ch. would be, &c.
66, 29, for ably read able.
69, 5, for Nisan 1 read Nisan 15.
,, 72, ,, 15, for Gregorian read Julian.
,, 97, 16, for requires read require.
99, 23, for superior read inferior.
114, 18, read with a Monday or a Saturday ; therefore, in
the third line from the bottom and in the
last line of the Table, &c.
120, 12, after required insert a comma.
151, 11, for 995 read 905
152, 11,' for 245-231 read 241-235.
186, 12, for Tishri read ; Tishri 1.
,, 197, ,, 6, after Succoth insert a semicolon.
,, 263, ,, 18, for upon read to.
280, in tn-o last lines of Table V., for 3775975 and 4469944 read
2775875 and 3469844.'
287, in moladfor Cycle 290, forferia 9 read 2.
( n ) , f n + 1 1 . | n | , / n + 1 1
427, wf.n.for J g J and J~J-[ re(1(1 [4] rf {~ i T"j
439, line 27, for 621-509 read 621-569.
,, in f.n. second line from bottom, for Muhammadan days
read years.
441, line 9, for -970224 read -970224 Y.
447, in heading to Ch. VI. for is read said to be.
,, 517, line 17, after number insert of days.
524, 13, for 1196 read 1196 + 1.
537, 12, for Megillak read Megillath.
. - 25, for Calandar read Calendar.
540, 14, for 36 read 46.
547, 21, for Ka'ab read Ka'ba.
CHAPTEE I
1, It is only reasonable to suppose that the Hebrews, when
dwelling in the land of Egypt, employed the Egyptian method of
reckoning time. They would naturally have acquired the custom
from a people with whom they had for a long time been familiar.
It is true that they had actually sojourned in Egypt for only two
hundred and ten years,* but their forefathers Abraham, Isaac, and
Jacob had been in constant communication with that country.
The Egyptians commenced their year with the month Thoth at the
time of the Autumnal Equinox, and whether the Hebrews had or had
not adopted this custom, it is quite certain that, so far as their
religious ceremonial observances were concerned, a change took place
at the time when they obtained their freedom. Just before their
departure from Egypt the command of God came to Moses and Aaron
that the month then current, which had not long commenced, should
be to them " the beginning of months," t that is to say, it was in
future to be accounted as the first month of the year. This occurred
in the Spring season at or about the time of the Vernal Equinox ;
and this month has been retained ever since by the Jews as the first
of the Legal or Ecclesiastical year for the regulation of all their Fasts
and Festivals.
If, however, the Hebrews had been in the habit of commencing
their year at the time of the Autumnal Equinox, in common with the
Egyptians of which there can be but little if any doubt it would
be long before the whole nation would become accustomed to the
innovation, t It was from this cause, in all probability, that for civil
* For the Sojourning of the Hebrews in Egypt, see Note at the end of this Chapter.
t Exodus xii. 1.
* Kwald, " Antiquities of Israel," p. 344.
4 THE JEWISH CALENDAR
and political purposes the year had another commencement. The first
month of this civil year was the seventh of the Legal year, and
corresponded to the Thoth of the Egyptians. After the time of the
Captivity in Babylon it was called Tishrl.
2. The first month of the Ecclesiastical year, " the beginning of
months," is called in the Hebrew Scriptures " the Abib." The article
is always used in the Hebrew text, though invariably omitted in the
English authorised version. In later times this month was called
Nisan, Nehemiah ii. 1, Esther iii. 7, and so Josephus tells us* that
" in the month Xanthicus, so called by the Macedonians, which is by
us called Nisan, on the fourteenth day of the Lunar month when the
Sun is in Aries, the Law ordained that we should every year slay that
sacrifice which was called the Passover ; for in this month it was that
we were delivered from bondage under the Egyptians." +
3. In the early Hebrew Scriptures the months are generally
described according to their numerical order in the Ecclesiastical year;
thus we have
" The first month," spoken of in Genesis viii. 13, Leviticus
xxiii. 5, Numbers xxviii. 16, and in many other passages.
" The second month," Genesis vii. 11, Exodus xvi. 1.
" The third month," Exodus xix. 1.
* " Antiq.," iii. x. 5.
f With respect to the two commencements of the year, compare the Jewish practice with
that of both the Anglican and Roman Churches. The civil year now commences on
January 1st, the liturgic year on Advent Sunday. "It is the peculiar computation of the
Church to begin her year, and to renew the annual course of her service, at the time of
Advent, therein differing from all other accounts of time whatsoever. The reason of which
is, because she does not number her days, or measure her seasons, so much by the motion of
the sun, as by the course of our Saviour : beginning and counting on her year with Him,
who, being the true Son of Righteousness, began now to rise upon the world, and as the
day-star on high, to enlighten them that sat in spiritual darkness" (Wheatley, "Book of
Common Prayer," ch. v. sect. i. p. 203).
"Tempus quod Dominicse Nativitatis memoriam antecedit, ideo Adventus nuncupatur,
quia totus ejus Ecclesiasticus ordo juxta contemplationem Adventus Domini dispositus est "
(Rupertus, " De Divin. Offic.," lib. iii. cap. i.).
In the eleventh century the custom of computing the year from Easter was introduced,
and became common from about A.D. 1300 to 1500. " Ut autem apud nos duplex anni
primordium est, alterum civile a Januario, alterum Ecclesiasticum a mense Paschali, sic illi
civilem annum auspicati sunt a Tisri mense Lunari autumnal!, Ecclesiasticum a Nisan verno.
mense " (Petavius, " Rat. Temp.," pt. ii. lib. i. cap. vi. ; torn. ii. p. 22).
THE JEWISH CALENDAR 5
" The seventh month," Leviticus xxiii. 24, 34, 39, Numbers xxix. 1.
All the twelve months are thus designated by numeration in
1 Chronicles xxvii. 2-5, where the names of David's captains for
each month are recorded.
Four times in the Pentateuch "the Abib " is mentioned without
the affix " the first month."
Exodus xiii. 4. " This day came ye out in the month Abib."
Exodus xxiii. 15. " In the time appointed of the month Abib."
Exodus xxxiv. 18. "In the time of the month Abib, for in the
month Abib thou earnest out from Egypt."
Deuteronomy xvi. 1. " Observe the month of Abib."
In the Book of Kings the names of three of the months are given,
together with their numerical order
1 iii. 1. " In the month Zif, which is the second month."
1 viii. 2. " In the month Ethanim, which is the seventh month."
1 vi. 38. " In the month Bui, which is the eighth month."
These four the Abib, Zif, Ethanim and Bui are the only months
of which the names are specified before the time of the Captivity.
The names have reference to the seasons of the year at which they
occurred.
The Abib is the month of corn,* or of new fruits ; so the Vulgate
renders Exodus xiii. 4, " Hodie egredimini mense iiovarum frugum."
And the Septuagint, lv fjujvl TMV vttuv, " the month of new things."
Zif is the month of flowers.
Ethanim may be the month of fruit, but the meaning of the word
is doubtful.
Bui is the month of rain.
4. During the Captivity in Babylon, and after that time, mention
is made of seven months by name, including Nisan, as the Abib was
now called. The numerical order of the month as it stands in the
Ecclesiastical year is also sometimes specified.
Esther iii. 7. " In the first month, that is, in the month Nisan."
In Nehemiah ii. 1 Nisan is mentioned by name, without the numerical
prefix.
* Die Gerstenreife : ripe barley. Laz. Bemlavkl, " Zur Berechnung des Judischen
Kulenders," p. 26, !>/.
6 THE JEWISH CALENDAR
Esther vii. 9. " In the third month, that is, in the month Si van.'
In Baruch i. 8, this month is mentioned by name only.
Nehemiah vi. 15, and 1 Maccabees xiv. 27. "The month 'Elul.''
without the number.
Zechariah vii. 1. " In the fourth day of the ninth month, even in
Chislthi." In Nehemiah i. 1, and 1 Maccabees i. 54, this month is
mentioned by name only.
Esther ii. 16. "In the tenth month, which is the month Tebeth."
Zechariah i. 7, and 1 Maccabees xvi. 14. "In the eleventh month,
which is the month Schebhat."
Esther viii. 12, and 2 Maccabees xv. 3G. "The twelfth month,
which is the month Adhar."
The remaining five months are not mentioned either in the sacred
Books or in the Apocrypha. They are found in the Talmud and in
other Hebrew writings. One only, Marheshwan, the eighth month, is
mentioned by Josephus, (" Antiq.," i. iii. 3).
The origin of the names used after the Captivity is said by some
writers to be Chaldaic, but is more probably Syrian. Eight of them
differ from the Syriac but slightly, as will be seen from the following
list. The names are given according to the transliteration of Dr.
Sachau in the Athar-ul-Bakiya, or " Vestiges of the Past," by
al-Birdni.
MONTHS OF THE HEBREW ECCLESIASTICAL, YEAH.
Before
tVi*>
After the Captivity.
/-^_,
bH6
Captivity.
Hebrew.
Syriac.
CO]
1
The Abib
Nte&o
Nisan
Mai-
2
Zif
Iy4r
lyar
Apr
3
Shvun
Haziran
Maj
4
Tammiiz
Tammuz
Jun
5
Abh
Abh
Julv
6
'Elul
Ilul Aug
7
Ethanim
Tishri
Teshrin I. Sepl
8
Bui
Marheshwan
Teshrin II. Octc
9
Kislew
Kanftn I. Nov
10
Tebeth
Kanun II. Deci
11
Schebhat
Shebat
Jan
12
Adhar
Adhar Feb
Corresponding to
August Septembe i
September October
October November
November December
December January
January Februa ry
February March
THE JE WISH CALENDAR 7
The Syriac names are given by Scaliger,* and by Beveridge ; t the
latter has them in both Syriac and Roman characters. The variations
in spelling are but slight.
Bevan conjectures \ that some of the Syriac names were derived
from the names of deities, and refers to Ezekiel viii. 14, where
Tammuz is mentioned : " Then he brought me to the dopr of the
gate of the Lord's house which was toward the north : and, behold,
there sat women weeping for Tammuz."
Jerome interprets the word by Adonis, who, he says, is in Hebrew
and Syriac called Tammuz. The Vulgate has " plangentes Adonidem."
The Septuagint retains Tammuz, in its Greek form. The worship of
Tammuz was general in Asia, particularly in Assyria. It spread to
Egypt, Greece, and Italy, and has been identified with that of Adonis,
the Sun-god. His death and restoration to life were celebrated by
annual festivals.
Lucian, as quoted by Parkhurst in his Hebrew Lexicon,:, gives an
account of these festivals ; he says, " The Syrians affirm that what the
boar is reported to have done against Adonis was transacted in their
country ; and in memory of this accident they every year beat them-
* " De Emen. Temp.," lib. iv. p. 241.
t " Institutiones Chronologic, " Appendix, p. 259.
\ In Smith's " Dictionary of the Bible," Art. Month., vol. ii. p. 417.
S (V. Milton, "Paradise Lost," bk. i. 446 :
" Thammuz came next behind,
Whose annual wound in Lebanon allur'd
The Syrian damsels to lament his fate
In amorous ditties all a summer's day ;
While smooth Adonis from his native rock
Kan purple to the sea, suppos'd with blood
Of Thammuz yearly wounded ; the love tale
Infected Sion's daughters with like heat ;
Whose wanton passions in the sacred porch
Ezekiel saw, when, by the vision led,
His eye surveyed the dark idolatries
Of alienated Judah."
Adonis was said to die and to revive again every year. He was killed by a wild boar in
Lebanon, from which the river named after him descends
" llepetitaque mortis imago
Annua plungoris peraget simulamina."
(Ovid, " Met.," x. 726.)
8 THE JEWISH CALENDAR
solves and lament, and celebrate frantic rites ; and great wailings are
appointed throughout the country ; and after they have beaten theni-
M>IVPS, and lamented, they first perform funeral obsequies to Adonis,
as to one dead, and afterwards on the next, or another day, they feign
that he is alive, and ascended into the air or heaven, and shave their
heads, as the Egyptians do at the death of Apis ; and whatever women
will not consent to be shaved are obliged, by way of punishment,
to prostitute themselves during one day to strangers ; and the money
thus earned is consecrated to Venus." Parkhurst adds to this trans-
lation of the passage, " From this account we may form a tolerably
just notion of the manner in which the Jewish idolatresses lamented
Thammuz."
It was one of these abominations transacted at Jerusalem that the
prophet Ezekiel beheld, in a vision, as he sat in his house with the
elders of Judah, in the sixth year of the captivity of Jehoiachin.
Rawlinson, on Herodotus i. o'15, says that the Assyrians had a
month called Sin, which may correspond to Siwan.
Marheshwan is Hebrew, and indicates a month in which rainy
weather prevails.
So far as regards the correspondence between the Hebrew months
and our own, the Table just given must be taken with some latitude.
Although the Hebrew months now fall usually as therein indicated,
partly in one of our months, partly in another, yet it is quite possible
that the whole of some Hebrew month may correspond to, or be included
by one of our own. Thus in A.D. 1897, Siwan corresponded with
June ; Siwan 1 was June 1, Siwan 30 was June 30. So, too, the whole
of Tammuz was included in July ; the first day of that month was
July 1, the last day was July 29, Tamrnuz being a month of twenty-
nine days. Such correspondence does not, however, occur fre-
quently.
5. It will be gathered from what has been said that the ancient
Hebrew year consisted, usually, of twelve Lunar months;* and, taking
the average length of a Lunation at twenty-nine and a half days, there
would be 354 days in an ordinary Lunar year. It must, however,
. ' v - 7. " Solomon had twelve officers over all Israel, which provided victuals
for the King and his household ^each man his month in a year made provision." Also,
1 Chron. xxvii. 1-15, where we find described in detail for twelve months, "the courses of
those that served the king month by month throughout all the months of the year. "
THE JEWISH CALENDAR 9
be distinctly understood that the ancient Hebrew calendar was not
permanently fixed. The Lunar year falls short of the Solar year by
nearly eleven days, and, because the Hebrew festivals were regulated
not by the Moon alone, but also by the state of the harvests which
depend upon the seasons, that is, upon the influence of the Sun, it
became necessary to reconcile the length of the year when measured
by Lunations to its length when measured by the motion of the
Sun.
For this purpose an extra month was- intercalated once in about
every three years. In later times seven months were intercalated
regularly in the course of every nineteen years. In this way the
Lunar year was brought into accord with the Solar, and the calendar
was made to correspond to the seasons.
There are indications in the Scripture that this was the case ; that
the year was accounted by Moses to be governed by the Sun as well as by
the Moon. Thus, at the very beginning, in the account of the Creation,
we read, Genesis i. 14, 16, "And God said, Let there be lights in the
firmament of the heaven to divide the day from the night ; and let
them be for signs and for seasons ; and for days and years. . . . And
God made two great lights ; the greater light to rule the day, and the
lesser light to rule the night." God did not say, "Let the lesser
light be for years." Both the greater and the lesser light are included
as the signs of the seasons.
There is clear reference to the yearly harvests, and therefore to
the seasons which are governed by the sun, in Exodus xxxiv. 22,
"Thou shalt observe the feast of ingathering at the year's end." Also
in Deuteronomy xiv. 22, " Thou shalt truly tithe all the increase of
thy seed that the field bringeth forth year by year."
Scaliger,* and Frank! show that the year was Luni-Solar, from
the precise details which are given in Genesis concerning the months
and days of the Deluge.
6. It was absolutely necessary for the due observance of the
religious ceremonies, the Fasts and Festivals of the Hebrews, that
the year should be made Luni-Solar. The great Feast of the Pass-
over, upon which all the other Feasts depend, was, by the Levitical
Ij;i\v, to commence not only " at even " on the fourteenth day of the
* " De Ememlatione Temporum," lib. iii. p. 220.
\ "Novum Systema Chronologiae," cap. i. Jj ix. p. 0.
,0 THE JEWISH CALENDAR
Abib, but it was to be kept at the same season of the year as that
which was current when it was first instituted. All tradition pointed
to the Spring season as the time, and accordingly Josephus says,
as already stated (Art. 2), that the Festival was kept when the Sun
was in Aries. Now the day when the Sun enters the Sign Aries is
called the day of the Vernal Equinox, and therefore, in the words
of Lindo,* " the proper season for keeping the Passover is the Full
Moon of the Vernal Equinox, or after the Sun has entered Aries ; it
must be kept while the Sun is in that Sign, but it is indifferent at
what period of it the Full Moon happens." It has been universally
held by the Jewish Babbis that the fourteenth day of the Abib was
intended to mean the day of the Full Moon which came next after the
day of the Vernal Equinox, and that it has always been so understood.
If that be the case the New Moon itself, of which the fourteenth day
was accounted the day of Full Moon, might be before, or upon, or
after the day of the Equinox ; and although there is a difference
of opinion as to whether the Abib began with the New Moon which
preceded, or with that which followed the day of the Equinox, it is
probable that it was made to begin with whichever of the two Moons
were the nearer to the day of the Equinox.
#
7. However this may be, there is no doubt that the Feast was kept
at the time of Full Moon, and the question naturally arises, How did
the Hebrews in the old time determine when the Moon was New, so
that they might correctly reckon the days to the fourteenth ?
The answer must be that in all probability they were sometimes, if
not often, wrong by at least one day; perhaps even by two; unless,
indeed, some special guidance were given to their Priests in this
matter. Of such guidance there is no hint in the Scriptures. No
instructions were given in the Books of the Law as to the method
by which either the New Moon, or its fourteenth day, were to be
found. No doubt it was done from the first, as we know that it was
done in later times, by actual observation, that is, the Moon was
assumed to be New when its crescent became first visible. Whether
this were so or not before and during the time that the first Temple
was standing, it is an established fact that it was so after the Captivity
in Babylon, and that great care was bestowed upon these observations.
Special watchers were appointed, men of good repute, who were sent
* " Jewish Calendar for Sixty-four Years," p. 5.
THE JE WISH CALENDAR ^ i
to the summits of the highest hills in the neighbourhood of Jerusalem
to look for the first appearance of the New Moon. So soon as the
crescent became visible they lighted fires, the smoke of which could be
seen from the city. This method after a time had to be forsaken, for
the Samaritans, in their national enmity to the Jews, deceived them
by lighting false signal-fires before the crescent of the New Moon
had become actually visible. This artifice was soon discovered, and
recourse was then had to special messengers.
Professor Graetz states * that while the custom of indicating the
first appearance of the crescent by these signals prevailed the fires
"could be seen on the Mount of Olives, on Mount Sartaba (Alexan-
drion), on Mount Tabor, and so on, as far as Beth-Beltis on the
Babylonian frontier. On the day when the New Moon was expected
the Babylonian community looked out for the signal, and repeated it
for the benefit of those who lived afar. The congregations in Egypt,
however, Asia Minor, and Greece, could not use bonfires ; they were
uncertain as to the day on which the New Moon fell, and therefore
they kept two days instead of one."
Hence arose the custom, to which further reference will be made
hereafter, of observing two Neomenise, or days for celebrating the Full
Moon t d\ post, Article 89).
8. Maimonides in the " Kiddusch hachodesch," caps. ii. and iii.,
gives an account of the Watchers and of their duties, as well as the
results of the reports that they brought to the Council at Jerusalem.
Riccioli, quoting from many authorities,! but more especially from
E. Jehuda, says that when the watchers had made their report to the
Synhedrion certain figures delineating the phases of the Moon were
exhibited to them. These figures had been drawn by Gamaliel upon
the wall of an upper chamber. They were asked by the Priest,
pointing to the different figures, which phase, or appearance, they
had seen. Is it this? Is it that? If the Rabbis were satisfied that
the witnesses had actually seen the crescent they proclaimed the New
* " History of the Jews," vol. ii. p. 366.
t It may be noted here that Latin writers are careful to distinguish between the time of
the actual or at least the computed conjunction of Sun and Moon, and the day upon which
the festival of the New Moon was observed. For the former the word Novilunium is employed,
for the latter Neomenia, from the Greek vv^r\ia.
I " Chronologia Reformata," lib. xii. p. 13. He says of K. Jehuda, that he was " Author
Misnae Talmtulicae anno fere 100 post Christi ascensionem."
I2 THE JEWISH CALENDAR
Moon by sound of trumpets, and twice repeated the word Mekudash
" Consecrated." * Swift runners were then sent to all places not more
than ten days' journey from Jerusalem to give notice that the important
day had been determined. Kiccioli adds the words, "And yet, as we
have shown previously, it is possible that the first appearance of the
Moon might not take place till the third or fourth day after the true
Conjunction." t
It is quite true that, even if the atmosphere were clear and the
sky free froiii clouds, the New Moon could not possibly be seen before
Sunset on at least the second day after the true Conjunction.
If, then, the Hebrews counted the fourteenth day of the Moon
from this first visibility, as is generally supposed, it would really
be the fifteenth or sixteenth day of the true Moon ; and in this way
would be actually nearer to the time of the true Full Moon than if
they had been able to see the Conjunction itself, and had kept the
Feast on the fourteenth day reckoned from that event.
The average interval of time between the actual New and Full
Moon is more than fourteen days and eighteen hours, so that the
Moon has not only entered upon her fifteenth day at the time she
becomes Full, but is within less than six hours of entry upon her
sixteenth day.
9. Whatever may have been the method of measuring time adopted
by the ancient Hebrews there is a want of any evidence I that, before
the time of the Babylonish Captivity, they possessed an acquaintance
with even the fundamental laws of astronomy, or of the true motions
of the earth and of the heavenly bodies. The names of the four
months, which have been given as in use before the Captivity, prove
that the year was Solar as well as Lunar, for these names have
reference to the seasons at which they respectively occurred.
In 1 Samuel xx. 5 it is recorded that David announced, " To-
morrow is the New Moon," and it has been argued from this that
he must have had some knowledge of astronomical computation, since
the Moon was not visible for one or two days before the Conjunction,
* Maimonides says that the Chief of the Council pronounced the word, and all the people
repented it twice (" Kiddusch hachodesch," cap. i. vii. p. 348).
t " Posse tamen Lunae pi-imam phasiui non contingere nisi 3 aut 4 die post verurn Novi-
lunium ostendiraus, lib. iv. Almagesti, cap. 3" (" Chron. Ref.," lib. xii. p. 13).
J Except, perhaps, some obscure passages with reference to the tribe of Isachar (c. ix>.s/.
Art. 15. p. 21).
THE JEWISH CALENDAR 13
and certainly had not yet been proclaimed. Little weight can be
attached to this ; for, although Lunations vary in length, yet the
variation between two successive Lunations never attains to two hours.
If David knew, as he would know, when the last New Moon occurred,
he must have been ignorant indeed if he could not predict with some
certainty the day upon which the next might be expected.
One thing is clear that the commencements of the Hebrew months
were governed by the New Moons, or rather by the first visibility of
the Moon the phase which she was assumed to present when New.
We know, also, that the year was rendered Luni-Solar by the inter-
calation of an extra month as necessity for it arose. In this way the
seasons at which the Fasts and Festivals were observed would be, year
by year, restored to their proper places.
10, The rules which determined these intercalations were formed
as follows :
One of the Jewish ordinances was that a sheaf of Barley should be
offered before the Lord as the first fruits of the harvest. This was
to be done in the Abib, or month Nisan, immediately after the
Passover, on the second day of unleavened bread, which is the six-
teenth day of the month.* If it were found, before this day had
arrived, that the Barley would not be then ripe it was evident that
the season, according to the reckoning by Lunar months, had been
accounted as arriving too early in the year. It must be made to come
later. The first day of the Abib is approaching ; the first day of the
new year ; the beginning of months. But, by the Sun, the Spring
season has not arrived ; the Barley is not ready for the reapers ; the
lambs for the Passover are not yet fit to be killed. The first day of
* Josephus, ' Antiq.," iii. x. 5. In Leviticus xxiii. 11 it is called " the morrow after the
Sabbath." There has always been some difference of opinion as to the meaning of this
phrase. It is generally considered, both by Jews and Christians, that the Sabbath here
mentioned is the first day of holy convocation of the Passover, to which reference is made
in verses 6 and 7 of the same chapter : " In the fifteenth day of the same month is the feast
of unleavened bread unto the LORD : seven days ye must eat unleavened bread. In the first
day ye shall have an holy convocation : ye shall do no servile work therein."
In the Septuagint version the Hebrew words are rendered by >'/ ivavpiov r//e 7rptur;e, " the
morrow of the first day," that is, the day after the first day of the festival.
There is a passage in the Book of Joshua, v. 11, which confirms the view that the day in
question was Nisan 16 : " They did eat of the old corn of the land, on the morrow after the
Passover, unleavened cakes, and parched corn in the self-same day."
For a full discussion of the question and the opinions of various authorities see the article
" Pentecost," by Samuel Clark, in Smith's " Dictionary of the Bible," Note b.
I4 THE JEWISH CALENDAR
the ceremonial year must be postponed till the next Lunation com-
mences. The current year which is coming to a close must be
increased in length by another month.
11. Some authorities state that the extra month was intercalated
whenever the first day of the Passover happened to occur before the
day of the Vernal Equinox.* This may have been the case in later
times, but it is probable that the ancient Hebrews were content with
noticing that the New Moon which, if no correction were made, would
be the first in the Spring season, w T as coming too soon ; that the
Spring had not actually arrived ; and that, in order to keep the great
Festival at the appointed time they must wait for the next Moon.
12. The method of forming the months and years which has been
indicated continued in use among the ancient Hebrews only while
they dwelt in their own land. After the dispersion f thej* were com-
pelled to employ astronomical calculations for the purpose of fixing
the times of Fasts and Festivals, as they had no means of rapid com-
munication with their co-religionists scattered throughout the civilised
world.
For this purpose Cycles were employed. The first that was used
appears to have been that of eighty-four years, formed by adding the
Octaeteris of Cleostratus to the seventy-six years of the Callippic
Cycle.! Whether this were so or not must, however, remain
* Prideaux, " Connection of History," vol. i. p. 0.
t The dispersion of the Jews throughout -the world is very commonly dated from the siege
and fall of Jerusalem, A.D. 70. It had, however, commenced long before this event. Large
colonies of Jews were formed in Egypt under the Ptolemies ; by Ptolemy Soter in particular.
After the death of Alexander the Great, B.C. 323 or 324 (the exact date is disputed) Ptolemy
took Jerusalem, and carried many Jews to Alexandria. Strabo says that they occupied a
considerable portion of that city, and were so numerous that they had a governor of their
own who protected their laws and customs, as though he were a ruler of a free republic.
There were also many Jews in Cyrene; we read in Acts of the Apostles vi. 8 that the Cyrenian
Jews had a synagogue of their own in Jerusalem. Antiochus the Great, who was very friendly
to the Jews, removed two thousand families from Mesopotamia and Babylonia where they
were in danger, and settled them in fortified places in Phrygia and Lydia ; allotted to them
lands and possessions, and discharged them from the liability to taxation for ten years
(Josephus, " Antiq.," xii. 3 ; Prideaux, " Connection of History," vol. iii. p. 155). In the time
of Cicero there were many wealthy Jews in Italy (" Orat. pro L. V. Flacco," vol. ii. p. 176).
In the Acts of the Apostles, iii. 9-11, there is a long list of countries from which foreign Jews
had assembled at Jerusalem .
\ Ideler, " Handbuch," bd. i. p. 571, gives as the authority for this statement Epiphanius,
" Ho?res," li. ch. 26, p. 448.
THE JEWISH CALENDAR 15
doubtful, because during very many years more than six centuries
after the time when astronomical computations were first made the
method by which the New Moons and Festivals were determined was
kept as a profound secret, certain astronomical rules being handed
down by tradition from Patriarch to Patriarch,* but not made public.
About the middle of the third century of the Christian Era Kabbi
'Adda bar Ahaba of Babylon t was anxious to deliver the foreign
communities from their uncertainty as to the precise days on which
the Festivals were to be observed. Hitherto they had been entirely
dependent upon the messages they received from the Synhedrion in
Palestine. With this purpose in view he made astronomical computa-
tions, adopting the calculations of Hipparchus (made circa B.C. 146),
for the length of a Lunation, namely, 29d. -l'2h. 44m. 3'3s., and for
the Tropical or true Solar year the mean length of 365d. 5h. 55m.
'2-V 4385s. (v. post, Art. 19). About the same time his contemporary,
Rabbi Samuel, or Mar-Samuel, called also Arioch and Yarchinai,t
who had studied astronomy under Persian instructors, drew up a
Calendar for determining the New Moons. He refrained, however,
from making public the method he employed, fearing to disturb the
unity of Judaism, which might suffer if the foreign communities
became independent of the chief Council in Palestine with regard to
these matters.
He adopted the less scientific Julian year of Sosigenes, 365d. 6h.
13. In A.D. 358 Eabbi Hillel II. reformed the Jewish Calendar.
According to the testimony of Rabbi Hai Gaon,;, who lived in the
eleventh century, he finally established it as it is now in use among
the Jews. Isidore Loeb says that he finds it difficult to believe that
this tradition is exact. *\ He does not contest the statement that
* Cj. Graetz, vol. ii. p. 579.
t Lazarus Bendavid, p. 32, says that he was President of the Academy of Sora [in Arabia
Deserta, on the borders of Mesopotamia] in A.D. 250. Ideler gives the date of his birth as
A.D. 183 ("Handbuch," bd. i. p. 574).
\ Graetz, ii. p. 523. Lazarus Bendavid says that he also was President of the Sora
Academy (p. 36). Ideler, bd. i. p. 574, says that he died in A.D. 250.
S Sosigenes was an Egyptian astronomer who assisted Julius Caesar in the correction of
the Roman Calendar, B.C. 46.
|| Gaon = Illustrious. It is a title of honour.
T " Tables du Calendrier Juif," p. 5. " Nous avons peine a croire cette tradition soit
parfaitement exacte. Sans contester que Hillel II. ait contribue^ dans une large mesure, a la
creation du calendrier juif, il nous parait impossible d'admettre que le calendrier actuel ait
1 6 THE JE WISH CALE.\ 7). I K
Hillel II. contributed in a large measure to the foundation of the
Jewish Calendar, but maintains the impossibility of admitting that the
actual Calendar, as it now is, could have been formed so early as the
time of Hillel. In his opinion it was not finally settled till after the
fifth century, when the Talmudic Period, so called, had come to a
close.
Whether Hillel II. did really bring the Calendar into its present
shape must remain uncertain, in spite of the efforts of many learned
scholars to solve the question. It is known that both in Palestine and
Babylon the old fashion of observing the Moon remained in use till the
middle of the fourth century.* This, in some measure, confirms the
opinion of Loeb.
It has been stated t that Hillel II. was a direct descendant from
Gamaliel, who was President of the Synhedrion when S. Peter and the
Apostles were called before that assembly (Acts of the Apostles, v. 34),
and at whose feet S. Paul was brought up and " taught according to
the perfect manner of the law of the fathers" (II)., xxii. 3). L. M.
Lewisohn has shown that this tradition is erroneous, t though it is true
that Hillel became President of the Synhedrion w r hen he was about
eighty years of age.
The following account of the circumstances which induced him to
make public his Calendar and method of computation is given by
Graetz. After describing the terrible sufferings of the Jews under
Constantius in the middle of the fourth century, this historian
continues: "The miserable condition of the Jews was the occasion of
an act of self-renunciation on the part of the Patriarch Hillel. which
has never yet been thoroughly appreciated. The custom had prevailed
up to now of keeping secret the computation of the New-Moon and
leap-year, and of making known the times of the Festivals to the
communities in the neighbouring lands by announcing them by
messengers. During the persecutions under Constantius this method
had proved itself both impracticable and useless. Whenever the
exist^, tel que nous Taverns, tlu temps de Hillel. On a de nombreuses preuves que ce calen-
drier n'etait pas encore en usage, au moins dans quelques-unes de ses parties, dans les temps
talmudiques. . . . Le calendrier actuel a done ete acheve apres 1'epoque talmudique, c'est-a-
dire apres le V e siecle."
Hamburger, " Real-Enclycopadie, 1 ' vol. ii. p. 628.
t Prideaux, vol. iv; p. 616.
J " Geschichte des jiidischen Kalenderwesens," p. 23.
" History of the Jews," vol. ii. p. 579.
THE JEWISH CALENDAR 17
Synhedrion was prevented from fixing the date of the leap-year, the
Jewish communities in distant countries were left in utter doubt
concerning the most important religious decisions. In order to put a
stop to all difficulty and uncertainty, Hillel II. introduced a final and
fixed Calendar ; that is to say, he placed at every one's disposal the
means of establishing the rules which had guided the Synhedrion up
till then in the calculation of the Calendar, and the fixing of the
festivals. With his own hand the Patriarch destroyed the last bond
which united the communities dispersed throughout the Koman and
Persian empires with the Patriarchate. He was more concerned for
the dignity of the continuance of Judaism than for the dignity of his
own house, and therefore abandoned those functions, for which his
ancestors, Gamaliel II. and Simon his son, had been so jealous and
solicitous. The members of the Synhedrion were favourable to this
innovation ; they only desired that the second day of the Festivals,
which had always been celebrated by the communities not situated
in Palestine, should not be disregarded. Jose addressetl to the
Alexandrian communities an epistle containing the following words :
' Although we have made you acquainted with the order of the
Festivals, nevertheless change not the custom of yotir ancestors '
(i.e., to observe certain of the New Moons and Festivals upon two days).
The same recommendation was also made to the Babylonians
' Adhere closely to the customs of your fathers.' This advice was
conscientiously followed, and the second day is observed by all the
non-Palestinian communities even at the present time."
14. Professor Graetz does not take the same view as Isidore Loeb
with respect to any further correction of the form and methods of the
Calendar. He says: " The method of calculating introduced by Hillel
is so simple and certain that up to the present day it has not required
either emendation or amplification, and for this reason is acknowledged
to be perfect by all who are competent to express an opinion on the
subject, whether Jews or non-Jews. The system is based on a Cycle
of nineteen years, in which seven leap-years occur.* Ten months in
every year are invariable, and consist alternately of twenty-nine and
* It must not be supposed that these, so called, leap-years are similar to our own. The
" leap-years " of the Professor's translator are generally called Embolismic or Intercalary.
They have thirteen months, and consist of either 383, 384, or 385 days, according to circum-
stances which will be explained.
3
t g THE JEWISH CALENDAR
thirty days [this should be thirty and twenty-nine] ; the two autumn
months which follow Tishri (the most important of all the months),
are left variable, as being dependent on certain circumstances in
Astronomy and Jewish Law. ... It has not been ascertained how
much of this system was invented by Hillel and how much he owed to
tradition ; for it is indisputable that certain astronomical rules were
regarded as traditional in the patriarchal house; in any case Hillel
appears to have laid Samuel's calendar under contribution."
And yet it is certain that Hillel did not adopt the year of E.
Samuel, but that of E. 'Adda. All the authorities are agreed upon
this point, and it is the astronomical length of the year which is
employed by the Jews to this day. Thus, B. Abraham Zacuth, as
quoted by Selden,* says: "The President Hillel, the son of Jehuda
the President, composed the annual computus according to the
astronomical teaching of B. 'Adda, to be employed by us even till
Messiah the Son of David shall come."
AWt'^-- SOJOURN OF THE ISRAELITES IN EGYPT. There is frequent
misapprehension concerning the duration of the sojourn in Egypt.
This arises from an imperfect understanding of the references made to
it in the Scriptures. We read in Exodus xii. 40, " The sojourning of
the children of Israel in Egypt was four hundred and thirty years."
In Genesis xv. 13 there is recorded the prediction of God to Abram
that "his seed should be afflicted four hundred years." S. Stephen,
quoting from Genesis, speaks of the seed of Abram being " evil-
entreated in a strange land for four hundred years" (Acts of the
Apostles vii. 6).
The four hundred and thirty years of Exodus xii. do not refer to
the length of time that the Israelites dwelt in Egypt, reckoned from
the date when Jacob and his sons went there out of Canaan ; they are
the number of years reckoned from the departure of Abram out of
Chaldaea. The four hundred years of Genesis xv. are reckoned from
the birth of Isaac, when the promise of God was made to Abram thirty
years after the patriarch had entered Canaan. This fact is recognised
by the Septuagint version of Exodus xii. 40, " The sojourning of the
children of Israel, which they sojourned in the land of Egypt, and in
* " Dissertatio," cap. xvii. p. 79. He quotes from the Sepher luchasln, fol. 50a, and trans-
lates the Hebrew thus: "Hillel Princeps films R. Jehudse Principis composuit rationem
Intercalationis, seu computum annalem juxta doctrinam astronomicam Rab Adda, a nostris
adhibendam usque dum venerit Messias filius David."
THE JEWISH CALENDAR i 9
the land of Canaan, was four hundred and thirty years," where the
addition of the words, " and in the land of Canaan," is to be
observed.*
This is confirmed by S. Paul, Galatians iii. 17, " This I say, that
the law which was four hundred and thirty years after, cannot dis-
annul the covenant that was confirmed before of God in Christ, that it
should make the covenant of none effect."
With reference to this, S. Augustin says,t "The prophecy was
made to Abram that his seed should sojourn in a strange country, and
be afflicted four hundred years not that they were to be under the
Egyptian persecution for four hundred years, but that it would be four
hundred years [from the time of the promise] before it came to an
end." S. Augustin also says that he computes the four hundred and
thirty years from the seventy-fifth year of the age of Abram, when the
first promise was made to him by God, till the time when the children
of Israel came out of Egypt.
The actual time that elapsed from the entry of Jacob into Egypt to
the Exodus was two hundred and ten years,! for, according to the
Jewish computation,
The interval from the birth of Abram to the
birth of Moses, was 420 years.
Moses was eighty years of age when the
Exodus took place, Exod. vii. 7 80 ,,
500
And, Abraham was one hundred years old when
Isaac was born, Gen. xxi. 5 100 ,,
Isaac was sixty when Jacob was born, Gen.
xxv. 26 60 ,,
Jacob entered Egypt when he was one hundred
and thirty years old, Gen. xlvii. 9 130 ,,
290
* // <~t KctToiKijffic; rail' i/iaij' 'l<rpj}\ >}i> Kar<i>icr]ffav 'ev yy A.lyfiirT'[t KUI ii> yi) \avaur tV//
ciKoaut rpiaKovra.
t " De Civitate Dei," lib. xvi. cap. iv.
J Josephus erroneously makes it 215 years, in " Antiq.," ii. xv. 2.
20 THJ: //:// 'ASH CALENDAR
The difference, or 500 290 = 210 = the time that the Israelites
actually dwelt in Egypt.
It is but fair to add that although this account is very generally
received by modern chronologers, yet it is not universally credited as
correct. Frankius, for example, maintains strongly that the sojourn
in Egypt lasted for four hundred years from the time that Jacob went
there, and that the four hundred and thirty is to be reckoned from the
time that Joseph was sold into bondage.*
The editors of " L'Art de Verifier les Dates " are convinced that
the belief is well founded which makes the sojourn to have been for
four hundred and thirty years from the entry of Jacob to the year of
the Exodus, exclusive,* thus adding thirty years to the period assigned
by Frankius.
* " Novum Systema Chronologies Fundamentalis," p. 155.
t Pt. i. torn. i. p. 364.
CHAPTEE II
ELEMENTS OF THE JEWISH CALENDAE
15. THE HOUR is not divided by the Jews into minutes and
seconds, but into 1080 equal parts called Chalakim. These are the
Ostenta, or Scrupulae of Scaliger and other writers.
The number 1080 possesses certain advantages ; being of the form
2 3 x 3 3 X 5, it has (3 + 1) (3 + 1) (1 + 1), or 32 divisors, including
unity and itself.*
Strauchius states t that Aben Ezra (on Exodus xii.), claims these
divisions as "the divisions of Israel," and that according to Eabbi
Samuel they were brought down from heaven by Isachar, the son of
Jacob. Selden quotes I the words of E. Samuel, according to Abraham
Zucuth in luchasin, fol. 40a, which he translates thus : "Isacharem
ascendisse in firm amentum, et secum deduxisse partes 1080."
S. Jerome says that " the sons of Isachar were learned and erudite
men skilled in the knowledge of time. They were Doctors, Computists,
and Masters, both for the celebration of the Festivals, and for other
matters ; and so in the benediction of Isachar it is said, ' He bowed his
shoulder to bear, and became a servant unto tribute ' ' (Genesis
xlix. 15).
The Septuagint Version has tytvi'iBt] avtjp -ytw/oyoe, " became an
agriculturist." Is it possible that there is a remote reference here to
* Maimonides, " Kiddusch hachodesch," cap. vi. 2 ; De Veil's trans, p. 368. " Hora autem
disti ihuitur in scrupulos mille et octaginta. Quid ita vero? quia numero in isto licet
dimidiam, quartam, et octavam pavtem reperire ; tertiam, sextain, nonans ; itemque quintam
et decimam, atque alias bene multas, qnarum suum quseque nomen habet."
t " Breviarium Chronologicum," lib. i. cap. i. 4.
* " Dissertatio," cap. i. p. 2.
22 THE JEWISH CALENDAR
the ripening of the Barley, one of the determinants in the old times for
the celebration of the Passover ?
In Deuteronomy xxxiii. 19, Moses says of Isachar, " They shall
call the people unto the mountain : there they shall offer sacrifices of
righteousness : for they shall suck of the abundance of the seas, and of
treasures hid in the sand." The Jewish commentators understand this
to mean " treasures hidden in the Law."
In 1 Chronicles xii. 32 it is said of the children of Isachar that they
were men " which had understanding of the times, to know what Israel
ought to do." This is explained as meaning, that they were skilful in
computing the periods of the Sun and Moon, and in ascertaining the
proper times for the feasts and solemnities. Josephus paraphrases the
passage thus " who foreknew what was to come hereafter."*
Maimonides refers to those who wrote in the old times, and says
that they were learned men of the tribe of Isachar, but that none of
their writings have come down to us.
Scaliger t asserts that, although the division of the hour into 1080
parts was claimed by the Jews as their own, it was employed by other
Eastern nations, including the Samaritans, Arabians, and Persians.
He gives no proof of this, and quotes no authority for the statement.
A still smaller division of time is the Bega ; 76 Begai'm are equal to
one Chalak.
It is easy to convert Chalakim and Kegai'm into minutes and
seconds, or the reverse ; for we have
1 hour = 60 min. =. 3600 sees. = 21600 thirds.
= 1080 ch. = 82080 reg.
So that 1 min. = 18 ch. = 1,368 reg.
and 1 sec. = 22'8 reg.
Tables I. and II. show, respectively, the equivalents of Chalakim in
minutes and seconds, and of minutes and seconds in Chalakim and
Regaim.
16. THE DAY is divided into twenty-four hours, which are
numbered from to 23. The Jews have no special names for the days
of the week except for the seventh day, which is Schabbath (Sabbath),
* "Antiquities," vii. 2, 2 (vol. i. p. 346).
t " De Emend. Temp.," lib. i. p. 5, D.
THE JEWISH CALENDAR 23
meaning " a day of rest." For technical purposes the days are
numbered 1, 2, 3, 4, 5, 6, 7, Sunday being the first day, Monday the
second day, and so on to Saturday, the seventh day, which is the
Sabbath.
For Calendar purposes these days may be distinguished as feria 1,
feria 2, &c.
The Jewish day commences at Sunset, but for computations of the
Calendar it is assumed to commence at 6 p.m., for the Meridian of
Jerusalem. This is in the evening of the preceding Christian Civil
day, thus anticipating by six hours the commencement, at Midnight,
of the Christian Civil day ; but six hoars later than the commencement
of the Astronomical day at Noon. This is in agreement with the
ancient record of Genesis i. 5, " The evening and the morning were the
first day." Hence the Jewish Sabbath, feria 7, commences in the
evening of our Friday and terminates in the evening of Saturday.
The commencements of the months of the years, follow the same
rule.
It may be well to notice here the difference between " Corre-
spondence" and "Coincidence" as those terms will be employed
hereafter. When a Jewish day is said to " correspond " to a Christian
day reference is made to the last eighteen hours of the former and to
the first eighteen hours of the latter, periods which in both cases
include the twelve hours of day-time as distinguished from night-time.
Thus, the Jewish feria 1 is said to " correspond" to our Sunday ;
but feria 1 does not " coincide " with Sunday. The twenty-four hours
of feria 1 " coincide " with the twenty-four hours which elapse between
6 p.m. of our Saturday and 6 p.m. of Sunday.
In the same way, the Jewish year 6179 is said to " correspond " to
the Christian year 2419, and that its first day will be Monday,
October 1, A.D. 2418. It will be seen at once that the " correspondence "
extends only to the last nine months of the Jewish year 6179, and to
the first nine of A.D. 2419. The " coincidence " is really from 6 p.m.
of Sunday, September 30, 2418, to 6 p.m. of Friday, September 21,
2419.
The following Synopsis for three days may assist in indicating the
difference between the Jewish Calendar method of noting the hours
and our own ordinary Civil notation :
THE JEWISH CALENDAR
Jewish Notation.
(1. h. ch.
3
6
9
9 540
12
18
18 810
200
260
2 12
2 18
2 19 270
300
360
1
1
1
1
1
1
1 15
1
1
3 12
&c.
equivalent to
Ordinary Civil Notation.
h. in
Saturday ... 6 p.m.
9 p.m.
Sat.-Sun. .. Midnight.
Sunday .. 30 a.m.
3 30 a.m.
6 a.m.
9 a.m.
Noon.
12 45 p.m.
6 p.m.
Midnight.
6 a.m.
Noon.
1 15 p.m.
6 p.m.
Midnight.
6 a.m.
Sun.-Mon.
Monday
Mon.-Tues.
Tuesday
d-c.
It must be very distinctly understood that such an expression as,
for example, 7d. 3h. 540ch., when used to indicate the instant of time
at which some event takes place on a particular day of the week, means
nothing more than that 3 hours 540 chalakim of the seventh day of the
week have elapsed. Thus, if any event, such as the time of a Con-
junction of the Sun and Moon, be noted as occurring at 7d. 3h. 540ch.,
this does not mean that seven whole days, together with 3h. 540ch. of
the next day have elapsed since some fixed time, but simply that the
event takes place upon the seventh day of the week when 3h. 540ch. of
that day have elapsed, the instant when the event occurs being equiva-
lent to 9h. 30m. p.m. on a Friday in our own Civil notation, because
the seventh Jewish day commences at 6 p.m. on our sixth day.
If, however, it be expressly stated that the interval of time since
some fixed standard is 7d. 3h. 540ch., then it does mean that seven
whole days, together with 3h. 540 ch. of the eighth day have elapsed.
17. All time, for purposes of the Jewish Calendar, is computed
according to local time at Jerusalem ; that is, the computations are
made for the Meridian of Jerusalem. Maimonides quotes, as the
reason for this, Isaiah ii. 3 : " Out of Zion shall go forth the law, and
the word of the Lord from Jerusalem.*
"Kiddusch hachodesch," cap. i. viii. (De Veil, trans., p. 344).
THE JEWISH CALENDAR 25
At Jerusalem, Solar time is 2h. 21m. in advance of Greenwich
time. In other words, when it is 2h. 21m. p.m. at Jerusalem, it is
only Noon at Greenwich (v. post, Chap. IV. Article 47).
18. The Jewish MONTH is of two forms Astronomical and Civil.
The Astronomical Month is the mean length of a Lunation, or
Synodical Month ; its duration is taken as
29d. 12h. 793ch.,* or 29d. 12h. 44m. 3'3s.,
which only differs from the latest computation of Elger by '649 of a
second.
No variation has ever been made from this computation in the
Jewish Calendar. It was adopted, as previously stated, by the Rabbis
Samuel and Hillel II. from the computations of Hipparchus.
The Civil months consist of either 30 or 29 days ; but, before giving
the number of days in each of the months, it will be necessary to
speak of the year which, with the Jews, varies in length to a far
greater extent than that which exists between the common and
Bissextile year of the Christian Calendar.
19. THE YEAK. Although the Jews have adopted as the basis of
their Calendar the Metonic Cycle of nineteen years, or 235 mean
Lunations, yet their computation is more accurate than that of Meton.
He reckoned the mean length of the Tropical year to be 365d. Gh.
19m. 15}^s. ; the Rabbis 'Adda and Hillel II. employed the year of
Hipparchus, consisting of 365d. 5h. 55m. 25'4385s., or 365d. 5h.
OTch. 48reg.t
Dr. Sachau, in his Annotations at the end of his translation of
al-Biruni, says * that there can be no doubt as to the origin of this
year, for it can be exactly obtained through dividing by 19 the length
of 235 Synodical months of Hipparchus, thus
235 Lunations = 6939d. 16h. 595ch.
= 19 (365d. 5h. 997ch. 48reg.).
Petavius says that some assert the year of Babbi 'Adda to have
been 363d. 5h. 595ch. 48reg. These figures are clearly erroneous.
* Maimonides, ' Kid. bach.," viii. i. p. 375. Talmud, Megillath. v. 1.
t Scaliger, lib. iv. p. 279, A. Lazarus Bendavid, Art. 27, p. H2. Ad. Schwarz, p. 65, Ac.
t P. 3H7.
5; " De Emen. Temp." lib. ii. cap. xliii. p. 5)1.
,6 THE JEWISH CALENDAR
The 3 in the units place for the days inust be a misprint for 5, and
the 5 in the units place for the chalakini should be 7, for, a few lines
further on, Petavius says that the difference between the Solar year of
E. 'Adda and twelve Lunations, or 354d. 8h. 876ch., is lOd. 21h. 121ch.
If the interval of time which, he says, some have assigned to the year
of E. 'Adda were right, the difference would be only 8d. 21h. 119ch.,
which is absurd. In other passages he gives the length correctly.*
The nineteen years of the Jewish Cycle, whether they be Civil or
Astronomical, are divided into Common and Embolismic years. Of the
former there are twelve in every Cycle, each consisting of twelve Lunar
months. Of the latter there are seven, each consisting of thirteen
Lunar months.
The Embolismic years stand, in the numerical range of the cycle,
as,
3, 6, 8, 11, 14, 17, 19.t
This order, according to Dr. Sachau,J has only become canonical
since the time of Maimonides. It is not mentioned by al-Biruni.
Scaliger, and others, give, as a Latin version of the Hebrew
memorial for this order of intercalation, the words, "Ter, ter, bis,
ter, ter, ter, bis " " third, third, second, third, third, third, second."
Insomuch as the first year of their Era is accounted by the Jews in
their chronology as the first year in the first Cycle of nineteen years, it
is only necessary, in order to find the Cycle and position in the Cycle
of any given year, to divide the number representing the given year by
19. - The quotient will give the Cycle, the remainder will give the
position of the year in the Cycle.
If the remainder be one of the numbers given above, then the year
is Embolismic. If it be any other number, the year is Common. If
there be no remainder the year is the last in the Cycle, and is therefore
Embolismic.
This maybe reduced to the following general rule: If H denote the
( 7 TT -i- IS)
year, then it is Embolismic when s - -\ [j is greater than 11.
* E.g., ii. xlv. p. 93.
t Maimonides, " Kid. hach.," vi. xi. p. 370.
I "Annotations on al-Biruni," p. 390.
S Lib. vii. p. 626, B.
|| That is, the remainder after dividing 7 H + 13 by 19.
THE JEWISH CALENDAR 27
20. The arrangement, or system, of the Embolismic years in the
Cycle is not arbitrary. They are introduced when the accumulated
excess in the estimated mean length of the Solar years over the length
of twelve mean Lunar months attains to one month, or as near to
that point as possible. The exact coincidence of the 19 years of
an Astronomical Cycle with 235 Lunations, according to the: Jewish
estimation of the mean lengths of the true Solar or Tropical year, and
of a Lunation, may be shown as follows :
d. h. ch. reg.
Estimated length of the Tropical year ... 365 5 997 48
of twelve Lunations .. 354 8 876
Excess of one Tropical year 10 21 121 48
two years 21 18 243 20
three 32 15 364 68
Consequently,.
At the end of the 3rd year there would
be a deficit 32 15 364 68
But the 3rd year has a thirteenth month 29 12 793
So that the deficit is reduced to 3 2 651 68
At the end of the 6th year there would
be a further deficit for three years ... 32 15 364 68
35 17 1016 60
But the 6th year has a thirteenth month 29 12 793
So that the deficit is reduced to 6 5 223 60
At the end of the 8th year there would
be a further deficit for two years ... 21 18 243 20
27 23 467 4
But the 8th year has a thirteenth month 29 12 793
So that now there is an Excess of 1 13 325 72
During the next three years, the 9th,
10th, llth, there would accumulate
a deficit of . 32 15 364 68
THE JEWISH CAI.EXDAR
cl. h. ch. i\r.
would be a deficit 31 2 38 72
But the llth year has a thirteenth month 29 12 793
Which reduces the deficit to 1 13 3i>:> 7'2
At the end of the 14th year there would
be a further deficit for three years ... 32 15 364 68
34 4 690 64
But the 14th year has a thirteenth month 29 12 793
So that the deficit is reduced to 4 15 977 64
The deficit for the next three years, 15th,
16th, 17th, is 32 15 364 68
So that at the end of the 17th year it
would be '. 37 7 262 56
But the 17th year has a thirteenth month 29 12 793
So that the deficit is reduced to 7 18 549 56
During the next two years, 18th, 19th,
there would accumulate a deficit for
two years 21 18 243 20
29 12 793
But the 19th has a thirteenth month 29 12 793
And the Coincidence is exact
21. The Jewish computation of the Metonic Cycle differs from that
used in the Christian Calendar, for, in the first place, the Jewish Civil
year commences in the Autumn, with the first day of the month Tishri.
In the second place, the Cycle used by the Jews does not commence
simultaneously with the Cycle of our Golden Numbers, but two years
and three to four months earlier. Hence every Number in the Jewish
Cycle of nineteen years corresponds to two of our Golden Numbers,
partly to the one, partly to the other.
For example : The Jewish year 5656 commenced in the evening of
THE JEWISH CALENDAR 29
September 18, A.D. 1895, its first day being said to correspond to
September 19. It closed in the evening of September 7, A.D. 1896.
It was the thirteenth year in a Cycle, for the remainder is 13 when
5656 is divided by 19. But the Golden Number for A.D. 1895 was xv.,
and for 1896 it was xvi.
So again, the next Jewish year 5657 commenced on September 7,
1896, and ended on September 27, 1897. It was the fourteenth year in
a Jewish Cycle ; but the Golden Number in the Gregorian Calendar for
1896 is xvi., and for 1897 it is xvii.
In the same way it will be found that every year in the Jewish
Cycle has a number which differs by 2 for the first part, and by 3 for
the latter and greater portion of the year, from the Golden Numbers
of the two corresponding Christian years.
22. There is another and more important difference between the
Calendar years of the Jews and Christians. While the latter have
only two forms for the Civil year namely, the common year of 365
days and the Bissextile of 366 the Jews have no less than six. Their
Common and Embolismic years are each subject to three different
forms. The Common year may contain 353, 354, or 355 days ; the
Embolismic may have 383, 384, or 385. This variation is rendered
necessary by a regulation of the ceremonial law, which will have to be
presently explained. It prohibits the first day of the year from falling
upon either the first, fourth, or sixth day of the week Sunday,
Wednesday, or Friday. Hence, if the first day of a year fall, by
computation, on one of these days, its commencement must be post-
poned to the following day ; in other words, the previous year must be
lengthened by one day. Sometimes the commencement of a year has
to be postponed for two days, for other reasons which also will be
explained.
On these accounts the year has three separate forms, each of which
may belong either to a Common or to an Embolismic year, so that
there are six forms in all.
COMMON YEABS, of twelve Lunar Months.
(1) The Ordinary, or Eegular Common year. The months have
thirty and twenty-nine days alternately, six of each. A year of this
form has therefore 354 days.
3
(2) The Imperfect, or Deficient Common year. A year of this
form has 353 days. The year is not shortened by taking away its last
day, but the third month, Kislew, is shortened by one day. It has
only twenty-nine days, the normal number being thirty.
(3) The Perfect, or Abundant Common year. In a year of this
form, which has 355 days, the extra day is obtained by making the
second month, Marheshwan, to have thirty instead of twenty-nine days.
EMBOLISMIC YEAES, of thirteen Lunar Months.
(4) The Ordinary, or Eegular Embolismic year has an intercalated
month of thirty days. It therefore contains seven months of thirty,
and six of twenty-nine days, or 384 days in all.
(5) The Imperfect, or Deficient Embolismic year. The third
month; Kislew, has only twenty-nine days instead of thirty as in
the Deficient Common year. This loss of one day, with the addition
of the thirty that are intercalated, gives to a year of this form 383
days.
(6) The Perfect, or Abundant Embolismic year. The second
month, Marheshwan, is increased in length from twenty-nine to
thirty days, as in an Abundant Common year. This increase, with
the addition of the thirty intercalated da} r s, gives 385 days to a year
of this form.
23. Whenever an additional month is intercalated, that is to say
seven times in every nineteen years, it invariably comes next after
the fifth month of the Civil year, the last but one of the Ceremonial
year. It comes next before Adhar, whose name and place it takes.
Adhar itself, in these Embolismic years, is called Adhar scheni, Second
Adhar, or Ve-Adhar, that is " after Adhar." The intercalated month
has always thirty days, while Adhar itself, now become Adhar scheni,
retains its usual length of twenty-nine days.*
Al-Birunl f says : " They added these days as a complete month
[i.e., thirty days] , which they called the first Adhar, whilst they called
the original month of this name the second Adhar, because of its
following immediately behind its namesake."
* Maimonides, " Kid. hach.," viii. 5. " Anno intercalari, quoniam Adar nuiuerantur
duo, primus eorum fit plenus, cavus alter." De Veil, trans., p. 376.
t P. 63.
THE JEWISH CALENDAR 31
It is necessary to be particular with respect to this fact, for the
very reverse is sometimes stated or implied. But a great mistake is
made when it is said that Ve-Adhar is the intercalated month, and
that it has only twenty-nine days, while a thirtieth day is added
to Adhar. With respect to this error, Meier Koenick says that most
of the chronologists are mistaken in supposing that Adhar II., or
Ve-Adhar, is the intercalary month ; the month Adhar in Common
years, and Adhar II. in Embolismic years are identical. He states
I distinctly that in Embolismic years Adhar I. has thirty days and is
the intercalary month, and that the second Adhar, or Ve-Adhar, has
twenty-nine days.*
Al-Biruni says : t " According to another opinion, the first Adhar
is the original month, the name of which, without any addition, was
used in the Common year, and the Second Adhar is to be the Leap-
month in order that it should have its place at the end of the
year, for this reason, that, according to the command of the Thora, t
Nisan was to be the first of their months. This, however,
is not the case. That the Second Adhar is the original month is
evident from the fact that its place, and length, the number of its
days, the feast and fast-days which occur in it, are not liable to any
changes. And of all these days nothing whatsoever occurs in the
First Adhar of a leap-year. Further, they make it a rule that, during
the Second Adhar, the Sun should always stand in the Sign of Pisces,
whilst in the First Ahhar of a leap-year he must be in Sign of
Amphora."
The fact that, in an Embolismic year, all the Fasts and Festivals
which are proper to Adhar are observed in Ve-Adhar is sufficient
proof that the additional month is formed by the intercalation of
thirty days before Adhar and not after it. It proves, moreover, that
a day is not added to Adhar in Embolismic years, but that in such
* "System der Zeitrechnung," p. xxviii. " Adar der Iste hat 30 Tage, 1st das Schaltmonat.
Der 2te Adav oder Veadar hat 29 Tage. Der meisten Chronologen irren, wenn sie der
Meinung sind, dass der Monat Adar der 2te oder Veadar der Schaltmonat sei, wo sei wohl
der veranderte Name Veadar dazu verleitete, welcher Name im Hebraischen noch einmal
Adar nur bedeutet. Der Monat Adar im gemeinen und der Monat Adar der 2te im
Schaltjahr sind identisch, beide haben nur 29 Tage, und in beiden werden auch die Feste,
die fur diesen Monat angeordnet sind, als z. B. das Hamansfest u. s. w. gefeiert. Der
Monat Adar der Iste ist der Schalt-Monat und hat 30 Tage."
t " Vestiges," p. 63.
t The Book of the Law.
32 THE JEWISH CALENDAR
years it has still twenty-nine days only ; and it is the original Adhar
which, in these years, is called Ve-Adhar, or Adhar scheni.
The authors of " L'Art de Verifier les Dates " * as w r ell as Ideler, *
Isidore Loeb, * and Lindo, appear to be in error in this respect.
24. The table on page 33 gives the number of days in the months
for each of the six different forms of the year ; the last column
contains the names as they are usually written in England.
25. It should be noticed here that the number of days from the
beginning of Nisan to the end of the year never varies. In each of
the six forms of the year the last six months contain 3 x 30 + 3 x 29,
or 177 days. The variations in the length of the year are caused by
the changes made during the first six months. In Common years the
months Marheshwan and Kislew vary from their regular length
when the year is deficient or abundant. In Embolismic years there
is the same variation in the length of these months as well as the
greater change caused by the addition of the Intercalary Adhar.
The following is the arrangement :
COMMON YEARS.
Deficient. From Tishri 1, inclusive, to Nisan 1, exclusive, 176 days.
Regular. 177
Abundant. 178
In each form : From Nisan 1, inclusive, to the end of the year,
177 days.
* Pt. ii. torn. ii. p. 115. "Dans leur annee extraordinaire il y en avait un treizieme
qu'on intercalait apres adar, et qu'on appelait par cette raison rcddur, le second adar; de
sorte que 1'annee extraordinaire avait treizemois."
t Band i. p. 541. "Man sieht also Thischri, Schebat, Adar im Schaltjahr, Xisan
Sivan und ab haben immer dreisig, Tebeth, Adar im Gemeinjahr oder Veadar im Schaltjahr,
Ijar, Thanius und Elul immer neum und zwanzig Tage."
J Tables du Calendrier luif, Paris, 1866, p. 4. "Dans les annees embolisniiques le. 6
mois a 30 jours au lieu de 29, et le mois supplemental a 29 jours ; de sorte que les aiinees
embolismiques ont 30 jours de plus que les annees communes."
S " Jewish Calendar for Sixty-four Years," p. 5. " In Embolismic years Adar has thirty
days, and the Intercalary month, Ve-Adar, twenty-nine."
THE JE WISH CALENDAR
33
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34 THE JE WISH CALENDAR
EMBOLISMIC YEARS.
Deficient. From Tishri 1, inclusive, to Nisan 1, exclusive, 206 days.
Regular. > 207 ,,
Abundant. ,, ,, 208 ,,
In each form: From Nisan 1, inclusive, to the end of the year,
177 days.
Also : Because from Nisan 1, inclusive, of any Civil year, H, to
Tishri 1, exclusive, of the following year, H + 1, there are always 177
days, therefore Tishri 1 of the year H + 1 is always the 163rd day
after Nisan 15 of the year H. For in every year, whether it be defi-
cient, regular, or abundant, Common, or Embolismic, there are
From Nisan 16 to 30 15 days.
'lyar has always 29 ,,
Sivan 30
Tamniuz ,, 29 ,,
Abh 30
'Elul 29
162
and Tishri 1 of the next year is the 163rd day. It will be found here-
after that use is made of this fact in computing the date of the
Passover.
26. The Astronomical Lunar year is also of two forms Common
and Embolismic. These forms, unlike those of the Civil years, are
constant ; they are not divided into regular, deficient, and abundant
lengths.
The Common Astronomical year is the duration of time occupied
by twelve Lunations, namely,
354d. 8h. 876ch.
or, 354d. 8h. 48m. 40s.
The Embolismic Astronomical year is the duration of thirteen
Lunations, namely,
383d. 21h. 589ch.
or, 383d. 21h. 32m. 43'3s.
35
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THE JE WISH CALENDAR
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THE JEWISH CALENDAR
37
27. In the preceding Table, which is given as an example of eight
consecutive Jewish years, the commencement of each month must be
understood as taking place six hours earlier than the corresponding
Gregorian day. Thus, Tishri, A.M. 5650, is entered in the Table as
corresponding to September 26, A.D. 1889. It commences at 6 p.m.
on September 25,* which is six hours before the commencement of
the Civil day, September 26. In fact, Tishri 1, A.M. 5650, really
coincides with six hours of September 25, and eighteen hours of
September 26. So it is throughout the Table.
28. It will be useful, for purposes of reference, to collect here in a
tabular form the leading elements of the Jewish Calendar.
(1) The Common Civil year, Eegular 354 days.
Deficient 353
Abundant 355
The Embolismic Civil year, Regular 384
Deficient 383
Abundant 385
(2) The Astronomical month 29d. 12h. 793ch.
= 29d. 12h. 44m. 3'3s.
(3) Twelve Astronomical months 354d. 8h. 876ch.
= 354d. 8h. 48m. 40s.
(4) Thirteen 383d. 21h. 589ch.
= 383d. 21h. 32m. 43'3s.
(5) Cycle of nineteen years 6939d. 16h. 595ch.
=6939d. 16h. 43m. 3'3s.
From these figures we obtain the remainders after subtracting
seven days as often as possible :
(6) For the Astronomical month Id. 12h. 793ch.
(7) Twelve Astronomical months 4d. 8h. 876ch.
(8) Thirteen ,, 5d. 21h. 589ch.
(9) Cycle of nineteen years 2d. 16h. 595ch.
(10) two Cycles 5d. 9h. HOch.
(11) three Cycles Id. Ih. 705ch.
(12) four Cycles 3d. 18h. 220ch.
* 6h. 34m. for the Latitude of London.
THE JEWISH CALENDAR
Compare with these
a. Mean Julian year . 365d. 6h. Om.
b. Cycle of nineteen mean Julian years 6939d. 18h. Om.
c. Mean Gregorian year 365d. 5h. 49m. 12s.
d. Cycle of nineteen mean Gregorian years... 6939d. 14h. 34m. 48s.
e. Cycle of 400 Gregorian years 146097d.
Hence we have-
CIS) The excess of a mean Julian year above
a Jewish Common Astronomical year
(14) The excess of a Jewish Embolismic
Astronomical year above a mean
Julian year
(15) The excess of nineteen mean Julian
years above Cycle of nineteen
Jewish years
(16) The excess of the Jewish Cycle of
nineteen years above nineteen mean
Gregorian years
lOd. 21h. llm. 20s.
= 10d. 21h. 204ch.
28d. 15h. 32m. 43'3s.
=28d. 15h. 589ch.
Od. Hi. 26m. 56'6s.
Od. Hi. 485ch.
Od. 2h. 8m. 15'3s.
Od. 2h. 148'59ch.
29. Inasmuch as the Jewish Cycle of nineteen years is shorter by
Ih. 485ch. than nineteen mean Julian years, it follows that ever since
the formation of the Jewish Calendar the close of every Cycle has
retrogressed from the Julian Calendar. In other words, the com-
mencement of every Jewish Cycle of nineteen years comes a little
nearer to the beginning of the Julian year than did the commencement
of the previous Cycle. This retrogression will amount to one day in
less than 315 years. Hillel formed the Calendar in A.D. 358 ; since
that time 1542 years have elapsed, and therefore (measuring by Jewish
Astronomical years) the commencements of the present Jewish years
ought to have approached nearer to the commencements of the Julian
years by nearly five days.
On the other hand, if the mean length of the true Solar year be taken
as 365d. 5h. 48m. 46s., the value of nineteen true Solar years will be
6939d. 14h. 26m. 34s. The length of the Jewish Astronomical Cycle
THE JEWISH CALENDAR 39
of nineteen years exceeds this interval of time by 2h. 16m. 29'3s. It
follows that the commencement of every Jewish Cycle conies a little
later, with reference to true Solar time, than the commencement of the
preceding Cycle. This advance will amount to a whole day in a little
less than 201 years. Assuming, then, that the Calendar of Hillel was
correct, both by Sun and Moon, in the year 358, it follows that all the
Jewish Fasts and Festivals are now about seven days later in the year
by the Sun than they were at that time. Unless some correction be
made, the time will arrive when the first day of the Jewish year will
have left the season of the Autumnal Equinox, and have advanced to
the Winter ; while the Feast of the Passover instead of being observed
in the Spring will be transferred to the Summer. It will not, however,
be till A.D. 6372 that the error will amount to a whole month, and
may then be easily corrected by dropping an Embolismic month.*
30. Table III. shows the Astronomical duration of time in the
Jewish Common and Embolismic years ; and Table IV. shows the
time elapsed at the close of each year of a Cycle. By Table V. the
duration of any given number of Jewish Cycles may be found. These
are all according to Astronomical computation, and must not be
confused with the lengths of the Civil years and Cycles. Table V.
will be used as follows :
Kequired the Astronomical duration of 327 Cycles.
300 Cycles = 2081906d. 21h. 300ch.
20 = 138793d. 19h. 20ch.
7 = 48577d. 19h. 925ch.
327 = 2269278d. 12h. 165ch.
* ( 'i'. Isidore Loeb, " Tables de Cal. Juif," p. 6.
CHAPTEE III
THE JEWISH MUNDANE ERA
31. MOLED, pi. MOLEDOTH, is a Hebrew word meaning renewal,
rejuvenescence. It would be properly applied to the phase of the
Moon at the instant of time when her Conjunction with the Sun takes
place. It is, however, commonly used not for the actual time of New
Moon, but for the computed time, which governs the commencement
of each month, and, thence, the commencement of each year and of
each Cycle.
Thus, the Molad* for any month is the computed time of New
Moon which determines the Astronomical commencement of the
Lunation, as distinguished from the Civil commencement of the
month, which is affected by other considerations. The Molad for
a year is the Molad for the first month of that year. The Molad for
a Cycle is the Molad for the first month of the first year of that Cycle.
The Molads are not expressed in full ; that is to say, they do not
give the whole interval of time elapsed since the commencement of
the Jewish Era, but only the feria, or day of the week, and the time
upon that day at which the computed New Moon occurs. Thus : If
it be stated that the Molad for a certain year is 5d. 13h. 259ch. it
means that the first New Moon of that year occurs, by computation,
on feria 5, at 13h. 259ch. after the commencement of that day,
corresponding to Thursday, 7h. 14m. 23s., a.m.
32. It must always be remembered that the computed time of
New Moon, for the Jewish Calendar, is not the time of the actual
Conjunction of the Sun and Moon. The length of a Lunation, as
* The Anglicised form of the word as it is usually employed.
4
THE JEWISH CALENDAR 41
adopted by the founders of the present permanent Calendar, is a
constant quantity, whereas the Lunations of the true Moon of the
Heavens are variable in their duration. The Moon of the Jewish
Calendar is a mean or average Moon moving uniformly, such as the
artificial Moon of Hilarius, which is used in the Julian and Gregorian
Calendars of the Christian Church.
The present Calendar is called permanent because no alteration
can be made in any Jewish law, including the Calendar, except by the
Great Synhedrion, and only when the Assembly is at Jerusalem. The
Calendar, therefore, must, of necessity, remain permanent, and can be
subjected to no correction until such time as the Synhedrion shall
again be able, under the Will of God, to meet in the Holy City a
time to which many look forward with hope and expectation.
33. The Jews do not reckon the commencement of their Mundane
Kni from the day upon which they believe that the world was created,
although the contrary to this is very often erroneously stated.
They hold that the world was created by God at the time of the
Autumnal Equinox, September 21, in the year of the Julian Period
954, B.C. 3760, and that the Sun and Moon were formed on the fourth
day of the week at 15h. measured from 6h. of the preceding evening,
that is, at 9h. in the morning of feria 4, Wednesday.* But the
Mundane Era, the Calendar, and the computation for New Moons do
not start from this point. They commence from 'a fictitious or
imaginary Moon, the first Moon of an imaginary or anticipative year
next preceding the year of the creation of the world. 1 The first day
of this imaginary Moon, if it had existed, would have been in the year
of the Julian Period 953, on the second day of the week, feria 2, at
5h. '204ch. after the commencement of that day, that is, at llh. 204ch.
p. m-. for the Meridian of Jerusalem.
This day corresponds to Monday, October 7, B.C. 3761, and the
time to Jlh. 20m. p.m., or 40m. before the close of that Julian day at
midnight. This day and hour is the Jewish Epoch, or Commencement
of the Era, from which all computations for the Calendar are made.
* Genesis i. 16, 19. "And God made two great lights, and set them in the firmament of
heaven . . . and the evening and the morning were the fourth day."
t Compare with this the commencement of the Dionysian Paschal Cycle ; it does not
commence simultaneously with the first year of the common Christian Era, but is reckoned
from the preceding year, its first day being January 1, B.C. 1.
4 2 THE JEWISH CALENDAR
34. It is not clear how the exact day and hour were determined,
neither is it known when this Epoch was first introduced. It is
possible that Eabbi 'Adda or Eabbi Samuel may have computed
backwards from the Molad of some year or Cycle as actually observed
by themselves or by Persian astronomers, and that their reckoning
was adopted by Hillel II. ; or Hillel himself may have made an
independent computation of the New Moons, reckoning backwards
from the first New Moon of the Cycle current when he formed the
Calendar ; that is to say, from the Molad for the Jewish year 4105,
the first in the 217th Cycle, which was 2d. 4h. 204ch. The day of the
New Moon of Tishri in that year corresponded to Monday, Sep-
tember 24, A.D. 344.
However this may be, it is from the Molad for Tishri in the year
of the Julian Period 953, 2d. 5h. 204ch., Monday, October 7, B.C. 3761,
that the commencements of all the years of the Jewish Calendar, as
determined by Hillel, are computed.*
This Molad is said by Scaliger, Petavius, and others to be called
the Molad TOHU, answering to the Greek x a( >e> " confusion," " nothing-
ness."! It is generally called the Molad BeHaRD,t or B'HaRaD.iJ
35. The passage which has just been quoted, in a footnote, from the
" Kiddusch hachodesch " may seem opposed to the statement that the
Era is reckoned from an imaginary, anticipative year the year which
would have next preceded that of the creation of the world had there
been then any measure of time.
The explanation, if indeed the matter can be explained, is some-
what complicated.
* Maimonides, "Kiddusch hachodesch," De Veil's trans., cap. vi. 8, p. 369. "Jam exordium
putandi ducendum est ab prima post constitutum mundum luna nova. Ea fuit ad secundam
hebdomadse noctem post horam quintam, et consequentis horse scrupulum quartum et ducen-
tesimuin : character est 2. 5. 204. Ab hac oportet luna nova putandi initium repeti."
t Scaliger, " De Emend. Temp.," lib. vii. p. 631, C. " Tohu enim ipsis est, quod veterebus
Graecis \uot;. J '
Petavius, lib. ii. cap. xlvi. torn. i. p. 93. " Novilunium porro conficti illius anni vocnnt
novilunium Tohu, id est confusionis, sive Nihili, quod tune luna nondum esset a Deo comlitu.
Acciditque novilunium illud feria II., hora 5, 204, ab initio noctis."
So, too, Petav., vii. cap. xvii. p. 387. "Ac novilunium Tohu, hoc est confusionis et inane,
sive fictivuni, vocant illud istum."
Adolf Schwarz, p. 50.
I Isidore Loeb, p. 5. col. 2.
S L. Bendavid, p. 13, 12. Adolf Schwarz, p. 50, note 2. According to the Hebrew
method of numeration the letter B stands f or 2 ; H for 5 ; R for 200 ; D for 4.
THE JEWISH CALENDAR 43
De Veil, in a note on the passage quoted, asks the question :
" How can it be possible that the first New Moon after the Creation
occurred on the second day, when we have it laid down in the Law that
the luminaries were created on the fourth day, and man upon the
sixth day ? " In order to " untie this knot " he consulted the Hebrew
Commentaries on Maimonides, and found that it was "very necessary
to know that God completed the creation of the first man at the third
hour of the sixth day from the foundation of the world." [He
evidently means the third hour of the day-time, as distinguished from
the night-time ; this would be more usually called the fifteenth hour,
being measured from six o'clock on the preceding evening]. "For
God gathered together the earth out of which He formed the first
man during the first [thirteenth] hour of that day ; and prepared it
during the second [fourteenth]. Since, therefore, from the time of
the first foundation of the world to that of the perfected man there
had elapsed five whole days and fourteen hours of the sixth day, we
must make it our business to know both the month to which those
days and hours belong, and also the first New Moon of that year to
which the month belongs. From the time therefore of that New
Moon, which occurred when the second [fourteenth] hour of the sixth
day was ending, there must be subtracted four days, eight hours, and
eight hundred and seventy-six chalakim (4d. 8h. 876ch.), which is the
excess of a Common Lunar year of twelve months above an exact
number of weeks ; and we find that the first New Moon of the year
which preceded the creation of man occurred on the second day of the
week, when five hours and two hundred and four chalakim of its night
had elapsed. ' Its character [Molad] is therefore 2d. 5h. 204ch. And
certainly, by computing those years which have elapsed since the
creation of the world, this anticipative year may be determined. In
this manner it seems to me that the passage is explained."
The explanation may not be quite so clear to others as it is to
De Veil. He does not say why the New Moon, from the Molad of
which he subtracts the excess of a Common year, is set down at
6d. 14h. Och., that being the time at which the creation of the first
man was completed. Scaliger and Petavius profess to throw some
light upon this point. The former says- 1 " that the New Moon, whose
Molad is 2d. 5h. 204ch., is called Novilimium Tohu. It is a mathe-
* (G<1. 14h. Och.)-(4d. 8h. 876ch.) = 'J<1. oh. '204ch.
f "De Emend. Temp.," viii. p. 631. C.
\
44 THE JEWISH CALENDAR
matical anticipation, Tr/ooXijTratg fu&qftartKfi. But by the Jews this
New Moon is called Neomenia 'rrmrXifewz ; so it is said to be 'criirAi&c
<rf A/;i>ic " [a rebuking, or upbraiding of the Moon]. "For the Jews
have a Folk-lore (fingunt) that the Moon, being jealous of the Sun,
expostulated with God because the Sun shone together with her.
For every ruling power is impatient of a consort. And, being
severely rebuked by God, was shut up in darkness, and not permitted
to shine until man was created. So for two days she did not appear,
which indeed is indicated by their New Moon Tohu."
The way in which Scaliger takes Tohu as indicative of this is clear.
If the excess of a Common year, 4d. 8d. 876ch., be subtracted from
the time recorded by tradition for the creation of the Moon, namely
4d. 15h. Och., then the Molad for the Epoch would be 7d. 6h. 204ch ;
but it is 4d. Oh. 204ch., which is obtained by subtracting the excess of
a Common year from Gd. 14h. Och. Therefore the interval of time
between 4d. 15h. Och. and 6d. 14h. Och., or two whole days all but one
hour, must have been lost to the Moon. In other words, she was
punished by being shut up in darkness for forty-seven hours !
Of course Scaliger places no faith in this Folk-lore. He speaks of
it as being utterly ridiculous. And it is hardly necessary to say that
no Jewish scholar treats the myth that has been so ingeniously
invented with any more respect.
Petavius relates very much the same story.* His method of
reasoning is somewhat complicated, but the substance of his account
is as follows : He says that such of the Jews as adopt a particular com-
putation (that is, those who take .for the Epoch, Monday, October 7,
B.C. 3761, which was not always universally adopted), consider that
the Sun and Moon were created together in the first year of the
world, at the time of the Autumnal Equinox, namely, on feria 4, at
the fifteenth hour from the beginning of the night, that is, at 9 in the
morning of Wednesday. The Moon was then endowed with a bright-
ness equal to that of the Sun ; but, when she spoke contemptuously,
and said that one luminary was quite enough for the world, she was
punished by God for her presumption, and not suffered to shine for
one day and twenty-three hours, nearly two whole days. Consequently
the beginning of the first actual Lunar month, and of the first year,
was delayed till the fourteenth hour of feria 6, that is to 8 a.m. on
Friday morning.
* " De Emend. Temp.," lib. ii. cap. xlv. p. !>;}.
45
Assume then, he continues, that the Sun and Moon were created
together on September 24, at 9h. a.m., in the year of the Julian
Period 954. The Sunday letter was E, and the day was, therefore,
Wednesday.
If this had been the commencement of the first actual Lunar
month the Molad for Tishri would have been 4d. 15h. Och. ; but the
commencement was delayed to the fourteenth hour of Friday,
September 26 : and the Molad from which to reckon would become
the sum of 4d. 15h. Och., and Id. 23h. Och., or 6d. 14h. Och.
If there had been a Lunar year preceding this it would have con-
sisted of 354d. 8h. 876ch., the excess of which above an exact number
of weeks is 4d. 8h. 876ch., which would be the Molad for Tishri in the
fictitious, anticipative year, answering to 953 of the Julian Period.
This is the Molad Tohu, from whence the Era is made to commence.
Thus it appears, he continues, that one day and twenty-three hours,
being the interval which elapsed between the first shining of the Sun
and the first shining of the Moon, is counted as though it were a whole
year ; and this, Petavius asserts, is the rule of the Jewish Masters
"Dies unus in anno pro anno computatur." The statement is
incorrect ; the Jewish masters hold no such doctrine. Moreover, the
saying does not apply, for the interval to be accounted for is not Dies
unus, but two days all but one hour.
The argument from the Molads will be better understood when the
method by which they are computed has been developed.
36. The fact is that Jewish chronologists are not in exact agree-
ment as to the year which is to be taken for the commencement of the
Era. There are three opinions with respect to it.
First, that which may be taken as the orthodox or generally
received view, that Adam was perfected on the sixth day, when five
whole days and fourteen hours had elapsed from the first instant of
creation. These days belong to the end of a year which terminated
at the moment when Adam was perfected by God, and, " Why
should they be lost ? " Why should they not be reckoned as forming a
part of the Era ? If they be counted as they ought to be we shall
have (6d. 14h. Och.)-(4d. 8h. 876ch.) as the Molad for the day, which
would have been Tishri 1 in this year, and that is the proper Epoch
from which the Era should be reckoned.
The second opinion is that the Epoch should be the instant of the
4 6 THE JE \VJSH CALENDAR
perfecting of Adam, namely, the fourteenth hour of the sixth day, and
the Era, which then might properly be called Era.Adami, must be
computed from that Epoch. This would make a difference of one
year in dating, so that, for example, Annus Mundi 5657 would be
Annus Adami 5656.
The third opinion is that no year ought to be counted at all until it
is completed, so that the year of the Creation is the year 0. This
makes a difference, from the Calendar, of two years in dating, and
those who adopt this view would call A.M. 5657 the year 5655.
This is analogous to the contention of some, who still maintain
erroneously that the first year of the Christian Era was the year 0. A
fallacy which has been repeatedly exposed.
37. The Jewish Era of the Calendar is, consequently, Mundane,
commencing with Monday, October 7, B.C. 3761.
Hence, if 3761 be subtracted from the number representing any
Jewish year, then the year of the Lord, which will be found is that
which in its Autumn season* begins to coincide with it. Thus : For
the Jewish Mundane year, or A.M., 5606, we have 5606 3761 = 1845 ;
showing that A.M. 5606 commenced some time in the Autumn of
A.D. 1845, and consequently ended some time in the Autumn of 1846.
If the procedure be reversed, the Jewish year coinciding with any
given year of the Lord may be found. That is, if 3761 be added to
the year of the Lord, then the Jewish year, which commences in the
Autumn of the given year, will be known. Thus : For A.D. 1864, we
have 1864 + 3761 = 5625, showing that in the Autumn of 1864 the
Jewish year 5625 had its commencement.
In establishing the correspondence between Jewish and Christian
dates, care must be taken to ascertain precisely the Christian year to
which the month in the Jewish date belongs. Suppose, for example,
that it were required to find the Christian year in which Nisan 15, of
A.M. 5660, occurs. It would not be correct to say that A.D. 1899 is
the year required because 56603761 = 1899. This equation only shows
that A.M. 5660 began in the Autumn of 1899.1 The last three months
of 1899 must have elapsed before Nisan 15 of A.M. 5660 could have
been reached, for this day always occurs in the Spring ; accordingly,
* August, September, October. The Je%vish Civil years are variable in length, but never
of the same length as the Julian or Gregorian Civil years.
t It began six hours before Tuesday, August 24, Julian = September 5. Gregorian.
THE JEWISH CALENDAR 47
it is in the Spring of A.D. 1890 that the Nisan 15 in question
occurred.*
The first four months of every Jewish Civil year, beginning with
Tishri 1, may have either 117, 118, or 119 days, according to whether
the year be Deficient, Kegular, or Abundant. This applies both to
Common and Embolismic years. Suppose some given year, H, to be
abundant, so that its first four months have 119 days, and let Tishri 1
correspond to September 6 in the Christian year Y. December 31 will
be the 118th day of the Jewish year H. These 118 days of the
Christian year Y will cover the 30 days of Tishri, the 30 of
Marheshwan, the 30 of Kislew, and 28 of Tebeth. The last, or 29th
day of this month Tebeth, and all the remaining months of the Jewish
year H, fall within the Christian year Y + l.
It does not appear that the custom of dating from the creation of
the world was generally employed by the Jews till towards the end of
the fourteenth century. It is possible that this Era may have been
originally suggested by Maimonides, who died A.D. 1204. Bartolocci
says that it was introduced gradually in his time,t but it is not by
any means established that it was used at all in his time.
It is very generally said that previous to the fourteenth century the
Jew employed the Era of the Seleucidae. M. Schwab is strongly
opposed to this, and insists that this Era, called by the Jews the Era
of Contracts, was only used when it was forced upon them by the
Syrian Kings. When they obtained their freedom under the Has-
monaean princes they at once abandoned this method of dating.
That is his opinion, the reasons for which are stated hereafter in
Chapter IX., Megillath Ta'anith, Day xvi.
The Era of the Seleucidae is still used by the Jews of Yemen, or
Southern Arabia.
38. Schwarz refers} to the confusion of ideas that exists with
respect to the true meaning of the Molads. In illustration of this he
* Saturday, April 1, Julian = April 14, Gregorian. With regard to the error which may
be made see pout, Article 68.
t " Bibliotheca magna Hebraica," part ii. p. 430. " ^Era contractuum maxime fuit in
usu apud Hebrseos, perduravitque usque ad tempora K. Mosis Bar Maimonis, quo tempore
jam paulatim introductus erat mos numerandi ab aera creationis mundi et seorsim dimissa
(era contractuum, ita ut hodie omnino cessaverit in Synagoga." The quotation is not taken
direct, but from Ideler, " Handbuch," bd. i. p. 568.
J " Der Jiidische Kalendnr," p. 58, footnote 1.
48
quotes the definition of the word as given by Ideler. " Molad that
is birth of the new luminary, called New Moon ; but not the true
Conjunction which we call New Moon, only the time at which the
Moon first becomes visible, after the Conjunction, in the evening
twilight, which the Greeks call vov/mrivta. The reckoning gives the
Molads so that, as a rule, the crescent of the Moon is visible on the
day which the Molad indicates."*
Thus Ideler very distinctly asserts that the Molad gives the day
upon which the New Moon first becomes visible an extraordinary
mistake, for, as previously stated, the Molad gives the time of Conjunc-
tion with the Sun of an artificial Moon moving uniformly in the
heavens, and has nothing to do with the first visibility of the crescent
of the true Moon. Ideler is correct in stating that the Molad does
not give the time of the true Conjunction ; and he is also correct
when he says beyond the passage quoted by Schwarz " that i,he
interval between any two successive Molads is the mean duration of a
Synodical month, 29d. 12h. 793ch." The very fact of this interval
being a constant quantity proves that the Moon of the Molads is sup-
posed to move uniformly, which is not the case with the true Moon of
the Heavens, whose Lunations are variable in length. But if the
Moon of the Molads move uniformly, how can the Molad indicate the
first visibility of the true Moon which does not move uniformly ?
Moreover, even if the true Moon did move uniformly, the interval of
time which elapses between her actual Conjunction with the Sun and
her first visibility in the evening twilight could not by any possibility
be a certain definite, constant quantity.
Schwarz adds that, to his regret, he is unable to refer to Lazarus
Bendavid, and therefore he cannot say whether Ideler obtained from
Bendavid or from Auerbach this " piece of wisdom " " Weiseheit."
There is no doubt but that he took it from L. Bendavid, who says :
"Moled (birth, i.e., of the Moon), New Moon, that is to say, the
instant of the visible Conjunction of the Sun and Moon.t He con-
* " Handbuch," Band 1, p. 543. " Moled, Geburt. namlich des neuen Lichts, heist der
Neumond, aber nicht gerade die Conjunction, die wir unter Neumond verstehen, sondern die
Zeit, wo der Mond nach der Conjunction zuerst wieder in der Abenddiinimerung sichtbar
wird, was die Griechen vovin]via nannten. Die Bechnung gibt namlich die Moleds so, dass
in der Kegel die Mondsichel au dem Tage erscheint, auf den der Moled trifft."
t " Zur Bevechnung und Geschichte des Jiidischen Kalenders," p. 5, 6. " Moled
(Geburth, sc. des Mondes), Neumond, heist der Augenblick der scheinbaren Conjunction von
Sonne und Mond."
THE JEWISH CALENDAR 49
tinues, as does Ideler, "The interval from one Molad to another is,
according to the Talmudists and Maimonides, fixed at 29d. 12h. 793ch."
39. COMPUTATION OF THE MOLADS. The length of a Jewish
Astronomical month, 29d. 12h. 793ch., exceeds an exact number of
weeks by Id. 12h. 793ch. Consequently, if the Molad for Tishri in
any given year be known, the Molads for all the months in that year
will be found by the successive additions of Id. 12h. 793ch.* Seven
days, and all multiples of 7, are to be rejected whenever the sum of
the days, hours, and Chalakim amounts to or exceeds 8 days. The 7
is not, however, to be rejected from such a Molad as 7d. 15h. 60ch., for
this, as previously explained, indicates a certain time upon the seventh
day, and not that the seventh day is completed and the eighth is
entered. It is evident that 7 cannot be subtracted until the last
hour of the seventh day has elapsed.
It would, perhaps, prevent a confusion of ideas upon this point if
the feriae of Molads were printed in Roman numerals, reserving the
Indian numerals for the hours and Chalakim, thus : iv. 7. 819, or
vii. 15. 60. This, however, is not the custom.
Take now, for an example, the method of obtaining the Molads for
the months of the first year of the Jewish Era, when the Molad for
Tishri was 2d. 5h. 204ch. ; in other words, this month commenced,
Astronomically, upon the second day of the week, when 5h. 204ch. of
that day had elapsed.
d. h. ch.
Molad of Tishri 2 5 204
Add 1 12 793
Marheshwan 3 17 997
Add 1 12 793
Kislew 5 6 710
Add 1 12 793
Tebeth 6 19 423
Add 1 12 793
Schebhat 1 8 136
Add 1 12 793
* Maimonides, " Kid. hach.," vi. 7. " Sicque licet consequentium reperire mensium lunam
novam vel ad infinitum tempus." De Veil, trans., p. 369.
5
5 o THE JEWISH CALENDAR
(1. h. ch.
Molad of 'Adhar 2 20 929
Add 1 12 793
Nisan 4 9 642
Add 1 12 793
'lyar 5 22 355
Add 1 12 793
Siwan 7 11 68
Add 1 12 793
Tammuz 1 23 861
Add 1 12 793
Abb 3 12 574
Add 1 12 793
'Elul 5 1 287
Add 1 12 793
,, Tishri in the next year 6 14
If this process be continued the Molads for all the months from the
commencement of the Jewish Era may be found, care being taken to
add Id. 12h. 793ch. for 'Adhar I., as well as for 'Adhar II., in the
Embolismic years.
The process may be shortened ; there is no necessity to make all
these successive additions in order to find the Molad for any given
month of a year. It is evident that for the sixth month, for example,
six times Id. 12h. 793ch. is to be added to the Molad of the first
month of the year ; while for the tenth month the addition must be
(Id. 12h. 793ch.) x 10 ; seven, and multiples of seven, being rejected
from the days when they exceed seven.
Table VI. shows the additions that are to be made to the Molad of
Tishri in any given year, H, in order to obtain the computed Molad for
any month in that year.
For example : Given that the Molad of Tishri in the year 5659 is
6d. 4h. 704ch., find the Molad for Tammuz in the same year.
First ascertain whether the year be Common or Embolismic. The
THE JEWISH CALENDAR 51
division of 5659 by 19 leaves a remainder 16 ; therefore, the year is
common. The addition to be made to the Molad for Tishri in order
to obtain that for Tammuz in a Common year is, by the Table,
6d. 18h. 657ch. The sum is 12d. 23h. 281ch., from which 7d. may
be rejected, so that it becomes 5d. 23h. 281 ch., the Molad required.
The occurrence of New Moon is thus computed, Astronomically, to be
on feria 5, at 23h. 281ch. after that day has commenced. Now, feria 5
commences, formally, at 6 p.m. on the Christian fourth day of the
week, Wednesday, and when 23h. 281ch. of feria 5 have elapsed, the
time arrived at is 5h. 281ch., or 5h. 15m. 36|s. p.m. on Thursday, for
the meridian of Jerusalem.
40. MOLADS FOR YEARS. A Jewish Astronomical Common year
of twelve months contains 354d. 8h. 876ch. ; and an Astronomical
Embolismic year of thirteen months contains 383d. 21h. 589ch. These
intervals of time exceed an exact number of weeks by 4d. 8h. 876ch.
and 5d. 21h. 589ch. respectively. Therefore, if the Molad for any given
year be known, the Molad s for all succeeding years may be found by
the successive additions of 4d. 8h. 876ch. in the case of a Common
fear, and of 5d. 21h. 589ch. in the case of an Embolismic year.
Take, for an example of the method to be pursued, the first years
of the Jewish Era.
d. h. ch.
Molad of first year 2 5 204
This year was Common, therefore add 4 8 876
Molad of second year 6 14
This year was Common, add 4 8 876
Molad of third year 3 22 876
This year was Embolismic, add 5 21 589
Molad of fourth year 2 20 385
This year was Common, add 4 8 876
Molad of fifth year 7 5 181
This year was Common, add 4 8 876
Molad of sixth year . 4 131057
This year was Embolismic, add 5 21 589
5 2 THE JEWISH CALENDAR
d. h. ch.
Molad of seventh year 3 11 066
This year was Common, add 4 8 876
Molad of eighth year 7 20 362
If this process be continued the Molads for all succeeding years
may be found.
41. Just as the process for finding the Molad for any month in a
given year is shortened by making use of the Table of Additions,
Table VI., so the above process may be shortened if it be required to
find the Molad for any year of a Cycle, assuming that the Molad for
the first year of the Cycle be known. The Common and Embolismic
years maintain constant places in every Cycle, so that it is easy to form
a Table of Additions to be made to the Molad for the first year of any
given Cycle in order to ascertain the Molad for any other year in the
same Cycle.
This Table, VII., is obtained as follows :
Let the Molad for the first year of the given Cycle be M. For the
excess of a Common year, which is 4d. 8h. 876ch., write C.
For the excess of an Embolismic year, which is 5d. 21h. 589ch.
write E.
Then
d. h. ch.
Molad for second year =M + C =M + 4 8 876
Add excess of a Com. year C 4 8 876
Molad for third year =M + 2C =M + 1 17 672
Add excess of anEmb. year E 5 21 589
Molad for fourth year =M + 2C + E=M + 7 15 181
Add excess of a Com. year C 48 876
Molad for fifth year =M + 3C + E=M + 4 23 1057
Add excess of a Com. year C 48 876
Molad for sixth year =M + 4C + E=M + 2 8 853
Add excess of an Emb. year E 5 21 589
Molad for seventh year =M + 4C + 2E =M + 1 6 362
&c. &c.
THE JEWISH CALENDAR 53
It will, of course, be noticed that the Molad for the nib year of a
Cycle is not found by adding (n 1) (4d. 8h. 876d.) to the Molad for
the first year, because the addition for an Embolismic year differs from
that for a Common year.
42. MOLADS OF CYCLES. A Cycle of nineteen years contains
6939d. 16h. 595ch., according to Jewish Astronomical computation.
This interval of time is 2d. 16h. 595ch. in excess of an exact number of
weeks. Hence, if the Molad, M, for any Cycle be known, those for all suc-
ceeding Cycles will be found by the continued addition of this excess.
The Astronomical length of the Cycle being constant, the addition to
be made never varies. This, as will be seen hereafter, is not the case
with the Civil Cycle, which is of variable length.
A general formula for the addition to be made to the Molad, M, for
any Cycle, C, in order to find the Molad for any other Cycle, C + n, is
easily obtained, for
Molad for C + l will be M + 2d. 16h. 595ch.
C + 2 M + 2 (2d. 16h. 595ch.)
C + 3 M + 3(2d. 16h. 595ch.)
And, generally,
C + )i M + n (2d. 16h. 595ch.)
Table VIII. shows the required addition for any given number of
Cycles from one to six hundred, together with the number of years in
such Cycles. It is to be read thus : For seven more Cycles add to the
Molad for the given Cycle 4d. 19h. 925ch. The second column shows
that in seven Cycles there are 133 years.
By means of this Table, together with Table VII., the feria and
hour of the computed New Moon of Tishri for any year in the Jewish
Era is readily found. The additions will, as a rule, be made to the
Molad BeHaRD of the first Cycle, namely, 2d. 5h. 204ch.
Example. Required the Molad for Tishri in the year 5357.
Before the year 5357 commences there have elapsed 5356 years, or
281 Cycles and 17 complete years. Therefore 5357 is the eighteenth
year of the 282nd Cycle.
d. h. ch.
Molad BeHaRD 2 5 204
Add, for 200 Cycles 5 22 200
80 5 4 80
1 Cycle 2 16 595
For eighteenth year (Table VII.) 6 10 210
22 10 209
54 THE JEWISH CALENDAR
From the 22 days there are rejected 21, and the Molad required is
Id. lOh. 209ch. ; that is to say, the computed New Moon of Tishri in
the year 5357 occurs at lOh. 209ch. after the commencement of ferial.
Feria 1 commences at p.m. on the Christian Saturday, therefore the
Christian time of this New Moon will be Sunday at 4h. 209ch. a.m.,
or 4h. llm. 36fs.
Example 2. Eequired the Molad for Tishri in the year 5821.
Here 5820 years, or 306 Cycles and 6 years have expired.
d. h. ch.
Molad BeHaED 2 5 204
300 Cycles 1 21 300
6 2 3 330
For the seventh year 1 G 362
Molad required 7 12 116
43. If the Molad for any year or Cycle be known, that for the
preceding year or Cycle will be obtained by subtracting from the
known Molad the excess of the preceding year or Cycle ; for, if M be
the Molad for any year or Cycle, H, then
M = Molad for (H - 1) + excess of (H - 1)
/. Molad for (H - 1) = M - excess of (H - 1).
Example. The Molad for the year 5648 is Id. Oh. 856ch. ; that for
the year 5647 is required.
Because 5647 = 19 x 297 + 4, it is the fourth in a Cycle, and,
therefore, is a Common year. The excess of an Astronomical Common
year is 4d. 8h. 876ch. This cannot be subtracted from Id. Oh. 856ch.,
which must therefore be increased by 7. This can be done without
altering the day of the week. We have, therefore
d. h. ch.
Molad for 5648 8 856
Subtract excess of 5647 .. 4 8 876
Molad for 5647 3151060
44. It should be noticed that the day of the computed, or Astro-
nomical New Moon of Tishri does not always indicate the day of the
THE JEWISH CALENDAR 55
week, or feria upon which the Civil year, as distinguished from the
Astronomical year, actually commences. There are certain ceremonial
regulations, to he hereafter explained, which frequently cause the
commencement of the year to be postponed for one day, sometimes
for two days. This postponement indeed occurs more often than not.
The same thing applies, of course, to the commencement of the Civil
Cycle of nineteen years, and has an effect upon the number of days
contained in such Cycles.
The method of finding the length of the Civil Cycles will be given
when these regulations have been described.
Hence the necessity of attending to the difference between Novi-
lunium, the computed day of New Moon, and Neomenia, the day on
which the New Moon is celebrated. (See post, Chap. IV., Art. 47.)
45. In Article 36 the additions were indicated which must be made
to the Molad BeHaED in order to find the Molads for subsequent
Cycles. These Molads may now be computed. There are certain
facts, pointed out by Isidore Loeb,* which greatly facilitate the
calculation.
1. For computing the Chalakim.
The duration of one Astronomical Cycle is 6939d. 16h. 595ch.,
and the duration of two Cycles is 13879d. 9h. llOch. Therefore
the duration of two Cycles exceeds an exact number of weeks by
od. 9h. llOch.
Hence the Chalakim in the Molad for any Cycle, C + 2, will be
110 more in number than in the Molad for the Cycle C.
Now, in the Molad for the First Cycle the number of Chalakim
is 204 ; therefore, in the Molad for the Third Cycle there will be
204 + 110, or 314 ; in the Molad for the Fifth Cycle there will be
204 + 2 (110), or 424 ; and so on. Hence, for the Molads of the suc-
cessive^ Cycles with uneven numbers we have, for the Chalakim, an
Arithmetical Series of which the first term is 204, and the common
difference 110. This series may be easily written down, care being
taken to reject 1080 whenever it is possible to do so, this being the
number of Chalakim in one hour, which will of course be carried to
the hours.
The series for the Cycles with uneven numbers will therefore be
204, 314, 424, 534, 044, 754, 864, 974, (1084 - 1080, or) 4, 114, &c.
* " Tables du Calenclrier Juif," p. 6. Probleme i.
5 6 THE JEWISH CALENDAR
Again, for the Cycles with even numbers, the first term of the
series will be the number of Chalakim in the Molad for the second
Cycle ; this is found from the sum of
a. h. ch.
MoladBeHaED 2 5 204
Addition for one Cycle (Table VIII.) 2 16 595
4 21 799
The first term of the series for the Cycles with uneven numbers is,
therefore, 799 ; and, just as in the former case, writing now C + 1 for
C, and C + 3 for C + 2, the common difference is, as before, 110.
Therefore, the series is 799, 909, 1019, (1129 - 1080, or) 49, 159,
269, &c.
A check upon results may be obtained by observing that the nth
term of any Arithmetical Series, whose first term is a, and common
difference d, is a + (n V)d. Thus, the nth term of the first series
will be 204 + (n 1) 110, or HOn + 94. That of the second series,
for the even numbers, will be 779 + (n 1) 110, or IWn + 689. In
both cases 1080 will be rejected as often as possible.
Also, because the 1st, 2nd, 3rd, 4th, &c., terms of the first series
belong to the Cycles whose numbers are 1, 3, 5, 7, 9, &c., the nth
term of this series will belong to the Cycle whose number is In 1.
Thus, if the number of the Cycle be 99, the term of the series which
belongs to it will be the fiftieth, for 99 = 2 x 50 1. In this case
n = 50, therefore the number of Chalakim in the Molad of the ninety-
ninth Cycle is 110 x 50 + 94, or 5594, which becomes 194 when
5 x 1080 is rejected.
In the same way, because the 1st, 2nd, 3rd, 4th, Arc., terms of the
second series belong to the Cycles whose numbers are 2, 4, 6, 8, &c.,
the nth term of this series, for the even numbers, will belong to the
Cycle whose number is 2n. Thus, if the number of the Cycle be 98,
the term of the series which belongs to it will be the forty-ninth, for
98 = 2 x 49. In this case n = 49, and the number of the Chalakim
in the ninety-eighth Cycle is 110 x 49 + 689, or 6079, which becomes
679 when 1080 has been rejected five times.
The result of this is that the Chalakim in the Molad for any uneven
Cycle, as 1, 3, 5, &c., can never be in number other than one of the
terms of the Arithmetical Series 4, 14, 24 .... 1074, where the common
/*
(9
*
THE JEWISH CALENDAR 57
difference is 10 ; and the Chalakim in the Molad for any even Cycle,
as 2, 4, 6, &c., can never be in number other than one of the terms of
the series 9, 19, 29 .... 1079. For the Chalakim in the Molad for
any Cycle C + 2 exceed in number those in the Molad for the Cycle C
by 110, so that, if we write down the series of which the first term is
204, and common difference is 110, rejecting 1080 from any term when
it is possible to do so, we obtain the following system, the terms being
written consecutively in the horizontal lines :
204
314
424
534
644
754
864
974
4
114
224
334
444
554
664
774
884
994
24
134
244
354
464
574
684
794
904
1014
44
154
264
374
484
594
704
814
924
1034
64
174
284
394
504
614
724
834
944
1054
84
194
304
414
524
634
744
854
964
1074
104
214
324
434
544
654
764
874
984
14
124
234
344
454
564
674
784
894
1004
34
144
254
364
474
584
694
804
914
1024
54
164
274
384
494
604
714
824
934
1044
74
184
294
404
514
624
734
844
954
1064
94
After 94 the next term would be 204, and the series recurs ; so that
every term here written is included in the series 4, 14, 24 .... 1074.
By the substitution of the digit 9 for 4, whenever the latter occurs in
the units place, we have a similar system for those Cycles which are
evenly numbered, as 2, 4, 6, &c. Every number in this system will be
covered by one of terms of the series 9, 19, 29 .... 1079.
2. For Computing the Hours.
The length of three Astronomical Cycles is 3(6939d. IGh. 595ch.),
or 20819d. Ih. 705ch. This interval of time is Id. Ih. 705ch. in
excess of an exact number of weeks.
Therefore the number of hours in the Molad for any Cycle, C + 3,
is greater by unity than the number in the Molad for the Cycle C,
assuming that nothing be carried from the Chalakim to the column of
hours. If, however, the sum of the Chalakim be equal to or be greater
than 1080, then 1 hour will be carried from such sum. In this case
the number of hours in the Molad for C + 3 will be greater by 2 than
the number in the Molad for the Cycle 3.
Now, in order to obtain the Molad for C + 3, the whole amount to
be added to that for C, on account of three Cycles, is (by Table VIII.),
Id. Ih. 705ch. ; and 705 = 1080 - 375 ; therefore it is only when the
Chalakim in Cycle C are in number equal to or greater than 375 that
THE JE WISH CALENDAR
1 hour will be carried forward. But as no term in either of the series
for the Chalakim is, or ever can be, 375, it is sufficient to say that the
hours in the Molads of the Cycles, C, C +3, C + 6, C + 9, &c.,
increase by unity if the Chalakim in the respective terms be less than
375, but increase by 2 if the number be equal to or greater than 375,
that is if the number be greater than 374.
The computation for the hours may therefore be distributed into
three series, namely, those for the Cycles whose numbers are
1, 4, 7, 10, 13, &c.
2, 5, 8, 11, 14, &c.
3, 6, 9, 12, 15, &c.
And it will be found, when the Computation is made, that for
Cycle 1 .... the hours are .... 5, and Chalakim less than 375
1 + 3, or 4, 5 + 1, or 6, ,, more
4 + 3, or 7, 6 + 2, or 8, ,,
7 + 3,orlO, 8 + 2, or 10, less
10 + 3, or 13, 10 + 1, or 11, more ,,
13 + 3, or 16, 11 + 2,01-13,
16 + 3, or 19, 13 + 2, or 15, less
., 19 + 3, or 22, 15 + 1, or 16, &c.
Ac. &c.
So, again, it will be found that for
.... 21, and Chalakim more than 375
21 + 2,oi-23, ,, ,,
23 + 2, or 25 I ,
ij iu ,, -less ,,
= Id. In. j
1-+ 1, or 2, ,, more ,,
2 + 2, or 4,
4 + 2, or 6, ,, less ,,
6 + l,oi- 7, ,, &c.
&c.
Cycle 2 . .
. . the hours are
2 + 3,
or 5,
ti
- 5 + 3,
or 8,
f
8 + 3,
or 11,
,,
,. H + 3,
or 14,
14 + 3,
or 17,
17 + 3,
or 20,
,,
Also for-
Cycle 3 ...
3 + 3, or
6 + 3, or
!> + 3, or 12,
12 + 3, or 15,
15 + 3, or 18,
18 + 3, or21,
21 + 3, or 24,
. the hours are .... 14, and Chalakim less than 375
6, 14 + 1, or 15, ,, more ,,
9,
15 + 2, or 17,
17 + 2, or 19,
19 + 1, or 20,
20 + 2, or 22,
(22 + 2, or 24
"( = Id. Oh.
+ l,or 1,
&c.
less
more
less
&c.
THE JEWISH CALENDAR
59
3. Computation for the Days.
Since the excess of three Cycles over an exact number of weeks is
Id. Ih. 705ch., the number of days in the Molad for any Cycle, C,
must be increased by unity in order to find the number of days in the
Molad for the Cycle C + 3. But, if the hours and Chalakim in the
Molad for Cycle C amount to, or are greater than 22h. 375ch., then
the number of days for the Molad of C + 3 will be two more than the
number in that for Cycle C ; because, if 22h. 375ch., or more, be added
to Id. Ih. 705ch., the sum of the hours and Chalakim will either
"amount to or be greater than 24h., so that one day would have to be
earned to the sum of days.
The computation for the days may, however, be made even more
rapidly than by this process, in the following manner :
Let H and h be the hours in the Molads for C and C + 3
respectively. If H be less than h, the days in the Molad for C are
to be increased by unity to give the days in the Molad for C + 3. If
H be greater than h, the increase is to be 2.
It is assumed that the columns of hours and Chalakim, as
exhibited in Table IX., have been written before the days are com-
puted.
This computation will be distributed into three series, in the same
way as the three series for the hours.
Thus we have, for
Cycle 1
days are
2, hours n.vfi 5 :
this is less than 6 of Cycle 4
, 1
+ 3,
or 4,
2
+
1.
or 3,
6;
8 . 7
, 4
+ 3,
or 7,
3
+
1.
or 4,
8;
.
10
10
, 7
+ 3,
or 10,
4
+
1.
or 5,
10;
:
11
13
, 10
+ 3,
or 13,
5
i
1,
or6,
il;
13
16
, 13
+ 3,
or 16,
6 +
1,
or7,
13;
,
15
19
. 16
+ 3,
or 19,
7
+
1.
or 1,
15;
,
16
22
, 19
+ 3,
or 22,
1
+
1,
or2,
16;
18
25
, 22
+ 3,
or 25,
2
1
1,
or 3, &c.
&c
tfrc.
&c.
Again, it will be found that for
Cycle 2 ..*... the days are .... 4,
2 + 3, or 5, 4+1, or 5,
5 + 3, or 8, .. 5 + 2, or 7,
8 + 3, or 11, .. + 1, or 1,
11 + 3, or 14, .. 1 + 1, or 2,
14 + H. or 17. .. 2 + 1, or 3,
17 + 3, or 20, .. 3 + 1, or 4,
<fec. &c.
4, and hours are 21 ; less than 23 of Cycle <>
23 ; more
1
2 :
4;
less
H
11
14
17
20
6o
THE JEWISH CALENDAR
f
. 7, and hours are 14;
less than 15 of Cycle 6
7+'r,
or 1, , 15 ;
,,
17
9
1 + 1,
or 2,
17;
,,
19
12
2 + 1,
or 3,
19;
,,
20
15
3 + 1,
or 4,
20;
,,
22
18
4 + 1,
or 5,
22;
more
21
5 + 2,
or7,
0;
less
1
24
0+1,
or 1,
etc.
&c.
Arid, lastly, for
Cycle 3 ..... the days are
34-3, or 6,
6 + 3, or 9,
9 + 3, or 12,
12 + 3, or 15,
15 + 3, or 18,
18 + 3, or 21,
21 + 3, or 24,
&c.
Following the method here described Table IX. is formed. The
first column gives the number of the Cycle, from 1 to 528 ; the
second gives the year which, in the Mundane Era, corresponds to the
first year of each Cycle ; and the third column gives the Molad for the
Cycle, commencing with BeHaED, 2d. 5h. 204ch., the Molad for the
first Cycle of the Era.
The Chalakim for all the Cycles with uneven numbers are first
written down ; next, the Chalakim for all the Cycles with even
numbers. The hours are then computed ; first, for the series of
Cycles with numbers 4, 7, 10, 13, &c. ; then, for those with the
numbers 2, 5, 8, 11, &c. ; and next, for those with the numbers 3, 6,
9, 12, &c. The days in the three series are computed in the same
order.
It will be remembered that 1080ch. are always to be carried forward
to the column of hours, as 1 hour ; that 24 hours are to be carried
forward as 1 day ; and that 7 is to be rejected from the feria, or
number of the day, when the number amounts to or exceeds 8 days.
The results thus obtained may be tested by employing the Table
VIII. of Additions to be made to the Molad for any Cycle in order to
find the Molad for any subsequent Cycle.
Thus, for Cycle 41,
MoladBeHaKD ........................... 2 5
Add for 40 Cycles ........................... 2 14
204
Molad for Cycle 41 4 19 244
46. It has been demonstrated by Bene Martin * that the Molad s
do not recur in the same order until 36288 Cycles, or 689472 years
* " Mgmoire sur le calendrier hebrai'que." Angers, 1863, p. 106.
6i
have elapsed. The same thing was shown by al-Birimi nine hundred
years ago.* The proof is very simple.
An Astronomical Cycle contains 6939d. 16h. 595ch. or 6939 8575 .
5184
The numerator and denominator in the fraction have no common
measure, therefore the fraction will not vanish till the whole quantity
is multiplied by 5184. In other words, 5184 is the least number of
Cycles which contains an interval of time that can be expressed in
integral days without any horary appendices. The computed Con-
junction of Sun and Moon, for the Molad of Tishrl, will not return to
the same day of the week, and same time of the day, until seven times
this number of Cycles have elapsed, that is, not till after 36288 Cycles,
or 689472 years, have passed.
Observe that 6939 - - A x 5184 = 35975251, a number which
5184
is of the form In + 4 ; the least multiple which will bring this
number to the form In is 7.
More will be said upon this subject when the question of Perpetual
Calendars, so called, is discussed.
The following is the demonstration given by Kene Martin
Molad BeHaED =2 5 204= 57444ch ......... a.
Cyclical excess =2 16 595= 69715ch .......... b.
Chalakim in 7 days = 7 x 24 x 1,080 = 181440ch .......... c.
Let x be the required number of the Cycle whose Molad is again to
be 2 5 204.
The Molad for Tishri in year 1 of Cycle 1 ...... = a.
The Molad for Tishri in year 1 of Cycle 2 ...... = a + b.
The Molad for Tishri in year 1 of Cycle 3 ...... = a + 2b.
And, generally,
The Molad for Tishri in year 1 of Cycler ...... = a + (x T)b.
The value of a + (x 1)6 must be such that, when the greatest
possible integral number of weeks is taken away from it, the remainder
may be a.
* Dr. Sachau's trans., "Vestiges," p. 153.
62 THE JEWISH CALENDAR
Let p be this number of weeks, then cp is the number of Chalakirn
in p weeks, and we have
a + (x 1)& cp = a
, _ cp _ 181440 36288
~ b ~ 69715 P ' 13943^
This fraction is in its lowest terms, therefore 13943 is the least
possible value of p, since x, and therefore x 1, is an integer. Hence,
x 1 = 36288 ; that is to say, 36288 Cycles, or 689472 years must
elapse before the Molad for Tishrl will be again 2 5 204.
CHAPTER IV
RULES OF THE JEWISH CALENDAR AS NOW ESTABLISHED
47. Hitherto the Molads, or the day of the week and the time
upon that day, when the computed New Moons will occur for the
Cycles, the years of the Cycle, and the months of the year, have been
calculated. The instant of time indicated by the Molad is the
Astronomical commencement of the month, the year, or the Cycle,
according to the estimated mean value of a Lunation in the Jewish
computation. This, of necessity, involves in the Molad the fractions
of a day ; but, as with the Julian and Gregorian Calendars, so with
the Jewish no fractions of a day can be admitted, and the Calendar
months commence, as do the days, at a fixed time, namely ; at six in
the evening for the Meridian of Jerusalem. They do not, however,
always, or indeed most frequently, commence upon the day indicated
by the Molad. The ancient ordinances which govern the Jewish holy
days compel this fluctuation.
When it is said that the Calendar days commence at six in the
evening for the Meridian of Jerusalem, it must be understood that this
formal time refers to the Calendar and the Calendar only. It does not
mean that the Civil days in any given locality, as, for example, in
London, or in Canton, commence at that particular local time which
coincides with 6 p.m. at Jerusalem. The longitudes of London and
Canton differ respectively from that of Jerusalem to the extent that when
it is six in the evening at Jerusalem, it is 3h. 39m. in the afternoon at
London, and llh. 12m. in the night at Canton ; the former being
2h. 21m. to the west, and the latter 5h. 12m. to the east of Jerusalem.*
Boughly speaking, the Civil day commences at sunset, local time, at
* Longitude of Canton, 113 20' E. of Greenwich.
64 THE JE WISH CALENDAR
any given place; so that, as Lazarus Bendavid says,* "A Calendar
composed for the Ganges can be used by the Jews on the Mississippi,
as all look to their own Meridian only." He points out that
Christopher Wolff is quite wrong with regard to this matter, t and that
a similar mistake has been made by many subsequent writers. He
says that Waser especially does not seem to have mastered the subject.
There are certain laws, to be hereafter explained, which frequently
cause the postponement of Tishri 1 from the feria indicated by the
Molad to the next day, and even to. the day after the next ; Waser,
therefore, according to Bendavid, proposes this case: "Assume that
the New Moon of Tishri occurs for the Meridian of Paris on feria 3, at
8h. 40m. 20s. ; the local time at Moscow would then be llh. 4m. 20s.
At Paris the New Moon would be celebrated on Tuesday, but the Law
which is called GaTKaD ADU " (see post, Article 52 (2) ) " would cause
the celebration to be postponed at Moscow till the Thursday following."
This, of course, could not be permitted, and upon this Wolff founds
the hypothesis that everywhere the modern Jews go by the Meridian
of Jerusalem. But, says Bendavid, "I should like to know how the
Meridian of Paris concerns the Jews in Moscow."
The facts are very simple, and there is no real difficulty involved.
The Calendar is formed according to the Meridian of Jerusalem.
Its rules are all framed with respect to that Meridian, and that only.
If Tishri 1 be postponed it is because the computed Molad has a
particular value at Jerusalem. What may be the corresponding local
time at Paris, or Moscow, or on the banks of the Ganges is not con-
sidered. The Jews everywhere, are to commence their months, and
years, and Cycles with the day determined for Jerusalem, but the hour
of that day at which they commence their service is determined by the
latitude, upon which the time of sunset depends, and the local time at
the place where they dwell. We have precisely the same effect in our
own Gregorian Calendar. That Calendar is framed for the Meridian
of Rome, which is 12 30', or, in time, fifty minutes, east of Greenwich;
our Easter Sunday does not commence at 50m. past 12h. on Saturday
night; it commences at midnight, that is, it commences when it is
midnight with us, not when it is midnight at Home. The Christians
* '' Zur Berechnung des Jiidischen Kalenders," p. 51, ft. " Ein Kalender am Ganges
verfertigt, ist fur die Juden am Mississippi-Flutz brauchbar, da alle nur auf ihren Meridian
Riictsicht nehmen."
t In the " Elementa Chronologica," 339, 6.
THE JE WISH CALENDAR 65
in Alexandria use the same Calendar and observe Easter on the same
day as the Komans and ourselves, but they commence their Sunday 69
minutes earlier than we commence it.
So it is with the Jews; their days and their Festivals begin
according to the local time, determined by the position of the place.
In regulating the time when any given day will commence the
question of twilight is taken into consideration. It is lawful to
lengthen all days, especially those of rejoicing, either at their beginning
or their end.* The only exception to this is Kippur, the great Day
of Atonement, which is unalterable. It is observed as a strict Fast,
and, as no one is allowed to fast for more than twenty-four hours, this
clay cannot be lengthened. The service on the eve is sometimes begun
a few minutes earlier, but not the Fast. On the other hand, Tishri 1,
for example, which is a Festival day, may begin at 5.30 p.m., although
sunset does not take place till after six o'clock. So with respect to the
Sabbath. It is not announced that "the Sabbath commences" but
that " the service commences " at such and such an hour. If any one
be engaged, for example, in writing a letter on Friday evening, he is
not bound to leave off his occupation at the exact time announced.
Although no work is done upon the Sabbath a license of about fifteen
minutes is allowed, and the writing, or other occupation, may be
continued during the permitted margin.
Inasmuch as the Jewish Civil and religious day is not reckoned
from an absolutely fixed time, as with ourselves, but from evening to
evening, the commencement of the day varies according to the time of
the year and according to the latitude of the place. Thus, if the Sun
set for the latitude of London at 8 p.m. in the month of June, it will
not set till 10 p.m. in the North of Scotland, and be still later in the
Shetland Isles.
Rules for the commencements of the Sabbaths and Festivals for
the latitude of London were formed by Eabbi David Nieto,t but there
was a difficulty, until recently, as to the time at which these days
should close. Dr. Joseph Jacobs, the Editor of the Jewish Year
Book, says that the ancient Eabbinical rule is that the day is at an end
when three stars of the second magnitude can be seen in the heavens, t
* With respect to lengthening Feasts and not lengthening Fasts, compare the old maxim
of the Canonists "Favores sunt ampliandi, et odiosa sunt restringenda."
t Haham of the Sephardim, that is, Chief Rabbi of the Spanish Jews. He died in
London, January 10, 1728.
\ Year Book for 5658, A.D. 1897-1898, p. 18.
6
66 THE JEWISH CALENDAR
Within the last twenty years Dr. Friedlander in England, M. Hirsch
in France, and Dr. Zuckermann in Germany, have determined astro-
nomically how many degrees T^elow the horizon the Sun must have
sunk before three stars of the second magnitude can be seen. This
was a point of the Law which had not been previously determined.
The time at which the Sabbaths close in London was settled by the
very Rev. Dr. Adler, the late Chief Rabbi, according to the formula of
Dr. Friedlander.
48. Under the reformed Calendar the ancient customs are not all
observed in their integrity. For instance, in former times watchers
were employed to observe the first appearance of the Moon's crescent,
and when their report had been received and verified the day of New
Moon was publicly proclaimed. But under the reformed Calendar the
day, not of the true Moon but of a mean Moon supposed to move
uniformly in the heavens, is Astronomically computed ; and the New
Moon is celebrated, with certain exceptions to be described, upon the
day itself when the computed Conjunction occurs. The chief of these
exceptions is that if the computed Conjunction take place upon a
Sunday, a Wednesday, or a Friday, its celebration is postponed to the
following day. For the reason of this rule see post, Article 49 (2) , and
for further exceptions Articles 51, 52.
The reformed Calendar was undoubtedly an innovation, and, as
Schwarz observes,* there is nothing in the history of the Jews with
which it can be compared. It was a necessity in order to preserve the
integrity of their religious observances, and for their very existence as
a distinct and separate people. The communities, scattered in different
countries, were no longer ably to rely upon the receipt of messages
from the chief Council in Palestine, and, without a fixed Calendar,
would have been equally unable to determine the time for their solemn
Feasts, New Moons, and assemblies, the observance of which upon
certain days was enjoined by the Law, to whose dictates they were
devotedly attached.
In order to understand how great the innovation was the rules as
now established rules which have been kept undoubtedly since the
time of Hillel, and probably for a much longer period must be con-
sidered, and compared so far as possible with the requirements of the
Mosaical Law.
* " Der Jiidische Kalender," p. 58.
THE JE WISH CALENDAR 5 7
49. LEADING RULES OF THE REFORMED CALENDAR.
1. The fifteenth day of the month Nisan, the day observed as that
of the Full Moon after the Sun has entered the Sign Aries, generally
known as the First Day of the Passover, Azyma, or the First of the
Days of Unleavened Bread, is never allowed to fall upon feriae 2, 4, or 6,
Monday, Wednesday, or Friday.
This is a Rabbinical rule. It is a fact, as Stofrler remarks,* that
the Levitical Law nowhere expressly prohibits these days for the
celebration of the First Day of the Passover. He states that the
regulation was not made till after the building of the second Temple.
If it were then made it is probable that it was because it was found
difficult, without such a rule, to carry into effect the laws which are
expressly laid down concerning other Festivals and Fasts. The
Passover regulates all other solemnities of the year, just as Easter
determines the observance of the Christian holy days ; and therefore it
is arranged in such a manner that no other Festivals or Fasts should
occur upon days when it would be in some cases impossible, in others
highly inconvenient to observe them properly.
There are good reasons for the rule. It is necessary to guard
against any day upon which work has to be done falling on the Sabbath,
feria 7, since work of every description is strictly prohibited on that day.+
Again, it was desirable to prevent a Sabbath, and any other day
upon which all work must cease, from following each other consecutively.
Two such days coming together would give rise to great practical
inconvenience in the social life of the people ; no fire could be lighted ;
no food could be cooked; nothing could be carried from one place to
another; no journey could be made exceeding two thousand paces in
length. Perhaps the most important consideration was that no dead
body could be buried, while in a hot and sultry climate like that of
Palestine it was highly essential that burial should take place so soon
as possible after death. \
* In the '' Calendarium Bomanum Magnum," Prop, xli., F. f. 74. " Deviant enim a
Mosaica constitutione qua nunquam Pascha celebrant die Lunse, die Mercurii, et die
Veneris, quos lex nusquam prohibet . . . sed per constitutiones a legis peritis et Judicibus
eorura emanatas in secunda templi instauratione, sequentibus intrudunt diebus."
t Exodus xxxv. 2. " Six days shall work be done ; but on the seventh day there shall
be to you an holy day, a Sabbath of rest to the Lord : whosoever doth work thereon shall
be put to death."
Cf. also Exodus xx. 8-11, and xxxi. 14, 15; Leviticus xxiii. 3; Deuteronomy v. 12-15.
In Numbers xv. 32-36, there is recorded the stoning of a man who gathered sticks on the
Sabbath day.
{ See post, on the Sabbath, Article 75.
68 THE JEWISH CALENDAR
The Hebrew letters forming the word BaDU are employed as
"memoria technica" to indicate the prohibited feriae for Nisan 15,
namely 2, 4, and 6, Monday, Wednesday, Fridaj 7 . In the Hebrew
method of numeration B = 2, D = 4, U = 6.
2. It will be remembered that Tishrl 1 in any Jewish Civil year,
H + 1, is always the 163rd day after Nisaii 15 in the preceding year,
H, (Article 25). Now 163 is of the form In + 2 ; therefore, rejecting
the In days, or n complete weeks, it is only necessary to add 2 to the
feria of Nisan 15 in any year H, in order to find the feria of Tishri in
the year H + 1.
Hence, if Nisan 15 were allowed to fall upon either feria 2, 4, or 6,
then the following Tishri 1 would occur either on feria 4, 6, or 1,
Wednesday, Friday, or Sunday. These days w r ould be inconvenient.
It is the first day of the Civil year, and the first day of the seventh
month of the Sacred or Religious year. It is a day upon which all work
is strictly prohibited.* Now if it were observed upon a Friday, or a
Sunday, there would be two days of rest coming together, for Friday
immediately precedes, and Sunday immediately follows the Sabbath.
Moreover, if Tishri 1 were allowed to fall upon a Sunday, then
Tishri 14 would be a Sabbath, and the next day, Tishri 15 is Succoth,
the Feast of Tabernacles, upon which no work might be done,! so that
again there would be two days of rest occurring consecutively.
If Tishri 1 were observed upon a Wednesday, then the great Day of
Atonement, the fast Kippur, which is observed upon the tenth day of
this month, would fall upon a Friday. All work upon this day is
forbidden,! and because the day following is the Sabbath there would
again be two days of rest coming together. It is chiefly with respect
to this important day that the arrangements are made.
The social inconvenience arising from the occurrence of two con-
secutive Sabbaths, or days of rest, would be more especially felt in the
* Leviticus xxiii. 24, 25. " In the seventh month, in the first day of the month, shall
ye have a Sabbath ... ye shall do no servile work therein."
t Leviticus xxiii. 34, 35. " The fifteenth day of this seventh month shall be the Feast
of Tabernacles for seven days unto the Lord. On the first day shall be an holy convocation:
ye shall do no servile work therein." Also, Numbers xxix. 12.
} Leviticus xxiii. 27, 28. "On the tenth day of the seventh month there shall be a
day of Atonement : it shall be an holy convocation unto you : and ye shall afflict your
souls, and offer an offering made by tire unto the Lord. And ye shall do no work in
that same day: for it is a day of Atonement, to make an Atonement for you before the
Lord your God."
THE JE WISH CALENDAR 69
month Tishri, which is always in the Autumn. The heat in Palestine
is then intense, so that the food cooked on the preceding working day
would not keep in good condition for the two non-working days. It
must, however, and does, frequently happen at other seasons of the
year that there are two consecutive days of rest. Thus, when Nisan 1
falls upon feria 1, Sunday, which is not prohibited, it follows imme-
diately after the ordinary weekly Sabbath. If it fall upon feria 7, the
Sabbath itself, then Schabuoth, the Feast of Weeks, which is fifty
days afterwards (Pentecost), must occur upon feria 1, Sunday, which
immediately follows the Sabbath.
In fact, the Rabbinical rule with respect to the prohibited days
appears to have been made with especial regard to the season of the
year at which the month Tishri occurs ; the month of which the tenth
day is the great Day of Atonement.
The memorial letters for the days on which it is forbidden to
celebrate Tishri 1 are ADU, feria 1, 4, and 6. A = 1, D = 4, U = 6.
3. Because the First Day of Unleavened Bread, Nisan 15 cannot
be upon either feria 2, 4, or 6, therefore Schabuoth, or Ashereth, the
Feast of Weeks, which is fifty days after Nisan 15, cannot be upon
either feria 3, 5, or 7, Tuesday, Thursday, or Saturday ; for fifty days
exceed an exact number of weeks by one day.
This rule is remembered by the letters of the word GaHaZ.
G = 3, H = 5, and Z = 7.
4. The Feast of Lots, or Purim, always precedes Nisan 15 by
thirty days, or four weeks and two days ; therefore Purim cannot be
upon either feria 7, 2, or 4, Saturday, Monday, or Wednesday.
The word for this is ZaBaD.
5. Because Tishri 1 cannot be upon either feria 1, 4, or 6, there-
fore Kippur, the Day of Atonement, observed upon Tishri 10, cannot
be upon either feria 3, 6, or 1, Tuesday, Friday, or Sunday.
The memorial letters are AGU.
Collecting the results of the above rules, it appears that the
prohibited days are, for Passover 2,4,6. BaDU.
Tishri 1 1,4,6. ADU.
Kippur 1,3,6. AGU.
Schabuoth 3,5,7. GaHaZ.
Purim 2, 4, 7. ZaBaD.
70 THE JEWISH CALENDAR
Also, if the feria of Nisan 15 be F.
that of Tishr! 1 will be F +
Kippur F + 4.
Schabuoth ,, F + 1.
Purim F + 5.
Since F indicates the same week-day as F + 7, therefore F + 4 and
F + 5 are respectively equivalent to F 3 and F 2. The Purim
whose feria is F + 5, or F 2 is the Purim which precedes Nisan 15 ;
it is in the same Civil year as Tishrl 1, but in the Sacred or Ecclesiastical
year which precedes that commencing with Nisan 1.
50. These five rules, concerning the feriae upon which certain of
the chief solemnities cannot fall, are Political. There are other rules
which may be called Astronomical, inasmuch as they are in a great
measure due to the method employed in the construction of the
Calendar. They are of importance, for the form or variety of the year,
that is the number of days which it contains, depends upon them as
well as upon ADU.
This, however, does not apply to the question, Is the year Common
or Embolismic ? The answer to that question is determined by the
position of the year in the Cycle. The places of the Embolismic years
are fixed and, as already stated, are those which stand in the numerical
order
3, 6, 8, 11, 14, 17, 19,
while the remaining twelve years in the Cycle are Common.
51. Every Jewish year is of the form In + x, where x may be
either 3, 4, 5, 6, or 0. No year can have anj ? other value for its
number of days, for the six forms of the year are :
1. Common Deficient, having days 353, or In + 3.
2. ,, Regular, ,, 354, or In + 4.
3. ,, Abundant, ,, 355, or In + 5.
4. Embolismic Deficient, ,, 383, or In + 5.
5. ,, Regular, 384, or In + 6.
6. ,, Abundant, ,, 385, or 7??
Consideration will first be given to those facts arising from Astro-
nomical computation which, like ADU, frequently cause the first day of
THE JEWISH CALENDAR 7 i
the year to differ from the day indicated by the Molad, that is, from the
day Astronomically computed for the Conjunction of the Sun and Moon.
The reason why no year is allowed to commence with either feria 1,
4, or 6 has already been assigned. If the feria of the Molad, as found
by computation, fall to either of these forbidden days, then Tishri 1 is
postponed to the next day. It will frequently happen that an Astro-
nomical postponement of Tishri 1 will have to be made from a lawful
to an unlawful day ; in that case a further postponement takes place,
so that there occurs a postponement of two days from the day indicated
by the Molad.
The postponement is never made, under any circumstances, for
more than two days.
Another fact, to which attention should be given, is that the first
day of any year or Cycle is never allowed to retrogress from the feria
indicated by the Molad. If it cannot be observed on the day found by
computation it is invariably advanced ; it is observed a day, or two
days later ; it is never observed earlier than the day indicated by the
Molad.
52. The following are the rules with respect to the Astronomical
postponement. They are given in the " Kiddusch hachodesh " of
Maimonides, vii. 2-6.
1. If the computed New Moon of Tishri occur upon any day of the
week so late as, or later than, 18h., reckoned from 6 p.m. of the pre-
ceding evening (for the Meridian of Jerusalem), that is to say, if it
occur upon any day of the week at Noon, or later than Noon, then the
following day is to be taken for the celebration of that New Moon, and
is to be Tishri 1, always provided that the following day in question is
not one of the days forbidden for Tishri 1. If it should be one of the
forbidden days, namely Sunday, Wednesday, or Friday, then Tishri 1
must be further postponed to one day later.
The memorial word for this rule is YacH. Y = 10 ; cH = 8.
The reason for the rule is as follows : Although the Jewish Civil
day commences at 6 p.m., yet, for the purpose of computing the
Conjunctions of the Sun and Moon, the days commence at the preceding
Noon. The Astronomical time, thus measured, shows an advance of
six hours upon Civil time. Hence, if Civil time upon any given day be
18h., it is Astronomically 24h. ; or, a whole day from the preceding
Noon. On that account the New Moon which occurs at Noon, or later
7 2 THE JEWISH CALENDAR
i haii Noon is not reckoned as falling upon the feria indicated by the
Molad, but upon the following feria.
For example : In the Jewish year 5340 the Molad for Tishri 1 is
by computation Id. 23h. 1079ch. " In other words, 23h. 1079ch. of
feria 1, Sunday, have elapsed before the Conjunction takes place.
These hours and parts of an hour are reckoned from six in the evening
of feria 7, Saturday ; and the time at which the computed Conjunction
takes place falls just within the limits of the Civil day, feria 1. By
Astronomical reckoning feria 1 commenced six hours earlier, and the
time elapsed since this Astronomical commencement is 29h. 1079ch. ;
in other words, feria 2 has not only been entered, but more than five
hours of its duration have elapsed.
Tishri 1 is therefore postponed to the next day ; from Sunday,
September 20, A.D. 1579, to Monday, September 21 ; these being the
corresponding Gregorian dates.
For another example : The computed Molad for the New Moon of
Tishri in the year 5797 is 7d. 22h. 35ch., or, the computed Conjunction
occurs upon a Saturday at 22h. 35ch., measured from 6 p.m. of Friday.
The time measured from Noon of Friday is therefore 28h. 35ch.,
equivalent to 4h. 35ch. in the afternoon of Saturday. By Astronomical
reckoning the next day, Sunday, feria 1, has commenced and more
than four hours of its duration have elapsed. The celebration of this
New Moon, or Tishri 1, does not take place upon the day indicated by
the Molad, but is postponed to the next day, Sunday, Astronomically.
Sunday, however, is forbidden by ADU, and therefore the celebration
has to be further postponed, Politically, to feria 2, Monday. This day
corresponds to the Gregorian date September 22, A.D. 2036.
2. If in a Common year * the computed Molad for Tishri fall to a
Tuesday, feria 3, so late as, or later than, 9h. 204ch., that is to say, if
the Molad be greater than 3d. 9h. 203ch., then Tishri 1 is to be post-
poned ; and because it cannot be upon feria 4, Wednesday, on account
of ADU it must be further postponed to Thursday, feria 5.
If the Molad be less than 3d. 9h. 204ch. by even 1 Chalak there
is no need for any postponement.
The memorial word for this rule is GaTEaD. G = 3 ; T = ( .> :
R = 200 ; D = 4.
The reason for this rule is as follows : Let the computed Molad
* Observe that this rule does not apply to Embolismic years. It belongs to Common
years only.
THE JE WISH CALENDAR 73
for Tishri in a Common year, H, have a value not less than
3d. 9h. 204ch. The duration of an Astronomical Common year is
354d. 8h. 876ch., which exceeds In weeks by 4d. 8h. 876ch. The
Molad of Tishri for the following year, H + 1, will have for its
minimum value the sum of 3d. 9h. 204ch. and 4d. 8h. 876ch., or
7d. 18h. Och. ; that is to say, if the computed Molad for H be not
less than 3d. 9h. 204ch., then, that for H + 1 will not be less than
7d. 18h. Och. The rule YacH, concerning the 18 hours, intervenes.
Feria 1 is Astronomically entered, and the celebration of the first New
Moon of H + 1 must be postponed to that day, that is, from Saturday
to Sunday. But Sunday is a prohibited day, and Tishri 1 is further
postponed Politically to Monday by ADU.
This postponement of the first day of H + 1 lengthens the pre-
ceding year, H, by two days. If, therefore, the year H had been
allowed to commence with a Tuesday, as indicated by its computed
Molad, it would have contained 356 days ; for its last day is a Sunday
(because H + 1 commences with a Monday), and it is a Common
year. But no Common year can have more than 355 days. It must
therefore be shortened by at least one day. It cannot be shortened
by cutting off its last day, for that would make H + 1 to commence
with a Sunday, which is prohibited. It cannot be shortened by
cutting off its last two days, for that would make H + 1 to commence
with a Saturday ; but the feria of H + 1 is not less than 7d. 18h. Och.,
therefore YacH prevents it from commencing with a Saturday. And
again H cannot be shortened by cutting off its last three days, for
that would not only cause H + 1 to commence with a prohibited day,
Friday, but would also cause the first day of H + 1 to retrogress from
its Molad, which is never permitted. If H were shortened at its close
by more than three days it would have less than 353 days, which is
impossible.
It appears, then, that the year H cannot be reduced from 356 days
by cutting off any of the days with which it terminates. Nothing
therefore remains possible but to shorten it at its commencement. Its
first day must be postponed from Tuesday, feria 3, to Wednesday,
leria 4 ; and, because Wednesday is a prohibited day, there must be a
further postponement to Thursday, feria 5. This reduces the number
of 356 days to 354, the year commencing with a Thursday and ter-
minating with a Sunday. It is, therefore, a Common Regular year,
and can be of no other form.
74 THE JEWISH CALENDAR
The reason why this rule does not apply to an Embolismic year is
that the Astronomical duration of such a year exceeds an exact number
of weeks by 5d. 21h. 589ch. Suppose that the Molad of an Embolis-
mic year, H, be, at the least, 3d. 9h. 204ch., and be not greater than
3d. 17h. 1079ch., so that it does not come under the rule YacH. The
Molad of the following year, H + 1, will vary from 2d. 6h. 793ch. to
2d. 15h. 588ch,* and however it may vary between these limits the
year H + 1 will commence with feria 2, Monday, to which there is no
impediment. Consequently the year H will end with a Sunday, and
if it commence with a Tuesday, as indicated by the Molad, it will
have six more days than an exact number of weeks. Being Embolis-
mic its form will be In + 6, and it will have 384 days, which is quite
consistent with the length of an Embolismic Regular year. Such a
year may therefore commence with a Tuesday, feria 3, even if the Molad
exceed 3d. 9h. 204ch., so long as it do not exceed 3d. 17h. 1079ch.
As an example, take the Embolismic year 5660. It is the seven-
teenth year of the 298th Cycle. Its computed Molad is 3d. 13h. 300ch.
By the addition of 5d. 21h. 589ch. the Molad for the next year, 5661,
is found to be 2d. llh. 9ch. Therefore, 5661 commences with feria 2,
Monday, and 5660 must terminate with a Sunday. This being the
case, if 5660 commence with a Tuesday, as indicated by the Molad, it
has In + 6, or 384 days. It is an Embolismic Regular year, and no
rule of the Calendar is transgressed.
But suppose now that the rule GaTRaD were applied to this Em-
bolismic year, and that it were not allowed to commence till Thursday.
It must still end with a Sunday, on account of the Molad for the
following year falling to a Monday. It could only have 382 days,
which is impossible because no Embolismic year ever has less than
383 days.
3. If the computed Molad for Tishri in a Common year which
follows next after an Embolismic year exceed 2d. 15h. 588ch., that is
to say, if it amount to 2d. 15h. 589ch., or be greater than this, then
Tishri 1 is to be postponed from feria 2, Monday, to feria 3, Tuesday.
If the Molad be less than 2d. 15h. 589ch. by even one Chalak then
there is no need for any postponement.
* 3 9 204 3 17 1079
5 21 589 5 21 589
2 6 793 2 15 588
THE JEWISH CALENDAR 75
The memorial words for this rule are BaTU ThaKPhaT.
B = 2 ; TU = 15 ; Th = 400 ; K = 100 ; Ph = 80 ; T = 9.
The reason for the rule is as follows : Let the Molad for some
given year, H, be 2d. 15h. 589ch., or be greater than this, and let the
preceding year, H 1, be Embolismic. The excess of an Astrono-
mical Embolismic year over an exact number of weeks is 5d. 21h.
589ch. ; if this excess be subtracted from the Molad of H, which may
be increased by 7 without altering the feria, the remainder will be the
Molad for H 1. The minimum value of this remainder will be
3d. 18h. Och.* The first day of H 1 must therefore be postponed to
feria 4, Wednesday, because the limit 18h. is reached. It must be
further postponed to feria 5, Thursday, on account of ADU.
If, therefore, the Molad of H attain to, or be greater than
2d. 15h. 589ch., the preceding year, H 1, must have commenced with
a Thursday, feria 5, and being Embolismic, that is to say, being of one
of the forms In + 5, In + 6, or In days, it must have had for its last
day either a Monday, a Tuesday, or a Wednesday. Consequently
the next year, H, could only have for its first day a Tuesday, a Wed-
nesday, or a Thursday. Wednesday is impossible, it is forbidden by
ADU. Thursday, feria 5, is impossible, for the Molad of H falls to
feria 2, and postponement can never take place for more than two
days. The only alternative is Tuesday, feria 3.
Hence the rule is that if the Molad of any year which follows an
Embolismic year fall to feria 2, and the hours and Chalakim exceed
15h. 588ch., then, Tishri 1 must be postponed to feria 3.
4. The five rules, BaDU, ADU, YacH, GaTEaD, and BaTU
ThaKPhaT, which have reference to the postponement of Tishri 1,
are called the five Dechiyyoth of the Jewish Calendar. It will be
convenient to place their results in a collective form :
(1) BaDU. . . . Nisan 15, never on Monday, Wednesday, or
Friday.
(2) ADU. . . . Tishri 1, never on Sunday, Wednesday, or Friday.
(3) YacH. ... If the Molad for Tishri* fall to any day so late as
or later than 18h., Tishri 1 is postponed to the next day.
d. h. ch.
* Minimum value = 2d. 15h. 589ch., equivalent ... 9 15 589
Subtract 5 21 589
3 18
7 6 THE JEWISH CALENDAR
(4) GaTKaD. ... If the Molad for Tisbri fall, in a Common year,
on a Tuesday so late as or later than 9h. 204ch., Tishri 1 is postponed
to the next day, and thence by ADU to Thursday.
(5) BaTU ThaKPhaT. . . .If in a Common year which follows
next after an Embolismic year the Molad for Tisbri fall upon a Monday
so late as or later than 15h. 589ch., Tishr! 1 is postponed to Tuesday.
53. The rules which determine the feria with which any given
year can possibly commence must now be considered. These rules
will, for convenience of reference, be first stated in a tabulated form ;
the reasons for them will be given afterwards. They are partly
Political, partly Astronomical.
The length or form of any given year is found by ascertaining, in
the first place, whether it be a Common or an Embolismic year, and
in the second place, by finding the ferise with which it commences and
terminates.
An example will illustrate the method to be employed.
Find the form of the Jewish year 5616.
(a) The division of 5616 by 19 gives a remainder 11, with a
quotient 295. The year is therefore the eleventh in the 296th Cycle.
Its place in the Cycle shows that it is Embolismic, and must be of the
form 378 + x, where the value of x has to be found.
(b) To find the feria with which the year commences.
Molad BeHaED 2 5 204
Add for 200 Cycles elapsed 5 22 200*
90 4 1 630
5 6 10 815
,, the eleventh year 6 (> 339t
Molad for Tishri, 5616 3 22 28
The computed New Moon occurs on feria 3, or Tuesday, and as
the hours and Chalakim attain to 18h. and more, the celebration is
postponed by YacH to Wednesday, and is further postponed by ADU
toThursday.
The first day of the year 5616 is therefore a Thursday.
(c) To find the feria with which the year terminates we must find
that with which the next commences.
* Table VIII. t Table VII.
THE JEWISH CALENDAR 77
Molad for Tishri, 5616 3 22 28
Add the excess of an Erubolismic year 5 21 589
Molad for Tishri, 5617 2 19 617
The computed New Moon for Tishri, 5617, falls to feria 2, or
[onday, and Tishri 1 is postponed to Tuesday by BaTU PhaKPhaT
well as by YacH.
(d) Insomuch as the first day of 5617 is a Tuesday the last day of
J16 must be a Monday. But it commences with a Thursday, as
lown by (b). Therefore, its integral number of weeks, or 378 days,
srminate with a Wednesday. It has five more days, namely Thurs-
day, Friday, Saturday, Sunday, and Monday. Its length is therefore
378 + 5, or 383 days. Its form is In + 5. It is an Embolismic
Deficient year.
Example 2.
Lacoine in his " Tables de Concordance des Dates," p. 36, gives
the form of the year 4668 as C.D., that is " Commune deficiente."
Isidore Loeb in his " Tables du Calendrier Juif " (Tableau XII.) gives
the form as 5a, that is, " Commune abondante," commencing with
feria 5, or Thursday. Meier Kornick in his " System der Zeitrech-
nung," p. 117, makes Nisan 15 in 4667 to be March 31, and in 4668
to be March 20, from which it may be deduced that he considers
Tishri 1 in 4668 and 4669 to have corresponded respectively to Thursday
September 10, A.D. 907 and Tuesday, August 30, A.D. 908. He there-
fore makes the year 4668 to commence with a Thursday and terminate
with a Monday, and therefore to be a Common Abundant year.
Is Lacoine right, or are Isidore Loeb and Kornick right ?
The division of 4668 by 19 gives a quotient 245, and a remainder
13. The year in question is therefore the 13th of the 246th Cycle.
BeHaED 2 5 204
Add for 200 Cycles 5 22 200
40 2 14 40
5 6 10 815
thirteenth year 2 12 724
Molad for Tishri, 4668 5 16 903
Add excess of a Common year 4 8 876
Molad, for Tishri, 4669 3 1 699
7 8 THE JF.ll/S// CALENDAR
From this it is evident that the year 4608 commenced with
feria 5, Thursday, and the next year with feria 3, Tuesday ; so that
4668 must have terminated with a Monday. It therefore has five
days more than an exact number of weeks, and is a Common Abundant
Year. Isidore" Loeb and Kornick are right ; Lacoine is in error.
Example 3.
Lazarus Bendavid, in "Zur Berechnung des Jiidischen Kalenders,"
p. 97, gives a so-called " Calendarium Perpetuum," from which it
appears that the year 4868 is to have its first day and its length
determined by the symbol hR, which means that it commences with a
Thursday and is " regel massige," or regular. Is this correct?
This year is found in the usual way to be the fourth in the 257th
Cycle.
BeHaED 2 5 204
Add for 200 Cycles 5 22 200
50 1 11 590
. 6 2 3 330
fourth year 7 15 181
Molad for Tishrl, 4868 5 9 425
Excess of a Common year 4 8 876
Molad for Tishri, 4869 2 18 221
Consequently the year 4868 commences with a Thursday, and it must
terminate with a Monday ; for the Molad of 4869 falling to feria 2, or
Monday, but having more than 18 hours, comes under the rule YacH,
causing Tishri 1 in this year to be Tuesday. The year 4868 has
therefore 355 days, and ought to be marked h.U, meaning Thursday,
" uebershussig," or abundant.*
54. The following Table shows the week-day with which a year
of given form, In + x, can commence and terminate, and the con-
sequent week-day with which the year that follows it will commence.
It may be read thus : A year of 353 days can only commence with
* This is not a misprint in the " Calendarium Perpetuum " ; hU, cannot be substituted
for hR .without vitiating the result for other years. It is a failure in this form of Perpetual
Calendar, which passes under a title to which it has no real claim. The error arises from n
source which will be explained when " Perpetual Calendars " are considered in Chapter VI.
THE JE WISH CALENDAR
79
a Monday or a Saturday. If it commence with a Monday it will
terminate with a Wednesday; if it commence with a Saturday it will
terminate with a Monday. The following year must then commence
in the one case with a Thursday, in the other with a Tuesday.
The Proof of the Statements contained in the Table will be given
directly afterwards.
FIEST AND LAST DAYS POSSIBLE FOE THE JEWISH YEARS,
AND FIEST DAYS OF THE FOLLOWING YEAE.
Length of the year H,
in days.
First day of H.
Last day of H.
First day of H + 1.
1
353 = In + 3
Monday
Saturday
Wednesday
Monday
Thursday
Tuesday
2
354 = In + 4
> M
Tuesday
Thursday
Friday
Sunday
Saturday
Monday
3
355 = In + 5
Monday
Thursday
Saturday
Friday
Monday
Wednesday
Saturday
Tuesday
Thursday
4
383 = In + 5
Monday
Thursday
Saturday
Friday
Monday
Wednesday
Saturday
Tuesday
Thursday
5
384 = 7n + 6
Tuesday
Sunday
Monday
8
385 = In
Monday
Thursday
Saturday
Sunday
Wednesday
Friday
Monday
Thursday
Saturday
PROOF OF THE STATEMENTS CONTAINED IN THE TABLE.
1. A Common Deficient year of 353 days can only commence with
a Monday or a Saturday.
It cannot commence with a Sunday, a Wednesday, or a Friday,
because these days are prohibited by ADU.
It cannot commence with feria 3, Tuesday, because if it did so
commence, its In days, containing n complete weeks, would terminate
with a Monday, and the last of its three remaining days would be a
So THE JEU'ISH CALENDAR
Thursday. In that case the following year would commence with a
Friday, which is a forbidden day for Tishri 1.
It cannot commence with feria 5, Thursday, for if it did so
commence its completed weeks would end with a Wednesday, and
the last of its three remaining days would be a Saturday. The next
year would then commence with feria 1, Sunday, which is a forbidden
day.
There is, however, nothing to prevent it from commencing with
feria 2, Monday, or with feria 7, Saturday, and with one or other of
these days it must commence. It will then end with a Wednesday or
a Monday, and the next year will commence with a Thursday or a
Tuesday, which are both lawful days.
2. A Common Eegular year, of 354 days, can only commence with
a Tuesday or a Thursday.
Such a year cannot commence with a Monday, feria 2, for if it did
so commence its In days would end with Sunday, feria 1, and the last
of its four remaining days would be a Thursday. The next year would
begin with a Friday, which is prohibited by ADU.
It cannot commence with a Saturday, feria 7, for its In days would
end with a Friday ; the last of the remaining four days would be a
Tuesday, and the next year would begin with a Wednesday, which is
prohibited.
There is nothing to prevent it from commencing with feria 3,
Tuesday, or feria 5, Thursday, in which case it would terminate with
a Friday or a Sunday, and the next year would commence with a
lawful day, Saturday or Monday.
3. A Common Abundant year, of 355 days, can only commence
with a Monday, a Thursday, or a Saturday.
Such a year commencing with one of these three days would ter-
minate either with a Friday, a Monday, or a Wednesday. The next
year would commence with one or other of the lawful days Saturday,
Tuesday, or Thursday.
But a year of 355 days cannot begin with a Tuesday, for its In days
would end with a Monday, and the last of the remaining five days
would be a Saturday. No year can end with a Saturday, because the
next year would begin with a prohibited Sunday.
4. An Embolismic Deficient year, of 383 days, contains, like a
Common Abundant year, five days more than an exact number of weeks.
It is therefore subject to the same restraint as a Common Abundant
THE JEWISH CALENDAR 8r
year, and cannot begin with a Tuesday. There is nothing to interfere
with its first day being a Monday, a Thursday, or a Saturday, and
with one or other of these three days it must begin.
5. An Embolismic Regular year, of 384 days, can only commence
with a Tuesday.
Such a year cannot commence with a Monday, a Thursday, or a
Saturday, for its In + 6 days would terminate with a Saturday, a
Tuesday, or a Thursday. The next year would begin with one of the
forbidden days, a Sunday, a Wednesday, or a Friday.
The only remaining day with which it can commence is feria 3,
Tuesday. In this case its In days would terminate with a Monday ;
the last of its remaining six days would be a Sunday. The next
year would then commence with a Monday, to which there is no
impediment.
6. An Embolismic Abundant year, of 385 days, can only commence
with a Monday, a Thursday, or a Saturday.
With respect to the years of the other five forms it has not been
necessary to consider any Astronomical reason why they cannot com-
mence with certain days. The Political rule ADU has sufficed. The
present case is different. A year of 385 days contains an exact number
of weeks, so that with whatever feria it may commence it will termi-
nate with the next preceding feria. Why, then, is it restricted as to
its commencement to the three days Monday, Thursday, and Saturday?
Why cannot it commence with a Tuesday? It would end with a
Monday, and the next year would begin with a Tuesday, which is
possible for a year of 354, or of 384 days. The latter is excluded
because there are never two consecutive Embolismic years. But why
should it not commence with a Tuesday, and be followed by a year of
354 days commencing also with a Tuesday ?
The reason is Astronomical. The impossibility arises from the
way in which the Calendar is constructed by the computation of
Molads.
In order that any year, H, may commence with a Tuesday, feria 3,
its Molad must not be less than 2d. 15h. 589ch., and not more than
3d. 17h. 1079ch. For if the Molads were less than 2d. 15h. 589ch. the
year would commence with a Monday, feria 2, as indicated by the
Molad, since the rule BaTU ThaKPhaT would not intervene to
postpone Tishri 1 to feria 3. Also, if the Molad were greater than
3d. 17h. 1079ch., that is to say, if it were 3d. 18h. Och., or more, then
7
82 THE JEWISH CALENDAR
YacH would intervene, and Tishri 1 would be postponed from Tues-
day, i'eria 8, to Thursday, feria 4.
Now the excess of an Astronomical Embolismic year above an
exact number of weeks is 5d. 21-h. 589ch. If, therefore, the Molad of
the Embolismic year, H, be from 2d. 15h. 589ch. to 3d. 17h. 1079ch.,
that of H + 1 will be from Id. 13h. 98ch. to 2d. 15b. 588ch.,* and,
whatever may be the variation between these limits, H + 1 will com-
mence with feria 2, Monday. But Monday is the day w r ith w r hich H
terminates, and it is impossible that this day can belong to both of the
years. Therefore H cannot terminate with a Monday, which is equi-
valent to saying that it cannot commence with a Tuesday, for it is
a year of 385 days, an exact number of weeks.
It can, however, commence with either a Monday, a Thursday, or
a Saturday, for the following year will commence with the same day,
and there is nothing to prevent its being followed by a year of 353 or
of 355 days, either of which may commence with a Monday or a
Saturday ; while a year of 355 days can also commence with a
Tuesday.
55. Collecting the results obtained from these rules it will appear
that the years, governed by their Molads and by the rules of the
Calendar, will commence with certain fixed days of the week according
to the annexed Table, which is to be thus read :
Tishri 1 will occur upon a Monday, when the Molad of the year is
not less than 7d. 18h. Och., and not greater than 2d. 15h. 588ch. This
rule applies to those Common years which follow next after an Embo-
lismic year, namely, the years whose numerical positions in a Cycle
are 1, 4, 7, 9, 12, 15, or 18.
It must be understood that in this, and in similar Tables, the
Regaim are neglected. There are 76 Eegaim in a Chalak, and when
the limit is given as, for example, 2d. 17h. 1079ch., the actual limit is
2d. 17h. 1079ch. 75r. It means that 2d. 18h. Och. (= 2d. 17h. 1080ch.)
must not be attained. This is the method adopted by Maimonides,
and, following him, by Petavius and others. Some modern writers, as
Dr. Adolf Schwarz or Dr. Sachau, the translator of al-Biruni, would
* 2 15 589 3 17 1079
5 21 589 5 21 589
1 13 us 2 15 588
THE JEWISH CALENDAR
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84 THE JE WISH CALENDAR
give the limits thus, from 2<1. 18h. Och. up to 2d. 15h. 589ch. When
given in this way there is some risk of supposing that the 589ch. may
be reached ; the fact being that if the Molad be greater than 2 15 588,
that is, if 2 15 589 be attained, the year will commence with a
Tuesday, and not with a Monday.
56. FURTHER EEGULATIONS WITH RESPECT TO THE COMMENCE-
MENT AND FORM OF THE YEARS.
Hitherto, the days have been considered with which the Jewish
years can commence ; these days have been determined thus far by
the Molads, and the rules ADU, YacH, GaTKaD, and BaTuThaKPhaT.
We now come to those which determine the length or form of the
successive years. These rules include the former, but they are further
developed, and place yet more restriction on the limits of the Molads.
They are given in Table X., called the Table of Day-Limits.
I. COMMON YEARS.
1. A Common year will commence with a Monday, and be Deficient,
353 days, if its Molad is found by computation to be so great as
7d. 18h. Och., and be not greater than Id. 9h. 203ch.
(a) The year will commence with a Monday if its Molad be so
great as or greater than 7d. 18h. Och., for Tishrl 1 is postponed from
feria 7 to feria 1 by YacH, and from feria 1 to feria 2 by ADU.
(6) The length of a Common year, H, is found by the addition
to its Molad of the excess of a. Common year above an exact number
of weeks, by which means the commencement of the next year, H + 1,
is found.
MoladofH 718 to 1 9 203
Excess of H.. 4 8 876 48 876
Molad of H + 1 5 2 876 to 5 17 1079
The feria for H + 1 being 5, and the maximum value of the hours
and Chalakim in the Molad not amounting to 5d. 18h., the year com-
mences with Thursday, the day indicated by , the Molad. Therefore
the last day of H must have been a Wednesday. As H commenced
with a Monday the last day of its completed weeks is a Sunday ; it
therefore contains three days more than an exact number of weeks,
THE JEWISH CALENDAR 85
namely, Monday, Tuesday, and Wednesday. It is therefore of the
form 350 + 3, or 353 days. It is Deficient.
It will be seen at once that if the superior limit of the Molad of H
had been so great as Id. 9h. 204ch., that is, if it had been even
1 Chalak greater than it is, then the limit for the Molad of H + 1
would have become 5d. 18h. Och. In such a case the commencement
of H + 1 would be postponed from feria 5, Thursday, to feria 7,
Saturday. This would have lengthened H by two days, making it to
consist of 355 days. Therefore the extreme limit for the Molad of
a Common year which commences with a Monday, and is Deficient, is
Id. 9h. 203ch.
2. A Common year which follows an Embolismic year will com-
mence with a Monday, and be Abundant, 355 days, if its Molad be not
less than Id. 9h. 204ch., and not greater than 2d. 15h. 588ch.
(a) Any year, whether it follows an Embolismic year or not, whose
Molad has these limits, will commence with a Monday. If the feria
be 1, then Tishri 1 is postponed from Sunday to Monday, by ADU.
If the feria be 2, Tishri 1 falls naturally to Monday ; it is only post-
poned by BaTU PhaKPhaT to Tuesday, when the Molad attains to
2d. 15h. 589ch.
The year in question therefore commences with a Monday.
(fc)MoladofH 1 9 204 to 2 15 588
Excess of H.. 4 8 876 48 876
Molad of H + l 6 18 to 7 384
Therefore, H+l commences with a Saturday, and the last day of
the year H must be a Friday. As H commences with a Monday its
completed weeks terminate with a Saturday, and it has an excess of
five over In days, namely, Monday, Tuesday, Wednesday, Thursday,
and Friday. It has therefore 355 days.
3. A Common year which follows a Common year will commence
with a Monday, and will be Abundant, 355 days, if its Molad be not less
than Id. 9h. 204ch., and not greater than 2d. 17h. 1079ch.
(a) If the feria be 1, Tishr! 1 is postponed to feria 2, Monday, by
ADU. If the feria be 2, Tishri 1 is not postponed by BaTU PHaK-
PhaT from Monday to Tuesday, because the year in question does not
follow an Embolismic year. Also, Tishri 1 is not postponed to Tues-
86 THE JE 1 1 y.s// C.U.E. \~D.IK
day by YacH because the maximum value of its Molad does not attain
to 2d.* 18h. Och.
The year will therefore commence witli a Monday.
(6) Molad of H 1 9 "204 to 2 171079
Excess of H 4 8 876 48 87G
Molad ofH + 1 6 18 to 7 2 875
Therefore H + 1 commences with a Saturday, and the last day of
H must be Friday. As H commences with a Monday it must have
355 days.
(c) But why is 1 9 204 the minimum Molad with which a
Common year following a Common year, and commencing with a
Monday, can have 355 days? Simply because all Common years
whose Molad is less than this have been proved under Kule 1 to have
only 353 days.
(d) And why is 2 17 1079 the maximum Molad for such a year'/
Because if the Molad attain to 2 18 Tishri 1 will be postponed to
Tuesday; so that the year could not fulfil the condition of commencing
with a Monday, no matter how many or how few days it might have.
4. A Common year which follows an Embolismic year will
commence with a Tuesday, and be Regular, or have 354 days, if its
Molad be not less than 2d. 15h. 589ch., and be not greater than 3d. 9h.
203ch.
(a) If the feria be 2, and the hours and Chalakim be not less than
15h. 589ch. Tishri 1 is postponed from Monday to Tuesday, in a year
which follows an Embolismic year, by BaTU PHaKPhaT. If the
feria be 3, Tishri 1 falls naturally to Tuesday so long as the maximum
value of the Molad does not attain to 3d. 9h. 204ch.
Therefore the year in question will commence with a Tuesday.
(6) Molad of H 2 15 589 to 3 9 203
Excess of H . 4 8 876 4 8 876
MoladofH + 1 7 385 to 7 17 1079
Hj-1, therefore, commences with a Saturday, and H ends with a
Friday. As it commenced with a Tuesday it has four days more than
an exact number of weeks. It has 354 days.
5. A Common year which follows a Common year will commence
THE JEWISH CALENDAR 87
with a Tuesday, and be Regular, 354 days, if its Molad be not less
than 2d. 18h. Och., and be not greater than 3d. 9h. 203ch.
(a) Such a year will commence with Tuesday for the reason given
in (4, a). Its Molad cannot be less than 2d. 18h. Och., for if it be less
than this it will commence with a Monday.
(b) Molad of H -218 to 3 9 203
Excess of H . 4 8 876 4 8 876
Molad ofH + 1 7 2 876 to 7 17 1079
H + l, therefore, commences with a Saturday, and the last day of H is
a Friday. As H commences with a Tuesday it must have 354 days.
From (4) and (5) it appears that all Common years which commence
with a Tuesday are Regular, or have 354 days ; and it may be noted
here that no year, whether it be Common or Embolismic, can
commence with a Tuesday except such years as are Regular that is,
no year commences with a Tuesday unless it have 354 or 384 days.
6. Every Common year whose Molad is not less than 3d. 9h. 204ch.,
and not greater than 5d. 9h. 203ch., commences with a Thursday, and
is Regular, 354 days.
(a) If the feria be 3, and the hours and Chalakim are not less
than 9d. 204ch. Tishri 1 is postponed from Tuesday to Wednesday
by GaTRaD, and further postponed to Thursday by ADU. If the
feria be 5, and the Molad be, as in this case, anything less than
5d. 18h. Och., Tishri 1 falls naturally to Thursday.
The year in question commences, therefore, with a Thursday.
(6)MoladofH 3 9 204 to 5 9 203
Excess of H 4 8 876 48 876
Molad of H + l 118 to 2 17 1079
Therefore, H + l commences with Monday, for if the Molad of H + 1
be not less than Id. 18h. Och. its first day is postponed from Sunday
to Monday ; also, Tishri 1 falls naturally to Monday if the feria be 2,
although the hours and Chalakim exceed 15h. 589ch., for H is, by
hypothesis, a Common year, so that H + l does not follow an
Embolismic year, and BaTU PHaKPhaT does not apply to it.
Because H + l commences with a Monday, H must end with a
88 THE JE WISH CALENDAR
Sunday. It has therefore 354 days, for it commences with a
Thursday.
7. Every Common year whose Molad is not less than 5d. 9h. 204ch.,
and not greater than 5d. 17h. 1079ch., commences with a Thursday,
and is Abundant, 355 days.
(a) Such a year commences naturally with a Thursday, feria 5, as
indicated by the Molad, for YacH causes no postponement till the
Molad 5d. 18h. Och. be attained.
(6) Molad of H 5 9 204 to 5 17 107 ( .)
Excess of H.. 4 8 876 48 876
MoladofH+1 218 to 3 2 875
Therefore, H + 1 commences with a Tuesday, and H terminates with
a Monday. As H commences with a Thursday it has five days more
than an exact number of weeks. It has 355 days.
8. Every Common year whose Molad is not less than 5d. 18h. Och.
and not greater than 6d. Oh. 407ch., will commence with a Saturday,
and be Deficient, 353 days.
(a) Since the minimum Molad is 5d. 18h. Och. Tishri 1 is postponed
by YacH from Thursday to Friday so long as the feria in the Molad
is 5. It is further postponed by ADU from Friday to Saturday. If
the Molad be 6, Tisrhi 1 is postponed from Friday to Saturday.
Therefore all such years must commence with a Saturday.
(6) Molad of H ' 518 to 6 407
Excess of H.. 4 8 876 48 876
MoladofH + 1 3 2 876 to 3 9 203
H + 1 commences with Tuesday, because the Molad is always less
than 3d. 9h. 204ch. H ends with Monday. It commences with
Saturday ; its In days end with Friday. It has three more days, and
therefore contains 353 days.
9. A Common year which is followed by an Embolismic year will
commence with a Saturday, and be Deficient, 353 days, if its Molad
be not less than 5d. 18h. Och., and be not greater thaii 6d. 9h. 203ch.
(a) Such a year must commence with a Saturday for the reason
assigned in (8, a).
THE JE WISH CALENDAR 89
(b) MoladofH 518 to 9 203
Excess of H.. 4 8 876 48 876
MoladofH + 1 3 2 876 to 3 17 1079
H + 1 is, by hypothesis, an Embolismic year. Although its maximum
Molad is more than 3d. 9h. 204ch. its first day is not postponed by
GaTKaD, which applies to Common years only.
The year H + 1 therefore commences with.feria 3, Tuesday, as
indicated by the Molad, and H ends with a Monday. As H
commences with a Saturday it has three days more than an exact
number of weeks. It has 353 days.
10. A Common year which is followed by a Common year will
commence with a Saturday, and be Abundant, 355 days, if its Molad
be not less than 6d. Oh. 408ch., and be not greater than 7d. 17h.
1079ch.
(a) If the feria be 6, Tishri 1 is postponed from Friday to Saturday
by ADU. If the feria be 7 there is no postponement from Saturday
because the maximum value of the Molad is less than 7d. 18h. Och.
The year, therefore, commences with a Saturday.
(6) MoladofH 6 408 to 7 171079
Excess of H 4 8 876 48 876
Molad ofH + ] 3 9 204 to 5 2 875
The year H + 1 is, by hypothesis, a Common year. Therefore when
the feria is 3, and the Molad not less than 3d. 9h. 204ch., as in this
case, Tishri 1 is postponed by GaTKaD, from Tuesday to Wednesday,
and thence to Thursday by ADU. When the feria becomes 4, Tishri 1
is postponed to Thursday by ADU. If the feria be 5 Tishr! 1 falls
naturally to Thursday so long as the Molad be less than 5d. 18h. Och.,
as it is here.
The year H + 1 begins, therefore, with a Thursday, and H ends
with a Wednesday. H, therefore, has 355 days, for it begins with
a Saturday and has five days more than an exact number of weeks.
(c) If the Molad be less than 6d. Oh. 408ch., even by one Chalak, the
Molad of H + 1 will not attain to 3d. 9h. 204ch. In such a case
H + 1 would begin with a Tuesday instead of with a Thursday. This
would shorten H by two days, reducing its number to 353. If, there-
90 THE JEWISH CALENDAR
fore, H be followed by a Common year it cannot be Abundant if its
Molad be less than Gd. Oh. 408ch.
11. Every Common year whose Molad is not less than 6d. 9h. 204ch.,
and not greater than 7d. 17h. 1079ch., will commence with a Saturday,
and be Abundant, 355 days.
(a) Such years commence with Saturday, because if the feria be 6
Tishri 1 is postponed by ADU from Friday to Saturday ; and if the feria
be 7 there is no postponement so long as the maximum value of the
Molad is less than 7d. 18h. Och.
(b) MoladofH 6 9
Excess of H . 48
Molad of H + l 318 to 5 '2 875
Therefore H + l commences with a Thursday, and H ends with a
Wednesday. It commences with a Saturday, its In days end with a
Friday. Its extra days are five, Saturday, Sunday, Monday, Tuesday,
and Wednesday. It has 355 days.
RULES EESPECTING THE COMMENCEMENT AND FOEM OF EMBOLISMIC
YEARS.
12. Every Embolismic year commences with a Monday and is
Deficient, 383 days, if its Molad be not less than 7d. 18h. Och., and
be not greater than Id. 20h. 490ch.
(a) The year commences with Monday for the reason assigned in
(1, a).
(6) MoladofH 7 18 to 1 20 490
Excess of H, Emb 5 21589 5 21 589
MoladofH + 1 6 15 589 to 7 171079
Therefore H+l commences with a Saturday, and H ends with a
Friday. As it begins with a Monday, and is Embolismic, it has 383
days.
13. Every Embolismic year commences with a Monday and is
Abundant, 385 days, if its Molad be not less than Id. 20h. 491ch., and
be not greater than 2d. 17h. 1079ch.
THE JEWISH CALENDAR 9 t
(a) ADU postpones Tishri 1 to Monday when the feria is 1. BaTU
THaKPhaT does not affect Embolismic years, therefore Tishri 1 falls
imturally to Monday when the feria is '2.
(i)MoladofH 1 20 491 to 2 171079
Excess of H 5 21 589 5 21 589
MoladofH + 1 7 18 to 1 15 588
H + 1, therefore, commences with Monday, for Tishri 1 is postponed
to that day whether the feria be 7 or 1 . H ends with a Sunday, and
as it begins with a Monday it must have 385 days.
14. Every Embolismic year whose Molad is not less than 2d. 18h.
Och., and not greater than 3d. 17h. 1079ch., commences with a
Tuesday, and is Kegular, 384 days.
(a) Because the minimum value of the Molad is 2d. 18h. Och.
Tishri 1 is postponed by YacH from Monday to Tuesday. When the
Molad becomes 3d. Oh. Och., but does not attain to 3d. 18h. Och.,
Tishri 1 falls naturally to Tuesday in an Embolismic year.
(6) Molad of H 2 18 to 3 171079
Excess of H 5 21 589 5 21 589
MoladofH + 1 1 15 589 to 2 15 588
H + 1, commences with a Monday, and H must end with a Sunday.
It therefore has six days more that an exact number of weeks. It has
384 days.
15. Every Embolismic year whose Molad is not less than 3d. 18h.
Och., and not greater than 4d. llh. 694ch., commences with a
Thursday, and is Deficient, 383 days.
(a) When the Molad is not less than 3d. 18h. Och., Tishri 1 is
postponed by YacH, and ADU, from Tuesday to Thursday. When the
feria is 4, it is postponed by ADU from Wednesday to Thursday.
Such a year must therefore commence with a Thursday.
(6) Molad of H 3 18 to 4 11694
Excess of H.. 5 21589 5 21589
Molad of H + 1 2 15 589 to 3 9 203
H + 1 follows H which is, by hypothesis, an Embolismic year;
92 THE JEWISH CALENDAR
therefore H + 1 is a Common year following an Embolismic year, and
must commence with a Tuesday, as demonstrated by (4, a). Conse-
quently H must end with a Monday, and, as it commences with a
Thursday, its In days end with a Wednesday. It has therefore five
extra days, Thursday, Friday, Saturday, Sunday, Monday, and its
form is In + 5, or it has 378 + 5 = 383 days.
This proof is given in some detail because both Dr. Adolf Schwarz
in " Der Jiidischer Kalender " p. 64, Table B, and Dr. Sachau in his
translation of the Athar-ul-Bakiya of al-Biruni, p. 152, who are
authorities, state that a year whose Molad has these limits consists,
when Embolismic, of 384 days. The former describes it as " 5r," the
figure indicating the feria, the letter standing for regelmassige, or
Regular. The latter says that it commences with feria 5, and is
" Intermediate," the term employed by this author for a Regular year.
It is beyond dispute that a year whose Molad is from 3 18 to 4 11
(594, both inclusive, must commence with feria 5, Thursday, whether
it be Common or Embolismic ; and it is equally beyond dispute that
an Embolismic year of 384 days, would, if it commenced with a
Thursday, end with a Tuesday ; for, 384 =ln + 6 ; the last day of the
completed weeks is a Wednesday ; the remaining days are Thursday,
Friday, Saturday, Sunday, Monday, and Tuesday. If therefore a year
which has 384 days commenced with a Thursday, that which next
follows would begin with a Wednesday, wiiich is impossible.
Moreover, it has been proved in Article 54, par. 5, that a year of 384
days can only commence with a Tuesday, so that an Embolismic year
which commences with a Thursday must hUve either 383 or 385 days.
That this is an error in the Table B, given by Dr. Schwarz at p. 64,
is made clear by an inspection of his Table K, pp. 82, 83, which gives
the sixty-one possible arrangements, or sequence of years for the
Jewish Cycle. This includes not only every possible form of a Cycle,
but also every possible form of a Jewish year ; there is not a single
Embolismic year which is marked 5R. Every Embolismic year in
that Table which commences with feria 5 is marked either as M.,
mangelhaft, Deficient, orU, iiberschiissig, Abundant. In fact, nothing
else is possible.
Petavius, in " De Doctrina Temporum," lib. vii. cap. xviii., under
the heading " Canones neomeniae Tisri in Embolimaeis annis," states
correctly that a year whose Molad has these limits commences with
a Thursdav and is Deficient.
THE JEWISH CALENDAR 93
16. Every Embolismic year whose Molad is not less that 4d. llh.
695ch., and not greater than 5d. 17h. 1079ch., will commence with a
Thursday, and be Abundant, 385 days.
(a) If the feria be 4 Tishri 1 is postponed to Thursday ; if it be
5 and the Molad be anything less than 5d. 18h. Och., Tishri 1 falls
naturally to Thursday.
(b) Molad of H 4 11 C95 to 5 17 1079
Excess of H . 5 '21 589 5 21 589
Molad of H + 1 3 9 204 to 4 15 588
H + 1 is a Common year, for it follows an Embolismic year, therefore
Tishri 1 is postponed by GaTRaD from feria 3 to feria 4, and thence
by ADU to feria 5 ; also when the Molad attains to 4d. Oh. Och. there is
a postponement to feria 5. If the feria be 5, and the Molad be not so
great as 5d. 18h. Och., Tishri 1 falls naturally to Thursday. H + 1
therefore, commences with a Thursday ; H ends with a Wednesday,
and as it commenced with a Thursday it has an exact number of
weeks, or 385 days.
17. Every Embolismic year whose Molad is not less than 5d. 18h.
Och., and not greater than 6d. 20h. 490ch., commences with a
Saturday, and is Deficient, 383 days.
(a) The minimum value of the Molad being 5d. 18h. Och., Tishri 1
is postponed from Thursday to Saturday by YacH and ADU. With
the Molad Gd. Oh. Och. to 6d. 17h. 1079ch. it is postponed by ADU from
Friday to Saturday, and if -it be greater than 6d. 17h. 1079ch., both
YacH and ADU are effective to postpone it from Friday to Saturday.
The year therefore begins with Saturday.
(b) Molad of H 5 18 to 20 490
Excess of H . 5 21 589 5 21 589
MoladofH + 1 4 15 589 to 5 171079
H + 1 commences with a Thursday; the last day of H is a
Wednesday, therefore it has 383, or In + 5 days for it commences
with a Saturday.
18. Every Embolismic year whose Molad is not less than 6d. 20h.
491ch., and not greater than 7d. 17h. 1079ch., commences with a
Saturday, and is Abundant, 385 days.
94 THE JE WISH CALENDAR
(a) When the feria is 6, Tishri 1 is postponed by ADU from Friday
to Saturday. When the feria is 7, Tishri 1 falls naturally to Saturday,
so long as the Molad does not exceed 7d. 17h. 1079ch. The year,
therefore, commences with a Saturday.
(b) Molad of H 6 20 491 to 7 171079
Excess of H 5 21 589 5 21 589
Molad ofH + 1 5 18 to 6 15 588
H 4- 1 commences with a Saturday, and the last day of H is a
Friday. It commences with a Saturday, therefore it has In + 0, or
385 days.
These results are called the Day-Limits of the years. They are
collected in Table X. The vertical argument in that Table refers to
the numbering of the demonstrations above.
It is important to notice that there are further restrictions on the
Day-Limits for a Common year following an Embolismic when it is
the first year in a Cycle. These restrictions will be explained in
Article 58.
57. Besides the commencement of the Civil year with Tishri, and
of the Ecclesiastical year with Nisan, the Jews have, for a particular
purpose, a third commencement, Schebhat 15, called Laylanot, the
First Day of the year of Trees, which occurs generally in one of the
Christian months January or February. It is unlawful to eat of the
fruit of a tree until the third crop is produced ; but because the crop
is produced annually, this law is so interpreted that it is made lawful
to eat of the crop of the third year. These years are reckoned from
Schebhat 15. Hence if a tree be planted at any time before that day
its first year is reckoned as terminating with that day, although the
tree may in fact have been planted for only a few wrecks, or even a few
days. Its third year w T ould then commence when it had been in
position only one year and a portion of another, and the fruit which is
produced during this nominal third year may be lawfully eaten.
To FIND THE LENGTH OF ANY GIVEN CYCLE.
58. This is done in a similar way to that by which the length of
any given year is found, namely, by ascertaining the feriae with which
the Cycle commences and terminates.
95
An Astronomical Cycle of nineteen years is a constant quantity
consisting of 6939d. 16h. 595ch., but a Civil Cycle of nineteen years is
variable in length. It must of necessity consist of an integral number
of days, and this number may be either 6939, 6940, 6941, or 6942 days,
that is, its length may be of one of the four forms 7N + 2, 7N + 3,
7N + 4, or 7N + 5, according to the feria with which it commences
and the number of times that Tishri 1 is postponed by the Dechiyyoth
in the course of the nineteen years.
6939 DAYS.
A Cycle of 6939, or In + 2 days cannot commence with a Monday,
because if it did so commence it would terminate with a Tuesday, and
the first year of the, next Cycle would commence with a Wednesday,
which is a day forbidden for Tishri 1.
It may commence with either a Tuesday, a Thursday, or a Saturday.
TUESDAY. Let C be the Cycle. It will commence with this
day if its Molad be not less than 2 15 589, and not greater than
3 1 484.
Molad of C 2 15 589 to 3 1 484
Add excess of C . 2 16 595 2 16 595
Molad of C + l 5 8 104 to 5 171079
C + l, therefore, commences with a Thursday and C ends with a Wed-
nesday; as, by hypothesis, it commences with a Tuesday, it has In + 2,
or 6939 days.
With reference to the limits assigned here to the Molad of C, it
must be noticed that although a Common year which follows an
Embolismic (as the first year of every Cycle), can commence with a
Tuesday if its Molad be from 2 15 589 to 3 9 203, (Article 56(4)),
yet when such a year is the first of a Cycle which has only 6939 days
the superior limit is reduced from 3 9 203 to 3 1 484. This
limit is obtained as follows : The next Cycle, C+l, must commence
with a Thursday if C commence with a Tuesday, and have In + 2
days. The maximum Molad for year or Cycle which commences with
a Thursday is 5 17 1079, for if the Molad be greater than this by
one Chalak the year will commence with a Saturday. Hence we have
96 THE JE WISH CALENDAR
Maximum Mclad for C + 1 5 17 1079
Subtract excess of C . . 2 16 595
Maximum Molad for C 3 1 484
THURSDAY. A Cycle of 6939 days can commence with this day if
its Molad be from 3 9 204 to 5 1 484.
Molad of C 3 9 204 to 5 1 484
Add excess of C 2 16 595 2 16 595
Molad of C + l 6 1 799 to 7 171079
C + l commences with a Saturday, therefore C terminates with a
Friday, and has In + 2, or 6939 days.
Here, again, the superior limit of the Molad for C is reduced,
namely, from 5 9 203 (Article 56(6)), to 5 1 484, obtained by
subtracting the excess of C from the maximum Molad which permits
a year to commence with a Saturday, that is, 7 17 1079. If this
Molad were increased by only one Chalak the first year of C + 1
would commence with a Monday ; C would terminate with .a Sunday,
and instead of having only 6939 days it would have 6941.
SATURDAY. A Cycle of 6939 days can commence with this day if
its Molad be from 5 18 to 6 22 1073.
MoladofC 5 18 to 6 221073
Add excess of C 2 16 595 2 16 595
Molad of C + l 1 10 595 to 2 15 588
C+l commences with a Monday, therefore C terminates with a
Sunday, and has In + 2 days.
The superior limit for the Molad of C is reduced from 7 17 1079
to 6 22 1073 in order that C + l may commence with a Monday.
The maximum limit for the Molad of C + l, which follows an
Embolismic year, is therefore 2 15 588, for if it were one Chalak
greater than this it would commence with a Tuesday. Subtracting
the excess of C from 2 15 588, to which 7 days may be added
without altering the feria, the remainder is 6 22 1073.
THE JE WISH CALENDAR 97
6940 DAYS.
A Cycle of 6940, or 7n + 3 days cannot commence with a Tuesday,
because it would terminate with a Thursday, and the next Cycle
would commence with a Friday, which is impossible.
It cannot commence with a Thursday, because the next Cycle
would commence with a Sunday, which is also impossible.
It may commence with a Monday or a Saturday.
MONDAY. A Cycle of 6940 days can commence with a Monday if
its Molad be from 7 18 to 2 15 588.
MoladofC 7 18 to 2 15 588
Excess of C . 2 16 595 2 16 595
Molad of C + l 3 10 595 to 5 8 103
C + 1 commences with a Thursday, and therefore C terminates
with a Wednesday, and has In + 3 or 6940 days.
In this case the ordinary limits for a Common year commencing
with a Monday requires no reduction.
SATURDAY. It can commence with this day if its Molad be from
6 22 1074 to 7 16 688.
MoladofC 6 22 1074 to 7 16 688
Excess of C . 2 16 595 2 16 595
Molad of C + l 2 15 589 to 3 9 203
C + l commences with a Tuesday, therefore C terminates with a
Monday, and has In + 3 days.
The ordinary limits for the Molad of a Common year following an
Embolisrnic year, to commence with Saturday, are 5 18 to
7 17 1079. Both of these limits have to be restricted for the first
year of a Cycle which is to have 6940 days. If the inferior Molad of
C + l were less than 2 15 589 by even one Chalak the year and the
Cycle would commence with a Monday, C would terminate with a
Sunday and have only 6939 days. The minimum limit for the Molad
of C is therefore 6 22 1074. With regard to the superior limit, if
it were one Chalak greater than 7 16 688 the Molad for C + l
would attain to 3 9 204, and in that case C+l would commence
with a Thursday, so that C would have In + 5 days.
98 THE JE\YISJf CALENDAR
6941 DAYS.
A Cycle of 6941, or In + 4 days cannot commence with a Monday
or a Saturday because, if it did so commence, it would terminate with
a Thursday or a Tuesday, and the next Cycle would commence with a
forbidden day, Friday or Wednesday.
It can commence with a Tuesday or a Thursday.
TUESDAY. It can commence with Tuesday if the limits for its
Molad be 3 1 485 and 3 9 203.
MoladofC 3 1 485 to 3 9 203
Excess of C . 2 16 595 2 16 595
5 18 to 6 1 798
C + 1 commences with Saturday ; C ends with Friday, and has
In + 4, or 6941 days.
The inferior limit for a Common year following an Embolismic
year is 2 15 589 ; but if it is to be the first year of a Cycle which
has 6941 days, this limit must not be less than 3 1 485, for if it
were even one Chalak less the Molad of C + 1 would not attain to
5 18 ; in that case Tishri 1 would not be postponed from feria 5
to Saturday ; C would terminate with a Wednesday, and have only
6939 days.
The superior limit requires no alteration.
THUESDAY. The ordinary limits are 3 9 204 and 5 17 1079,
but if a Cycle is to be one of 6941 days its inferior limit cannot be less
than 5 1 485.
MoladofC 5 1 485 to 5 171079
Excess of C . 2 16 595 2 16 595
Molad of C + l 7 18 to 1 10 594
C + 1 commences with Monday ; C terminates with Sunday, and has
In + 4, or 6941 days.
If the Molad of C were anything less than 5 1 485, that of C + 1
would be less than 7 18 and Tishri 1 would not be postponed from
Satin-da) 7 to Monday.
THE JE WISH CALENDAR 99
6942 DAYS.
A Cycle which has 6942 or In + 5 days can commence with a
Saturday only.
It cannot commence with a Monday, for- the Day-Limits which
permit of a year commencing with a Monday are 7 18 to
2 15 588, and it has been shown that with these limits a Cycle
is one of only 6940 days.
It cannot commence with a Tuesday, because it would terminate
with a Saturday, and the next Cycle would commence with a Sunday,
which is impossible.
It cannot commence with a Thursday, because the limits for the
Molad of a Common year so commencing are 3 9 204 to 5 17 1079.
MoladofC 3 9 204 to 5 171079
Excess of C.. 2 16 595 2 16 595
Molad of C + l 6 1 799 to 1 10 594
C + 1 would, therefore, commence with a Saturday, or with a Monday.
In the former case C would terminate with a Friday, and have only
In + 2 days ; in the latter case, it would end with a Sunday and have
only In + 4 days.
SATUBDAY. A Cycle of 6942 days can commence with this day.
The ordinary limits for the Molad of any year which commences
with a Saturday are 5 18 and 7 17 1079. In order that a Cycle
so commencing may have 6942 days the superior limit for the Molad of
its first year must be increased to 7 16 689, for if it be anything less
than this the next Cycle will not commence with a Thursday.
MoladofC 7 16 689 to 7 171079
Excess of C. 2 16 595 2 16 595
Molad of C + l 3 9 204 to 3 10 594
C + l begins with a Thursday ; C ends with a Wednesday, and has
In + 5, or 6942 days.
The fact that it is possible for a Cycle to contain so many as 6942
days is not always recognised. Dr. Schwarz, in one passage, speaks
of Cycles as though they could only contain 6939, 6940, or 6941
100
THI-: JEll'ISH CALENDAR
days,* but in line 61 of his " Tabel K," p. 83, he gives, as a possible
form of a Cycle, one which has its first year marked 7u, meaning that
it is a Common Abundant year, and commences with a Saturday ; the
last year of the same Cycle is marked as 5u, meaning that this
nineteenth year commences with a Thursday, and is an Embolismic
Abundant year. It therefore contains 385 days, or an exact number of
weeks, and because it commences with a Thursday it must terminate
with a Wednesday. In other words, the Cycle itself terminates with a
Wednesday, and as it commences with a Saturday it must contain
7N + 5, or 6942 days.
Such a Cycle is, however, of very rare occurrence. The only
Cycles which have had 6942 days since the commencement of the Era
are the 154th, and the 167th, and that only when the computation is
made according to the rules of the reformed Calendar.
The same thing will not occur again till the 547th Cycle is reached ;
its Molad is 7 17 1074. After that the 560th Cycle, whose Molad is
7 17 169, will also have 6942 days ; see Example 3, below.
The results which have been obtained are collected in the following
Table :
LIMITS FOE THE MOLADS OF CYCLES ACCORDING TO THE
NUMBER OF DAYS IN THE CYCLE.
Days in
Cycle.
First Day of
Cycle C.
. Molads :
The Limits are inclusive.
First Day of Cycle
C + l.
6939
Tuesday
Thursday
Saturday
2
3
5
lo
9
18
589
204
to
to
to
3
5
6
1
1
22
484 Thursday
484 Saturday
1073 Monday
6940
Monday
Saturday
7
6
18
2-2
1074
to
to
2
7
15
16
588 Thursday
688 Tuesday
6941
Tuesday
Thursday
3
5
1
1
485
485
to
to
3
5
9
17
203
1079
Saturday
Monday
6942
Saturday
7
16
689
to
7
17
1079
Thursday
* In the German text, " Der Jiidische Kal.," p. 78, the figures are 3639, 3640, and 3641.
" Daher riihrt auch die veranderliche Lange des Mondcyclus, der bald 3639, bald 3640,
zmveilen gar 3641 Tage ziihlt." These are evidently misprints for 6939, 6940, and 6941.
THE JEWISH CALENDAR 101
The method of finding the lengths of any given Cycle is illustrated
by the following examples :
Example 1. Required the numher of
BeHaRD
days in the 295th Cycle.
2 5 204
Add for 200 Cycles elapsed
5 22 200
4 1 630
3 18 220
Molad for 295th Cycle 1 23 174
Add for 1 Cycle 2 16 595
Molad for 296th Cycle 4 15 769
From this it appears that the 295th Cycle commences with a
Monday, because feria 1, to which the Molad falls, is forbidden by
ADU. Also it must terminate with a Wednesday, for the next Cycle
commences with feria 5, Thursday, because feria 4, Wednesday, is
forbidden.
The 295th Cycle has therefore three days more than an exact
number of weeks, and is of the form 7n + 3, or has 6940 days.
Example 2. Find upon what date the 154th Cycle of the Era
would have commenced, and the number of days it would have con-
tained, if the rules of the Jewish Calendar, as now established, had
been then in force.
BeHaKD 2 5 204
Add for 100 Cycles elapsed 2 23 100
50 1 11 590
3 11 705
Molad of 154th Cycle 7 17 519
Add for 1 Cycle 2 16 595
Molad of 155th Cycle 3 10 34
The 154th Cycle would, therefore, have commenced with a
Saturday, and it must have terminated with a Wednesday, because
the feria in the Molad for the next Cycle is 3 and the hours and
Chalakim exceed 9h. 204ch., so that the rules GaTRaD and ADU
io2 Till-. JEU'ISH CALENDAR
postpone the commencement of the first year of this Cycle to
Thursday.*
The 154th Cycle had, therefore, five days more than an exact number
of weeks, and if the rules had been in force would have had 6,942
days.
Example 3. Find the feria with which the 560th Cycle will com-
mence, and the length of the Cycle.
BeHaKD 2 5 204
Add for 500 Cycles elapsed 7 19 500
50 1 11 590
9 3 41035
Molad of 560th Cycle 7 17 169
Add for 1 Cycle 2 16 595
Molad of 561st Cycle 3 9 764
The 560th Cycle will commence with a Saturday, and it will
terminate with a Wednesday, for the next Cycle begins with a
Thursday, Tishri 1 being postponed by GaTEaD and ADU from feria
3 to feria 5. The Cycle will, therefore, have five days above an exact
number of weeks, and be of the form 7n + 5, or will have 6942 days.
* The first year of every Cycle is a Common year following an Embolismic year, and
therefore comes within the rule GaTEaD.
CHAPTEK V
THE SEQUENCE OF YEAES
59. The following statements, which refer to the possible and
impossible sequence of years, may be deduced from the rules which
have been previously given. They result, in fact, from the method in
which the Calendar is constructed by means of Molads, and from the
law which prohibits the celebration of Tishrl 1 upon certain days of
the week.
The Numbers and Letters in the margin refer to the proofs.
These will be given after the statements have been made.
I. A Deficient year, whether it be either Common or Embolismic,
cannot be followed by a Deficient year-.
a. b, 353 cannot be followed by 353.
c. d. 353 cannot be followed by 383.
e. f. g. 383 cannot be followed by 353.
II. A Regular year, whether Common or Embolismic, cannot be
followed by a Regular year.
a. b. 354 cannot be followed by 354.
c. d. 354 cannot be followed by 384.
e. 384 cannot be followed by 354.
III. An Abundant year, whether Common or Embolismic, can, with
certain exceptions, be followed by an Abundant year.
a. 355, commencing with Monday, can be followed by 355.
103
io 4 THE JEWISH CALENDAR
b. c. Not, if it commence with Thursday or Saturday.
d. e. 355, commencing with Monday or Saturday, can be followed
by 385.
/. Not, if it commence with Thursday.
g. h. 385, commencing with Monday or Saturday, can be followed
by 355.
i. Not, if it commence with Thursday.
IV. A Deficient year, whether Common or Embolismic, can, with
certain exceptions, be followed by a Kegular year.
a. b. 353, whether commencing with Monday or Saturday, can be
followed by 354.
c. 353, commencing with Saturday, can be followed by 384.
d. Not, if it commence with Monday.
e. f. 383, commencing with Thursday or Saturday, can be followed
by 354.
g. Not, if it commence with Monday.
V. A Regular Common year can be followed by a Deficient year,
with certain exceptions.
a. 354, if it commence with Thursday, can be followed by 353.
b. Not, if it commence with Tuesday.
c. 354, if it commence with Thursday, can be followed by 383.
d. Not, if it commence with Tuesday.
VI. A Regular Embolismic year cannot be followed by a Deficient
year,
a. 384 cannot be followed by 353.
VII. A Deficient year can, with certain exceptions, be followed by an
Abundant year.
a. 353, if it commence with Monday, can be followed by 355.
b. Not, if it commence with Saturday.
c. 353, if it commence with Monday, can be followed by 385.
d. Not, if it commence with Saturday.
e. f. 383, commencing with Monday or Saturday, can be followed
by 355.
g. Not, if it commence with Thursday.
THE JEWISH CALENDAR 105
VIII. An Abundant year can, with certain exceptions, be followed by
a Deficient year.
a. 355, if it commence with Monday, can be followed by 353.
b. c. Not, if it commence with Thursday or Saturday.
d. e. 355, if it commence with Monday or Saturday, can be followed
by 383.
/. Not, if it commence with Thursday.
g. h. 385, if it commence with Monday or Saturday, can be followed
by 353.
i. Not, if it commence with Thursday.
IX. An Abundant year, with certain exceptions, can be followed by
a Regular year. .
a. b. 355, if it commence with Thursday or Saturday, can be
followed by 354.
c. Not, if it commence with Monday.
d. 355, if it commence with Thursday, can be followed by 384.
e. f. Not, if it commence with Monday or Saturday.
g. 385, if it commence with Thursday, can be followed by 354.
h. i. Not, if it commence with Monday or Saturday.
X. A Regular year, whether it commence with Tuesday or Thursday,
can be followed by an Abundant year.
a. b. 354, commencing with Tuesday or Thursday, can be followed
by 355.
c. d. 354, commencing with Tuesday or Thursday, can be followed
by 385.
e. 384, which can only commence with Tuesday, can be followed
by 355.
It is hardly necessary to add that, according to the arrangement of
the Cycle in the established Calendar, it is impossible for two Em-
bolismic years, or for three Common years, to be consecutive.
PROOFS OF THE FOREGOING STATEMENTS.
The days of the week upon which the Jewish years, according to
their form, can commence, will be found in Article 54, page 79.
The limits of the Molads are taken from the colbcted Table X.
They result from the rules specified in Article 50.
ro6 THE JEWISH CALENDAR
In the following proofs H is the given year, H + 1 the next year,
and H -I- 2 the year after H + 1.
I. 353 cannot be followed by 353.
a. Let 353 commence with a Monday, and, if possible, let it be
followed by 353.
MoladofH ............... 718 to 1 9 203
Excess of H, Com. ... 4 8 876 4 8 876
Molad of H + 1 .. 5 2 . 876 to 5 17 1079^ m ,
Excess of H + 1 4 8 876 4 8 876 ( '
Molad of H + 2 211 672 to 3 2 875
Therefore H + 2 must begin with a Monday or Tuesday, and
H + 1 must end with a Sunday or Monday. It commences with a
Thursday, and may therefore have 354 or 355 days, but it cannot have
353.
b. Let 353 commence with a Saturday, and, if possible, let it be
followed by 353.
MoladofH 518 to 6 407
Excess of H, Com. ... 4 8 876 4 8 876
Molad of H + 1 3 2 876 to 3 8 203J T Be ^ ns
Excess of H + 1, Com. 4 8 876 4 8 876 1 -
Molad of H + 2 7 11 672 to 7 16 1079
Therefore H + 2 must begin with a Saturday, and H + 1 must end
with a Friday. It commences with a Tuesday, and may therefore have
354 days, but it cannot have 353 or 355.
353 cannot be followed by 383.
c. Let 353 commence with a Monday, and, if possible, let it be
followed by 383.
(See a, above.
MoladofH + 1 5 2 876 to 5 17 1079.! Begins
Excess of H + 1, Emb. 5 21 589 5 21 589 (Thursday.
Molad of H+2.. 4 385 to 4 15 588
THE JEWISH CALENDAR 107
Therefore H + 2 commences with a Thursday, arid H + 1 must end
with a Wednesday. It begins with Thursday, and therefore has 385
days, but it cannot have 383 or 384.
d. Let 353 commence with a Saturday.
(See b, above.
MoladofH + 1 ......... 3 2 876 to 3 8 203^ Begins
Excess of H + l,Emb. 521 589 521 589 [Thursday.
MoladofH + 2 ......... 1 385 to 2 5 792
Therefore H + 2 begins with a Monday, and H + 2 must end with
a Sunday. It begins with Tuesday, and therefore has 384 days, but it
cannot have 383 or 385.
383 cannot be followed by 353.
e. Let 383 commence with a Monday, and, if possible, let it be
followed by 353.
MoladofH ............... 718 to 1 20 490
Excess of H, Emb. ... 521 589 521 589
Molad of H + 1 ......... 6 15 589 to 7 17 1079 -j Q B , egms
Excess of H + 1, Com. 418 876 418 876 (k
Molad of H + 2 ......... 4 385 to 5 2 875
Therefore H + 2 commences with a Thursday, and H + 1 must end
with a Wednesday. It commences with a Saturday, and can only have
355 days. It cannot have 353 or 354.
/. Let 383 commence with a Thursday, and, if possible, let it be
followed by 353.
MoladofH ............... 318 to 4 11 694
Excess of H, Emb. ... 521 589 521 589
Molad of H + 1 ......... 215 589 to 3203
Excess of H + 1, Com. 4 8 876 48 876 ( -
MoladofH + 2 ......... 7 385 to 7 16 1079
Therefore H + 2 commences with a Saturday, and H + 1 must end
with a Friday. It commences with a Tuesday, and can only have 354
days. It cannot have 353 or 355.
io8 THE JEWISH CALENDAR
<j. Let 383 commence with a Saturday, and, if possible, let it be
followed by 353.
MoladofH ............ 518 to 6 20 490
Excess of H, Emb. ... 521 589 521 589
Molad of H + 1 ......... 415 589 to 5 17 1079 m
Excess of H + 1, Com. 4 8 876 4 8 876 ( '
Molad of H + 2 ......... 2 385 to 3 2 875
Therefore H + 2 will commence with a Monday, or a Tuesday, and
H + l must end with a Sunday or a Monday. It commences with
Thursday, so that it may have 354 or 355 days, but it cannot have
353.
II. 354 cannot be followed by 354.
a. Let 354 commence with a Tuesday, and, if possible, let it be
followed by 354.
MoladofH ............... 215 589 to 3 9 203
Excess of H, Com. ... 4 8 876 4 8 876
Molad of H + l ......... 7 385 to 7 17 1079 1 Q B , egms
Excess of H + 1, Com. 4 8 876 48 876 i bi
Molad of H + 2 ......... 4 9 181 to 5 2 875
Therefore H + 2 must commence with a Thursday, and H + l
must end with a Wednesday. It commences with a Saturday, and
therefore must have 355 days ; but it cannot have 354 or 353.
b. Let 354 commence with a Thursday, and, if possible, let it be
followed by 354.
MoladofH ............... 3 9 204 to 5 9 203
Excess of H, Com. ... 4 8 876 4 8 876
Molad of H + 1 ......... 718 to 2 17 1079
Excess of H + 1, Com. 4 8 876 4 8 876 l Monda y-
Molad of H + 2 5 2 876 to 7 2 875
Therefore H + 2 must commence either with a Thursday or a
THE JEWISH CALENDAR 109
Saturday, and H + 1 must end with a Wednesday or a Friday. It
commences with a Monday ; so that it may have 353 or 355 days, but it
cannot have 354.
354 cannot be followed by 384.
c. Let 354 commence with a Tuesday, and, if possible, let it be
followed by 384.
Molad of H + 1 .. 7 385 to 7 17 1079 | Se *' a j ve '
Excess of H + 1, Emb. 5 21 589 5 21 589 (
MoladofH + 2 ......... 521 974 to 6 15 588
Therefore H + 2 must commence with a Saturday, and H + 1 must
end with a Friday. It commences with Saturday, and therefore has
385 days ; but it cannot have 384 or 383.
d. Let 354 commence with a Thursday, and, if possible, let it be
followed by 384.
Molad of H + 1 ......... 7 18 to 2 17 1079 j Se 6 ' ^ b Ve -
Excess of H + 1, Emb. 5 21 589 5 21 589 I
MoladofH + 2 ......... 615 589 to 1 15 588
Therefore H + 2 must commence with a Saturday or with a
Monday, and H + 1 must end with a Friday or a Sunday. It com-
mences with a Monday. Therefore it may have either 383 or 385
days, but it cannot have 384.
384 cannot be followed by 354.
e. A year of 384 days can only commence with a Tuesday, and, if
possible, let it be followed by 354.
MoladofH ............... 218 to 3 17 1079
Excess of H, Emb. ... 521 589 521 589
Molad of H + 1 . , 1 15 589 to 2 15 588
Excess of H + 1, Com. 4 8 876 4 8 876 (l
MoladofH + 2 ...... 6 385 to 7 384
Therefore H + 2 must begin with a Saturday, and H + 1 must
no THE JE U'ISH CALENDAR
with a Friday. It commences with Monday, and can only have 355
days. It cannot have 354 or 353.
III. 355, if it commence with Monday, can be followed by 355 .
a. MoladofH ............ 1 9 204 to 2 15 588*
Excess of H, Com. ... 4 8 876 48 876
Molad of H + 1 5 18 to 7 384-; Q B , e ^ ms
ExcessofH + l.Com. 4 8 876 48 876 ( k
Molad of H + 2 ...... 3 2 876 to 4 9 180
Therefore H + 2 commences with a Tuesday, or with a Thursday,
and H + 1 must end with a Monday or a Wednesday. It commences
with a Saturday, so that it may have 353 or 355 days, but it cannot
have 354.
b. Let 355 commence with a Thursday.
MoladofH ............... 5 9 204 to 5 17 1079
Excess of H, Emb. ... 4 8 876 4 8 876
Molad of H + 1 . . 218 to 3 2 875 -' rp
Excess of H + 1, Com. 4 8 876 48 876 '- -
Molad of H + 2 ......... 7 2 876 to 7 11 671
Therefore H + 2 commences with a Saturday, and H + 1 must
end with a Friday. It commences with a Tuesday, and therefore can
only have 354 days ; it cannot have 355 or 353.
c. Let 355 commence with a Saturday.
MoladofH ............... 6 408 to 7 17 1079
Excess of H, Com. ... 4 8 876 4 8 876
Molad of H + l ......... 3 9 204 to 5 2 875 m
Excess of H + 1 Com. 4 8 876 4 8 876 ( ^
Molad of H + 2 ......... 718 to 2 11 671
Therefore H + 2 must commence with a Monday, and H + l must
* Notice that H must follow an Erabolismic year, because it is assumed to be itself followed
by a Common year. The superior limit is therefore 2 15 588.
THE JE WISH CALENDAR 1 1 1
end with a Sunday. It begins with a Thursday, so that it has 354
days, and cannot have 355 or 353.
355, if it commence with Monday or Saturday, can be
followed by 385.
d. Let 355 commence with Monday.
MoladofH 1 9 204 to 2 17 1079*
Excess of H. Com. ... 4 8 876 48 876
MoladofH + 1 518 to 7 2 875 ] G B . egl ? s
Excess of H + lEmb. 521 589 521 589 I b
MoladofH + 2 415 589 to 6 384
Therefore H + 2 commences with a Thursday, or with a Saturday,
and H + 1 must end w r ith a Wednesday or a Friday. It begins with
Saturday ; so that it may have 383 or 385 days ; but it cannot have
384.
e. Let 355 commence with a Saturday.
MoladofH 6 9 204 to 7 17 1079
Excess of H, Com. ... 4 8 876 4 8 876
MoladofH + 1 3 18 to 5 2 875 jm? egil j s
Excess of H + 1, Emb. 5 21 589 5 21 589 I - 1
MoladofH + 2 215 589 to 4 384
Therefore H + 2 commences with a Tuesday, or with a Thursday,
and H + 1 must end with a Monday or a Wednesday. It begins with
a Thursday, and may have 385 or 383 days. It cannot have 384.
/. Let 355 commence with a Thursday.
MoladofH 5 9 204 to 5 17 1079
Excess of H, Com 4 8 876 48 876
MoladofH+1 218 to 3 2 875J rr Be ^ ns
Excess of H + 1, Emb. 521 589 521 589 l 1
MoladofH + 2 115 589 to 2 384
* H may follow either a Common or an Embolismic year because H + 1 is, by hypothesis,
Embolismic.
1 1 2 THE JE WISH CALENDAR
Therefore H + 2 must begin with a Monday, and H + 1 must end
with a Sunday. It begins with Tuesday, and therefore has 384 days.
Hence, 355 commencing with a Thursday cannot be followed by 385
or by 383.
385, commencing with Monday or Saturday, can be
followed by 355.
ff. Let 385 commence with Monday.
MoladofH ............ 1 20 491 to 2 17 1079
Excess of H, Emb. ... 5 21 589 521 589
MoladofH + 1 ......... 718 to 1 15
Excess of H + 1, Com. 4 8 876 48 876 l iv -
MoladofH + 2 ......... 5 2 876 to 6 384
Therefore H + 2 may commence with a Thursday or a Saturday,
and H + 1 must end with a Wednesday or a Friday. It commences
with a Monday, and therefore can have 355 or 353 days ; but it cannot
have 354.
h. Let 385 commence with Saturday.
MoladofH ........ ".... 6 20 491 to 7 17 1079
Excess of H, Emb. ... 521 589 521 589
Molad of H + 1 . . 5~18 to 6 15 588 f Begi j s
Excess of H + 1, Com. 4 8 876 48 876 I b;
Molad of H + 2 ......... 3 2 876 to 4 384
Therefore H + 2 begins with a Tuesday or a Thursday, and H + 1
must end with a Monday or a Wednesday. It commences with a
Saturday, and can have 355 or 353 days, but it cannot have 354.
i. Let 385 commence w r ith Thursday.
MoladofH ............ 4 11 695 to 5 17 1079
Excess of H, Emb. ... 521 589 521 589
Molad of H + 1.. 3 9 204 to 4 15- m
Excess of H + 1, Com. 4 8 876 48 876 ( lnursda y-
MoladofH + 2... 718 to 2 384
THE JEWISH CALENDAR 113
Therefore H + 2 must begin with a Monday, and H + 1 must end
with a Sunday. It commences with a Thursday ; it can therefore only
have 354 days, so that if 385 commence with a Thursday it cannot be
followed by 355 or by 353.
IV. to X. It will be found that the proofs of these statements,
are included in those which have been given above.
IV. a. Proof included in La.
b. 1.6.
c. La".
d. I.e.
e. I/
/ - M I*-
g. ,, I.e.
V. a. Il.b.
b. ILa.
c. Il.d.
d. II.c.
VI. ll.e.
VII. a. La.
b. 1.6.
c. ,, I.e.
d. I.d.
e. I.e.
/ n 1.9.
g. I/
VIII. a. IILa.
b. Ill.b.
c. ,, III.c.
d. Ill.d.
e. ,, IlI.e.
f. HI./.
g. ,, III.*/.
7i. III./i.
i. III.2.
IX. a. III.6.
6. IILc.
c. ,, IILa.
d. III./.
ii4 THE JEWISH CALENDAR
e. Proof included in III.cZ.
/. lll.e.
g. III.*.
h. III.?.
L III A
X. a. ,, II. a.
ft. II. ft.
c. ,, II. c.
d. ILdf.
e. ,, II.c.
In the following Table of collected results all those years are entered
which can possibly follow a year of the form given in the first column
when the latter commences upon the day of the week given in the
second column.
It is to be understood that no sequence of years, other than such
as are here expressed, is possible. Thus : It is impossible that a year
of 354 days can follow a year of 385 days when the latter commences
with a Saturday ; therefore, in the third line from the bottom of the
Table, 354 does not appear.
A Year
of Days.
Having for First
Day.
Can be followed by a Year having Days in
Number.
353 Monday 354 i 355
Saturday 354 |
354 Tuesday 355
Thursday 353 355
355 Monday 353 355
Thursday 354
Saturday 354
383 Monday 355
Thursday 354
Saturday 354 355
384 Tuesday ; 355
385 Monday 353 i 355
Thursday 354
Saturday 353 355
383
383 |
383
384
384
385
385
385
385
385
Reference to
Proof.
I.n I.c
I.ft I.d
ILa II c
Il.b ll.d
Ill.fl lll.d
III.& Ill.f
III.c. Ili.e
I./
Lf
Il.e
HI..'/
m.i
III./i
THE JEWISH CALENDAR 115
60. It may be well to observe here that, in attempting to prove
statements such as the foregoing, there may be a temptation to adopt
a method which will seem to be both short and simple. It might be
said, for example If a year of 354 days commence with a Tuesday its
last day must be a Friday, and the next year will commence with a
Saturday ; this is a day which is possible for the commencement of
years having 353, 355, 383, or 385 days ; therefore 354 can be followed
by either of these years.
It has, however, been proved, in V.a, that, when the Molads are
-considered, it is impossible for 354, commencing with a Tuesday, to be
followed by 353 ; and, in V.c, that it is impossible for it to be followed
by 383.
The method, if attempted, therefore fails in this case. It fails also
in three other cases. It would show that 353 commencing with a
Monday might be followed by 383 ; that 383 commencing with a
Monday might be followed by 353 ; and that 384 commencing, as it
always does, with a Tuesday, might be followed by 353. Each of
these sequences is proved by the Molads to be impossible.
Reliance, therefore, must not be placed upon such a method, although
it gives correct results in ten out of fourteen cases. Thus : It will
show that 353 commencing with a Saturday can be followed by 354
or by 384. For if 353 commence with a Saturday it must end with a
Monday, and the next year will commence with a Tuesday ; this is
a day which is possible for the commencement of both 354 and 384,
but not possible for the commencement of any other year. This
method therefore proves, in this instance correctly, that not only can
353 be followed by 354 or by 384, but also that such must be the
sequence ; the former, if 353 be followed by a Common year ; the
latter, if it be followed by an Embolismic year.
CORRESPONDENCE BETWEEN JEWISH AND CHRISTIAN DATES.
61. Guided by the foregoing regulations the Christian dates
corresponding to Tishrl 1, for any consecutive number of years, may
be computed. If the computation be not made from the commence-
ment of the Jewish Era it must begin from some year in which the
Christian date of Tishrt 1 is known. Assuming that no such date is
known, it may be found by means of the formula of Dr. Gauss, which
u6 THE JEWISH: CALENDAR
will be described hereafter, or by the method of " Days Elapsed," of
which examples will now be given.
Required the Christian date corresponding to Tishri 1 of the year
5611.
Let it be assumed as known that the Molad BeHaRD is 2d. 5h.
204ch., that is, the Era commenced at 5h. 204ch. after the commence-
ment of feria 2, and that the day corresponded to Monday, October 7,
B.C., 3761.* The Jewish feria commences six hours earlier than our
own Civil week-day, that is to say, it commences at 6 p.m.
It is also known that, according to Jewish Astronomical computation
the mean length
d. h. ch.
Of a Lunation is 29 12 793
Of a Common year 354 8 876
Of an Embolismic year 383 21 589
Of a Cycle 6939 16 595
These, then, are the known facts by means of which the Christian
date of Tishri 1 in the given year is to be found. Attention must, of
course, be paid to the established rules of the Jewish Calendar.
1. The Christian year, in the Autumn of which A.M. 5611
commences, is A.D. (5611-3761), or 1850 ; t the Jewish year
terminates in the Autumn of 1851.
2. The division of 5611 by 19 gives a quotient 295, and a remainder
6, showing that the given year is the sixth in the 296th Cycle.
Consequently there had elapsed 295 complete Astronomical Cycles and
5 complete Astronomical years before the New Moon occurred by which
Tishri 1, A.M. 5611, is governed.
3. To find the time in days, hours, and Chalakim, contained in these
295 Cycles and five years.
In the first five years of every Cycle there are four Common years,,
and one Embolismic year.
We have then, by actual multiplication,
d. h. ch.
295 Astronomical Cycles = 2047208 10 565
4 Astro. Com. years = 1417 11 264
1 Astro. Emb. year = 383 21 589
The sum = 2049009 19
* Article 33, p. 41. f Article 37, p. 46.
THE JE WISH CALENDAR 1 1 7
The same result is obtained if the values be taken from the Tables
V. and IV., thus :
a. h. ch.
200Cycles 1387937 22 200
90 624572 1 630
5 34698 10 815
First 5 years of next Cycle 1801 8 583
The sum 2049009 19 338
This, then, is the actual interval of time elapsed, according to Jewish
Astronomical computation, since the commencement of the Era up to
the occurrence of the New Moon of Tishri, A.M. 5611.
If we add 5h. 204ch. to this interval of time the sum will denote the
time elapsed from 6 p.m. on Monday, October 7, B.C. 3761, up to the
occurrence of the New Moon of Tishri, A.M. 5611. This sum is
2049010d. Oh. 542ch. The New Moon therefore occurred upon the
2049011th day, at 542ch. after the commencement of that day.
4. This number of days, when divided by 7, is found to contain
6 days more than an exact number of weeks. The days commenced
with a Monday, feria 2, and the complete weeks terminated, therefore,
with a Sunday, feria 1. The last of the 6 remaining days would be a
Saturday, feria 7, and the Molad for Tishri A.M. 5611 is expressed by
7 542, or, Saturday at Oh. 242ch. past six o'clock in the evening.
As the same Molad is found for Tishri 1, A.M. 5611, by the ordinary
method (Article 42), it may be concluded that the work up to this point
is correct, thus :
Molad BeHaKD 2 5 204
Excess of 200 Cycles 522 200
90 4 1 630
5 6 10 815
,, for sixth year 2 8 153
7 542
The feria in this Molad being 7, and the hours and Chalakimnot
amounting to 18h., no postponement is required by any of the rules of
the Calendar. Tishri 1 is celebrated upon the day indicated, namely,
the Saturday which has been found to be the 2049011th day of the
Era ; Monday, October 7, B.C. 3761 being the first of these days.
n8 THE fEU'ISH CALENDAR
5. The corresponding day in the Christian Calendar must now be
found. This will be done, as usual, by Julian computation, in order
to avoid any difficulty which might be caused through the nominal
days dropped in the Gregorian Calendar.
Dividing 2049011 by 1461, the quotient gives 1402 quadriennial
periods, and 689 days which = 1 year + 324 days.
The interval of time is therefore 4 x 1461 + 1, or 5609 Julian years
+ 324 days.
From October 7 to December 31, both inclusive, B.C. 3761 is a
period of 86 days ; therefore 3760 Julian years and 86 days elapsed
before the Christian Era commenced ; there remain 1849 complete
years and 238 days of the next year, A.D. 1850.
The Julian date corresponding to Tishri 1, A.M. 5611 is, therefore,
the 238th day, or August 26, in A.D. 1850. The corresponding
Gregorian date is August (26 + 12), or September 7.
This demonstration has been given in considerable detail in the hope
that it may be thoroughly understood. In actual practice the work
would be much abbreviated, thus :
(1) A.M. 5611 = A.D. (5611-3761) = 1850.
(2) Jewish years elapsed = 5610 = 295 Cycles + 5 years.
= 2049009d. 19h. 338ch.
Add ........................ 5h. 304ch. in order to
obtain the time elapsed, by Astronomical computation, from 6 p.m.
Monday, October 7, B.C. 3761. The sum is
2049010d. + Oh. + 542ch.
The New Moon occurred, therefore, very shortly after the commence-
ment of the 2049011th day of the Era.
(3) For the corresponding Julian date, which is in the Autumn of
A.D. 1850.
From October 7 to Dec. 31, B.C. 3761, both inclusive = 86 d.
From January 1, B.C. 3760, to December 31, A.D. 1849) _
there are 5609 Julian years ........................... J~
2048773
Subtracting this number of days from the total number required,
namely 2049011, the remainder is 238. The day required is therefore
the 238th of the Julian year 1850 ; or August 26, A.D. 1850, Julian =
September 7, Gregorian.
THE JEWISH CALENDAR 119
As another example, with the calculation made from a different
basis, let the date be required at which Tishri 1 occurred in A.D. 1897,
to be computed from the Molad 2d. 4h. 204ch. as adopted by Hillel
for Tishri 1, A.M. 4105, corresponding to the Julian date, Monday,
September 24, A.D. 344.
(1) A.D. 1897 = A.M. (1897 + 3761) = 5658.
(2) The number of Astronomical years elapsed be'tween the New
Moons of Tishrl, A.M. 4105 and A.M. 5658, is 1553, or 81 Cycles + 14
years.
These 14 years are the first fourteen in a Cycle because the division
of 4105 by 19 shows that 4105 was the first year in a Cycle. Five of
the fourteen years are therefore Embolismic, and nine are Common.
The interval of time between the computed New Moons is, therefore,
the sum of
d. h. ch.
80 Cycles 555175 4 80*
1 Cycle 6939 16 595
9 Common years 3189 7 324 t
5 Embolismic years 1919 11 785
567223 15 704
that is, the New Moon of Tishri, A.M. 5658, occurred on the 567224th
day, at 15h. 204ch. after that day had commenced.
This number of days is an exact number of weeks, and because the
first of these days was a Monday, the last of them was a Sunday ; but if
the computed New Moon occur upon a Sunday Tishri 1 is postponed
to Monday, which will be the 567225th day. This feria is confirmed
by the Molad of A.M. 5658, which may be found in the usual way.
Dividing 5658 by 19 the quotient is 297, and the remainder is 15.
It is therefore the fifteenth year of the 298th Cycle.
BeHaKD 2 5 204
Add for 200 Cycles 5 22 200
90 4 1 630
7 4 19 925
,, fifteenth year 5 19 29
7 19 908
* Table V. t Table III.
120 THE JEWISH CALENDAR
As the hours exceed 18, Tishrl 1 is postponed to Sunday, and thence
to Monday.
(3) The time elapsed from Monday, September 24, A.D. 344,
inclusive, to the end of that year is 99 days, and from the commence-
ment of 345 to the end of 1896 there are 1552 Julian years, or 566868
days. The total number of days up to the end of 1896 is, therefore,
566967.
Subtracting this total from 567225, the remainder is 258. The
required date for Tishrl 1 is, therefore, the 258th day of A.D. 1897,
Monday, September 15, Julian; the corresponding Gregorian date is
Monday, September 27. The week-day is found to be correct, if a
further test be required by the Sunday Letter for 1897, Julian E,
Gregorian C.
To FIND THE CHRISTIAN DATE CORRESPONDING TO NISAN 15 OF
ANY GIVEN JEWISH YEAR.
62. It will be remembered that Nisan 15 in any Jewish year, H,
invariably precedes Tishri 1 of the year H + 1 by 163 days.
Consequently, to find the date of Nisan 15 in the year H nothing
more is required than to subtract 163 from the Christian date of
Tishri 1 in the year H + 1, this date being expressed by its serial
number as a day of the year.
The idea may occur to some that it would be just as easy to add to
the date of Tishri 1 the number of days that elapse before Nisan 15 in
the same Jewish year is reached. This indeed may be done ; but
it must be kept in mind that the number of days from Nisan 15 to
Tishri 1 is constant, while the number from Tishri 1 to Nisan 15 is
variable. Thus :
Tishri 1 to Nisan 15 in a year of 353 days 190 days.
354 191
355
383
384
385
192
220
221
222
The former method is therefore to be preferred as less liable to error.
Much less labour is involved, especially when the work is consecutive.
A Table of consecutive days, for which it is only necessary to
calculate (by subtraction of 163) the first line, may very easily be
THE JEWISH CALENDAR
formed ; by its means the date of Nisan 15 may be written down at
once when the date of Tishri 1 is known.
It must always be remembered that the months of Nisan and
Tishri which occur in any one given Christian year belong, the former
to the Jewish year H 1, the latter to the Jewish year H.
Calculation for the first line of the Table.
August 20 = January 232 in a Christian Common year,
Subtract 163
January 69 = March 10.
August 20 = January 233 in a Leap-year.
163
January 70 = March 10.
In fact, no difference in the date assigned to Nisan 15 can, in any case,
arise from Leap-years, because the intercalated day occurs before the
interval between March and September.
The Table is to be read thus : If, in any given Christian year the
Tishri 1 which belongs to the Jewish year H occur upon August 20,
then, in the same Christian year the Nisan 15 which belongs to the
preceding Jewish year H 1 will have occurred upon March 10.
TABLE FOE COEEESPONDENCE OF DATES BETWEEN TISHEI 1
AND NISAN 15.
Tishri 1 of
year H.
Nisan 15 of
H-l.
Tishri 1 of year
H.
Nisan 15 of
H-l.
Tishri 1 of year
H.
Nisan 15 oi
H-l.
August 20
March 10
September 6
March 27
September 23
April 13
21
11
7
28
24
14
22
12
8
29
25
15
23
13
9
30
26
16
24
14
10
31
27
17
25
15
11
Ap
il 1
28
C
18
26
16
12
2
29
;
-,
19
27
17
13
3
30
20
28
18
14
4 Oct
ber 1
21
29
19
15
5
2
22
30
20
16
6
o
23
31
21
17
7
4
24
Septei
nber 1
22
18
8
5
25
2
23
19
9
6
M
3
24
20
10
7
27
4
25
21
11
8
28
5
26
22
12
it
n
122 THE JEWISH CALENDAR
From these figures it appears that if D be the day of September in
any Christian year which corresponds to Tishri 1, then D + 21 is the
day of March which corresponds to the Nisan 15 which occurs in the
same Christian year. Thus :
Let Tishri 1 = October 3 = September 33 = D
Then Nisan 1 = March (D - 21) = March 54 = April 23.
On the other hand, if d be the day of March which corresponds to
Nisan 15, then d 21 is the day of September which corresponds to
Tishri 1. Thus :
Let Nisan 15 = April 4 = March 35 = d
Then Tishri 1 = September (d-21) = September (35-21) = 14.
As a check upon the feria, or week-day found for Nisan 15, it may
be noticed that, because 163 is of the form In + 2, the feria of Nisan
15 in any given Christian year is always less by 2 than the feria of the
Tishri 1 which occurs in the same Christian year. In other words the
feria of Nisan 15 in the Jewish year H is less by 2 than the feria of
Tishri 1 in the year H + 1. Thus :
If Tishri 1 be on Monday, feria 2, (or 9), Nisan 15 is on Saturday, feria 7.
,, Tuesday, ,, 3, ,, Sunday, ,, 1.
Thursday, 5, Tuesday, ,, 3.
Saturday, ,, 7, ,, Thursday, ,, 5.
63. The computation for a^series of years may now be made. This
will be done, by way of example, for three Cycles, the 296th, 297th,
and 298th, commencing with A.M. 5606 (see pp. 123-125).
The first object is to find the Molads for the successive years, by
means of which the feria for Tishri 1 is determined. This will be
effected by, first, finding the Molad for A.M. 5606, and then, as usual,
by the successive additions of 4d. 8h. 876ch. as the excess for Common
years, and of 5d. 21h. 589ch. as the excess for Embolismic years.
As the work now proposed is consecutive it will not be necessary
to employ the shortened method of finding the Molads, which was
described in Article 41. If, however, there be any doubt as to the
correctness of the results obtained they may be tested from time to
CYCLE 296.
Years of
Cycle.
A.M.
Molad.
Week-day.
Tishri l.
Cause of Postponement,
if any take place.
1
5606
4 15 701)
4 8 876
Wednesday
Thursday
ADI .
2
5607
2 565
4 8 876
Monday
Monday
3 Emb.
5608
6 9 361
5 21 589
Friday
Saturday
ADU.
4
5609
5 6 950
4 8 876
Thursday
Thursday
5
5610
2 15 746
4 8 876
Monday
Monday
6 Emb.
5611
7 542
5 21 589
Saturday
Saturday
7
5612
5 22 51
4 8 876
Thursday
Saturday
YacH and ADU.
8 Emb.
5613
3 6 927
5 21 589
Tuesday
Tuesday
9
5614
2 4 436
4 8 876
Monday
Monday
10
5615
6 13 232
4 8 876
Friday
Saturday
ADU.
11 Emb.
5616
3 22 28
5 21 589
Tuesday
Thursday
YacH and ADU.
12
5617
2 19 617
4 8 876
Monday
Tuesday
YacH.
13
5618
7 4 413
4 8 876
Saturday
Saturday
14 Emb.
5619
4 13 209
5 21 589
Wednesday
Thursday
ADU.
15
5620
3 10 798
4 8 876
Tuesday
Thursday
GaTBaD and ADU.
16
5621
7 19 594
4 8 876
Saturday
Monday
YacH and ADU.
17 Emb.
5622
5 4 390
5 21 589
Thursday
Thursday
18
5623
4 1 979
4 3 876
Wednesday
Thursday
ADU.
19 Emb.
5624
1 10 775
Sunday
Monday
ADU.
4 15 769
3 19 6
Molad of 5624
1 10 775
CYCLE 297.
Cause of Postponement
if any take place.
Years of . ,,
Cycle.
Molad.
\Veek-day. Tishri 1.
Ill
1
2
3 Emb.
4
5
<} Emb.
7
8 Emb.
<>
10
11 Emb.
12
13
14 Emb.
15
16
17 Emb.
18
I'.i Emb.
5624
5625
5626
5627
5628
5629
5630
5631
5632
5633
5634
5635
5636
5637
5638
5639
5640
5641
5642
5643
1 10 775
5 21 589
Saturday
Wednesday
Monday
Saturday
Thursday
Monday
Sunday
Thursday
Wednesday
Monday
Friday
Thursday
Monday
Saturday
Friday
Tuesday
Saturday
Friday
Wednesday
Saturday
Thursday
Monday
Monday
Thursday
Monday
Monday
Saturday
Thursday
Monday
Saturday
Thursday
Tuesday
Saturday
Saturday
Thursday
Monday
Saturday
Thursday
ADU.
YacH and ADU.
ADU.
YacH and ADU.
ADU.
ADU.
YacH.
ADU.
GaTRaD and ADU.
YacH and ADU.
ADU.
ADU.
7 8 284
4 8 876
4 17 80
4 8 876
2 1 956
5 21 589
7 _>;) 4<;r>
4 8 876
5 8 261
4 8 876
2 17 57
5 21 589
1 14 646
4 8 876
5 23 442
5 21 589
4 20 1031
4 8 876
2 5 827
4 8 876
6 14 623
5 21 589
5 12 132
4 8 876
2 20 1008
4 8 876
7 5 804
5 21 589
6 3 313
4 8 876
3 12 109
4 8 876
7 20 985
5 21 589
6 18 494
4 8 876
4 3 290
Test for the last Molad f M ], ft ? o ( 5 t
( Add for 1 (
Molad
024
1 10 775
2 16 595
3ycle
of 5643
4 3 290
Years of
Cycle.
HI
3 Emb.
6 Emb.
7
s Kmb.
1
10
11 Emb.
14 Emb.
IS
10
17 Emb.
is
19 Emb.
A.M.
Molad.
Week-day.
Tishri 1.
Cause of Postponement
if any take place.
5643
4 3 290
5 21 589
5644
3 879
4 8 876
Tuesday
Tuesday
5645
5646
7 9 675
4 8 876
4 18 471
5 21 589
Saturday
Wednesday
Saturday
Thursday
ADU.
5647
3 15 1060
4 8 876
Tuesday
Thursday
GaTRaD and ADU.
5648
1 856
4 8 876
Sunday
Monday
ADU.
5649
5 9 652
5 21 589
Thursday
Thursday
5650
4 7 161
4 8 876
Wednesday
Thursday
ADU.
5651
1 15 1037
5 21 589
Monday
Monday
5652
7 13 546
4 8 876
Saturday
Saturday
5653
4 22 342
4 8 876
Wednesday
Thursday
ADU.
5654
2 7 138
5 21 589
Monday
Monday
5655
1 4 727
4 8 876
Sunday
Monday
ADU.
5656
5 13 523
4 8 876
Thursday
Thursday
5657
2 22 319
5 21 589
Monday
Tuesday
YacH.
5658
1 19 908
4 8 876
Sunday
Monday
ADU.
5659
6 4 704
4 8 876
Friday
Saturday
ADU.
5660
3 13 500
5 21 589
Tuesday
Tuesday
5661
2 11 9
4 8 876
Monday
Monday
5662
6 19 885
5 21 589
Friday
Saturday
ADU.
Cycle
5 17 394
Thursday
Thursday
I. '^ Mo,ad of 5626
4 3 290
2 IB 595
Molad of 5662 . . G 19 885
i 2 6 THE JEWISH CALENDAR
time by means of Table VIII. of " Additions to be Made." It will
certainly be wise to test the Molad of every last year of a Cycle, for if
a mistake be made anywhere in this consecutive work it will of
necessity run on unless it be corrected.
To find the Molad for Tishri, A.M. 5606.
The division of 5606 by 19 gives a quotient 295, and a remainder 1.
The year is therefore the first in the 296th Cycle, and 295 complete
Cycles had elapsed before its commencement.
d. h. ch.
Molad BeHaKD 2 5 204
Excess for 200 Cycles 5 22 200
90 4 1 630
5 6 10 815
Molad for Tishri, A.M. 5606 = 4 15 769
This affords a point of departure, and the computation for the feriae
of Tishri 1 can now be made for the whole Cycle.
64. The corresponding Christian dates for Tishri 1 must now be
found. Reference should be made to the method of finding the length
of the Jewish year described in Article 53. The question whether
the Christian year in which Tishri 1 occurs be Bissextile or not must
be taken into account.
The year with which the computation commences is A.M. 5606.
It is necessary to find, by the process illustrated in Article 61, the
Christian date of Tishri 1 for this year.
1. A.M. 5606 = A.D. (5606-3761) = 1845.
2. Years elapsed = 5605 = 295 Cycles.
d. h. ch.
200 Cycles = 1387937 22 200
90 = 624572 1 630
5 = 34698 10 815
295 Cycles = 2047208 10 565
THE JEWISH CALENDAR 127
This is the actual time elapsed from the commencement of the Era
to the computed New Moon of Tishri, 5606.
The day of New Moon by computation is therefore the 2047209th
day of the Era = (In + 3)rd day ; it must be a Wednesday, because
the first day of the Era "was a Monday, so that the completed weeks
end with a Sunday. The celebration of this Moon, on Tishri 1, is
postponed by ADU to Thursday, day 2047210 of the Era.
3. The Christian date required is in the Autumn of A.D. 1845.
From October 7, B.C. 3761, to the end of that year = 86 days, and
from the commencement of B.C. 3760 to the close of A.D. 1844 there
are 5604 Julian years, or 2046861 days ; the sum of the two intervals
is 2046947 days. The difference between this number and 2047210
is 263. The day required is, therefore, the 263rd of A.D. 1845
= Thursday, September 20, Julian = October 2, Gregorian. The
Julian Sunday Letter is G ; the Gregorian is E.
Having thus obtained a basis from which the computation can
commence, the work may proceed. Gregorian dates will be now
employed, the years being subsequent to A.D. 1582. The Sunday
Letter of the Christian year is added, in order that the day of the week,
as given, may be verified if it be thought necessary.
A.M. 5606. The first day is Thursday ; the last must be Sunday,
for the next year has been found (Table, above) to commence with a
Monday. The form of the year is, therefore, In + 4, so that it has
354 days, being a Common year, for it is the first in a Cycle.
The Gregorian date for Tishri 1 in this year has been found to be
October 2, 1845.
The date for Nisan 15 will be found when that for Tishri 1 in the
next year has been determined.
A.M. 5607. First day Monday. This day must be October
(2 + 354), A.D. 1845, because the last year, A.M. 5606, was found to
contain 354 days.
October (2 + 354) = October 356 = September 386 *
Subtract for the year 1846 t 365
Tishri 1, 5607 = September 21, 1846. Monday. D.
* The 356th of October is the 386th of September ; the latter is used because 365 cannot
be subtracted from 356.
t This subtraction is really for the number of days from September 1, 1845, to September
1, 1846, including the month of February, 1846, which has no day intercalated.
J2 8 THE JEWISH CALENDAR
For the length of the year : It begins with a Monday, and ends
with a Friday because Tishri 1, in the next year, has been found to be
a Saturday. It, therefore has 5 days more than an exact number of
weeks, and being a Common year its form is 350 + 5. It has 355
days.
Nisan 15 of 5606 occurs 163 days earlier than Tishri 1 of 5607, and
may now be found.
September 21, 1846 = January 264
Subtract 163
January 101 = April 11, Saturday.
This date might be taken direct from the Table in Article 62, and,
because by the use of that Table, the dates for Nisan 15 can be written
down at once when the results of the computation are collected, it will
not be necessary to continue calculating them.
5608 Emb, First day, Saturday. This day must be September
21, 1846 + 355 days, for the last year was found to contain 355 days.
September 21 + 355 = September 376
Subtract for 1847 365
Tishri 1, 5608 = September 11, 1847. Saturday. C.
Length of the year : It commences with a Saturday, and ends with a
Wednesday, for the next year has been found to begin with a
Thursday. It is Embolismic, and is of the form In + 5. It has 383
days.
The method of computing ought now to be understood, and the
work may be continued in an abbreviated manner. It should be
remarked that the Last day, and the Length of each year is not to be
written until the first day of the following year has been noted.
THE JE WISH CALENDAR
129
Years
of
Cycle.
A.M.
First Day.
Sun-
day
Letter.
Last Day.
Length.
4
5609
Thursday, Sep. 11 + 383 = Sep. 394
Days in 1848... 366
A
Sunday
350+4=354
September 28,1848
5
5610
Monday, Sep. 28 + 354 = Sep. 382
365
G
Friday
350+5 = 355
September 17, 1849
G
5611 Emb.
Saturday, Sep. 17 + 355 = Sep. 372
365
F
Friday
378+7 = 385
September 7, 1850
1
5612
Saturday, Sep. 7 + 385 = Sep. 392
365
E
Monday
350+3 = 353
September 27,1851
S
5613 Emb.
Tuesday, Sep. 27 + 353 = Sep. 380
Days in 1852... 366
C
Sunday
378+6 = 384
September 14,1852
r9
5614
Monday, Sep. 14 + 384 = Sep. 398
365
B
Friday
350+5 = 355
Sep. 33
= October 3,1853
10
5615
Saturday, Sep. 33 + 355 = Sep. 388
365
A
Wednesday
350+5 = 355
September 23, 1854
11
5616 Emb.
Thursday, Sep. 23 + 355 = Sep. 378
365
September 13,1855
G
Monday
378+5 = 383
12
5617
Tuesday, Sep. 13 + 383 = Sep. 396
Days in 1856... 366
September 30, 1*56
E
Friday
350 + 4 = 354
10
130
THE JE \VISH CALENDAR
Years
of
Cycle
A.M.
First Day.
Sun-
day
Letter.
Last Day.
Length.
13
5618
Saturday, Sep. 30 + 354 = Sep. 384
365
D
Wednesday
350+5 = 355
September 19, 1857
14
5619 Emb.
Thursday, Sep. 19 + 355 = Sep. 374
365
C
Wednesday
378+7 = 385
September 9, 1858
15
5(520
Thursday, Sep. 9 + 3&5 = Sep. 394
365
B
Sunday
350+4 = 354
September 29, 1859
16
5621
Monday, Sep. 29 + 354 = Sep. 383
Days in 1860... 366
-
G
Wednesday
350+3 = 353
September 17, 1860
17
5622 Emb.
Thursday, Sep. 17 + 353= Sep. 370
365
September 5, 1861
F
Wednesday
378+7 = 385
18
5623
Thursday, Sep. 5 + 3a5 = Sep. 390
365
September 25,1862
E
Sunday
350+4 = 354
19
5624 Emb.
Monday, Sep. 25 + 354 = Sep. 379
365
September 14,1863
D
Friday
378+5 = 383
CYCLE 297.
1
5625
Saturday, Sep. 14 + 383 = Sep. 397
Days in 1864... 366
Sep. 31
= October 1,1864
B
Wednesday
350+5 = 355
2
5626
Thursday, Sep. 31 + 355 = Sep. 386
365
September 21,1865
A
Sunday 350 + 4 = 354
THE JE ll'ISH CALENDAR
Years
of
Cycle.
A.M.
First Day.
Sun-
day
Letter.
Last Day.
Length.
3
5627 Emb.
Monday, Sep. 21+354 = Sep. 375
365
September 10,1866
G
Sunday
378+7 = 385
4
5628
Monday, Sep. 10+385 = Sep. 395
365
September 30,1867
F
Wednesday
350+3 = 353
5
5629
Thursday, Sep. 30+353 = Sep. 383
Days in 1868... 366
September 17,1868
D
Sunday
350+4 = 354
6
5630 Emb.
Monday, Sep. 17+354 = Sep. 371
365
September 6, 1869
C
Sunday
378+7 = 385
7
5631
Monday, Sep. 6+385 = Sep. 391
365
September 26, 1870
B
Friday
350+5 = 355
8
5632 Emb.
Saturday, Sep. 26+355 = Sep. 381
365
A
Wednesday
378+5=383
September 16, 1871
9
5633
Thursday, Sep. 16+383 = Sep. 399
Days in 1872... 366
F
Sunday
350+4 = 354
Sep. 33
= October 3, 1872
10
5634
Monday, Sep. 33+354 = Sep. 387
365
September 22,1873
E
Friday
350+5 = 355
11
5635 Emb.
Saturday, Sep. 22+355 = Sep. 377
365
September 12,1874
D
Wednesday
378+5 = 383
132
THE JE WISH CALENDAR
Years
of
Cycle.
A.M.
First Day.
Sun-
day
Letter.
Last Day.
Length.
12
5636
Thursday, Sep. 12 + 383 = Sep. 395
365
C
Monday
350 + 5 = 355
September 30,1875
13
5637
Tuesday, Sep. 30 + 355 = Sep. 385
Days in 1876... 366
A
Friday
350 + 4 = 354
September 19, 1876
14
5638 Emb.
Saturday, Sep. 19+354 = Sep. 373
365
G
Friday
378+7 = 385
September 8, 1877
15
5639
Saturday, Sep. 8 +385 = Sep. 393
365
September 28, 1878
F
Wednesday
350+5 = 355
16
5640
Thursday, Sep. 28 +355 = Sep. 383
365
E
Sunday
350+4 = 354
September 18, 1879
17
5641 Emb.
Monday, Sep. 18 + 354 = Sep. 372
Days in 1880... 366
September 6, 1880
C
Friday
378+5 = 383
18
5642
Saturday, Sep. 6 +333 = Sep. 389
365
B
Wednesday
350+5 = 355
September 24, 1881
19
5643 Emb.
Thursday, Sep. 24 + 355 = Sep. 379
365
A
Monday
378+5 = 383
September 14,1882
THE JE WISH CALENDAR
CYCLE 298.
133
Years
of
Cycle.
A.M.
First Day.
Sun-
day
Letter.
Last Day.
Length.
1
5644
Tuesday, Sep. 14+383 = Sep. 397
365
G
Friday
350+4 = 354
Sep. 32
= October 2,1883
2
5645
Saturday, Sep. 32+354 = Sep. 386
Days in 1884... 366
E
Wednesday
350+5 = 355
September 20, 1884
3
5646 Emb.
Thursday, Sep. 20+355 = Sep. 375
365
September 10, 1885
D
Wednesday
378+7 = 385
4
5647
Thursday, Sep. 10+385 = Sep. 395
365
C
Sunday
350+4 = 354
September 30, 1886
5
5648
Monday, Sep. 30+354 = Sep. 384
365
September 19, 1887
B
Wednesday
350+3 = 353
6
5649 Emb.
Thursday, bep. 19 +353 = Sep. 372
Days in 1888... 366
September 6, 1888
G
Wednesday
378+7 = 385
7
5650
Thursday, Hep. 6+385 = Sep. 391
365
F
Sunday
350+4 = 354
September 26,1889
8
5651 Emb.
Monday, Sep. 26+354 = Sep. 380
365
September 15, 1890
E
Friday
378+5 = 383
'34
Yean
of
Cycle
A.M.
First Day.
Sun-
day
Letter
Last Day.
Length.
9
5652
Saturday, Sep. 15+385 = Sep. 398
365
Sep. 33
= October 3,1891
D
Wednesday
350+5 = 355
10
5653
Thursday, Sep. 33+355 = Sep. 388
Days in 1892... 366
September 22,1892
B
Sunday
350+4 = 354
11
5654 Emb.
Monday, Sep. 22+354 = Sep. 376
365
A
Sunday
378+7 = 385
September 11, 1893
12
5655
Mondav, Sep. 11 +385 = Sep. 396
365
G
Wednesday
350+3 = 353
Sep. 31
= October 1,1894
13
5656
Thursday, Sep. 31 +353 = Sep. 384
365
F
Monday
350+5 = 355
September 19, 1895
14
5657 Emb.
Tuesday, Sep. 19+355 = Sep. 374
Days in 1896... 366
D
Sunday
378+6 = 384
September 8, 1896
15
5658
Monday, Sep. 8 +384 = Sep. 392
365
September 27,1897
C
Friday
350+5 = 355
16
5659
Saturday, Sep. 27+355 = Sep. 382
365
B
Monday
350+3 = 353
September 17, 1898
THE JE WISH CALENDAR
'35
Years
of i A.M.
Cycle.
18
19
First Day.
17 5660 Emb. , Tuesday, Sep. 17+353 = Sep. 370
5661
5662 Emb.
1 i 5663
Monday, Sep. 5+384 = Sep. 389
Days in 1900, Greg.... 365
Saturday, Sep. 24+355 = Sep. 379
Thursday
Sun-
day
Letter.
Last Day.
Length.
;p. 370
365
er 5, 1899
A
Sunday
378+6 = 384
jp. 389
... 365
G
Friday
350+5 = 355
>er 24,1900
:p. 379
365
F
Wednesday
378+5 = 383
>er 14,1901
Collecting the results thus found, we obtain the following
Calendar, with respect to Tishrl 1 and Nisan 15, for the three
Cycles 296, 297, 298, A.M. 5606 to 5662; A.D. 1845 to 1901.
Julian and Gregorian dates are now both inserted.
136
JEWISH CALENDAR
^co
'S
ft
53
Pn
w
02
Length
of Year.
CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO
00000000000600060600060606000000000000
1845-1864.
2
5
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5
w
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'g^ t^^t^^ g^^^'S^^I 1 !^
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rH rH(?q 1 1 C* i-l i 1 l-t fH i-(
CO t- X OS -| <N CO - - - t- / - = - r, r-: -
S
s si 1 1 Is
THE JE WISH CALENDAR
'37
ength
f Year.
cococo
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_
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56
I 1 " 1 !
s i a
a 4 a ?
l i
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SHE
11 1 1
-*
1 1
2 : 2
iHi-H(M
138
THE JE WISH CALENDAR
s -~
sg
g*
K re
re
O X O 00 C C
co co co co cc co
x io s x
CO CO CO CO
c 5 ' -s s a
CO CO CO CO CO
Jo
x x oc
X
X 1 X X X X GO
i 1 1 1
1 1 1 1 i
rH
cT
2 ^
of
t-- ^
I s
1
'*" 'R '^
. < en" *< <!
^J w
T i i - *
' .. "S
1 b? _L *
?: a '
h^
cc
^; d
S
Q "?
^^
< i
B
CO co
w
a
1 1 1 i 1 1 1 1 1 1
*
O o: X w o c:
i I i 1 C<I
WI C ? C O LO 1C
H
1C ts
>o >c
"a
a
W? UJ U5 US 5 IQ >O >C W 5
THE JEWISH CALENDAR 139
CHECKS UPON KESULTS.
65. In addition to the tests suggested in Article 62 for the feria of
Nlsan 15, and for the Molads in Article 63, a useful check upon the form
or length of the successive years is obtained in the following manner:
Let the seven feriae be treated as in repeated order, thus :
1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, &c.
Take the feria of any year H, and count from it, exclusive, in the
positive direction, that is to say, from left to right, to the place of the
feria, inclusive, of the next year, H + 1. Call the number of places
so counted " the difference " of the year H.
For example : Let H commence with a Thursday, feria 5, and H + 1
with a Monday, feria 2. The number of places counted in the positive
direction from 5 exclusive, to 2, inclusive, is four. Again, if H com-
mence with a Saturday, feria 7, and H + 1 with a Tuesday, feria 3,
the difference in the number of places from 7 to 3 is three.
Then, for a Common year, H :
If difference be 3, H is Deficient 353 days.
,, 4, ,, Eegular 354 ,,
5, ,, Abundant 355 ,,
For an Embolismic year, H :
If difference be 5, H is Deficient 383 days.
,, 6, ,, Kegular 384 ,,
,, 7, ,, Abundant 385 ,,
Thus, for Cycle 297,
AM. 5625 begins with feria 7, next year with 5, d = 5 ... 355
5626 5, 2, 4 ... 354
5627 Emb. 2, 2, 7 ... 385
5628 2, 5, 3 ... 353
5629 5, 2, 4 ... 354
5630 Emb. 2, 2, 7 ... 385
5631 2, 7, 5 ... 355
5632 Emb. 7, 5, 5 ... 383
5633 5, 2, 4 ... 354
5634 2, 7, 5 ... 355
5635 Emb. 7, 5, 5 ... 383
5636 5, 3, 5 ... 355
140 THE JE WISH CALENDAR
5637 begins with feria 3, next year with 7, d = 4 ... 354
5638 Emb. 7, 7, 7 ... 385
5639 7, 5, 5 ... 355
5640 5, '2, 4 ... 354
5641 Emb. 2, 7, 5 ... 383
5642 7, 5, 5 ... 355
5643 Emb. 5, 3, 5 ... 383
66. A check upon the Christian dates found, in successive years,
for Tishri 1 is obtained from a consideration of the respective lengths
of the Jewish and Christian years. There are only two forms of the
latter, 365 and 366 days, while there are six different forms of the
Jewish year 353, 354, 355, 383, 384, and 385 days. Hence, there are
twelve possible combinations that can be made between a Jewish and
a Christian year ; for the months which are covered by the Jewish
year, commencing and terminating always in the Autumn, invariably
include the whole of the month of February, and this February may,
or may not, have an intercalated day.
Let the Jewish year H have 353 days, and let Tishri 1 of the year H
occur on a day whose serial, number is D in the Christian Y. Then
1. If Y + 1 be a common Christian year of 365 days, February
29 will not occur in the course of the 353 days of H, and H + 1 must
commence in Y + 1 earlier than H commences in Y, that is, earlier
than D,'by 365-353, or 12 days.
2. But if Y + 1 be a Bissextile year, February 29 will be included
in the course of the 353 days of H, and H + 1 must commence in the
year Y + 1 earlier than D by 366353, or 13 days.
3, 4. If the year H have 354 days, H + 1 will commence in
Y + 1 earlier than H commences in Y by 365 354, or 11 days, if
Y + 1 be a Common year, but 366354, or 12 days, if Y + 1 be
Bissextile.
5, 6. If the year H have 355 days, H + 1 will commence in
Y + 1 earlier than H commences in Y by 365 355, or by 366 355,
that is, by 10, or by 11 days according to whether Y + 1 be a Common
or a Bissextile year.
7, 8. On the other hand, if the Jewish year H be Embolismic,
and have 383 days, then Tishri 1 of H + 1 will occur later than
Tishri 1 of H by either 383-365, or 383-366 days, that is, by 18
or by 17 days, according to whether Y r + 1 be a Common or a Bissextile
year.
THE JEWISH CALENDAR 141
9, 10, 11, 12. So too with respect to the Jewish years of 384
and 385 days. In the one case Tishrl 1 of H + 1 will be either 19 or
18 days later than Tishri 1 of H ; in the other case it will be either
20 or 19 days later.
These twelve possible combinations may be reduced to a very
simple rule.
Let 7w + x be the value in days of a Jewish Common year, H, so
that x may be either 3, 4, or 5. Also, let 7N + x be the value in days
of a Jewish Embolismic year, so that x may be either 5, 6, or zero.
Then
For Common years,
(a) If H commence in the Christian year Y, and Y + 1 has 365
days, H + 1 will commence in Y + 1 earlier than H commenced in Y
by 365 (In + x) days.
(6) If Y + 1 has 366 days, H + 1 commences in it earlier than H
commenced in Y by 366 (In + x} days.
For Embolismic years,
(c) If Y + 1 has 365 days, then H + 1 commences in it later than
H commenced in Y by (7N + x) 365 days.
(d) If Y + 1 has 366 days, then H + 1 commences in it later than
H commenced in Y by (7N + #) 366 days.
67. It appears from the Tables given in Articles 54, 55, pp. 79, 83,
that there are fourteen possible combinations of the forms of the year
with the week-days upon which those years can commence. A Table
can be formed which will show the week-day for every day in every
month of these fourteen combinations.
The first two columns in Part I. of this Table XI. are a repetition
of the first two in the Tables above. The remaining columns, headed
with the names of the months, show which column of week-days in
Part II. is to be employed.
Although thirty days are given in each of these seven columns,
only twenty-nine, of course, are required for those months which have
only that number of days. It must also be remembered that in
Deficient years, whether Common or Embolismic, Kislew has only
twenty-nine days instead of the thirty which it contains in Kegular
and Abundant years ; while in Abundant years, both Common and
Embolismic, Marheshwan has thirty days instead of the twenty-nine
which it has in Deficient and Kegular years.
142 THE JEWISH CALENDAR
The following example, of which the full work is given, will illus-
trate the way in which the Table is to be used.
Find the week-day for Kislew 13 in the Jewish year 5611.
a. The division of 5611 by 19 gives a quotient 295, and a
remainder 6. It is therefore an Embolismic year.
b. The Molad of 5611 is the sum of
d. h. ch.
BeHaKD 2 5 204
Excess of 200 Cycles 5 22 200
90 4 1 630
5 , 6 10 815
For a sixth year 2 8 853
7 542
There is no reason for postponing Tishri 1 from feria 7 ; the first
day of the given year is, therefore, Saturday.
c. An Embolismic year which commences with a Saturday may
be one of either 383 or 385 days. To ascertain which of these forms
appertains to A.M. 5611 it will be necessary to find the day of the
week with which the next year commenced.
Moladfor5611 7 542
Excess of an Emb. year 5 21 589
Molad for 5612 5 22 51
Tishri 1 is postponed by YacH and ADU from feria 5 to feria 7,
Saturday. The previous year, 5611, therefore, ended with a Friday,
and as it commenced with a Saturday, it is of the form In + 0, or has
385 days.
All the required facts are now established, and we may proceed to
use the Table.
Eefer to Line 14 of Part I., which is for an Embolismic year of
385 days commencing with a Saturday. Under the heading Kislew
the figure 4 appears in this line. Therefore, Column 4 in Part II. is
to be employed. It shows that Kislew 13 is a Monday.
THE JEWISH CALENDAR 143.
If the question had been proposed with the required facts given
the day would have been found thus :
Tishri 1, 5611 is a Saturday = feria 7
Add for Tishri 2 to Tishri 30 29
,, ,, Marheshwan 30
Kisle\v 1 to Kislew 13 13
79
and because 79 = In + 2, the week-day required is Monday.
68. If the feria, or week-day, be required for any date in a Jewish
month occurring in some given Christian year, care must be taken to
ascertain precisely the year to which the Jewish month belongs (see
Article 37, p. 46) ; if this be not done there is liability to error.
Example.
Upon which day of the week does Nlsan 15 occur in A.D. 1900?
By the addition of 3761 to 1900, we find that the Jewish year
corresponding in part to A.D. 1900 is 5661 ; that is, the year 5661
commences at some time in the Autumn of A.D. 1900.
It is very clear that the Nisan 15 which occurred during the course
of A.D. 1900 must have belonged to the Jewish year 5660.
The division of 5660 by 19 gives a quotient 297, and a remainder
17. The year is therefore the seventeenth in a Cycle, and is Embolis-
mic. Its Molad is the sum of :
d. h. ch.
BeHaKD 2 5 204
Excess of 200 Cycles 5 22 200
90 4,1 630
7 4 19 925
And, for a seventeenth year 7 12 701
3 13 500
There is nothing to cause the postponement of Tishri 1 from feria 3,.
Tuesday.
For the Molad of the next year, the addition of 5 21 589 gives
2 11 9, and Tishri 1 is a Monday. Consequently 5660 must have
i 4 4 THE JEWISH CALENDAR
ended with a Sunday ; and, as it begins with a Tuesday and is
Embolismic, it is of the form In + 6, or has 384 days.
Line 11 of the Table, Part I., refers us to Column 7 of Part II. for
the month Nisan, from which it is seen that Nisan 15 occurs upon a
Saturday.
It may perhaps be well to show how the error may arise, to the
possibility of which reference was made at the commencement of this
Article, and in Article 37.
Suppose that the Nisan 15 occurring in A.D. 1900 has been
erroneously taken as belonging to the Jewish year 1900 + 3761, or
5661 ; the week-day would have been found to be Thursday, which is,
of course, wrong. Thus :
BeHaKD .................................... 2 5 204
Excess for 297 Cycles ..................... 7 19 675
17 years elapsed ............... 6 10 210
Moladof5661 .............................. 2 11 9 Monday.
Add for a Com. year ........................ 4 8 876
Moladof5662 .............................. 6 19 985
Tishri 1 of 5662 is postponed by ADU from feria 6, Friday, to
feria 7, Saturday. Therefore 5661 terminates with a Friday ; and, as
it began with a Monday and is a Common year, it is of the form
350 + 5, or has 355 days.
Refer to Line 5 of Part I. of the Table ; it tells us that Column 5
of Part II. is to be used for Nisan ; the 15th day of the month appears
to be Thursday, which is wrong.
69. There is, however, a simpler method even than this ; for, by
the employment of the seven first letters of the Alphabet as Day-Letters,
a Calendar may be formed Table XVI. which will show the day of
the week for any day of any month when the feria for Tishri 1 and
the form of the year are known.
Numerical values must be given to the seven Letters according to
the feria for Tishri 1 : Thus, if Tishri 1 be feria 5, A will be 5 and
THE JEWISH CALENDAR 145
be the Thursday Letter, B will be 6 and be the Friday Letter, C
will be 7 and be the Saturday Letter, &c., according to the following
system :
TlSHBI 1.
= Feria 2.
= Feria 3.
= Feria 7.
A .
B .
C .
D .
E .
F .
G
A
3
A
5
A .
7
B
4
B
6
B .
1
C
5
C
7
C .
2
D
6
D
1
D .
3
E
7
E
2
E .
4
F
1
F
3
F .
5
G
2
G
4
G .
6
The Calendar, Table XVI., is to be used as in the following
examples :
1. Kequired the week-day for Kislew 13 in the year 5611, which has
385 days ; Tishri 1 is a Saturday.
Part VI. of the Calendar, which belongs to a year of this form,
must be used.
Because Tishri 1 = feria 7, and Kislew 13 is in a line with C, it is
a Monday, for C = '2 when A = 7.
2. Required the week-day for Tammuz 29 in the year 5659, which
commenced with a Saturday, and had 353 days.
Part I. of the Calendar must be used.
Here again Tishri 1 is on feria 7, .'. A = 7, and Tammuz 29, which
is on the line with G, is feria 6, or Friday.
3. Nisan 15, in the year 5660, which commenced with a Tuesday
and had 384 days.
Part V. of the Table. A = 3 ; Nisan 15 = E = 7 = Saturday.
11
CHAPTEK VI
KEBIOTH. PERPETUAL CALENDARS. SIXTY-ONE FORMS OF THE CYCLE
70. It is usual in Jewish Calendars and Year-Books to describe
the year by means of three characters. The first on the right (the
Hebrew language is written from right to left), gives the feria with
which the year commences ; that in the middle is the initial letter of
the word which defines the form or length of the year; and that
on the left gives the feria for Nisan 15, the First Day of Unleavened
Bread.
The combination of these three characters is called the Kebia of
the year, a word derived from the Aramaic root Keba, meaning " Settle-
ment, ""or "Determination (sc., of the Feasts)."*
Tables have been formed of the Kebioth for a series of years. One
of these is given by al-Birunit for A.M. 4754 to 5285 inclusive,
A.D. 993 to 1524. This Table, however, so far as the Jewish years
are concerned, contains only the feria for Tishri 1, and the form of
the year.
The old chronologists seem to have believed that such Tables,
formed for a period of 247 (= 13 x 19) years, would serve in per-
petuity, because they thought that after that time had elapsed all the
Kebioth would return in the same cyclical order as before. This,
however, is erroneous, as will be proved.
The fourteen possible combinations of the year, in its different
forms, with the four week-days which are lawful for Tishri 1, would
be expressed as Kebioth in the following manner, the feriae for
Tishri 1 and Nisan 15 being here transposed, in order that the Table
* Ideler, i. p. 561. f Sachau, trans, p. 154.
146
THE JEWISH CALENDAR 147
may be read according to the customary way, that is, from left
to right :
The small letters indicate Common, and the capital letters indicate
Embolismic years : a, A = Abundant ; r, K = Regular ; d, D =
Deficient.
1 1 a 5
2 Id?
3 1 D 5
4 3 d 2
5 3 a 7
6 3 D 7
7 3 A 5
8 5 a 2
9 5 r 3
10 5 D 2
11 5 A 7
12 7 r 5
13 7 A 2
14 7 R 3
If, therefore, a year were described as having the Kebla, or Sign,
1, a, 5, it would indicate that Tishri 1 occurs on feria 1, Monday, that
the year is Common Abundant, or has 355 days, and that Nisan 15 is
on feria 5, Thursday.
PERPETUAL CALENDARS.
71, It is almost self-evident, perhaps quite self-evident, that the
old chronologists must have been perfectly aware of the fact that the
duration of the Civil Cycle of nineteen Civil years is a variable, while
that of the Astronomical Cycle is a constant quantity. Schwarz says*
that they consoled themselves under the idea that after every thirteen
Cycles, that is, after every 247 years, there takes place almost an exact
equalisation. In other words, they believed not only that every such
Cycle of 247 years contained the same. number of days, but also that
after every such 247 years the Kebioth would all return in the same
* " Der Jiidische Kalender," p. 78. " Schon die alien Chronologen f iihlten diese Unebenheit,
undsieberuhigten sich iiber dieses Schwanken bei clem Gedanken, dass nach 13 Mondcykeln,
<1. h. nach 247 Jahren, ein moglichst genauer Ausgleich eintritt. Ja, man ging in dieser
Behauptung so weit, anzunehmen, dass in clem unter clem Namen Iggul des R. Nachshon
Gaon bekannten grossen Cyklus alle Conjunctionen sich in derselben Ordnung wiederholen."
148 THE JEWISH CALENDAR
order. He says that this Cycle is known as the Iggul of Rabbi
Nachson Gaon (A.D. 881-889), and that they even went so far as to
believe that all the Conjunctions of the Sun and Moon were repeated
in the same order, after every 247 years.
Scaliger fell into this error. Though he is explicit in stating that
the Conjunctions do not return in the same order with respect to the
hours and the Chalakim, till after the lapse of many centuries,* yet he
positively asserts that after every 247 years the celebrations of the
New Moons will come back to the same days of the week.* As he
particularly addresses his communications to the young students it is
possible that he intends it for them only. If his statement were
allowed to pass without notice it might probably mislead some who
would not be at the trouble of ascertaining w r hether it can be verified.
The fact is that the commencement of the first year of these,
so-called, Great Cycles of 247 years has already changed its week-day
five times since the commencement of the Era, and a change will take
three times more before the year 7678 commences in A.D. 3917.
The changes which have already taken place are as follows :
Cycle 35 commenced with Tuesday ; Cycle 48 with Monday.
,, 83 ,, Saturday; ,, 96 ,, Thursday.
,, 141 ,, Monday : ,, 154 ,, Saturday.
168 Thursday ; ,, 181 ,, Tuesday.
,, 238 ,, Tuesday"; ,, 251 ,, Monday.
Those which will take place are
Cycle 286 commenced with Saturday ; Cycle 299 with Thursday.
,, 344 will commence with Monday ; ,, 357 ,, Saturday.
,, 358 ,, ,, Thursday; ,, 371 ,, Tuesday.
The ferise are computed according to the mean length of a Lunation
as estimated by Hipparchus, and adopted by Hillel II. for the Jewish
Calendar. They are also assumed as subject to the Dechiyyoth, or
* " De Emend. Temp.," lib. ii. p. ISf, B. ' Cum clico neomeniarum ferias in orbem redire
periodo 247 annorum, intelligo feriani, non autem horas. Nam in decem millibus, ant
amplius annorum, nunquam reperies duas neomenias, feria, horis, et scrupulis inter se
convenientes."
t Ib., p. 132, C et D. " Sciant igitur, adolescentes, in 247 annis, hoc est, Cyclis xiii, cmnes.
neomenias in easdem ferias recurrere. Nam periodus Judaica est annorum (591(5, qui 28
divisi dant 247 annos, in quibus fit orbis neomeniarum et feriarum, sicut feriarum tanlum
in 28 annis Solaribus."
THE JEWISH CALENDAR 149
rules which govern the postponement of Tishri 1 ; for it is upon these
data that the statement of Scaliger is based.
72. Lazarus Bendavid, to whom reference is frequently made by
Dr. Sachau in his Annotations on al-Biruni, though he is not considered
a great authority by the majority of Hebrew scholars, is equally mis-
leading. He gives a " Kalendarium Perpetuum," so called, by means
of which, he says, may be found the feria for the first day of any year
in the Jewish Era, as well as the form of any such year. He furnishes
full directions as to the way in which it is to be used, together with
several examples.*
This Calendar consists of thirteen lines for thirteen ordinary Cycles,
divided into nineteen columns for the years of the Cycle, thus forming
247 cells in which are placed the feria of Tishri 1, and the letter
indicating the form of the year for 247 consecutive years.
Bendavid goes beyond this. At p. 58, 45, he states plainly that
the Kebioth return after every 247 years, that is, after every thirteen
Cycles ; in other words, that the year P is in every respect identical
with the year P + 247. To show that this is so (which it is not), he
says that in 13 x 19 years there are 13 x 19 x 235 Lunations, or
New Moons, and, because the excess of a Lunation is Id. 12h. 793ch.
above an exact number of weeks, the retrograde movement of the
feria in the Molad after 247 years will be (Id. 12h. 793ch.) x 3055, or
4695d. 23h. 175ch., which is 6d. 23h. 175ch., or very nearly one whole
week, above an exact number of weeks. And so, the first day of
P + 247 must fall to the same feria as the first day of P ; also, that
which is true for P and P + 247 is true f or P + 1 and P + 248 ; for
P + 2 and P + 249 ; and so on throughout.
To this argument he adds a footnote,! " The Perpetual Calendar
attached to this work is based upon the above [argument] . It is
taken out of the book ' Lebusch Haschacor ' (The Black Eobe), No. 428,
p. 151, by the Rabbi Mardochai Japhi. The inventor of this Calendar,
* " Zur Berechnung uncl Geschichte des Jiidischen Kalenders," p. 97, "Calendarium Per-
petuum ; " and pp. 98, 99, " Schliissel und Gebrauch des ewigen Kalenders."
t P. 61. " Darauf grtindet sich das Calendarium Perpetuum, das diesem Werke ange-
hiingt 1st. Es ist aus dem Buche Lebushch Haschachor (Schwarzes Gewand), No. 428, p. 151,
des K. Mardochai Japhi entnommen. Der Erfinder desselben ist nach Bartoloccius ein mir
unbekannter R. Gabriel de Sorano. Nirgends findet man aber einen Beweis dafiir. Ich
weist nicht, was Waser, a. a. o. meint, wenn er sagt : ' Es komine erst alles in 689472
Jahien wieder in Ordnnng.'"
according to Bartolocci, was Kabbi Gabriel de Sorano,* but I have
never found a proof of that. I know not what Waser, in another
passage, means when he says : ' It comes all over again in order in
689472 years.'"
All this is most remarkable. No account whatever is taken of the
905 Chalakim required to bring 6d. 23h. 175ch. up to seven complete
days ; and yet these 905ch., occurring as they do once in every 247
years, must in process of time accumulate till they amount to an
interval of time sufficient to shift the week-day, and so entirely destroy
the perpetuity of the Calendar.
Our author's difficulty about the 689742 years, to which Waser
makes reference, would have been removed if he had made the simple
calculation which was given in Article 46, page 61.
73. It is quite easy to show that the belief of the old chronologers,
and the statements of Scaliger and Lazarus Bendavid are erroneous.
The duration of an Astronomical Cycle of 235 Lunations, or 19
years, is 6939d. 16h. 595ch. Its excess above a complete number of
weeks is 2d. 16h. 595ch. Consequently, the excess of thirteen Astro-
nomical Cycles will be (2 16 595) x 13, or 34 23 175 ; this is
6d. 23h. 175ch. more than an exact number of weeks, as Bendavid
says, and will be the excess after 13 x 19, or 247, years have elapsed.
The addition of 905ch. would bring the excess to exactly one week.
This being the case, it is evident that the Molad for Tishri at the
commencement of every Cycle of 247 years will have retrogressed, or
been diminished, by 905ch., and the question becomes, simply, How
long can this retrogression continue before it has amounted to a length
of time sufficient to change the week-day for Tishri 1 ? In some cases
the retrogression may continue for many hundreds, even thousands, of
years, without producing a change. In other cases the change will
occur after a comparatively short period.
Assume, for the sake of the argument, that the Molad of some year
H is 7 18 904 ; then, the Molad of the year H + 247 will be 905ch.
less, that is, it will be 7 17 1079. Clearly, H will commence with a
Monday, and H + 247 with a Saturday. Here a period of one Great
Cycle of 247 years has been sufficient to shift the week-day for Tishri 1.
Assume, again, that the Molad of H is 7 20 554; the year will
* Rabbi Gabriel de Sorano is utterly unknown.
THE JEWISH CALENDAR 151
commence with a Monday. Before the week-day for Tishri 1 can be
shifted to Saturday this Molad must be reduced, at least, to 7 17 1079.
The necessary reduction amounts to 2h. 555ch., or 2715 Chalakim.
This is exactly 3 x 905. Therefore the retrogression must take place
three times, which will occupy 3 x 247, or 741 years.
Once more, assume that the Molad of H is 7 17 1079 ; this year will
commence with a Saturday ; in order that the week-day for Tishri 1
may be shifted to the next possible day in retrogression, namely,
Thursday, the Molad must retrogress to, at least, 5 17 1079 ; that is, it
must retrogress to the extent of 48 hours, or 51840 Chalakim. Now,
57 x 995 is not sufficient to cover this amount, and therefore it will
require no less than 58 x 13 x 19, or 14326 years to effect the change.
This is a long period ; but, however long it may be, the change
must come if time endure. And no Calendar can be properly called
" Perpetual " whether it fail after 247, or after a thousand times 247
years.
From the examples thus given it will be seen that, in order to find
when a change of week-day for the commencement of a Great Cycle of
13 x 19 years will take place, it is only necessary to consider the limits
of the Molad which, together with the Dechiyyoth, or five laws, deter-
mine the feria for Tishrt 1. Take the difference between these limits ;
reduce the days and hours to Chalakim ; divide the whole number of
Chalakim by 905. If there be no remainder the quotient will give the
number of times that 247 years must be repeated before a change of the
week-day, which will always be retrogressive, can take place. If there
be any remainder, even of only one Chalak, the quotient must be
increased by unity, for in that case it will take another Cycle of 247
years to effect the change.
74. In Table XII., which is a scheme for showing when the
changes have taken place, and when they will again take place, the
horizontal argument gives the number of the ordinary Cycles of
nineteen years, from 1 up to 391, in an Arithmetical Series whose
common difference is 13. The vertical argument gives the inter-
mediate years.
It may be used for finding the feria with which any Cycle of the
Jewish Era commences, up to the 403rd, that is, up to the year 7639
inclusive.
If the number of the given Cycle, for which the feria of Tishri 1
THE JEU'ISff CALENDAR
is required, be amongst the numbers in the horizontal argument, then
the feria is found immediately beneath it in the first line of the Table,
which is marked by the zero in the vertical argument. If, however,
the number of the given Cycle be not found in the horizontal argument,
search for the next less number which does appear ; and, in the vertical
argument, find the number representing the difference between the
given Cycle and the next less. In the same line with this number,
and in the column under the next less number to that of the given
Cycle, will be found the feria with which the given Cycle commences.
Thus : For the 241st Cycle The next less number in the horizontal
argument is 235, and 245 231 = 6. In the line which is marked 6,
and in the column under 235, is the figure 5. The 241st Cycle com-
mences with feria 5, Thursday.
The ferise are in Roman characters when a change takes place,
namely, for Cycles 48, 96, 154, 181, and 251, which have already elapsed,
and for Cycles 299, 357, and 371, which are in the future.
The feriae are calculated according to the reformed Calendar, that
is, on the assumption that the Molad of the first Cycle of the Jewish
Era was 2 5 204, that the excess of a Cycle above an exact number of
weeks is 2 16 595, and that, for purposes of computation, the Dechiy-
yoth have always been in force. This method of computation is analogous
to that for the Julian Period, which assumes that Leap-years have
been observed regularly once in every four years, from B.C. 4713, and
will so continue to be observed for a total period of 7980 years.
The following is the computation for the Molads of Cycles where
changes of the feria occur.
Cycle 35. BeHaRD 2 5 204 Cycle 48. BeHaRD 2 5 204
30 Cycles 3 16 570 40 Cycles 2 14 40
4 , 3 18 220 7 4 19 925
35th Cycle 2 15 994
Tishri 1 is postponed by BaTU ThaK-
PhaT to feria 3.
Cycle 83. BeHaRD 2 5 204
80 Cycles 5 4 80
2 59 110
48th Cycle 2 15 89
Tishri 1 is not postponed from feria 2.
83rd Cycle 5 18 394
Tishri 1 is postponed by YacH to feria
6, and by ADU to feria 7.
Cycle 96. BeHaRD.
90 Cycles
2 5 204
4 1 630
6 10 815
96th Cycle 5 17 569
Tishri 1 is not postponed from feria 5.
THE JEWISH CALENDAR
'S3
Cycle 141. BeHaED 2 5 204
100 Cycles 2 23 100
40 . 2 14 40
141st Cycle 7 18 344
Tishri 1 is postponed by YacH and
ADU to feria 2.
Cycle 154. BeHaED 2 5 204
100 Cycles 2 23 100
50 1 11 590
3 1 1 705
154th Cycle 7 17 519
Tishri 1 is not postponed from feria 7.
Cycle 168. BeHaRD 2 5 204
100 Cycles 2 23 100
60 7 9 60
7 . 4 19 925
168th Cycle 3 9 209
Tishri 1 is postponed to feria 5, by
GaTBaD.
Cycle 181. BeHaED 2 5 204
100 Cycles 2 23 100
80 . 5 4 80
181st Cycle 3 8 384
Tishri 1 is not postponed from feria 3.
Cycle 238. BeHaED 2 5 204 Cycle 251. BeHaED 2 5 204
200 Cycles 5 22 200
30 3 16 570
7 4 19 925
238th Cycle 2 15 819
Tishri 1 is postponed to feria 3 by
BaTU PhaKPhaT.
200 Cycles 5 22 200
50 1 11 590
251st Cycle 2 14 994
Tishri 1 is not postponed from feria 2.
Cycle 286. BeHaED 2 5 204 Cycle 299. BeHaED 2 5 204
200 Cycles 5 22 200 200 Cycles 5 22 200
80 5 4 80 90 , 4 1 630
5 6 10 815 8 7 12 440
286th Cycle 5 18 219
Tishri 1 is postponed by YacH and
ADU to feria 7.
299th Cycle 5 17 394
Tishri 1 is not postponed from feria 5.
Cycle 344. BeHaED 2 5 204 Cycle 370. BeHaED...
300 Cycles 1 21 300 300 Cycles
40 2 14 40 60
3 1 1 705 9
344th Cycle 7 18 169
Tishri 1 is postponed to feria 2, by
YacH and ADU.
2 5 204
1 21 300
7 9 60
3 4 1035
370th Cycle 7 16 519
Tishri 1 is not postponed from feria 7.
1 54 THE JEWISH CALENDAR
Cycle 358. BeHaBD ,. 2 5 204 Cycle 371. 370th Cycle as
300 Cycles 1 21 300
50 1 11 590
7 , 4 19 925
above 7 16 519 1
1 Cycle 2 16 595
358th Cycle 3 9 939 371st Cycle 3 9 34
Tishri 1 is postponed from feria 3 to Tishri 1 is not postponed from feria 3.
feria 5 by GaTRaD.
The change of style in the Christian Calendar, made in October,
A.D. 1582, took place during the course of the 282nd Jewish Cycle
just after the year 5343, the fourth of that Cycle, had commenced.
This change does not affect the present question, for it made no altera-
tion in the feriae or current names of the week-days, but affects their
monthly date only.
75. It should now be evident that the only way in which any
approach to a Perpetual Calendar can be made is by considering the
Molads of the successive Cycles, and the limits to which they are con-
fined in order that the first year of a Cycle may commence with one of
the four days which are not forbidden by ADU, and also that the
remaining eighteen years of the Cycle may follow each other according
to some particular sequence.
Such a Calendar, instead of containing only thirteen lines, will be
found to contain sixty-one.
The limiting values for the Molads which allow Tishri 1 to fall upon
a given week-day, and also the form or length of the year when Tishri 1
does so fall, are given in Table X. This, however, is not sufficient for
the present purpose. It is necessary that the limits be further
developed ; for it is quite possible that the Molad for Tishri may be
such as would cause the first day of a Cycle to be, say, Monday, the
number of days in the first year to be 355, the total number of days in
the Cycle to be 6940,* and yet the forms of the remaining years vary in
their sequence.
It remains, then, to investigate the Molads, and to ascertain the
* There are no less than 4624 variations in the Molad for Tishri which permit of these
three conditions being fulfilled. The Molad, as will be seen hereafter, may be from 1 9 204
to 2 15 589, both inclusive ; that is to say, it may be 1 9 204, 1 9 209, 1 9 214,
1 9 219, &c., up to 2 15 589. The figure in the units place of the Chalakim must always,
be either a 4 or a 9, for the first year in a Cycle.
THE JE WISH CALENDAR
'55
sequence of years which they, in connection with the Dechiyyoth, will
permit. In other words, it is required to find the limits within which
the Molads must be confined in order that a Cycle may be of a
particular type.
The work may appear somewhat tedious, and will involve some
repetition of what has been said before ; but the subject requires careful
attention if it is to be understood.
In the first'place, consider the limiting values of the Molads which,
combined with the Dechiyyoth, cause a year to commence with a
given week-day. These are explained in Article 55, and stated in
the Table on page 83, as well as in Table X. ; it will save
trouble if those Tables be repeated in an abbreviated form here.
The twentieth year, which is the first of the next Cycle, is included
because the length of the nineteenth depends, when its first day is
fixed, upon the day with which the next year commences.
TABLE A.
Years of the Cycle.
Monday.
Tuesday.
Thursday.
Saturday.
1
3 6
8 11
14 17
19
7
18
2 18
3 18
5 18
1 4
7 9
12 15
18 20
7
18
2 15
589
3 9
204
5 18
2 5
10 13
16
7
18
2 18
3 9
204
5 18
The Table is to be read thus : The years 3, 6, 8, &c., . . . 19, will
commence with a Monday if the Molad be so great as or greater than
7 18 0, but so soon as the Molad attains to 2 18 0, that is, when
it exceeds 2 17 1079, the year will commence with a Tuesday. The
column for Monday is supposed to recur after that for Saturday.
76. Take now the very earliest limit which will permit a year to
commence with a Monday, that is, 7 18 0, and commencing with
this limit compute the Molads for the successive years of the Cycle,
adding also that for the twentieth year, which is the first of the next
Cycle.
Note the week-day with which each year commences, and thence
deduce the length of the year, thus determining the Sign for the year,
as 2d, 5r, &c.
The following is the result of the computation, the Molads being
156 THE JEWISH CALENDAR
obtained in the usual way by the addition of 4 8 87(5 for a Common
and of 5 21 589 for an Embolismic year.
The sixth and last columns of this computation, though inserted
here with the object of saving space, cannot be added at present.
TABLE B. TYPE 1.
Year of the
Cycle.
Molads.
First Day of
the Year.
Days in
Year.
Sign of
Year.
Molafl might be.
Possible
Addition.
1
7 18
Monday
353
2d
2 15 588
1 21 588
2
o 2 876
Thursday
354
5r
5 17 1079
15 203
3E
2 11 672
Monday
3a5
2 A 2 17 1079
6 407
4
19 181
Monday
353
2d 2 15 588
1 6 407
5
5 17 1057
Thursday
355
5 a 5 17 1079
22
6E
3 2 853
Tuesday
38*
3R
3 17 1079
15 226
7
2 362
Monday
355
2 a
2 15 588
15 226
8E
6 9 158
Saturday
383
7D
7 17 1079
1 8 921
9
5 6 747
Thursday
354
5r
5 17 1079
11 332
10
2 15 543
Monday
355
2a
2 17 1079
2 536
HE
7 339
Saturday
385
7 A
7 17 1079
17 740
12
5 21 928
Saturday
353
7d
7 17 1079
1 14 151
13
3 6 724
Tuesday
354
3r
3 9 203
2 559
14 E
7 15 520
Saturday
385
7A
7 17 1079
2 559
15
6 13 29
Saturday
355
7a
7 17 1079
1 4 1050
16
3 21 905
Thursday
354
5r
5 17 1079
1 14 174
17 E
1 6 701
Monday
383
2D
2 17 1079
1 11 378
18
7 4 210
Saturday
355
7 a 7 17 1079
13 869
19 E
4 13 6
Thursday
385
5 A
5 17 1079
1 4 1073
20
3 10 595
Thursday
5 17 1079 2 7 484
Every Cycle, the Molad of whose first year is 7 18 0, assuming
for the moment the possibility of such a Molad, will be of this Type,
which may be called the first Type.
TYPE 1.
Year of Cycle...
Sign of year ...
I
2d
2
or
3
2A
4
2d
5
5a
6
3B
7
2a
8
7D
9
oi-
lO
2a
11
7A
12
7d
13
3r
14
7A
15
7a
16
5r
17
2D
18 19
7a 5A
No Cycle, however, can possibly have 7 18 for its Molad. The
Molad may be 7 18 4, 7 18 9, 7 18 14, &c., and the question
THE JEWISH CALENDAR 157
arises whether any, and, if so, what addition may be made to the
Molad of the first year without altering the Type, that is, without
altering the feria with which any year in the Cycle commences, and
without altering the length of any year : in fact, without altering the
Sign of any one of the years : remembering always that any addition
made to the Molad of the first year will be the source of a similar
increment to the Molads of all the remaining years, including the
twentieth, or first of the next Cycle.
Such alteration will take place if the increment be sufficient to
raise the Molad of any one of the years to that limit which would
cause its first day to pass from its present to another feria.
We must therefore now ascertain what increment each of the
Molads can receive without causing any such passage to occur. This
must be done for each year throughout the Cycle. The least of all the
increments that can be made to the respective years will evidently be
the maximum increment that the original limit, 7 18 0, with which
we start, can receive. The sixth and last columns of Table B can
now be added as the computation goes on.
1. The first year will still commence with a Monday if its Molad
be increased from 7 18 to 2 15 588, which is the same as
9 15 588, since feria 2 and feria 9 represent the same week-day.
The first Molad may therefore be increased by 1 21 588.
2. The Molad of the second year is 5 2 876 ; this might be
increased to 5 17 1079 without altering the day, Thursday, with
which this year commences, and therefore without altering the length
of the first year. The possible increment is therefore 15 203.
The computation for the first two years in Table B would then
become
7 18 + 15 203 = 1 9 203 .'. Monday.
Add for a Common year. . . 4 8 876
Molad of second year 5 17 1079 Thursday.
3. The Molad of the third year is 2 11 672; this might be
increased to 2 17 1079, without altering the day, Monday, with
which the third year commences, and therefore without altering the
length of the second year. Consequently the possible increment to
the Molad of this third year is 6 407, and the original Molad y
'58
THE JEWISH CALENDAR
7 18 0, may be increased by this amount without causing, as yet,
any alteration : notice that it has already been ascertained that the
Molad of the second year, and therefore of the first so far as the
second is concerned, may be increased by 15 203 ; much more
then may it be increased by 6 407.
The computation for the first three years in Table B will now
become
7 18 + 6 407 = 1 407 Monday.
4 8 876
Molad of second year 5 9 203 Thursday.
4 8 876
Molad of third year 2 171079 Monday.
There is no alteration, as yet, in the days with which these three
years respectively commence, and therefore no alteration in the
lengths of the first two years.
4. The Molad of the fourth year is 1 9 181 ; this may be
increased to 2 15 588 without altering the day, Monday, with
which this year commences, and therefore without altering the
length of the preceding year. The possible increment is 1 6 407.
This increment is greater than can be allowed. It can only accrue
through the addition of 1 6 407 to the original Molad, 7 18 ;
and we have seen that any addition greater than 6 407 to that
Molad would alter the Type of the Cycle.
This will be seen at once if we compute the first four years under
the idea that this larger addition can be made :
7 18 + 1 6 407 = 2 407 Monday.
4 8 876
Molad of second year ...6 9 203 Saturday.
4 8 876
Molad of third year, E.... 3 17 1079 Tuesday.
5 21 589
Molad of fourth year 2 15 588.
.Monday.
THE JEWISH CALENDAR 159
The Type is altered ; instead of being 2 d, 5 r, 2 A, 2 d, it becomes
2 a, 7d, 3R, 2 a.
Clearly this addition is too great, and it need not be further
considered.
5. The Molad of the fifth year is 5 17 1057; this might be
increased to 5 17 1079 without altering the day, Thursday, with
which the year commences, and therefore without altering the length
of the fourth year. The possible increment is 22. This
increment, being less than that which has been already found pos-
sible for the preceding years, will not make any alteration in the Type,
as yet. The computation will become
7 18 + 22 = 7 18 22 Monday.
4 8 876
Molad of second year ... 5 2 898 Thursday.
4 8 876
Molad of third year, E . . . 2 11 694 Monday.
5 21 589
Molad of fourth year ... 1 9 203 Monday.
4 8 876
Molad of fifth year 5 17 1079 Thursday.
The sequence of the Signs of the years remains precisely the same.
The Type is not altered.
If the increase to the original Molad, 7 18 0, were only one
Chalak more than 22, then the Type would be altered ; the
Molad of the fifth year would become 5 18 0, and this year would
commence with a Saturday. The length of the fourth year would be
increased by two days ; its Sign would become 2 a instead of 2 d ; the
Type would be vitiated.
It is evident, then, that, so far as we have yet ascertained, the
maximum increment to the Molad of the first year can only be
22 Chalakim, if the Type is to be preserved. As this is but a small
increment it is not unlikely that nothing smaller will be required.
The remaining years must, however, be tested.
160 THE JE WISH CALENDAR
It is not necessary to give the full details for the remaining years.
The possible increments for each of them are set down in the last
column of Table B. They are all greater than 22, and there-
fore they are all too great.
It appears, then, that this addition of 22 Chalakim still retains
the function of being the maximum that can be made to the
original Molad, 7 18 0, without altering the Sign of any one of the
years of the Cycle. In other words, all Cycles which have for the
Molad of their first year any value which is not less than 7 18-0,
and not greater than 7 18 22, will be of the same Type. This
is given as Type I. in the first line of the collected Types, Table
XIII.
By adding together the number of days specified by the Signs of
the years, or the number pertaining to each year as actually stated
in Table B, above, the total number of days in the Cycle is ascer-
tained. In the present case Type 1 the sum of the days is 6940 ;
and every Cycle whose Molad is within the limits 7 18 and
7 18 22, both inclusive, will consist of this . number of days
according to the Civil computation.
The possible Molads within these limits are 7 18 4, 7 18 9,
7 18 14, and 7 18 19. It so happens that during the first 7650
years of the Jewish Era there is no Cycle which commences with a
Monday whose Molad comes within this range. There is consequently
no Cycle, amongst all those years, which is of Type 1, so far as the
arrangement or sequence of the years is concerned, though there are
many which, with a different sequence, have 6940 days.
77. TYPE 2.
The inferior limit for the Molad of the first year of a Cycle of the
second Type will be 7 18 23. The superior limit will be found in a
similar way to that for Type 1.
The computation is given below, by which it will be seen that
the increment, 2 513, which may be made to the Molad of
the tenth year is the least, and therefore this is the greatest that
can be made to the original Molad, 7 18 23, which then becomes
7 20 536.
The limits for a Cycle of Type 2 are therefore 7 18 23 and
7 20 536, both inclusive.
THE JEWISH CALENDAR
TYPE 2.
161
Year of the
Cycle.
Molads.
First Day of
the Year.
Days in
Year.
Sign of
Year.
Molad might be.
Possible
Addition.
1
7 18 23
Monday
353
2d
2 15 588
1 21 565
2
5 2 899
Thursday
354
5r
5 17 1079
15 180
3E
2 11 695
Monday
385
2 A
2 17 1079
6 384
4
1 9 204
Monday
355
2a
2 15 588
6 384
5
5 18
Saturday
353
7d
7 17 1079
1 23 1079
6E
3 2 876
Tuesday
384
3E
3 17 1079
15 203
7
2 385
Monday
355
2 a
2 15 588
15 203
8E
6 9 181
Saturday
383
7D
7 17 1079
1 8 898
9
5 6 770
Thursday
354
5r
5 17 1079 11 309
10
2 15 566
Monday
355
2a
2 17 1079
2 513
HE
7 362
Saturday
385
7 A
7 17 1079
17 717
12
5 21 951
Saturday
353
7d
7 17 1079
1 14 128
13
3 6 747
Tuesday
354
3r
3 9 203
2 536
14 E
7 15 543
Saturday
385
7A
7 17 1079
2 536
15
6 13 52
Saturday
355
7a
7 17 1079
1 4 1027
16
3 21 928
Thursday
354
5r
5 17 1079
1 14 151
17 E
1 6 724
Monday
383
2D
2 17 1079
1 11 355
18
7 4 233
Saturday
355
7a
7 17 1079
13 846
19 E
4 13 29
Thursday
385
5 A
5 17 1079
1 4 1050
20
3 10 618
Thursday
5 17 1079
2 7 461
If the course of the years be traced through any Cycle whose
Molad is not less than 7 18 23 and not greater than 7 20 536,
it will be found that such Cycle is of this Type, and, like Type 1,
has 6940 days.
This forms the second line in Table XIII.
78.
TYPE 3.
This Type will commence with 7 20 537 as the inferior limit for
the Molad of the first year of the Cycle.
The computation, made as before, gives the following result :
12
162
THE JE WISH CALENDAR
Year of the
Cycle.
Molads.
First Day of
the Year.
Days in
Year.
Sign of
Year.
Molad might be.
Possible
Addition.
1
7 20 537
Monday
353
2d
2 15 588
1 19 51
2
5 5 333
Thursday
354
5r
5 17 1079
12 746
3E
2 14 129
Monday
385
2 A
2 17 1079
3 950
4
1 11 718
Monday
355
2a
2 15 588
3 950
5
5 20 514
Saturday
353
7d
7 17 1079
1 21 565
6E
3 5 310
Tuesday
384
3B
3 17 1079
12 769
7
2 2 899
Monday
355
2a
2 15 588
12 769
8E
6 11 695
Saturday
383
7D
7 17 1079
6 384
9
5 9 204
Thursday
355
5 a
5 17 1079
8 875
10
2 18
Tuesday
354
3r
3 9 203
15 203
11
7 2 876
Saturday
385
7A
7 17 1079
15 203
12
6 385
Saturday
353
7d
7 17 1079
17 694
13
3 9 181
Tuesday
354
3r
3 9 203
22
14 E
7 17 1057
Saturday
385
7 A
7 17 1079
22
15
6 15 566
Saturday
355
7a
7 17 1079
1 2 513
16
4 362 | Thursday
354
5r
5 17 1079
1 17 717
17 E
1 9 158 i Monday
383
2D
2 17 1079
1 8 921
18
7 6 747 i Saturday
355
7 a
7 17 1079
11 332
19 E
4 15 543
Thursday
385
5 A
5 17 1079
2 537
20
3 13 52
Thursday
5 17 1079
2 4 1027
From this computation it appears that the least of all the
increments that can be made is 22, which can be added to
the Molads of both the years 10 and 11. The original Molad with
which this Type commences may therefore be increased by this
amount, and the limits for Type 3 are 7 20 537, and 7 20 559,
both inclusive.
There are only six possible Molads which can come within these
limits ; the feria and hours being in each 7 20, and the Chalakim,
respectively, 534, 539, 544, 549, 554, 559.
In the first 403 Cycles, covering 7647 years of the Era, there
occurs no Cycle of this Type.
The fourth Type will commence with 7 20 560 as the inferior
limit for the Molad of its first year.
79. If this process be continued it will be found that there are,
in all, 61 possible Types for the Cycles, and 61 only. It is perhaps
unnecessary to give the computations for the remaining Types, as the
method has been sufficiently indicated. The computation for Type 61
will, however, be stated. It starts with 7 16 689 for the Molad
THE JE WISH CALENDAR
163
of its first year, and it will be seen that the maximum increment
which this Molad can receive, without changing the Type, is
1 390, being the increment that can be made to the Molad
of the first year.
This raises the superior limit to 7 17 1079, and the next Type
would start with 7 18 0, which is the inferior limit for Type 1, so
that the whole series of Types will now recur in the same order
as before.
TYPE 61.
Y-roJtiio Molad ,
First Day of
the Year.
Days in
Year.
Sign of
Year.
Molad
might be.
Possible
Addition.
1 7 16 689
Saturday
355
7a
7 17 1079
1 390
2 51 485
Thursday
354
5r
5 17 "1079
16 594
3E 2 10 281
Monday
3a5
2 A
2 17 1079
7 798
4 1 7 870
Monday
353
2d
2 15 588
7 798
5 5 16 666
Thursday
355
5a
5 17 1079
1 413
6E 3 1 462
Tuesday
384
3B
3 17 1079
16 617
7 1 22 1051
Monday
353
2d
2 15 588
16 617
8E 67 847
Saturday
383
7D
7 17 1079
10 232
9 5 5 356
Thursday
354
5r
5 17 1079
12 723
10 2 14 152
Monday
355
2a
2 17 1079
3 927
HE 6 22 1028
Saturday 385
7 A
7 17 1079
19 51
12 5 20 537
Saturday
383
7d
7 17 1079
1 21 542
13 3 5 333
Tuesday
354
3 r
3 9 203
9 950
14 E 7 14 129
Saturday
385
7 A 7 17 1079
3 950
15 6 11 718
Saturday
355
7 a
7 17 1079
6 361
16 3 20 514
Thursday
354
5 r
5 17 1079
1 21 565
17 E 15 310
Monday
383
2D
2 17 1079
1 12 769
18 72 899
Saturday
355
7 a 7 17 1079
15 180
19 E 4 11 695
Thursday
385
5 A
5 17 1079
6 384
20 3 9 204
Thursday
5 tt 1079
2 8 875
The final results for all the Types are set out in Table XIII.
80. The following Table C will, so far as the limits are concerned,
supply the want of the computations for Types 4 to 60. It shows,
in the last column, the year of the Cycle which is capable of receiving
that increment which is the least. It will be observed that in nineteen
of the Types there are two years, each of which may receive the same
increment. This is an important fact of which further notice will be
taken.
164
THE JE WISH CALENDAR
TABLE C.
Type.
First Limit.
Possible Increment.
Second Limit.
Year, of which
Molad may be
increased.
1
7
18
22
7
18
22 5
2
7
18
23
2
513
7
20
536 10
3
7
20
537
22 7
20
559 13 or 14
4
7
20
560
3
927
1
407 3
5
1
408
4
1004
1
5
332 9
6
1
5
333
2
536
1
7
869 18
7
1
7
870
1
413
1
9
203 2
8
1
9
204
22
1
9
226 6 or 7
9
1
9
227
2
518
1
11
740 10 or 11
10
1
11
741
11
309
1
22
1050 15
11
1
22
1051
22 1
22
1073 19
12
1
22
1074
1
413
2
407 3 or 4
13
2
408
2
513
2
2
921 7 or 8
14
2
2
922
2
536
o
5
378 17
15
2
5
379
8
852
2
14
151
12
16
2
14
152
22
2
14
174
16
17
2
14
175
1
413
2
15
588 1
18
2
15
589
2
513
2
18
22 4 or 5
19
2
18
23
2
536
2
20
559 14
20
2
20
560
4
1004
3
1
484
20
21
3
1
485
3
927
3
5
332 9
22
3
5
333
22
3
5
355 13
23
3
5
356
22
3
5
378
17 or 1*
24
3
5
379
3
904
3
9
203
1 or 2
25
3
9
204
22 3
9
226
6
26
3
9
227
2
513 3
11
740
11
27
3
11
741
8
875
3
20
536
10
28
3
20
537
22 3
20
559
14 or 15
29
3
20
560
2
513 3
22
1073
18 or 19-
30
3
22
1074
1
413 4
407
3
31
4
408
2
513
4
2
921
8
32
4
2
922
8
875
4
11
717
7
33
4
11
718
22
4
11
740
11 or 12
34
4
11
741
2
513
4
14
174
15 or 1&
35
4
14
175
3
927
4
18
22
5
36
4
18
23
7
461
5
1
484 20
37
5
1
485
1
413
5
2
898 4
38
5
2
899
22
5
2
921
8 or 9
39
5
2
922
2
513
5
5
355
12 or 13
40
6
5
356
22
5
5
378
17
41
5
5
379
3
904
5
9
203
2
42
5
9
204
22
5
9
226
5 or 6
43
5
9
227
8
852
5
17
1079
1
44
5
18
2
536
5
20
536
9 or 10
45
5
20
537
22 5
20
559 14
THE JEWISH CALENDAR
TABLE C. (continued}.
165
Type.
First Limit.
Possible Increment.
Second Limit.
Year, of which
! Molad may be
increased.
46
5
20
560
2
513
5
22
1073
19
47
5
22
1074
1
413
6
407
2 or
3
48
6
408
7
461
6
7
869
18
49
6
7
870
3
927
6
11
717
7
50
6
11
718
22
6
11
740
11
51
6
11
741
2
513
6
14
174
16
52
6
14
175
8
875
6
22
1050
15
53
6
22
1051
22
6
22
1073
19 or 20
54
6
22
1074
3
904
7
2
898
4
55
7
2
899
22
7
2
921
8
56
7
2
922
2
513
7
5
355
13
57
7
5
356
22
7
5
378
16 or 17
58
7
5
379
3
927
7
9
226
6
59
7
9
227
4
1004
7
14
151
12
60
7
14
152
2
536
7
16
688
20
61
7
16
689
1
390
7
17
1079
1
1
7
18
The
Types
now
recur in
order.
81. Professor Nesselmann, in his " Beitrage zur Chronologic," *
gives a method of finding the sixty-one limits for the Molads of first
years which determine the sixty-one types of the Cycles. This method
is adopted by Adolf Schwarz, t who refers also to the " Jesod Olam," t
p. 216, and to Berl Goldberg's Chronological Tables, but relies chiefly
upon Nesselmann. The reckoning is not given by either of these
writers, but both supply the Table of results, which is similar to
Table XIII., though not precisely in the same form. It is not very
easy to follow their explanations of the process pursued.
Starting with the earliest Molad which permits a year to commence
with a Monday, 7 18 0, the successive years of a Cycle are computed
precisely as for Type 1, Table B, above.
Although an Astronomical, as distinguished from a Civil Cycle, may
commence with any one of the seven days of the week, as indicated by
its Molad (see Table IX.), yet a Civil Cycle can only commence with
some one of the four days which are lawful for Tishri 1. Also, before
* " Crelle Journal fur die Mathematik," Band 26, p. 59. Berlin, 1843.
t " Der Jiidische Kalender," p. 79.
\ By Rabbi Isaac Israeli ; an edition in Hebrew and German was published in Berlin in
1848.
1 66 THE JE ll'ISff CALENDAR
any change can take place from one day to another, whether it be for
the first or for any subsequent year of the Cycle, the Molad for the
year must pass the limit which confines Tishri 1 to the former of the
two days.
Thus : If the Molad for the year be 5 17 1079, the first day of the
year will be a Thursday, but so soon as the Molad passes this limit,
and attains to 5 18 0, the first day of the 'year is changed to
Saturday.
Now, there is nothing to prevent a Molad from indicating any one
of the seven week-days as the commencement of some Astronomical
year, and there is nothing to prevent a Civil year from commencing
with some one or other of the four possible week-days.
Thus, the first year of a Cycle may commence with a Monday, as
in Type 1 ; or it may commence with a Tuesday, as in Type 18 ; or
with a Thursday, as in Type 25 ; or with a Saturday, as in Type 44.
The same thing applies to every other year of the nineteen of the
Cycle, and also to the twentieth year, which must be taken into con-
sideration, because the day with which it commences is one of the
factors that determine the length of the nineteenth year.
Again : The value of the Molad for the first year of a Cycle, and
the week-day with which that year commences, determine the whole
Type, that is to say, determine the Molad, and thence the week-day, for
each of the remaining years of the Cycle, as well as for the twentieth
year, because the Molads of the successive years are found by making
certain additions, which are constant, to the Molad of the first year.
These additions are 4 8 876 for every Common year, and 5 21 589
for every Embolismic year. The result of these additions for any par-
ticular year of the Cycle has been given in Table VII.
It is evident, therefore, that there are 20 x 4, or 80 variations
which can take place in the Types, because a change in the Sign for
any one year will cause a change in the Type, and each one. of the
twenty years is capable of commencing with any one of four different
days.
It is, however, found, when the computation is made, that nineteen
of these 80 variations occur twice, thus reducing the total number of
different Types to 61.
The limits, within which the Mo-lads of the Cycles must fall, for
these sixty-one Types are found by Nesselmann in the following
manner :
THE JEWISH CALENDAR 167
The Molad of each year in Type 1, Table B (Article 76), is to be
subtracted from the particular day-limit (Table A, Article 75), the
attainment to which would cause the postponement of Tishrl 1.
The remainder is to be added to 7 18 0, the Molad taken for the
origin of the computation, and the sum gives the inferior limit for
the first year of one of the Types. The superior limit will, of course,
be less by one Chalak than the inferior limit of the next succeeding
Type ; not of the next Type that is found, but of the next Type after
all the inferior limits have been found and arranged in the numerical
order of their magnitude.
For example : A year will commence with a Saturday, whatever
may be its position in the Cycle, if the Molad be so great as or greater
than 5 18 0. Therefore all the Molads in Type 1 , Table B, are to
be subtracted from 5 18 0, and the remainder is to be added to
7 18 0. Thus, the Molad of year 11 in Type l.is 7 339 ; if
this be subtracted from 5 18 0, the minimum day-limit for Saturday,
the remainder is 5 17 741.* This, being added to 7 18 0, gives
the sum 6 11 741 as the inferior limit for one of the sixty-one
Types. When the Types are numbered in order of the magnitudes of
the Molads, it will be found that this is number 51.
With respect to Tuesday and Thursday, care must be taken to
make the subtractions from those day-limits which are proper to the
different years of the Cycle. Thus, Table B shows that those Common
years which follow next after an Embolismic year will commence with
a Tuesday if the Molad attain to 2 15 589 : this is under the rule
BaTU ThaKPhaT ; all other years, whether Common or Embolismic,
commence with a Tuesday, when the Molad attains to 2 18 0.
82. The process thus described will, perhaps, be better understood
when the following computations, which I have thought it well to-
give, are examined. The numbers on the left are the years of the
* Observe that 5 18 0, treated as a Molad, is identical with 12 18 0, because feria 5-
and feria 12 are identical ; so we have
12 18
- 7 339
5 17 741
+ 7 18
6 11 741
1 68
Cycle, and the twentieth year, the first of the next Cycle, is added.
The numbers on the right are the numbers which are attached to the
Types when they are arranged in order of magnitude, as in Tables C
(Article 80), and XIII.
I. MONDAY.
The day-limit for Monday in all years is 7 18 0.
the
or,
All the Molads in Table B are to be subtracted from 7
remainder is to be increased by 7 18 0.
This is equivalent to subtracting each of the Molads from
for it is the same thing, from 15 11 1080.
18
15
0, and
12 0,
i.
2.
3.
4.
5.
6.
7.
15
7
12
18
8.
9.
10.
11.
12.
13.
15 11
6 9
1080
158
14
14. lo
7
11
15
1080
520
4
7
15
5
18
11
2
1
2 2
15 11
5 6
922.
7
15. 15
6
20
11
13
560
1080
29
1080
876
204 25
1080
747
22
11
3
15
2
9
11
11
3 5
15 11
2 15
333.
1
16. 15
3
22
11
21
1051
1080
905
1080
672
1080
543
45
35
6
15
1
11
9
408 48
5 20
15 11
7
537.
4
17. 15
1
14
11
6
175
1080
701
1080
181
1080
339
10
58
7
15
5
2
11
17
899 55
1 11
15 11
5 21
741
7
18. 15
7
5
11
4
379
1080
1057
1080
928
...16
1080
210
7
2
15
3
18
11
2
23... 19
2 14
15 11
3 6
152
1
19. 15
4
7
11
13
870
1080
853
1080
724
40
1080
6
30
5
15
2
9
11
227 43
5 5
356
3
20. 15
3
22
11
10
1074
1080
362
1080
595
6
11
718 50
5
1
485
THE JE WISH CALENDAR
169
II. TUESDAY.
The day-limit for years 1, 4, 7, 9, 12, 15, 18, and 20 is 2 15 589.
For years 2, 3, 5, 6, 8, 10, 11, 13, 14, 16, 17, and 19 it is 2 18 0.
All the Molads in Table B which belong to the former years are to
be subtracted from 2 15 589, and the remainder is to be added to
7 18 0. This is equivalent to subtracting these Molads from
10 9 589, or, for it is the same thing, from 10 8 1669.
All the Molads in Table B which belong to the remaining years are
to be subtracted from 2 18 0, and this, through the addition of
7 18 to the remainders, is equivalent to the subtraction of the
Molads from 10 12 0, or from the same value, 10 11 1080.
7.
9.
12.
15.
18.
10
7
9
18
589
20. 10
3
8
10
1669
595
10. 10
2
11
15
1080
543
9
15
589 18
6
9,9,
1074 54
7
*>0
537
3
10
1
9
9
589
181
11. 10
7
11
1080
339
i
408 13
3
11
741
27
10
2
9
589
362
2. 10
5
11
2
1080
876
13. 10
3
11
6
1080
724
1
q
227 9
5
9
204 42
7
6
356
57
10
5
8
6
1669
747
3. 10*
2
11
11
1080
672
14. 10
7
11
15
1080
520
.->
a
922 39
1
408 5
2
*>0
560
9/n
10
8
21
1669
928
5. 10
5
11
17
1080
1057
16. 10
3
11
21
1080
905
4
11
741 34
4
18
23 36
6
14
175
52
10
6
9
13
589
29
6. 10
3
11
2
1080
853
17. 10
1
11
6
1080
701
8
20
560 29
7
9
227 59
2
5
379
15
10
7
9
4
589
210
8. 10
6
11
9
1080
158
19. 10
4
11
13
1080
6
3
5
879 24
4
9
922 32
5
99,
1074
47
170
THE JEWISH CALENDAR
III. THURSDAY.
The day-limit for the years 1, 2, 4, 5, 7, 9, 10, 12, 13, 15, 16, 18,
and 20 is 3 9 204.
For the years 3, 6, 8, 11, 14, 17, and 19, the day-limit is 3 18 0.
The Molads in Table B which belong to the former years are to be
subtracted from 3 9 204, and when 7 18 is added to the re-
mainder, the equivalent will be subtracting the Molads from 11 3 204,
which is the same as 11 2 1284.
The Molads which belong to the latter years are to be subtracted
from 3 18 0, and when 7 18 is added to the remainder an
equivalent is obtained by subtracting the Molads from 11 12 0.
1.
11
7
3
18
204
12. 11
5
2
21
1284
928
3. 11
2
11
11
1080
672
3
q
204 25
5
ej
356 ...40
2
408....
....13
2.
11
5
2
2
1284
876
13. 11
3
2
6
1284
724
6. 11
3
11
2
1080
853
6
o
408 48
7
90
560 4
1.
9
227....
.... 9
4.
11
1
3
9
204
181
15. 11
6
3
13
204
29
8. 11
6
11
9
1080
158
2
18
23 9
4
14
175 35
5
2
922....
39
5.
11
5
2
17
1284
1057
16. 11
8
2
21
1284
905
11. 11
7
11
1080
339
5
9
227 43
7
5
379 58
4
11
741....
....34
7.
11
2
2
1284
362
18. 11
7
2
4
1284
210
14. 11
7
11
15
1080
520
2
922 14
3
99
1074 30
3
30
560....
....29
9.
11
5
2
6
1284
747
20. 11
3
2
10
1284
595
17. 11
1
11
6
1080
701
-
90
537 45
7
16
689 61
3
,-
379
24
10.
11
2
2
15
1284
543
19. 11
4
11
13
1080
6
1
11
741... . 10
6
99
1074...
. 54
THE JE WISH CALENDAR
IV. SATURDAY.
The day-limit for Saturday in all years is 5 18 0.
All the Molads in Table B are to be subtracted from 5 18 0, and
the remainder is to be added to 7 18 0.
This is equivalent to subtracting the Molads from 13 12 0, and
insomuch as the subtractions for the Monday day-limit were all made
from 15 12 0, all that need be done is to throw back the feria in each
of the limits so found by two days. This gives the following result :
i.
2.
3.
4.
5.
6.
7.
8.
9.
10.
5
18
... 44
1
9
204
8
4
408 ..
31
5
fl
899
38
7
18
23
2
3
9
227
26
4
11
718. . .
. 33
7
9,
922
56
1
6
333
6
3
20
537
28
11.
12.
13.
14.
15.
16.
17.
18,
19.
20.
6
11
741
51
7
14
152
60
3
5
356
23
5
20
560
46
<;
22
1051
53
2
14
175
17
5
5
379
41
(i
7
870
49
1
22
1074
12
3
1
485
21
Eighty limits, or variations, have thus been found ; but when they
come to be arranged, and numbered in the order of their magnitude, so
as to form a Table identical with the first and second columns of
Table C, it is found that only 61 numbers are required, for 19 of these
variations occur twice.
Those which occur twice, and the computations under which they
occur, are the following :
Types.
Computations.
Types.
Computations.
4
Monday, 14, and Thursday, 13
34
Tuesday, 12, and Thursday, 11
9
Tuesday, 7,
6
35
Monday, 16,
15
10
Monday, 11,
10
39 Tuesday, 9,
8
13
Tuesday, 4,
3 40 Monday, 13,
12
14
Monday, 8,
7 43 Monday, 6,
5
19
Monday, 5,
4 45
Monday, 10,
9
24
Tuesday, 18,
17
48
Monday, 3,
2
25
Monday, 2,
1
54
Tuesday, 20,
19
29
Tuesday, 15,
14
58
Monday, 17,
16
30
Monday, 19,
18
172
The numbers attached to the ieriae in this Table are those of the
years of the Cycle, under the headings Monday, Tuesday, Thursday,
and Saturday, in the Computations I. II., III., and IV., which have
just been made. If this Table be compared with Table C, it will be
noticed that the Types which are here found to be duplicated are
always in advance by unity of those Types in Table C against which
are written, in the last column of that Table, the years of which the
Molads are capable of receiving the same increment.
The process of Nesselmann, which I have thus endeavoured to
explain, may appear to be shorter and simpler than that previously
suggested. It is shorter, so far as obtaining the limits for the Types is
concerned ; but, insomuch as each Type has afterwards to be computed
in full to obtain the Signs of the years, the work is not in reality
abbreviated.
It would be interesting to obtain a mathematical proof that there
must be sixty-one Types for the Cycles, and that there are not more
than sixty-one. This, however, cannot be done by any direct method.
The number can only be ascertained by actually counting how many
out of the 4 x 20 occur twice; this number being found to be nineteen,
the fact that there are sixty-one Types, and not more, must be accepted
as an arithmetical coincidence.
A check upon results which have been obtained may be made
by the use of Table XIII. combined with Tables XIV. and XV.
The first column, A, of Table XIV. is an Arithmetical Series
having zero for its first term, and 13 x 19, or 247, for its common
difference.
The second column, B, commencing with the Molad BeHaRD, is
an Arithmetical Series whose terms decrease regularly by 905 Chalakim,
the amount by which the Molads of Tishri retrogress after every 247
years (Article 73, page 150).
The first column, C, of Table XV. is an Arithmetical Series whose
first term is zero, and common difference 19.
The second column, D, of this Table is a repetition of part of
Table VIII., and shows the addition which has to be made to the
Molads for the multiples of 19.
These Tables are especially intended for finding the feria with
which any given Jewish year commences, and the form or length of
the year ; but, in the course of the process, there will also be found
the Molad for the first year of the Cycle to which the given year
THE JEWISH CALENDAR i 7s
belongs, the Type of the Cycle, and the position of the given year in
the Cycle.
The following is the method of using the Tables :
Let H be the given year.
1. In the first column, A, of Table XIV. search for the next less
number, N, to H, and note the Molad attached to it in column B,
which may be called b.
2. Subtract the number, N, from H, and note the remainder, R.
3. Find the number, n, next less to R in column C of Table XV. ,
and note, in column D, the addition to be made, which may be called d.
4. Add d to b ; the Sum, b + d, is the Molad of the Cycle to which
the given year H belongs.
5. Subtract n from R ; the remainder, r, is the place of the given
year in the Cycle.
6. In the column headed "Limits of the Molads," Table XIII. ,
find among the inferior limits that which is next less to b + d. The
Type of the Cycle is that in a line with this limit, and the form of the
year is that in the column headed by the number r, being the place of
the given year in the Cycle.
Examples.
(1) The year 1279.
H= 1279 = 19x67 + 6.
N = next less in Table XIV. = 1235 ... 2 1079 = b
R= 44 "
n = next less in Table XV. = 38... 5 9 110 = d
r= 6... 7 10
= Molad of first year of
the 68th Cycle.
The next limit less than b + d in Table XV. is 7 9 227, which
belongs to Type 59. This then is the Type to which the 68th Cycle
belongs.
The form of a sixth year in a Cycle of this Type is 3R ; therefore,
the given year 1279 commences with feria 3, Tuesday, and is a Regular
Embolismic year of 384 days. It therefore ends with a Sunday, and
i 7 4 THE JE WISH CALENDAR
the next year commences with a Monday, feria 2. Therefore Nisan
15 in the given year occurs on feria 2 2, or 9 2, = 7 = Saturday.
(2) The year 4372.
H = 4372 = 19 x 230 + 2
N = 4199 . . 1 14 1019 = b.
K= 173
n = 171 . .34 1035 = d.
r= 2 4 19 974 = Molad of Cycle 231.
The given year is the second in a Cycle.
The next less limit is 4 18 23, Type 36. The form of a second
year in a Cycle of this Type is 2a ; the given year commences with a
Monday and has 355 days. It therefore ends with a Friday, and the
next year commences with feria 7. Nisan 15 in 4372 occurs on feria
7 2, or Thursday.
(3) The year 5665 = 19 x 298 + 3.
H = 5665
N = 5434 . . 1 10 814 = b.
E= 231
n = 228 . .4 6 660 = d.
r = 3 5 17 394 = Molad of Cycle 299.
The given year is the third in a Cycle.
The next less limit is 5 9 227, Type 43. The form of a third
year in a Cycle of this Type is 7 A. The year begins with a Saturday,
has 385 days, and ends with a Friday. The next year begins with a
Saturday, and Nisan 15 in 5665 is on feria 7 2, or Thursday.
CHAPTER VII
JEWISH FASTS AND FESTIVALS
83. One of the leading features of the Jewish Law is the strict
observance demanded for the seventh day. It is to be a Sabbath, or
Day of Best from work of every kind. Brief reference was made to
this in Article 49, page 67.
It is impossible to determine with any positive accuracy whether
one day in seven was or was not observed by the Patriarchs. Some
consider that the " sanctification " of the day mentioned in Genesis ii.*
is only proleptic, or in anticipation, and is therefore to be understood
of the Sabbath which was afterwards enjoyed. This is supposed to be
the case because it is never mentioned during the time covered by
the patriarchal narrative. This, however, is but negative evidence,
and is no proof of the non-existence of the Sabbath as an institution
from the earliest times, any more than against its existence during the
four hundred and forty years from the time of Moses to that of David
during which, also, it is not mentioned.
The first actual record of the institution of the day as one to be
kept holy by the Israelites is in Exodus xvi. 22-30, in connection with
the gathering of manna. But, in that passage, Moses seems to speak
as though the institution had been previously made, and as though it
were already clearly known and recognised: "This is that which the
Lord hath said, To-morrow is the rest of the holy sabbath unto the
LORD." Others think there is reason for believing that " the statute
and ordinance " which God made, when He proved the people by the
* Genesis ii. 3. "And God Blessed the seventh day and sanctified it: because that in
it He had rested from all His work which God created and made."
J 7 6 THE JEWISH CALENDAR
waters of Marah, were with respect to the observance of this day,
Exodus xv. 25.
In the Fourth Commandment, which was given shortly after the
event at Marah, the ordinance is set forth distinctly, Exodus xxi. 8-11 ;
the reason there assigned for it being that "in six days the LORD made
heaven and earth, the sea, and all that in them is, and rested the
seventh day : wherefore the LORD blessed the seventh day and
hallowed it." When Moses, not long before his death, called all
Israel together, and rehearsed to them the statutes and judgments of
the LORD, he did not repeat this reason for the commandment, but
substituted the words, " Remember that thou wast a servant in the
land of Egypt, and that the LORD thy God brought thee out thence
through a mighty hand and by a stretched out arm, therefore the
LORD thy God commanded thee to keep the sabbath day,"
Deuteronomy v. 15.
84. We may gather from other passages in the Old Testament of
what kind were the provisions and penalties made respecting the
abstinence from labour. There are many such passages, but it is not
necessary to refer to more than a few of the most striking.
1. It was forbidden to do any work therein, and the penalty for
transgression was death.
Exodus xxxv. 2. " Whosoever doeth work therein shall be put to
death." We have an instance of the way in which this law was
carried into effect, Numbers xv. 32 : " And while the children of Israel
were in the wilderness, they found a man that gathered sticks upon
the sabbath day. And all the congregation brought him without the
camp, and stoned him with stones, and he died : as the LORD
commanded Moses."
2. No fire might be lighted.
Exodus xxxv. 3. "Ye shall kindle no fire throughout your
habitations upon the sabbath day."
3. No burden might be carried.
Jeremiah xvii. 21. "Thus saith the LORD : Take heed to yourselves
and bear no burden on the sabbath day, nor bring it in by the gates
of Jerusalem. Neither carry forth a burden out of your houses on the
sabbath day, neither do ye any work, but hallow ye the sabbath day,
as I commanded your fathers."
4. It was forbidden to buy or sell goods.
THE JEWISH CALENDAR 177
Neherniah x. 31. "If the people of the land bring ware or any
victuals on the sabbath day to sell, that we would not buy it of them
on the sabbath, or on the holy day."
Ib. xiii. 15. "In those days saw I in Judah' some treading wine-
presses on the sabbath, and bringing in sheaves, and lading asses ; as
also wine, grapes, and figs, and all manner of burdens, which they
brought into Jerusalem on the sabbath day : and I testified against
them in the day wherein they sold victuals."
5. Travelling was forbidden.
Exodus xvi. 29. " Abide ye every man in his place, let no man go
out of his place on the seventh day. So the people rested on the
seventh day."
The Jews were not permitted to make a journey on the Sabbath,
or on any of the great festivals which were kept as Sabbaths. The
distance that it was lawful to travel is not mentioned by Moses, but
it was considered by the Rabbins that it must never exceed two
thousand cubits, about seven hundred and fifty paces, or two-thirds of
a mile. Josephus, "Antiquities," xviii. cap. viii. 4, " Nor is it lawful
for us to journey, either on the sabbath day, or on a festival day."
Reference to this rule is made by Christ in His address to His
Apostles, S. Matthew xxiv. 20, " Pray that your flight be not in the
winter, neither on the sabbath day." It was usual to close the gates
of the cities and towns on this day, so that Christ might have had in
view the actual impediments that would have to be encountered if the
flight were on the Sabbath ; cf. Nehemiah xiii. 19 : " And it came to
pass, that when the gates of Jerusalem began to be dark before the
sabbath, I commanded that the gates should be shut, and charged that
they should not be opened till after the sabbath."
On the other hand, a blessing was promised to those who duly
observed the Sabbath.
Isaiah Iviii. 13, 14. "If thou turn away thy foot from the sabbath,
from doing thy pleasure upon My holy day ; and call the sabbath a
delight, the holy of the LORD, honourable ; and shalt honour Him, not
doing thine own ways, nor finding thine own pleasure, nor speaking
thine own words ; Then shall thou delight thyself in the LORD ; and I
will cause thee to ride upon the high places of the earth, and feed thee
with the heritage of Jacob thy father : for the mouth of the Lord hath
spoken it."
In Ezekiel xx. 12-24, the pollution of the Sabbath is described as
13
i 7 8 THE JEWISH CALENDAR
one of the great national sins which brought the wrath of God upon
the people. In verse 15 it is set down as one of the reasons why those
who rebelled in the wilderness were not allowed to enter the promised
land.
85. From the time when Nehemiah, after the return from the
Captivity in Babylon, " made a sure covenant, and wrote it, and the
princes, Levites, and priests set their seal unto it " (Nehemiah ix. 38),
from that time forward the Sabbath was most strictly observed. The
national sin, in this respect was eliminated. There was indeed one
sad exception in the apostacy, when " Wicked men went out of Israel,
who persuaded many, saying, Let us go and make a covenant with the
heathen that are round about us " [the Greeks under Antiochus
Epiphanes], 1 Maccabees i. 11 ; and when, six years later, Antiochus
in the hundred forty and third year of the kingdom of the Greeks,*
went up against Jerusalem, and defiled the sanctuary, and two years
afterwards burnt the city, so that " her feasts were turned into
mourning, her sabbaths into reproach, her honour into contempt,"
1 Maccabees i. 39. Yet even in this time of woe and desolation there
were many in Israel who remained faithful, " who were fully resolved
and confirmed in themselves, not to eat any unclean thing. Where-
fore they chose rather to die, that they might not be defiled with
meats, and that they might not profane the holy covenant : so then
they died," 1 Maccabees i. 62, 63.
The Sabbath was then, indeed, so scrupulously observed by the
faithful, that they would not even defend themselves from their
enemies on that day ; and we are told in 1 Maccabees ii. 34-38, as well
as by Josephus, " Antiquities," xii. cap. vi. 2, that "there were about
a thousand with their wives and children, w r ho were smothered and
burnt in certain caves to which they had fled, without resistance, and
without so much as stopping up the entrances into the caves. They
avoided to defend themselves on that day, because they were not
willing to break in upon the honour they owed the sabbath, even in
such distresses, f or our law requires that we rest upon that day."
Mattathias the Hasmonaean, the father of the great Judas who was
called Maccabaeus, decreed, in consequence of this event, that it was
lawful to fight even on the Sabbath. He told his followers " that
unless they would do so they would become their own enemies, by so
* Era of the Seleucidse, B.C. 170.
THE JEWISH CALENDAR 179
rigorously observing the law, while their adversaries would still
assault them on this day, and they would not then defend themselves,
and that nothing could then hinder but they all must perish without
fighting," "Antiq.," xii. cap. vi. 2. ''At that time therefore they
decreed saying, Whosoever shall come to make battle with us on the
sabbath day, we will fight against him : neither will we die all, as our
brethren that were murdered in the secret places," 1 Maccabees ii. 41.
86. Josephus tells us that in later times it was usual to spend the
'Sabbath day in the study of the Law, When Herod and Agrippa
were in Ionia, Nicolaus pleaded before them for the privileges of the
Jews, and said in the course of his speech, " The seventh day is set
apart from labour ; it is dedicated to the learning of our customs and
our laws, we thinking it proper to reflect on them as well as on any
[good] thing else, in order to our avoiding of sin," "Antiquities," xvi.
cap. ii. 3. In fact, from the time when the New Testament history
opens the strict observance of the Sabbath had become one of the
Jewish characteristics, so that in whatever country a Jew might be
found his nationality could be recognised by this alone.
Hospitality was encouraged on the Sabbath day. Indeed it was
not unusual for rich men to give a dinner upon the day ; but every-
thing had to be eaten cold, since nothing might be cooked upon
a Sabbath. It was such a feast that was attended by our Lord,
" when He went into the house of one of the chief Pharisees to eat
bread on the sabbath day," S. Luke xiv. 1. Nehemiah expressly
desired the people not to mourn and weep, but " Go your way, eat the
fat, and drink the sweet, and send portions unto them for whom
nothing is prepared : for this day is holy unto the Lord : neither be ye
sorry ; for the joy of the LOED is your strength," viii. 10.
Josephus, in the "Wars of the Jews," iv. cap ix. 12, speaks of the
.announcement of the beginning and ending of the Sabbath by the
sounding of a trumpet. This ceremony is not mentioned elsewhere.
He had been narrating the methods adopted by the Zealots against
Simon, during the sedition and civil war when Vespasian was pre-
paring to besiege the city. He says, " The Zealots threw their darts
easily from a superior place, and seldom failed of hitting their
enemies ; but having the advantage of situation, and having withal
erected four very large towers aforehand, that their darts might come
from higher places, one at the north-east corner of the court, one
i8o THE JEWISH CALENDAR
above the Xystus, the third at another corner, over against the lower
city, and the last was erected above the top of the Pastophoria, where
one of the priests stood, and gave a signal beforehand, with a trumpet
at the beginning of every seventh day, in the evening twilight, as also
at the evening when that day was finished, as giving notice to the
people when they were to leave off work, and when they were to go-
to work again."
Whiston, in his note upon this passage, vol. iv. p. 112, says that
Reland's conjecture here is not improbable that this was the very place
that has puzzled our commentators so long, called "Musach Sabbati,"
the " Covert of the Sabbath," if that be the true reading of 2 Kings
xvi. 18, "And the covert for the sabbath that they had built in the
house, and the king's entry without, turned he from the house of the
LORD for the king of Assyria"; because here the appointed priest
stood under a "covering" to proclaim the beginning and ending of
every Jewish Sabbath.
87. In addition to specifying especially the seventh day as a Day of
Best, the word Sabbath is also used for all the Jewish Feasts and Fasts
upon which work was forbidden. Thus :
Leviticus xix. 3. "Ye shall fear every man his father and his
mother, and keep my sabbaths," and verse 30, " Ye shall keep my
sabbaths, and reverence my sanctuary."
Leviticus xvi. 30, 31. " That day (the Day of Atonement), shall be
a sabbath of rest unto you, and ye shall afflict your souls by a statute
for ever." Also xxiii. 32.
Leviticus xxiii. 24. " In the seventh month, in the first day of the
month (Tishri 1), shall ye have a sabbath, a memorial of blowing of
trumpets, an holy convocation."
From the fifteenth day of the same month to the twenty-second,
inclusive, was the Feast of Tabernacles; "On the first day shall
be a sabbath, and on the eighth day shall be a sabbath," Leviticus
xxiii. 39.
88. THE FEASTS OF THE NEW MOONS.
Rosh-chodesh, or Renewal of the Month. On the first day of every
month the New Moon is celebrated with great ceremony, in accordance
with the Mosaical law, though these Festivals are not enumerated
among the days of solemn Feasts in Leviticus xxiii. In fact, the days.
of New Moon are not mentioned at all in that Book, or in Exodus, or
in Deuteronomy. Reference is, however, made to them in Numbers,
and frequently in other parts of the Scriptures. From the fact of their
being generally mentioned specifically it would seem that they were
distinguished from the other Feasts, and from the Sabbaths. Thus, in
1 Chronicles xxiii. 31, " And to offer all burnt sacrifices unto the LORD
in the sabbaths, in the new moons, and on the set feasts by number."
So also 2 Chronicles ii. 4, " . . . for the burnt offerings morning and
evening, on the sabbaths, and on the new moons, and on the solemn
feasts of the LOUD our God." They are separately mentioned in the
same way in 2 Chronicles viii. 13 and xxxi. 3 ; Ezra iii. 5 ; Nehemiah
x. 33 ; Isaiah i. 13, 14 ; Ezekiel xiv. 17 ; Hosea ii. 11, and elsewhere.
S. Paul recognises that there is a distinction, "Let no man judge
you in respect of an holy day, or of the new moon, or of the sabbath
days," Colossians ii. 16.
With respect to the ceremonies upon these days, they were
1. The sounding of trumpets. Numbers x. 10. " In the beginnings
of your months ye shall blow with the trumpets over your burnt
offerings, and over your peace offerings that they may be to you a
memorial before your God."
Psalms Ixxxi. 3. " Blow up the trumpet in the new moon, in the
time appointed, and on our solemn feast day."
Isaiah x. 10. " In the beginnings of your months ye shall blow with
the trumpets over your burnt offerings."
Cf. also 1 Samuel xx. 5 ; 2 Chronicles ii. 4 ; Ezra iii. 5 ; Nehemiah
x. 33.
2. Additions to the daily sacrifice were made, namely, two young
bullocks, a ram, and seven lambs, as a burnt offering, a kid as a sin
offering, with wine, and flour mingled with oil. Numbers xxviii. 11-15.
3. The purchase and sale of merchandise was stopped, as upon the
Sabbath.
Amos viii. 5. " When will the new moon be gone, that we may sell
corn?"
It would appear that it was customary for the people to attend the
service in the Temple, and to receive instruction in their religion and
laws from their prophets and teachers, for we read, in 2 Kings iv. 23,
that when the Shunammite was about to visit Elisha her husband
asked her, " Wherefore wilt thou go to him to-day? It is neither new
moon nor sabbath."
1 82 THE JEWISH CALENDAR
Isaiah Ixvi. 23. " And it shall come to pass that from one new moon
to another, and from one sabbath to another, shall all flesh come to-
worship before Me, saith the LORD."
Ezekiel xlvi. 3. " Likewise the people of the land shall worship at
the door of this gate before the LORD, in the sabbaths and in the new
moons."
89. The manner in which the day of New Moon, so called, was
determined by actual observation, and then consecrated, has been
described in Article 7, page 10. Although Hillel II. in A.D. 358 had
made known the method of Astronomical computation, yet the
custom of watching the heavens for the first appearance of the
crescent was retained for many years, and the New Moons were
announced as heretofore, messengers being dispatched to carry the
information. Special permission was given to these messengers to
break the law concerning the limit of a Sabbath-day's journey with
respect to the months Tishri and Nlsan, the most important as regards
the Festivals. It is reported that on a certain occasion Rabbi Akiba,
kept back no less than eighty messengers at Lydda, on account of the
Sabbath day, to the great indignation of Gamaliel II.
Those who lived in the neighbourhood of the Holy City kept the
celebration during one day ; but those who lived farther off, in places
which could not be reached by messengers, observed two days on certain
occasions, namely, the last day of every month which had thirty days,
as well as the first day of the next month.*
Maimonides says t that there were six months of which the New
Moons were indicated by messengers :
Nisan on account of the Passover.
Abh ,, ,, Fast for the destruction
of the Temple.
Elul New Moon of Tishri.
Tishri ,, Feast of Tabernacles.
Kislew ,, ,, Feast of Purification.
Adhar ,, ,, Purim.
* Horace refers to this custom in Sat. i. 9 :
" Memini bene ; sed meliore
Tempore dicam : hodie tricesima Sabbata : vin' tu
Curtis Judeeis oppedere ? "
t " Kiddusch hachodesch," cap. 3.
THE JEWISH CALENDAR 183
While the Temple was standing lyar was added on account of the
Second Passover, which those who were unable to keep the Feast on
Nisan 15 were allowed to celebrate on lyar 15.
The following are the months which have two Rosh-chodesh,
namely, their own first day, and the last day of the preceding month :
Marheshwan, in all years.
Kislew, in Abundant years, both Common and Embolismic.
Tebeth, in Regular and Abundant years, both Common and
Embolismic.
Adhar I., in Embolismic years.
Adhar II., in all years.
lyar, in all years.
Tammuz, in all years.
'Elul, in all years.
The five months Tishri, Schebhat, Nisan, Siwan, andAbh have only
one Rosh-chodesh.
90. The reason why two Rosh-chodesh were observed for certain
months, as explained by al-Blruni,* Lazarus Bendavid,t and Lindo,t
was this : A mean Lunar month, by Jewish Astronomical computation,
consists of 29d. 12h. 793ch., so that a Civil month of twenty-nine days
is 12h. 793ch. shorter, while one of thirty days is llh. 287ch. longer
than a Lunation. If, then, a Civil month has thirty days, these
llh. 287ch. really belong to the Lunar month which follows it, and
this part of a day ought to be observed as part of the first actual
twenty-four hours of the Lunation ; but it is contrary to principle to
keep a holy day during part only of a day, therefore the whole of the
thirtieth day must be kept. Again, the remaining 12h. 793ch. of the
first actual twenty-four hours of the Lunation fall within the first day
of the next Civil month ; these hours must be kept sacred ; and, for the
same reason that the whole of the thirtieth day is kept, the whole of
the first day is kept also.
Another cause for assuming the two Rosh-chodesh, especially after
the method of Astronomical computation had come into use, would be
the scrupulous anxiety of the Jews to fulfil the Law. The observance
of the New Moons was required, and if any error had crept into the
computation by which the day was determined, the observance of two
days would tend to its elimination.
* P. 156. t P. 11, 2. J P- 6-
184 THE JEWISH CALENDAR
In this connection an extra day is allotted to certain of the
Festivals.
Tishri 1 and 2 are both observed as Bosh Ha-schanah, the Com-
mencement of the year.
Tishri 15 and 16, as Succoth, or the Feast of Tabernacles.
Tishri 22 and 23. Feast of the Eighth day ; but the second day is
called the Feast of the Law.
The Passover has eight days in all, instead of seven, Nisan 15 to 22
inclusive.
Siwan 6 and 7 are both kept as Schabuoth, the Feast of Weeks.
This custom has existed since the time of the Babylonish Captivity,
and is still practised by the strict Jews. In the reformed Synagogue
the Festivals are observed upon one day only.
91. A detailed list of the days observed in each month of the Jewish
year will now be given.
All the Hebrew Sabbaths, Festivals, and Fasts commence in the
evening which precedes the midnight from which the corresponding
Christian Civil day begins.
TISHRI.
The first month of the Civil Year. The seventh month of the
Sacred or Religious year. The Sabbatical year, and the year of
Jubilee, both commence with this month.
Tishri has 30 days in all years.
Day of the
month.
1 and 2. Rosh Ha-schanah, " Caput Anni," or New Year. The first
and second days of this month are treated as though they were
but one day. In their combination they are termed " Yorna
Arichta," that is, " A day lengthened out," or "A long day."
Both days are kept with equal solemnity.
The Feast of Trumpets. Leviticus xxiii. 24, 25. "In the
seventh month, in the first day of the month, shall ye have a
sabbath, a memorial of blowing of trumpets, an holy convo-
cation. Ye shall do no servile work therein, but ye shall offer
an offering made by fire unto the LORD." Cf. also Numbers
xxix. 1-6 ; Ezra iii. 1 ; Nehemiah vii. 2, 9.
THE JEWISH CALENDAR 185
Day of the
month.
This Feast differed in several respects from the ordinary
Festivals of the New Moon. In addition to the usual daily
sacrifices, and to those which were offered at the celebration of
every New Moon, namely, two young bullocks, one ram, seven
lambs of the first year, and a kid,* it appears from Numbers
xxix. 1-6, that the latter offerings were doubled with the
exception of one bullock.
This was one of the seven days of Holy Convocation, Leviticus
xxiii. 24 ; the other six being Tishri 10, Tishri 15, Tishri 22,
Nisan 15, Nisan 21, and Siwan 6.
On ordinary occasions trumpets were blown in the Temple at
the time when the sacrifices were offered, but this was to be
" a day of blowing of trumpets," Numbers xxix. 1. There were
trumpets of two kinds, the straight and the ram's horn. The
former were used in the Temple only, but it was lawful for any
one, even for a child, to blow the ram's horn during this festival
unless it happened to fall upon the Sabbath day ; in that case,
the trumpets were blown in the Temple only.f
It was upon this day, according to tradition, that Abraham
prepared to offer his son Isaac for a burnt offering, Genesis
xxii. 2.
Theodoret, Comment, in Leviticus, Quoestio xxxii., says that
the feast was kept in commemoration of the thunder and
lightning on Mount Sinai at the giving of the Law.
The Rabbins have taught that upon these two days God
judges all men with respect to their actions during the past year,
and disposes the events of the year which is commencing.
Hence, these days have been called Days of Judgment, Days
of Remembrance, Days of Tribulation, Days of Penitence, and
Terrible days.
3. Fast of Guedaliah. In memory of his slaughter, and that of
the Jews who were with him at Mizpah, by Ishmael, " of the
seed royal." After King Zedekiah had been blinded and carried
away to Babylon, Guedaliah was appointed by Nebuchadnezzar
to rule over the people that were left in the land. Josephus
describes him as being of a kind and gentle disposition. He was
* Numbers xxviii. 11-15. f Maimonides, "R&sh Ha-schanah," bk. iv. 1.
1 86 THE JEWISH CALENDAR
Day of the
month.
warned by Johanan and others that Ishmael had been sent by
Baalis, King of the Ammonites, to kill him in order that
Ishmael himself, who was of the royal family, might rule in
Israel. He did not believe what they said, and was slain by
Ishmael and ten men who were his accomplices, after a great
feast at which he had entertained them ; 2 Kings xxv. 22-26 ;
Jeremiah xli. 1-3; Josephus, "Antiquities," x. cap. ix. 2, 3.
Al-Blruni says that Guedaliah was killed, together with
eighty-two people who were with him, in a cistern in which
the water collected until it rose above their heads.*
If this Fast fall upon the Sabbath, which will be the case
when Tishri falls upon a Thursday, it is observed on the
following day.
It appears from Megillath Ta'anith (see post, Article 115,
Day xvii.), that in the time of the Hasmonseans, Tishri 3 was
appointed to be a semi-festival on account of the suppression of
the Divine name from official documents.
7. Fast for the Golden Calf which the people compelled Aaron
to make in Horeb, when Moses was in the Mount. Exodus
xxxii. 1-35 ; Deuteronomy ix. 12-21 ; Nehemiah ix. 18 ;
Psalms cvi. 19.
10. Fast of Kippur, called also Ashura. The great day of
Atonement, or Expiation. One of the days of Holy Convocation.
The Fast commences half an hour before sunset on the evening
of the ninth day, and lasts till half an hour after sunset on the
tenth. It is sometimes called the White Fast. It is observed
in commemoration of the day upon which Moses came down
from Mount Sinai with the renewed Tables of the Law, after he
had obtained pardon for the sin of the Israelites in making and
worshipping the Golden Calf. The Fast was instituted that
atonement might be made for all the sins committed during the
past year, from the High Priest down to the humblest of the
people.! The account is given in Leviticus xvi. 29, xxiii. 27 ;
and Numbers xxix. 7.
* " Vestiges," p. 269.
t Al-Blrftni, p. 270, says sins " committed by mistake," as opposed to wilful sin.
THE JEWISH CALENDAR 187
Day of the
month.
Fasting upon this day is observed with the utmost strictness.
It is obligatory, while all other Fasts are voluntary. It is kept
as a Sabbath, or day of rest ; it is not lawful to wash, to anoint
oneself with oil, even to put on leather shoes. Women who-
have been recently confined, invalids who are dangerously ill,
and children under three years of age, are exempted from
the rule.
In the Talmud, Tishri 10 is called simply "the day." In
Acts xxvii. 9, it is 7j vrjorefa, " the fast " " when sailing was now
dangerous because the fast was now already past." The Rhem&
New Testament * has a marginal note on this passage : "It may
signify the Jews' fast of the seventh month, September, after
which navigation was perilous, winter approaching." So
Elsley, "Annotations," in loco, "This was the great fast of
Expiation." Dean Alford, in loco, says the same, and in his
" Chronology of the Book of the Acts," Prolegomena, ch. i. vi.
he gives the date as A.D. 58, A.U.C. 811. The corresponding
Jewish year, commencing with Tishri, was therefore A.M. 3819,
which was Embolismic. Consequently A.M. 3818 was a
Common year, and had only one Adhar. Therefore Tishri 10
in 3819 must have fallen about the time of the Autumnal
Equinox, when the weather is often stormy, and " sailing was
now dangerous." Dean Alford quotes Vegetius, "De Re Mili-
tari," iv. 39, to show that the usual season for sailing did not as
a rule close so early, "Ex die igitur tertio iduum Novembris
(November 11), usque in diein sextum iduum Martiarum, maria
clauduntur."
It was upon the Day of Atonement that the Scape-goat wa&
sent out into the wilderness, Leviticus xxi. 15, 20, 21. Two
goats were presented to the High Priest, at the door of the
Tabernacle, for a sin offering. He cast lots as to which should
be sacrificed, and which should be set at liberty. The latter,
after certain prayers had been said, and ceremonies performed,,
was charged with all the transgressions of the children of Israel,
was taken to the wilderness by a man appointed for the purpose,,
and was then suffered to escape.
* Fol. Ed. " printed in the year 1737," p. 319.
1 88 THE JE WISH CALENDAR
Day of the
month.
This is the only fast which was actually ordained by Moses.
All the other Fasts were instituted at later times.
15 and 16. Succoth. First and second days of the Feast of Taber-
nacles, or ingathering of harvest. Gk. amivoTriryla. This was
one of the three great Feasts upon which every male of the
children of Israel was commanded to appear before the Lord,
and to make their offerings, Exodus xxiii. 14-17 ; Deuteronomy
xvi. 16, " Three times in a year shall all thy males appear
before the LORD thy God in the place that he shall chose : in the
feast of unleavened bread, and in the feast of weeks, and in the
feast of tabernacles : and they shall not appear before the LORD
empty : every man shall give as he is able."
The Feast was kept in memory of the dwelling in tents in the
wilderness. Leviticus xxiii. 34-43 ; Deuteronomy xvi. 13 ;
Ezra iii. 4 ; Nehemiah ix. 15, 18. Josephus, "Antiq.," iii.
cap. x. 4.
The Feast lasted for seven days, but the first and last days
were the most solemn. The first day, Tishri 15, is a day of
Holy Convocation.
21. Hosana Raba, the Great Hosana. The seventh day of the
Feast of Tabernacles, which now lasts for nine days, the next
two being reckoned as a part of the Feast.
22. Schemeni Azereth. The Feast of Benediction. The day of
Solemn Assembly of the Congregation after the Feast of Taber-
nacles had been kept for seven days. Leviticus xxiii. 36,
" Seven days ye shall offer an offering made by fire unto the
LORD : on the eighth day shall be an holy convocation unto you :
it is a solemn assembly : and ye shall do no servile work
therein." Cf. also Nehemiah viii. 18. This is sometimes
called the Feast of the Eighth Day, i.e., of Tabernacles.
N 23. Simchath Thorah, the Feast of Rejoicing for the Law ; the
ninth day of the Feast of Tabernacles.
30. First Rosh-chodesh of Marheshwan.
THE JEWISH CALENDAR 189.
Day of the
month.
92. MARHESHVVAN.
Second month of the Civil, Eighth of the Sacred year.
It has thirty days in Abundant years : in Regular and Deficient
years it has only twenty-nine.
1. Second day of Rosh-chodesh.
6. Fast of Zedekia. His children were slain in his presence by
Nebuchadnezzar, and his own eyes were then put out ; 2 Kings
xxv. 7 ; Jeremiah xxxix. G, and lii. 10, 11.
30. In Abundant years only, this intercalated day is the first
Rosh-chodesh of Kislew.
93. KISLEW.
Third month of the Civil year ; ninth month of the
Sacred year.
It has thirty days in a Regular and in an Abundant year. It
has only twenty-nine in a Deficient year.
1. Rosh-chodesh. In Abundant years this is the second Rosh-
chodesh of Kislew.
8. Fast on account of the burning of the book written by Baruch
at the dictation of Jeremiah the prophet. Jeremiah xxxvi. 20-25.
20. Day of Prayer for rain.
25. Chanukka. First day of the Feast of the Dedication, or
Purification of the Temple. Lat. Encoenia. This Feast was
instituted by Judas Maccabaeus, and is celebrated for eight days
in honour of the restoration of the Temple after it had been
profaned by Antiochus Epiphanes, A.M. 3632, B.C. 128 ;
1 Maccabees i. 59, Josephus, " Antiq.," xii. cap. v. 4. Antiochus
had taken away all the treasures of the Temple. See post,
Article 115, Megillath Ta'anith, Day vi.
30. Eliminated in Deficient years. In Abundant and Regular
years it is the first Rosh-chodesh of Tebeth.
1 9 o THE JEWISH CALENDAR
Day of the
month.
94. TEBETH.
Fourth month of the Civil, tenth of the Sacred year. It
has twenty-nine days in all years.
1. In Deficient years this month has only one Rosh-chodesh.
In Kegular and Abundant years this day is the second Rosh-
chodesh.
8. Fast on account of the translation of the Holy Scriptures into
the Greek language : the Septuagint version.
Al-Blrunl gives an interesting account of the transaction.*
' ' After Nebukadnezar had conquered Jerusalem part of the
Israelites emigrated from their country, took refuge with the
King of Egypt, and lived there under his protection till the time
when Ptolimaeus Philadelphus ascended the throne. This King
heard of the Thora, t and its divine origin. Therefore he gave
orders to search for this community and found them at last in a
place numbering 30,000 men. He afforded them protection, and
took them into his favour, he treated them with kindness, and
allowed them to return to Jerusalem, which meantime had been
rebuilt by Cyrus, who had also revived the culture of Syria.
They left Egypt, accompanied by a body of his (Ptolimseus
Philadelphus') servants for their protection. The King said to
them : ' I want to ask you for something. If you grant me the
favour, you acquit yourselves of all obligations towards me. Let
me have a copy of your book, the Thora.' This the Jews
promised, and confirmed their promise by an oath. Having
arrived at Jerusalem, they fulfilled their promise by sending
him a copy of it, but in Hebrew. He however did not know
Hebrew. Therefore he addressed himself again to them, asking
for people who knew both Hebrew and Greek, who might
translate the book for him, promising them gifts and presents
in reward. Now the Jews selected seventy-two men out of
their twelve tribes, six men of each tribe, from among the
Rabbis and priests. These men translated the Thora into
Greek, after they had been housed separately, and each couple
had got a servant to take care of them. This went on till they
* " Vestiges," p. 24. f The Books of the Law.
THE JEWISH CALENDAR 19 j
Day of the
month.
had finished the translation of the whole book. Now the King
had in his hands thirty-six translations. These he compared
with each other, and did not find any difference in them, except
those which always occur in the rendering of the same ideas.
Then the King gave them what he had promised, and provided
them with everything of the best. The Jews asked him to
make them a present of one of these copies, of which they
wished to make a boast before their own people. And the King
complied with their wish. Now this is the copy of the Christians,
and people think that in it no alteration or transposition has
taken place. The Jews however give quite a different account,
viz., that they made the translation under compulsion, and that
they yielded to the King's demand only from fear of violence
and maltreatment, and not before having agreed upon inverting
and confounding the text of the book."
Josephus gives very much the same account, though some of
the details are varied.* He quotes a letter from Ptolemaeus to
Eleazar, the High Priest, in which the King expresses a wish to
do what he can for the benefit of the Jews settled in Egypt, and
to obtain for them a copy of the Hebrew Scriptures translated
into Greek. He asks that seventy-two elders may be chosen
out and sent to him for this purpose. Eleazer complied with
the request, and sent the elders with a copy of the Law written
in golden letters, of which " they made an accurate interpre-
tation, with great zeal, and great pains."
In consequence of this translation being made darkness was
spread over the world during three days and nights. The eighth
day of Te"beth was the last of the three dark days, and is
observed as a Fast.
There is some confusion of ideas with respect to this Fast, for
by some authors it is spoken of as a Feast ; thus Philo, who lived
in the first century, in the reign of Caligula, says that down to
his day there was a great annual festival held on the Island of
Pharos, in which not only Jews but others also took part, and
that it was celebrated in honour of the translation, t
Graetz, i., ch. xxiv. p. 530, makes the matter quite clear, and
explains the origin of the different views. " The Greek trans-
* " Antiquities," xii. cap. ii. 5. t "De Vita Mosis," lib.ii.
1 92 THE JEWISH CALENDAR
Day of the
month.
lation of the Torah might be looked upon as a temple erected to
the glory of God in a foreign land. The accomplishment of this
task rilled the Alexandrian and Egyptian Judseans with intense
delight : and they thought, with no little pride, that now the
vainglorious Greeks would at last be obliged to concede that
the wisdom taught by Judaism was at once more elevating and
of more ancient date than the philosophy of Greece. Their
satisfaction was doubtless enhanced by the fact that the noble
work owed in part its successful termination to the warm
sympathy of the friendly King, who then, as it were, opened a
new path for Judaism into Greece. It was natural, therefore,
that great rejoicings should take place among the Egyptian
Judseans on the day of presentation of the version to the King,
and that its anniversaries should be observed as holidays. On
that day it was customary for the Judseans to repair to the
Island of Pharos, where they offered up prayers of joyful thanks-
giving. . . . Later on this anniversary became a national
holiday, in which even the heathen Alexandrians took part.
" But far different was the effect produced by the translation
of the Torah into Greek upon the pious inhabitants of Judaea.
Greece was the object of their hatred on account of the sufferings
they had endured at her hands, and the indignities she had
inflicted upon their sanctuaries ; and they now feared, not
unnaturally, that the Law would be disfigured and perverted
by its translation into Greek. The Hebrew language in w r hich
God had revealed Himself upon Mount Sinai, alone appeared to
them worthy of being the means by which to transmit the
Divine teaching of the Torah. When the Law was presented
in a foreign tongue, the pious Judseans deemed Judaism itself
altered and profaned. Consequently the commemoration of the
translation, which was celebrated as a festival by the Judaeans in
Egypt, was kept by their brethren in Judaea as a day of national
mourning, similar to that upon which the golden calf had been
worshipped in the desert, and the day became numbered amongst
their fasts."
For further information concerning the Septuagint version,
and the traditions connected with it, reference may be made to
Ewald, " The History of Israel," vol. v. p. 249. He shows
that the translation effected under Ptolemy Philadelphus was
THE JEWISH CALENDAR 193
Day of the
month.
confined to the Pentateuch, and perhaps the Book* of Joshua.
The remaining Books of the Old Testament were translated at
a later, unknown time, and by unknown authors.
9. The Fast of Tebeth. The origin is unknown.
10. Fast. Nebuchadnezzar arrived at Jerusalem and commenced
the siege. Asarah Beteketh. 2 Kings xxv. 1, 2, "It came to-
pass in the tenth month, in the tenth day of the month, that
Nebuchadnezzar, king of Babylon, came, he, and all his host,
against Jerusalem and pitched against it ; and they built forts
against it round about. And the city was besieged unto the
eleventh year of king Zedekiah."
95. SCHEBHAT.
Fifth month of the Civil, eleventh month of the Sacred
year. It has thirty days.
1. Rosh-chodesh.
5. Fast for the death of the Elders who were coeval with Joshua,
the son of Nun. Judges ii. 10, " All that generation were
gathered unto their fathers : and there arose another generation
after them, which knew not the LORD, nor yet the works which
he had done for Israel."
15. Laylanot, First day of the new year of trees. See Article
57, p. 94.
23. Fast for the rebellion of the tribe of Benjamin. Judges
xix. 16 to xxi. 24.
30. First Rosh-chodesh of Adhar in Common years.
96. ADHAR I.
The intercalary month in Embolismic years. It has no
number as a month ; that is, it is not called the sixth month of
the Civil year, or the eleventh of the Sacred year. It has thirty
days.
14
i 9 4 THE JEWISH CALENDAR
Day of the
month.
There are no Festivals or Fasts observed in this month.
30. First Rosh-chodesh of Adhar II. in Embolismic Years.
97. ADHAR II., OB ADHAR SHENI.
The sixth month of the Civil year, the twelfth and last of
the Sacred year. This month is the original Adhar, and in
Common years is simply so called. It has twenty-nine days.
1. Bosh-chodesh, second day.
7. Fast for the death of Moses. Deuteronomy xxxiv. 5, 6, " So
Moses, the servant of the LORD, died there in the land of Moab,
according to the word of the LORD. And He buried him in a
valley in the land of Moab, over against Beth-peor ; but no man
knoweth of his sepulchre unto this day."
9. Fast in memory of the schism between the followers of
Shammai and Hillel. Al-Biruni says that 28,000 men were
killed, but this number is a great exaggeration.
Hillel, a Babylonian, was appointed by Herod in the year
B.C. 31 to be one of the presidents of the Synhedrion. He was
born about B.C. 75, and traced his descent on the mother's
side from the house of David. He was distinguished for
extraordinary gentleness, and for a profound trust in God, that
never wavered in the midst of trouble. The presidency of the
Synhedrion became hereditary in his family during four gene-
rations. The second place of honour, that of deputy to Hillel,
was given, at Herod's request, to Menahem, an Essene. He
soon withdrew in favour of Shammai, who was strict even to
excess in his religious observances.
The two Synhedrists, Hillel and Shammai, founded separate
schools, opposed to one another in many religious, social, and
judicial questions.* Graetz says nothing of the warfare which,
according to al-Btruni occurred between their respective fol-
lowers. The latter may perhaps refer to the subsequent strife
of the Zealots Kannaim a religious faction of whom Zadok,
of the school of Shammai, was the head.
* Graetz, vol. ii. pp. 96, 100, 131.
THE JE 1 1 7.S // CALENDAR 1 95
Day of the
month.
13. Thanith Esther. Fast of Esther. Esther iv. 16 and ix. 31.
Josephus, "Antiq.," xi. cap. vi. 8,9, "Esther sent to Mordecai
[to desire him] to go to Shushan, and to gather the Jews that
were there together to a congregation, and to fast and abstain
from all sorts of food, on her account, and [to let him know that]
she with her maidens would do the same. . . . Accordingly,
Mordecai did as Esther had enjoined him, and made the people
fast."
If the thirteenth be a Sabbath this Fast is kept on the
eleventh day.
14. Purim. The Feast of Lots. In memory of the deliverance of
the Jews from 4he plot of Hainan. Esther iii. 7, and ix. 24.
Haman, the Agagite, the enemy of the Jews, had devised a plan
for their destruction, and had cast lots, that is, Pur (a Persian
word), "to consume them and to destroy them." These lots
were cast by Haman in the first month of the year, and the lot
fell upon the twelfth month as favourable for his design. The
Jews therefore had time to prepare, and by help of Esther to
remove the bad impressions against them which had been raised
in the mind of Ahasuerus. It was upon Adhar 14 that the Jews,
led by Mordecai, smote their enemies and the ten sons of
Haman. Esther ix. 5-17.
15. Schuschan Purim. The second Purim ; the feast was kept at
Susa on the day after Adhar 14. Esther ix. 18.
On this day the half-shekel, payable by every Israelite, was
collected in the cities ; but on the twenty-fifth day in the
Temple. Exodus xxx. 13, " This they shall give, every one
that passeth among them that are numbered, half a shekel, after
the shekel of the sanctuary : an half shekel shall be the offering
of the LORD."
98. NISAN.
The seventh month of the Civil year, the first of the
Sacred year. It has thirty days.
1. Kosh-chodesh.
196 THE JEWISH CALENDAR
Day of the
month.
2. Fast for the sons of Aaron, Nadab and Abihu, who " died
before the LORD, when they offered strange fire before the
LORD in the wilderness of Sinai," Numbers iii. 4, and xxvi. 61.
The story of the offering of strange fire is told in Leviticus x. 1-7.
10. Fast for the death of Miriam, the sister of Moses and Aaron,
Numbers iii. 4.
The lamb of the Passover selected, and " kept up until the
fourteenth day," Exodus xii. 3, 6.
In the year when the Israelites were delivered from the
Egyptian bondage, this tenth day of Nisan fell upon the Sabbath.
The Sabbath next before the Passover is, upon that account,
called the Great Sabbath, and it is lawful to select the lamb for
the Paschal service even on the Sabbath day, should the 10th of
the month fall upon such a day, because the day of the month
when this was to be done is precisely specified,* without
reference to the fact that the tenth may be a Sabbath.
14. The Eve of the Passover. The lamb is slain and eaten in the
evening. Exodus xii. 2-10, Leviticus xxiii. 5, Josephus,
" Antiq." iii. cap. x. 5.
15. Pesach. The first day of the Feast of the Passover. First
Day of Unleavened Bread. In the New Testament it is called
?j IO/OTTJ TWV a^vfjunv, and the days from the fourteenth to the
twenty-first inclusive, i^ipai TUV au/uwv.
The feast was instituted to commemorate the deliverance of
the Israelites from their bondage in Egypt, with special reference
to the fact that when the angel of the Lord smote all the first-
born in Egypt, he passed over the dwellings of the Israelites,
the two sides being sprinkled with the blood of the lamb.
Exodus xii. 3-20, xiii. 6; Leviticus xxiii. 6. Josephus,
"Antiq." iii. cap. x. 5.
The modern Jews do not continue the actual sacrifice of the
Paschal lamb, which is represented in their service by the
roasted shankbone of a lamb.
* Maimonides, " Tractatus de Sacrificio Paschali," De Veil, trans, i. 19. p. 9. "Jam victima
paschalis ut sabbato consecraretur, concessum erat, quod huic.sacrificio dies status esset:
similiter nihil erat, cur suum quisquam solemne sacrum ipso die festo cousecrare religion!
haberet."
THE JEWISH CALENDAR 197
Day of the
month.
The Samaritans alone observe the rite according to the
ancient ceremonial. The High Priest, now resident at Nablus,
on the site of the ancient Samaria, performs the sacrifice.*
The Passover was one of the three great Feasts at which every
male was to appear before the Lord. Deuteronomy xvi. 16.
See Tishri 15 and 16, Succoth and Siwan 6, Schabuoth.
The Jews who do not dwell in Palestine add an additional day
to the seven between Nisan 15 and 22, in order to ensure that
all, throughout the world, should keep the festival at the same
time. The first two and the last two days are kept as Holy
Days of Solemn Assembly.
16. The second day of the Passover. The first sheaf of barley
harvest, gathered after sunset on the previous evening, to be
offered before the LOKD. This rite was instituted before the
Israelites had reached the promised land, but it was not to be
actually celebrated until they had come thither. Leviticus
xxiii. 10, 11. Josephus, " Antiq.," iii. cap. x. 5. See
Article 10, p. 13.
From this day commences the Sephira, or counting the days
of the Omer, the seven weeks which elapse between the Passover
and the Feast of Weeks, or Pentecost. No marriages are per-
formed during these days, except on the thirty-third day. See
lyar 18, Lag b'Omer. A special prayer is said in the evening
of Ntsan 16, and is continued throughout the fifty days, with a
declaration of the number of the day as it stands in the
numerical order of the fifty.
17-20. Third, Fourth, Fifth, and Sixth days of Unleavened Bread.
21. The last day of Unleavened Bread. A day of Holy Convoca-
tion. Exodus xii. 16, " In the first day there shall be an holy
convocation, and in the seventh day there shall be an holy
convocation to you ; no manner of work shall be done in them,
save that which every man must eat, that only may be done
by you."
* Jewish Year Book, 5659, A.D. 1898, pp. 285, 292.
198 THE JEWISH CALENDAR
Day of the
month.
22. Eighth day of the Passover. This is the additional day
observed by the Jews " of the exile," or those who dwell outside
of Palestine.
26. Fast for the death of Joshua, the son of Nun. Joshua xxiv. 29.
30. First Rosh-chodesh of lyar.
99. IYAR.
Eighth month of the Civil, second month of the Sacred
year. It has twenty-nine days.
1. Second Rosh-chodesh.
7. If the 7th be a Monday it is observed as the First Fast of
lyar : a Fast of three days for any wrong done during the Feast
of Passover. The three days are the Monday, the following
Thursday, and the next Monday. If lyar 7 be not a Monday,
then the Fast is kept in a similar way, but its first day is the
Monday next after the 7th. Thus, in the year 5659, A.D. 1899,
the Fast was kept on Monday, lyar 7 = April 17. In the
preceding year it was Monday, lyar 10 = May 2.
10. Fast for the death of the High Priest Eli, and for the loss
of the Ark which was taken by the Philistines. 1 Samuel iv.
11-18.
14. Pesach Scheni. Second Passover, ordained for those who,
through uncleanness or from other causes, are prevented from
keeping the Feast at the proper time in the month Nlsan. See
Article 115.
18. Lag b'Omer. Feast of the thirty-third of the Omer, reckoned
from Nisan 16, the second day of the Passover inclusive.
Ideler states* that an old tradition belongs to this day
concerning the pupils of the Rabbi Akiba, but he does not
narrate it.
* " Handbuch," i. 566.
THE JEU'ISH CALENDAR 199
Day of the
month.
The tradition is that a great mortality broke out among the
pupils of the Rabbi, on the first day of the Orner, and that it
ceased on this thirty-third day. Many of the stricter Jews
retain the custom of not cutting the hair during these days
to mark the mourning for the disciples of Akiba. He lived
in the second century of the Christian Era. He was put to
death with the most cruel torture by Turnus Kufus, the Governor
under the Emperor Hadrian, in or about A.D. 139. Graetz says *
that " the number of his hearers is exaggerated by tradition,
which recounts them as twelve thousand, and even double that
number ; but a more modest record represents them as amounting
to three hundred." He was one of the first compilers of the
Mishna, was considered the head of the spiritual regeneration of
Judaism, and was honoured as a legendary second Moses, t
28. Fast for the death of the prophet Samuel. 1 Samuel xxv. 1.
100. Si WAN.
Ninth month of the Civil, third of the Sacred year. It has
thirty-one days.
1. Bosh-chodesh.
4, 5. Sanctification of the people before the Giving of the Law.
Exodus xix. 10, 11, " And the LORD said unto Moses, Go unto
the people and sanctify them to-day and to-morrow, and let them
wash their clothes, And be ready against the third day."
6. Schabuoth. The Feast of the Congregation, or the Feast of
Weeks, called also Asartha = Pentecost, because it was appointed
to be held seven weeks, a week of weeks, after the Passover,
Exodus xxxiv. 22. It is the fiftieth day after Nlsan 15, therefore
called in Greek ii/mtpa rr\q TrevrrtKotrrri^, the reckoning being from
" the morrow after the Sabbath," Leviticus xxiii. 15, 16, that
is, from the first day of Holy Convocation of the Passover,
* Vol. ii. p. 357.
t " The Emperor Hadrian, 1 ' bv Ferdinand Gregorovicus ; trans, by Mary E. Robinson.
. 145.
200 7 ///; JE 1 1 Y.S7/ c I / LENDAR
Day of the
month.
Nisan 15, inclusive ; the word Sabbath being here used not for
feria 7, but for " a day of rest."
This was one of the three great Festivals at which every male
was to appear before the Lord.
The wheat harvest being now complete, one of the ceremonies
of the day was the offering of two loaves of leavened bread
"made from fine wheat flour, as first fruits unto the LOBD,"
Leviticus xxiii. 17. This bread was eaten in the Temple in the
evening, and nothing of it allowed to remain to the next day.
7. Second day of the Feast. According to the Law the Feast
of the Congregation lasted for one day only, but since the time
of the Babylonish Captivity the Jews in countries foreign to
Palestine have observed it during two days, to meet the
possibility of an error.
22.' Fast in memory of the idolatry and rebellion under Jeroboam
son of Nebat, who made Israel to sin. 1 Kings xii. 26-33,
xiv. 16.
27. Fast for the death of Chananya who was burned with the
scroll of the Law wrapped round him. He was the fourth of
the seven martyrs executed by Turnus Rufus, the Governor,
in the time of Hadrian ; Akiba, previously mentioned, being the
third. This was in or about A.D. 139.*
30. First Rosh-chodesh of Tammuz.
101. TAMMUZ.
Tenth month of the Civil, fourth of the Sacred year. It has
twenty-nine days.
1. Second Rosh-chodesh.
17. Scheba asar bethamuz. The Fast of Tammuz, kept in
memory of five great misfortunes, though they did not all
occur upon this day.
(1) Moses broke in pieces the first Tables of the Law.
Exodus xxxii. 19.
* Graetz, vol. ii. p. 431.
THE JEWISH CALENDAR 201
Day of the
month.
(2) Antiochus Epiphanes set up an image, " the abomination
of desolation," upon the altar. 1 Maccabees i. 54. This was
on the fifteenth day of the month Kislew.
(3) The Greeks under Antiochus destroyed the Books of the
Law. 1 Maccabees i. 56.
(4) The lamp which burned day and night in the Temple was
extinguished by King Ahaz. Al-Biruni ascribes this to Abh 28,
"in the days of the prophet Ahaz,"* which, Sachau says,
" seems to be a mistake for Ahaz the King." Gf. 2 Chronicles
xxix. 7, " They have shut up the doors of the porch, and have
put out the lamps, and have not burned incense nor offered
burnt offerings in the holy place unto the Lord God of Israel."
Scaliger, also, gives the day as Abh 28. t
(5) The destruction of the fortifications of Jerusalem when
Nebuchadnezzar besieged the city. This was on the ninth day
of the month at midnight.
If this Fast fall upon the Sabbath it is kept upon the next day.
102. ABH.
Eleventh month of the Civil, fifth of the Sacred year. It has
thirty days.
1. Kosh-chodesh. Fast for the death of Aaron the High Priest.
Numbers xx. 28.
9. Fast of Abh on account of the decree against the Fathers in
the wilderness that they should not enter into the promised
land, Numbers xiv. 23. Cf. Zechariah vii. 5, "When ye fasted
and mourned in the fifth and seventh month, even those seventy
years, did ye at all fast unto Me, even to Me? "
This Fast is still observed. If the ninth day of the month fall
upon the Sabbath, it is kept upon the next day.
On the same day took place the destruction of the first
Temple by Nebuchadnezzar, A.M. 3338, B.C. 422 ; and of the
second Temple by Titus, A.D. 70. It is called the Black Fast.
15. Tubeab. A minor Festival to commemorate the feast at
* " Vestiges," p. 276. f " De Emend. Temp.," lib. vii. p. 651, C.
202 THE JE WISH CALENDAR
Day of the
month.
Shiloh, and the reconciliation of the tribe of Benjamin.
Judges xxi. 13-23.
22. Commemoration of the wood-offering "to burn upon the
altar of the Lord," Nehemiah x. 34 ; xiii. 31. Called Xylophoria
by the Greeks. Josephus, "Wars," ii. cap. xvii. 6, " Now the
next day was the. festival of Xylophoria, upon which the custom
was for every one to bring wood for the altar, that there might
never be a want of fuel for that fire which was unquenchable,
and always burning." (See post, Article 115. Day IV.)
30. First Rosh-chodesh of 'Elul.
103. 'ELUL.
Twelfth month of the Civil, sixth of the Sacred year. It
has twenty-nine days.
1. Rosh-chodesh, second day.
7. Fast for the death of the Spies, who, with the exception of
Joshua and Caleb, brought an evil report of the promised land
to Moses, Numbers xiv. 36-38. Selden * places this Fast on the
seventeenth day of the month. Al-Biruni says that some Jews
place this fast on the Monday or Thursday which falls within the
last seven days before the beginning of the next year." t
According to Jacob ben Ascher this fast should be on 'Elul 17.
In the Megillath Ta'anith, 'Elul 7 is given as a semi-festival in
commemoration of the rebuilding of the Walls of Jerusalem by
Nehemiah. (See post, Article 115. Day II.)
104. In the following Calendar for the months the serial numbers
are given for the days of the years of all six forms. By means of
these numbers the feria for any day of any month may be found, if
the form of the year and the feria for Tishri 1 be known.
For example : Let the year be Common and Deficient, commencing
with a Monday. In such a year Tainmuz 17 has 282 for its serial
number, which = In + 2. The n complete weeks beginning with a
Monday must terminate with a Sunday, feria 1, and feria (1 -I- 2)
= feria 3 = Tuesday.
* " De Anno Civili," 1644, p. 36. f " Vestiges," p. 277.
THE JEWISH CALENDAR
203.
Again : Let the year be Embolismic and Abundant, commencing
with a Thursday. In such a year the serial number for II. Adhar 14
is 193 = In + 4. The complete weeks beginning with a Thursday
terminate with a Wednesday, feria 4 ; and feria (4 + 4) = feria 1
= Sunday.
105. The two Tables which follow the monthly Calendar show the
feriae for the Rosh-chodesh of each month, and for the principal Feasts
and Fasts. Under the headings "Deficient," "Regular," &c., the
leading numbers give the ferise with which each form of year is able
to commence. The remaining numbers in each column show the
feriae for the different days against which they are written.
Thus : If the year be Common and Deficient, and commence with
feria 7, the Fast of Guedaliah will be on feria 2 ; the Rosh-chodesh
of Tebeth on feria 4, &c.
Table XVII. gives the Christian dates for the chief Feasts and
Fasts, governed by that of Nlsan 15.
204
THE JEWISH CALENDAR
TISHRi.
Common Year.
Embolismic.
Def.
Reg.
Ab.
Def.
Reg.
Ab.
1
2
8
4
5
I\6sh-Ha-schana. Feast of Trumpets
Second day of the Feast ,,
2
3
2
3
2
3
2
3
2
3
2
3
4
5
Fast of Guedaliah
5
5
5 5
5
6
7
8
i Fast for the decree against those who made ]
6
6 C) 6
6
6
8
8
8
8
8
8
9
9
9
9
9
9 1 9
10
Ashura = Fast of Kippur. Day of Atonement
10
10
10 10
10
13
11
11
11
11
11
11
11
12
12
12
12
12
12
12
13
13
13 13
13
13
13
14
14
14 14
14
14
14
15
16
17
is
19
20
21
22
Succoth = Feast of Tabernacles = Scenopegia
Second day of the Feast
15
16
17
18
19
20
21
22
15
16
17
18
19
20
21
22
15
16
17
18
1!
20
21
22
15
16
17
18
19
20
21
22
15
16
17
18
19
20
21
22
15
16
17
18
19
20
21
22
Third
Fourth
Fifth
Sixth
Seventh ,, Hoshana Rabba
Schemeni Azereth = Feast of Benediction
23
Sinichath Thorah = Rejoicing for the Law
23
23
23
23
23 23
1M
25
(These eight days are all now reckoned
as forming the Feast of Tabernacles.)
24
25
24
25
24
25
24
25
24 24
25 25
26
26
26
26
26
26 26
27
27
27
27
27
27 27
K
28
28
28
28
28 28
29
30
First Rosh-chodesh of Marheshwan
29
30
29
30
29
30
29
30
29 29
30 30
THE JEWISH CALENDAR
205.
MAR^ESHWAN.
Common Year.
Embolismic.
Def.
Keg.
Ab.
Def.
Beg.
Ab.
1
2
Second Rosh-chodesh
31
32
31
32
31
32
31
32
31
32
31
32
3
33
33
33
33
33
33
4
34
34 34
34
34
34
5
6
7
Fast of Zedekia
35
36
37
35
36
37
35
36
37
35
36
37
35
36
37
88
36
37
8
38
38
38
38
38
38
9
39
39
39
39
39
88
10
40
40
40
40
40
40
11
41
41
41
41
41
41
12
42
42
42
42
42
42
13
43
43
43
43
43
43
*14
44
44
44
44
44
44
15
45
45
45
45
45
45
16
46
46
46
46
46
46
17
47
47
47
47
47
47
18
48
48
48
48
48
48
19
49
49
49
49
49
49
20
50
50
50
50
50
50
21
51
51
51
51
51
51
22
52
52
52
52
52
52
23
53
53
53
53
53
53
24
54
54
54
54
54
54
25
55
55
55
55
55
55
26
56
56
56
56
56
56
27
57
57
57
57
57
57
28
58
58
58
58
58
to
29
30
(Intercalated day, and First Rosh-chodesh |
of Kislew, in Abundant years ...
59
59
59
60
59
59
59
60
2O6
THE JEWISH CALENDAR
KISLEW.
Common Year.
Embolismic.
Def.
Reg.
Ab.
Def.
Beg.
Ab.
1
R6sh-eh6desh. Second day in Abundant years
60
60
61
60
60
61
2
61
61
62
61
61
62
3
62
62
63
62
62
63
4
63
63
64
63
63
64
5
64
64 65
64
64
65
6
65
65
66
65
65
66
7
8
9
' Fast. Yehoyakim burned the book written )
( by the prophet Jeremiah j"
66
67
68
66
67
68
67
68
69
66
67
68
66
67
68
67
68
69
10
69
69 70
69
69
70
11
70
70 71
70
70
71
12
71
71
72
71
71
72
13
72
72
73
72
72
73
14
73
73
74
73
73
74*
15
74
74
75
74
74
75
16
75
75
76
75
75
76
17
76
76
77
76
76
77
18
77
77
78
77
77
78
19
20
21
Prayer for rain
78
79
80
78
79
80
79
80
81
78
79
80
78
79
80
79
80
81
22
81
81
82
81
81
82
23
82
82
83
82
82
83
24
25
26
/ Chanukka = Feast of Purification of the |
Temple = Encoenia )
83
84
85
83
84
85
84
85
86
83
84
85
83
84
a5
84
85
86
27
86
86
87
86 .
86
87
28
87
87
88
87
87
88
29
30
f Eliminated in a delicient year. First R6sh- )
ch6desh of Tebeth in Regular and f-
( Abundant years )
88
~
88
89
89
90
88
88
89
89
90
THE JE WISH CALENDAR
207
Common Year. Kuibolisiuic.
'PTOTlP"rH
1 1 . 1 1 . X 11.
Def.
Beg.
Ab. Def.
Beg.
Ab.
1 I Kosh-chodesh. Second day in Regular 1 ftq
1 and Abundant years I
90
91
91 89
92 90
90 91
91 92
2 90
3 91
92
93 91 92 !3
4 92
,- 'First appearance of the darkness of three) ,..,
( days I
93
94
95
94 92
95 93
96 94
93 94
94 95
95 96
94
7 95
96
97 95
96 97
8 Fast, for Greek translation of the Scriptures 96
97
98 96
97
98
(> 07
( Asarah Beteketh. Fast of Tebeth. Xebn- )
10 -; chadnezzar commenced the siege of - 98
11 ( Jerusalem j QQ
98
99
100
101
99 97
100 98
101 99
102 100
98
99
100
101
99
100
101
102
12 100
13 101
102
103 101
102
103
14 102
103
104 102
103
104
15 103
104
105 103
104
105
16 104
105
106 104
105
106
17 105
106
107 105
106
107
18 106
107 108 100
107
108
19 107
108 109 107
108
109
20 j 108
109
110 108
109
110
21 109 110
111 10'.)
110 111
22 110 111
23 111 112
112 110
113 111
111
112
112
113
24 112 113
114 112
113
114
25 113
114
115 113
114
115
26 114
115
116 114
115
116
27 115 116 117 115
116
117
28 ' 116 117
118 116
117
118
29 117 11H
119 117
11H
119
208
THE JE WISH CALENDAR
SHEBHAT.
Common Year.
Embolisiuic.
Def.
Reg. Ab.
Def. Reg.
Ab.
1
2
Rosh-chodesh
118
119
119 120
120 121
118 119 120
119 120'. 121
3
120
121 122
120 121 122
4
121
122 123
121 122 12:5
5
Death of the Fathers in the time of Joshua
122
123 124
122 l'2:-5 124
6
123
124 125
123
124 1-2--,
7
124
125
126
124
125 1-2IV
8
125
126
127
125
126
127
9
126
127
128
126
127
12s
10
127
128
129
127
128
1-2'.}
11
128
129
130
128
129
130
12
129
130
131
129 130
131
13
130
131
132
130 ' 131
132
14
15
16
( R6sh-Ha-shana = Laylanot, New year of )
1 Trees /
131
132
133
132
133
134
133
134
135
131
132
133
132
133
134
133
134
135
17
134
135
136
134
135
136
18
135
136
137
135
136 137
11)
136
137
138
136
137
138
20
137
138
139
137
138
139
21
138
139
140
138
139
140
22
139
140
141
139
140
141
23
Fast for rebellion of tribe of Benjamin
140
141
142
140
141
142
24
141
142
143
141
142
143
25
142
143
144
142
143
144
26
143
144
145
143
144
145
27
144
145
146 ! 144
145
146
28
145
146 147 145
146
147
29
30
First Rosh-chodesh of Adhar
146
147
147 148
148 149
146
147
147
148
148
14'.t
THE JEWISH CALENDAR
209
ADHAR I.
Common Year.
Embolismic.
Def.
Reg.
Ab.
1
2
Eosh-chodesh
148
149
149
150
150
151
3
150
151
152
4
151
152
153
5
152
153
154
6
153
154
155
7
154
155
156
8
155
156
157
9
1
156
157
158
10
157
158
159
11
158
159
160
12
Intercalated month
159
160
161
13
14
15
16
in
Embolismic years.
It has
no Fast or Feast Day,
except the Eosh-chodesh.
160
161
162
163
161
162
163
164
162
163
164
165
17
164
165
166
18
165
166
167
19
166
167
168
20
167
168
169
21
168
169
170
22
169
170
171
23
170
171
172
24
171
172
173
25
172
173
174
26
173
174
175
27
174
175
176
28
175
176
177
29
30
First E6sh-ch6desh of Adh&r II
176
177
177
178
178
179
15
2IO
THE JEWISH CALENDAR
ADHAR II.
1
Rosh-chodesh, second day
2
3
4
5
6
7
Fast for death of Moses
8
9
fFast for the strife between followers of)
( Hillel and Shammai * j
10
11
12
13
Thanith Esther. Fast of Esther
Purim. Fast of Lots
1C
Schuschan Purim. Second Purim
O
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Common Year.
Ernbolisniic.
Def.
Keg.
Ab.
Def.
Keg.
Ab.
148
149
150
178
179
180
149
150
151
179
180
181
150
151
152
180
181
182
151
152
153
181
182
183
152
153
154
182
183
184
153
154
155
183
184
185
154
155
156
184
185
186.
155
156
157
185
186
187
156
157
158
186
187
188
157
158
159
187
188
189'
158
159
160
188
189
190
159
160
161
189
190
191
160
161
162
190
191
192
161
162
163
191
192
193
162
163
164
192
193
194
163
164
165
193
194
195
164
165
166
194
195
196
165
166
167
195
196
197
166
167
168
196
197
198
167
168
169
197
198
199'
168
169
170
198
199
200-
169
170
171
199
200
201
170
171
172
200
201 202
171
172
173
201
202 203
172
173
174
202
203
204
173 174
175
203
204
205
174
175
176
204
205
206
175
176
147
205
206
207
176
177
178
206
207
208
THE JEWISH CALENDAR
211
ISAN.
Common Year.
Embolismic.
Def.
Beg.
Ab.
! Def.
Beg.
Ab.
1
2
( R6sh-chodesh. Fast for death of Nadab 1
( and Abihu ... I
177
178
178
179
179
180
! 207
208
208
209
209
210
3
179
180
1H1 209
210
211
4
180 181
182 210
211
212
5
181
182
183 211
212
213
6
182
183
184 212
213
214
7
183
184
185 213
214
215
8
184
185
186 214
215
216
9
185
186
187
215
216
217
10
Fast for death of Miriam, sister of Moses... 186
187
188 216
217
218
11
187
188
189 217
218
219
12
.
188
189
190
218
219
220
13
189
190
191
219
220
221
14
Eve of Passover. Paschal Lamb slain 190
191
192
220
221
222
15
16
17
18
19
20
21
22
23
I Pesach. First day of Passover. First)
I day of Unleavened Bread I
191
192
193
194
195
196
197
198
199
192
193
194
195
196
197
198
199
200
193
194
195
196
197
198
199
200
201
221
! 222
223
224
225
226
227
228
229
222
223
224
225
226
227
228
229
230
223
224
225
226
227
228
229
230
231
Second day
Third :
Fourth ,,
Fifth
Sixth
Seventh ,, Last day of Unleavened Bread
( Eighth ,, observed by the Jews "of the }
( Exile" J
24
200 201 202 230
231
232
25
201 202 203
231
232
23?
2G
Fast for death of Joshua, son of Nun 202
203
204
232
233
234
27
203 204 205 233 234
235
28
204 205
206
234 235
236
2!)
205 206
207
235
236
237
30
First Rosh-chodesh of lyar
206
207
208
236 237
238
212
THE JEWISH CALENDAR
lYAB.
Common Year.
Embolismic.
Def.
Beg.
Ab.
Def.
Beg.
Ab.
1
R6sh-ch6desh, second day
207
208
209
237
238
239
2
208
20'.) 210
238
239
240
3
NOTE. First, Second, and Third Fast of
209
210
211
239
240
241
4
lyar on first Monday, and on the
following Thursday and Monday.
210
211 212
240
241
242
5
211
212 213
241
242
243
6
212
213
214
242
243
244
7
213
214
215
243
244
245
8
214
215 216
244
245
246
9
215
216
217
245
246
247
10
( Fast for death of Eli the High Priest,)
( and the taking of the Ark )
216
217
218
246 247
248
11
217
218
219
247 248
249
12
218
219
220
248
249
250
13
219
220
221
249
250
251
14
220
221
222
250
251
252
15
221
222
223
251
252
253
16
222
223
224
252
253
254
17
223
224
225
253
254
255
18
( Lag b'oiner. Feast of the thirty-third)
| day of the Omer j
224
225
226
254
255
25i>
19
225
226
227
255
256
257
20
226
227
228
256 257
888
21
227
228
229
257 258
259
22
228
229
230
258
259
2C.O
23
229
230
231
259
260
261
24
230
231
232
260 261
262
25
231
232
233
261
262
263
26
232
233
234
262
263
2(54
27
233
234
235
263
264
265
28
Fast for death of Samuel the Prophet ...
234
235 236
264
265
266
29
235
236
237
265
266
2(57
/'///: JEWISH CALENDAR
213
1
2
SiWAN.
Common Year.
Embolismic.
Def.
Reg. Ab.
Def.
Reg.
Ab.
R6sh-chodesh
236
237
237
238
238
239
266
267
267
268
268
269
3
4
5
6
7
-
f Scheloschah jeme hagbalah. Sanctifi-)
| cation of the People j
238
239
240
241
242
243
239
240
241
242
243
244
240
241
242
243
244
245
268
269
270
271
272
273
269
270
271
272
273
274
270
271
272
273
274
275
Second dav of Sanctification
| Schabuoth. Feast of the Congregation. )
( Pentecost I
Second day of the Feast
9
244
245
246
274
275
276
10
11
245
246
246
247
247
248
275
276
276
277
277
278
12
247
248
249
277
278
279
13
248
249
250
278
279
280
14
249
250
251
279
280
281
15
250
251
252 280
281
282
16
251
252
253 28 1
282
283
17
252
253"
254
282
283
284
18
253
254
255 283
284
285
19
254
255
256 284
285
286
20
255
256
257 1 285
286
287
21
256
257
258
286
287
288
22
Fast for Golden Calves of Jeroboam 257
258
259
287
288
289
23
258
259
260
288
289
290
24
259
260
261
289
290
291
25
260 261
262 290
291
292
26
27
28
Fast for death of R . Chananya
261
262
263
262
263
264
263
264
265
291
292
293
292
293
294
293
294
295
29
30
First Rosh-chodesh of Tammuz
264
265
265
2<;<;
966
967
294
295
295
296
296
297
214
THE JEWISH CALENDAR
TAMMUZ.
Common Year.
Embolismic.
Def.
Beg.
Ab. '
Def.
Keg.
Ab.
1
R6sh-chodesh, second day
266
267
268
296
297
298
2
267
268
269
297
298
299
3
268
269
270
298
299
300
4
269
270
271
299
300
301
5
270
271
272
300
301
302
6
271
272
273
301
302
303
7
272
273
274
302
303
304
8
273
274
275
303
304
305
9
274
275
276
304
305
306
10
275
276
277
305
306
307
11
276
277
278
306
307
308
12
277
278
279
307
308
309
13
278
279
280
308
309
310
14
279
280
281
309
310
311
15
280
281
282
310
311
312
16
281
282
283
311
312
313
17
Fast of Tammiiz .......
282
283
284
312
313
314
18
283
284
285
313
314
315
19
284
285
286
314
315
316
20
285
286
287
315
316
317
21
286
287
288
316
317
318
22
287
288
289
317
318
319
23
288
289
290
318
319
320
24
289
290
291
319
320
321
25
290
291
292
320
321
322
26
291
292
293
321
322
323
27
292
293
294
322
323
324
28
293
294
295
323
324
325
29
294
295
296
324
325
326
THE JE WISH CALENDAR
ABH.
Common Year.
Embolismic.
Def.
Keg.
Ab.
Def.
Beg.
Ab.
1
Rosh-chodesh. Fast for death of Aaron
295
296
297
325
326
327
2
296
297
298
326
327
328
3
297
298
299
327
328
329
4
298
299
300
328
329
330
5
299
300
301
329
330
331
6
300
301
302
330
331
332
7
301
302
303
331
332
333
8
9
1
( Fast for Decree against the Israelites in
the wilderness, and destruction of
First and Second Temples : called
( Fast of Abb.
302
303
304
305
303
304
305
306
304
305
306 !
307 [
332
333
334
335
333
334
335
336
334
335
336
337
2
306
307
308
336
337
338
3
307
308
309
337
338
339
4
6
( Tubeab. Reconciliation of tribe of)
( Benjamin j"
308
309
310
309
310
311
310
311
312
338
339
340
339
340
341
340
341
342
7
311
312
313
341
342
343
8
312
313
314
342
343
344
9
313
314
315
343
344
345
JO
314
315
316
344
345
346
1
315
316
317
345
346
347
2
Xylophoria. Wood offering for the Altai-
316
317
318
346
347
348
3
317
318
319
347
348
349
4
318
319
320
348
349
350
,5
319
320
321
349
350
351
6
320
321
322
350
351
352
7
321
322
323
351
352
353
-8
322
323
324
352
353
354
9
First Rosh-chodesh of Eliil . .
323
324
324
325
325
326
353
354
354.
355
355
356
2l6
THE JE WISH CALENDAR
ELUL.
Common Year.
Embolismic.
Def.
Keg.
Ab.
Def.
Beg.
Ah.
1
2
Kosh-chodesh, Second day
325
326
326
327
327
328
355
356
356 :!.->7
357 .V,s
3
327
328
329
357
358
359
4
328
329
330
358
359
360
5
329
330
331
359
360
361
6
7
8
/ Fast, Death of the Spies who brought an )
( evil report to Moses )
330
331
332
331
332
333
332
333
334
360
361
362
361
362
363
362
363
364
9
333
334
335
363
364
365
10
334
335
336
364
365
306
11
335
336
337
365
366
367
12
336
337
338
366
367
368
13
337
338
339
367
368
369
14
338
339
340
368
369
370
15
339
340
341
369
370
371
16
340
341
342
370
371
372
17
341
342
343
371
372
373
18
342
343
344
372
373
374
19
343
344
345
373
374
375
20
344
345
346
374
375
376
21
345
346
347
375
376
377
22
346
347
348
376
377.
378
23
347
348
349
377
378
379
24
348
349
350
378
379
380
25
349
350
351
379
380
381
26
350
351
352
380
381
382
27
351
352
353
381
382
383
28
352
353
354 ;
382
383
384
29
353
354
355 383
1
384
385
THE JEWISH CALENDAR
217
FERINE FOE NEW MOONS AND DAYS TO BE OBSERVED.
(ARTICLE 105.)
Month, and Day < Days to be observed. B.C.=K6sh- '
COMMON YEARS.
of Month.
Chodesh.
Deficient.
Begular. Abundant.
Tishri 1
3
10
15
21
23
30
Marheshwan 1
30
Kistew 1
Kislew 1
25
30
TSbeth 1
Tebeth 1
10
Schebhat 1
30
Adhar 1
13
14
15
Nisan 1
15
21
30
lyar 1
18
Siwan 1
6
30
Tammuz 1
17
Abh 1
9
30
'Elul 1
E.C. of Tishri
2
4
4
2
3
3
4
5
^
6
1
7
1
2
5t
1
2
3
3
2
4
5
/
1
3
2
3
3
4
7
2
2
7
6
1
1
2
3
6
4
6
5
6
7
5
6
7
1
1
7
2
3
6
4
2
5
6
1
7
1
1
2
3
5
5
3
2
4
4
5
6
2
7
1
3
2
3
4
2
3
4
5
5
4
6
7
3
1
6
2
3
5
4
5
5
6
5
1*
7
5
4
6
6
7
1
4
2
3
5
4
5
6
4
5
6
7
7
6
1
2
5
3
1
4
5
1
6
7
7
1
!
4
2
1
3
3
4
5
6
2
7
1
3
2
3
4
2
3
4
5
5
4
6
7
3
1
6
2
3
5
4
5
5
6
5
1*
7
5
4
6
6
7
1
2
5
3
4
6
5
6
7
5
6
7
1
1
7
2
3
6
4
2
5
6
1
7
1
1
2
7
2
2
7
6
1
1
9
3
4
7
5
6
1
7
1
2
h
1
2
3
3
2
4
5
1
&
4
7
1
3
2
3
3
4
Fast of Guedaliah
Day of Atonement
Feast of Tabernacles
Hoshana Raba
Feast of the Law
First E.C. of Marheshwan
Second ,,
First E.C. of Kislew
Second ,,
E.C. of Kislew
Purification of Temple
First E.C. of Tebeth
Second ,,
B.C. of Tebeth
Fast of Tebeth
E.C. of Schebhat
First E.C. of Adhar
Second ,, ,,
Fast of Esther
Purim
Schushan Purim
E.C. of Nisan
Passover
Seventh day of Passover
First E.C. of lyar
Second ,, ,, ...
Lag b'Omer
E.C. of Siwan
Feast of Weeks
First E.C. of Tammuz
Second ,, ,,
Fast of Tammuz
E.C. of Abh
Destruction of Temple
First E.C. of 'Elul
Second ,, ,,
* The Fast of Guedaliah falls to feria 7, and is observed on the next day.
t The Fast of Esther falls to feria 7, and is therefore kept on the previous Thursday.
2l8
THE JE WISH CALENDAR
FEBLE FOE NEW MOONS AND DAYS TO BE OBSERVED.
Month, and Day
of Month.
Days to be observed. R.C.=R6sh-
Chodesh.
EMBOLISMIC YEARS.
Deficient.
Regu-
lar.
Abundant.
Tishri 1
3
10
15
21
23
30
Marheshwan 1
30
Kislew 1
Kislew 1
25
30
Tebeth 1
Tebeth 1
10
Schebhat 1
30
Adhar I. 1
30
Adhar H. 1
13
14
15
Nisan 1
15
21
30
lyar 1
18
Siwan 1
6
30
Tammuz 1
17
Abh 1
9
30
'Elul 1
B.C. of Tishri .
2
4
4
2
1
3
3
4
5
1
6
1
7
1
2
3
4
2
3
4
5
5
4
6
7
3
1
6
2
3
5
4
5
5
6
5
1*
7
5
4
6
6
7
1
4
2
4
3
4
5
6
7
5
6
7
1
1
7
2
3
6
4
2
5
6
1
7
1
1
2
7
2
2
7
6
1
1
2
3
6
4
6
5
6
7
1
2
f
2
3
3
2
4
5
1
6
4
7
1
3
2
3
3
4
3
5
5
3
2
4
4
5
6
2
7
1
3
2
3
4
5
6
4
5
6
7
7
6
1
2
5
3
1
4
5
It
6
It
7
1
2
4
4
2
1
3
3
4
5
6
2
7
1
3
2
3
4
5
6
4
5
6
7
7
6
1
2
5
3
1
4
5
It
6
It
7
1
5
1
7
5
4
6
6
7
1
2
5
3
4
6
5
6
7
1
2
s:
2
3
3
2
4
5
1
6
4
7
1
3
2
3
3
4
7
2
2
7
6
1
1
2
3
4
7
5
6
1
7
1
2
3
4
2
3
4
5
5
4
6
7
3
1
6
2
3
5
4
5
5
6
Fast of Guedaliah
Day of Atonement
Feast of Tabernacles
Hoshana Baba
Feast of the Law
First B.C. of Marheshwan ...
Second ,, ,,
First B.C. of Kislew
Second ,, ,,
B.C. of Kislew
Purification of the Temple ...
First B.C. of Tebeth
Second ,, ,,
B.C. of Tebeth
Fast of Tebeth
B.C. of Schebhat
First B.C. of Adhar I
Second ,,
First B.C. of Adhar II.
Second ,, ,, ...
Fast of Esther
Purim
Schushan Purim
B.C. of Nisan
Passover
Seventh day of Passover
First B.C. of lyar
Second ,, ,,
Lag b'Omer
B.C. of Siwan
Feast of Weeks
First B.C of Tammuz
Second ,, ,, ...
Fast of Tammuz
B.C. of Abh
Destruction of Temple
First B.C. of 'Elul
Second , , .
* Fast of Guedaliah falls to feria 7 ; therefore observed on the next day.
t Fast of Tammuz, and fast of Abh fall to feria 7 ; therefore observed on the next day.
\ Fast of Esther falls to feria 7 ; therefore kept on previous Thursday.
CHAPTEE VIII
THE FORMULA OF DR. GAUSS FOR FINDING THE CHRISTIAN DATE OF
THE JEWISH PASSOVER
106. The " Berechnung des Jiidischen Osterfestes," by Dr. Gauss,
the celebrated German mathematician, was published in the " Monat-
liche Correspondenz vom Freyherrn von Zaeh," b. 5, p. 435. Gotha,
1802.
The formula is there given without any demonstration of the
method by which it was obtained. This demonstration was, however,
supplied by M. le Chevalier Casa Gresy in the " Correspondance
Astronomique, etc., du Baron de Zach," torn. i. p. 556. Genes,
1818.
The formula is given also by Dr. Adolf Schwarz in " Der Jiidische
Kalender," p. 72 (Breslau, 1872), but without demonstration.
The following is by no means a literal translation or transcript of
the contribution by Casa Gresy, neither does it pursue precisely the
same lines, but it must be understood that, with certain modifications,
it is derived from his paper upon the subject.
He commences with an account of the elements of the Jewish
Calendar, which need not be here repeated ; they have already been
fully described. It is only necessary to state again that the Jewish
Era commences with the Molad 2d. 5h. 204ch., or the fictitious New
Moon which is supposed to have occurred on Monday, October 7, in
the year of the Julian Period 953, B.C. 3761, at 5h. 204ch. after 6 in
the evening, that is, at llh. 204ch. p.m. ; and that the Christian Era
commenced at the midnight which was the commencement of the
year 4714 of the Julian Period, or Saturday, January 1, A.D. 1.
Every subsequent Julian year has commenced with the same day
220 THE JEWISH CALENDAR
of the month, but the commencement of the Jewish years is variable.
Tishri 1 may occur in either August, September, or October ; that is
to say, the year commences in the Autumnal season, but the actual
day with which it commences has to be determined for each year.
It follows that, because 4714 953 = 3761, any given Jewish year,
H, must commence in the Autumn of the Julian year H 3761.
Also, if B be the Julian year in which the Jewish year H terminates
and H + 1 commences in the Autumn, then B = H + 1 3761 =
H - 3760.
There is a reason for introducing the Jewish year H + 1. There
are invariably 163 days from the Passover in any year H to Tishri 1 of
the next year H + 1 ; so that if the Julian date of Tishri 1 in the
year H + 1 be found, the date of the Passover in the year H is
obtained at once by the subtraction of 163 days.
107, The day upon which Tishri 1 is to be observed is governed
by the day of the computed New Moon of Tishri, and in order to find
the Julian date for this New Moon in any given year H + 1, it is
necessary, in the first place, to ascertain the interval of time which
has elapsed since the commencement of the Jewish Era up to the
close of the year H. This interval must be measured in Julian Civil
years and parts of a year. The addition of one day to this interval
will give the date for the first day in the year H + 1.
Measured in Jewish years, the interval will, of course, be exactly
H years. Some of these H years w T ill be Common, and some will be
Embolismic.
Let e = the number of Common years in these H years,
andE = ,, Embolismic ,, ,,
so that e + E = H, or E = H e.
Each of the Common years is shorter by lOd. 21h. 204ch., and
each of the Embolismic years is longer by 18d. 15h. 589ch. than a
mean Julian year of 365d. 6h., the Jewish years being Astronomically
computed.
If, therefore, there be an interval of time which contains exactly
H Jewish years, the same interval when measured by Julian mean
years will contain
(a) H - e (lOd. 21h. 204ch.) + E (18d. 15h. 589ch.).
THE JEWISH CALENDAR 221
Also, because in every number of Julian Civil years, such number
not being a multiple of 4, there may be 18, or 12, or 6 hours less than
in the same number of Julian mean years, it follows that H Julian
mean years have, for their equivalent in Civil years, H + 6h. x (the
remainder after dividing H by 4) . In other words
H mean Julian years = ( H + 6h. x -, ) Civil Julian years.
\ ( 4 } r J
The interval of time under consideration must be measured by
Julian Civil years, and therefore this value must be substituted for H
in expression (a), which then becomes
<&) ...... H + Gh.j j | - e(10d. 21h. 204ch.) * + E (18d. 15h. 589ch.).
This, then, is the interval of time, measured in Julian Civil years
and parts of a year, from llh. 204ch. p.m. on Monday, October 7,
B.C. 3761, up to the termination of the Jewish year H, by the
Astronomical computation, that is, up to the termination of the last
Lunation of the year. By the addition of one day to this interval, the
integral part of the sum of the terms in the expression will give the
computed first day for the Moon of Tishrl in the next Jewish year,
H + 1, which is therefore indicated by
<c)...ld. + H + Gh.j ? 1 r - e (lOd. 21h. 204ch.) + E (ISA 15h. 589ch.).
It will be more convenient to reckon from Noon of October 1,
B.C. 3761, than from llh. 204ch. p.m. of October 7. The interval of
time between these two bases is 6 whole days and llh. 204ch. of
another day. Consequently, if the reckoning be made from Noon,
October 1, the Julian date for the first day of the computed Moon of
Tishrl in the Jewish year H + 1 will be indicated by the integral part
of the sum of the terms in the expression
(d) ............ 7d. llh. 204ch. + H + 6h. | ^ [ ^ - e (lOd. 21h. 204ch.)
+ E (18d. loh. 589ch.),
* There is a self-evident misprint here in the demonstration of Casa Gresy as given
in the " Correspondance du Zach." The third term of the expression is made -f- r< ' instead
-of <<.
222 THE JEWISH CALENDAR
in which the first term, Id., of expression (c) is increased by Gd.
llh. 204ch.
There is, however, no necessity for reckoning from so distant a
base as the Noon of October 1, B.C. 3761. The reckoning may be
made from the Noon of October 1 in the Julian year B, in which the
Jewish year H terminates, which is H years nearer to the required
date. If the reckoning be thus made, these H years must be dropped
from the expression (d), which then becomes
(e) 7d. llh. 204ch. + 6h. | =" j- ^ - e (lOd. 21h. 204ch.)
+ E(18d. 15h. 589ch.),
indicating the first day of the Moon of Tishri in the Jewish year
H + 1, measured from Noon, October 1, of the Julian year B.
If, in this expression, there be substituted for E its equivalent
H e, we have
7d. llh. 204ch. + 6h. I -* [ - e(10d. 21h. 204ch.)
( 4 ) r
- e (18d. 15h. 589ch.) + H (18d. loh. 589ch.),
or
(/) 7d. llh. 204ch. + 6h. I | - e (29d. 12h. 793ch.)
+ H(18d. 15h. 589ch.).
The number of Common years in H Jewish years, which number
is expressed by e, is the integral part of the quotient when 12 H + 17
is divided by 19 ; or
12 H + 17 | *
19
By substituting this value of e in the last expression, it becomes
... 7d. llh. 204ch. + 6h. | \ r ~ ^l<f~^ } ( 29d - 12h -
+ H(18d. 15h. 589ch.).
* See Note at the end of this Chapter.
THE JE WISH C A LEND. /A' 223
In order to reduce this expression to the formula of Gauss, it
must be noticed that
12 H + 171 Ifi 17 (12H + 17) \*
19~ "j == M 121 "1" -MT-frJ
_12 T? 17 1 ( 12 H + 17 I
~ 19 *" 19 19 ( 19 I r '
Substitute this value of ~Tq~ m expression (g], and it
becomes
7d. llh. 204ch. + 6h. { ?- } . - ^ H(29d. 12h. 793ch.)
\ 4 i Y JL\J
^ (29d. 12h. 793ch.) + | i^SjLlI I x (29d. 12h. 793ch.)
+ H (18d. 15h. 589ch.),
where the integral part of the sum of the terms expresses the number
of days reckoned from October 1 of the Julian year B to the first day
of the Moon of Tishri in the Jewish year H + 1, both days inclusive.
But the Moon of Tishri and the first day of the Jewish year most
frequently occur before October 1, and sometimes before September 1;
it will therefore be convenient to reckon the days from the first .day of
some month before the Autumnal season commences. It is a matter
of indifference, thus far, which of the earlier months be taken, but as
the Passover always occurs after March 1, it will be well to take that
day for the point of departure. If this basis be adopted, 214 days
must be added to the expression above, on account of the number of
days, contained in the Christian months, from March 1 to September
30, both inclusive.
Let this addition be made ; the first term of the expression then
becomes 221d. llh. 204ch.
* The equivalent of -. J" j- is thus obtained :
Let the integral part of the quotient of 12 H + 17 when divided by 19 be n, and the
f 12 H + 17 )
remainder, or - - be r.
Then 12 H + 17 = 19 n + r, or 12 H + 17 r = 19 H.
The value of { - If + 17 j- is therefore found by dividing 12H + 17 r by 19.
224 THE JEWISH CALENDAR
Also, for greater simplicity, write a for -j c - , and 6 for
Collect the similar terms ; reduce the hours and Chalakim to
fractions of a day ; and the expression becomes
c 4343 6 n 272953 313 .
C.1K _ I . I | _ ft ___ _ __ _ I I
98496 ^ 4 ^ 492480 98496
or
(I.) ...... 195-0440932 + -256 + 1-5542418 a - '003177794 H.
This is the First Formula of Dr. Gauss, for computing the New
Moon of Tishri of the year H + 1.
If, instead of the Jewish year H, the corresponding Julian year B
be employed, we have H = B + 3760 ; consequently
f 12 H + 17 1 J 12 B + 451371 f 12B + 12 )
~lgr~)V l ~T9~ ~jr' SE i~i9 JV
f H ) < B + 3760 ) ( B )
and 0, or - , becomes = = - -j [ .
(4jr ( 4 } r |4jr
In this way both a and b are expressed in terms of B, and it only
(1) 221d. llh. 204ch.-JJ(29d. 12h. 793ch.) = 221^^^.. - 26,
19 v 1080 x 24 ""19 X 1080 x 24
m 229596 - 207881 _ 21715 = 4343
19 x 1080 x 24 " 19 x 1080 x 24 98496'
10d - 12h - 793ch - 272953
/oo^ TOV, TOQ v, x
(2) (29d. 12h. 793ch.) =
(3) (29d. 12h. 793ch.) + 18d. 15h. 589ch.
= 4( 354d - 7h - 391ch. 354d. 8h. 876ch.)
A7
1 . A , . 1565 313
- - (Od. Ih. 48och.) = -
THE JEWISH CALENDAR 225
remains to substitute B + 3760 for H in the First Formula, which
then becomes
195-0440932 + -256 + 1-554218 a - "003177794 (B + 3760),
or
<II.) 183-0955877 + "256 + l'554218a - '003177794 B.
This is the Second Formula of Dr. Gauss for the New Moon of
Tishri.
These two formula are equivalent. They each give the computed
date for the New Moon of Tishri in the Jewish year H + 1, measured
in days reckoned from March 1, inclusive, of the corresponding Julian
year B, or H - 3760.
108. As the Feast of the Passover, Nisan 15, in the year H is 163
days earlier than Tishri 1 of the year H + 1, it is only necessary to
subtract this number of days from each of the two formulae, and we
have the computed date for Nisan 15 in the year H
<IIL) 32-0440932 + '25 b + T5542418a - '003177794H.
<IV.) 20-0955877 + "256 + l'5542418a - "003177794B.
It will be noticed that in each of the two formulae the first term
does not involve either H, B, a, or b, or any other variable. It is a
constant in each of the formulae.
With respect to the decimals : After substituting for H, B, a, and b
their values as determined by the given year in which the Julian
date of Nisan 15 is required, let M be the integral, and m the
decimal part of the sum of the terms.
M + m is obtained from whichever formula be employed ; and,
neglecting for the present the decimal part, m, the Julian date of
Tishri 1 will be the Mth day of March * as obtained from (I.) or (II.),
while that of Nisan 15 will be the Mth day of March as obtained from '
(III.) or (IV.), assuming that there be nothing in the rules of the
Jewish Calendar to cause a postponement from the computed day.
The important question of a possible postponement must now be
considered. The feriae 2, 4, and 6, Monday, Wednesday, and Friday,
-are forbidden for the Passover, and the feriae 1, 4, and 6, Sunday,
Wednesday, and Friday, are forbidden for Tishri 1.
The week-day for the Mth day of March can always be ascertained
* April 1, 2, 3, &c., are counted as March 32, 33, 34, *c.
16
226 THE JEM'ISH CALENDAR
by means of the Sunday Letter for the Christian year corresponding
to the given Jewish year, by the ordinary rules of the Julian Calendar.
This must first be done, and if a postponement from the Mth to the
next day be required, such postponement must be made.
There are, however, other rules besides ADU which may render
necessary a postponement of Tishri 1 from the computed day of New
Moon.
(1) Let n be the numerical value of the computed feria for Nisan 15
in the Jewish year H, counting Sunday as 1, Monday as 2, Tuesday
as 3, &c. In other words, let n be the numerical value of the week-day
for the Mth day of March as found by the formula.
Let t be the numerical value of the computed feria for Tishri 1 in
the following Jewish year H + 1.
Then ~ f n + 163 } f n + 2 t
~~\ 1 )r"l 7 )r'
because Tishri 1 in the year H + 1 is always 163 days later than
Nisan 15 in the year H.
The rule GaTRaD requires that if the computed time for the New
Moon of Tishri fall upon feria 3, Tuesday, so late as or later than
9h. 204ch. after 6 in the evening, that is, if it fall so late as or later
than 15h. 204ch. after Noon, and if also the year be Common, then
Tishri 1 has to be postponed to the next day, feria 4, Wednesday, and
thence, by ADU, to feria 5, Thursday.
Now, if it be found by the formula that t = 3, it is evident that n
must be 1, for- f ?l + 2 )
" 1 7 )V
.'. n = 1, or 8, or 15, &c.,
each of which numbers indicate feria 1.
If, therefore, n = 1, and the decimal part of the sum of the terms
in the formula, namely m, be equal to or greater than 15h. 204ch.,
that is to say, if m be equal to or greater than '6328703,* and if also-
* Let it be remembered that the formula measures the time elapsed from Noon.
1080
24
204
15-188
6328703
THE JEWISH CALENDAR 227
the year H + 1 be Common, then Nisan 15 of the year H, which is
found by the formula, must be postponed from the day found by the
formula to the next day, feria 2, Monday. This day is forbidden by
BaDU, and there must be a further postponement to feria 3, Tuesday.
(2) If Tishri 1 be found by the computation to fall upon feria 2,
Monday, so late as or later than 15h. 589ch. after 6 in the evening,
that is to say, so late as or later than 21h. 589ch. after Noon, and if
also the preceding year be Embolismic, then Tishri 1 is to be post-
poned to feria 3, Tuesday.
Now, if it be found by the formula that t = 2, it is evident that n
must be 7, for
t - 2 - | *L*. \
~\ 1 Ir'
..n = Q, or 7, or 14, &c.,
each of which values indicates feria 7.
If, therefore, n = 1, and the decimal part of the sum of the terms
in the formula be equal to or greater than 21h. 589ch., that is to say,
if m be equal to or greater than '897723765, and if also H be an
Embolismic year, then Nisan 15 must be postponed to the (M + l)th
day, which will be feria 1, or Sunday.
(3) There is one other rule of the Calendar, but it does not affect
the date given by the formula.
If the New Moon of Tishri, as computed, fall upon any day of the
week so late as or later than 18h. after 6 in the evening, that is to
say, so late as, or later than, Noon, then Tishri 1 is postponed to the
following day.
In this case n, or the feria of Nisan 15 in the preceding year H,
will also be a day later.
In the formula the reckoning of time is from Noon. It is made
from a point of departure six hours earlier than that of the Jewish
reckoning. But the rule regarding the eighteen hours has reference to
the Jewish reckoning. The value of M + m has in fact been augmented
by six hours, or "25 of a day.
No matter how great may be the sum of the decimals in the
formula, they can never by any possibility be greater than '9, and
when this sum is diminished by '25 in order to bring it back to the
Jewish Epoch, and so to bring it within the rule, it can never
possibly amount to '75 of a day, that is, to 18h. Therefore the
228
THE JEWISH CALENDAR
effect of this particular rule is entirely excluded when the formula is
employed ; .and it remains, so far as this rule is concerned, that the
Mth day of March will be the date of Nisan 15, the decimal being
neglected whether it be great or small.
In finding the dates of Xlsan 15 in the year H, or of Tishri 1 in the
year H + 1, by means of the formula, it will be seen that a, or
, which may be of any value from to 18, has to be
j- y / /*
multiplied by 1 '5542418; also, the multiplier both for H and for B is
003177794. The following Tables of Products will facilitate the
computation :
a
a x 1-5542418.
1
1-5542418
2
3-1084836
3
4-6627254
4
6-2169672
5
7-7712090
6
9-3254508
7
10-8796926
8
12-4339344
9
13-9881762
10
15-5424180
11
17-0966598
12
18-6509016
13
20-2051434
14
21-7593852
15
23-3136270
16
24-8678688
17
26-4221106
18
27-9763524
H or B. -003177794 x H or B.
1
003177794
2
006355588
3
009533382
4
012711176
5
015888970
6
019066764
7
022244558
8
025422352
9
028600146
11
034955734
12
038133528
13
041311322
14
044489116
15
047666910
16
050844704
17
054022498
18
057200292
19
060378086
109. Examples.
1. Find the Christian date corresponding to Nisan 15, A.M. 5578.
Here, H = 5578.
B = H - 3760 = 1818, for which the Julian Sunday Letter
is F, and the Gregorian is D.
The year is Embolismic, for 5578 = 298 x 19 + 16.
THE JEWISH CALENDAR 229
By Formula I.
(12H + 17) (66936 + 17)
-W\r=\- -lg--}r- 1(l -
i j\ =J 5578| =2>
(4Jr I 4 \r
The values of the terms in the formula are
The Constant = 32'0440932
a x 1-5542418 = 24 '8678688
b x -25 .. = 0'5
57-4119620
H x -003177794 = 17*7257349
39-6862271
The Julian date is therefore March 39, that is, April 8, a Monday,
for the Julian Sunday Letter is F. Feria 2 is forbidden for the
Passover, and the Festival is kept on feria 3, Tuesday, April 9.
The corresponding Gregorian date is April (9 + 12) = April 21,
A.D. 1818.
By Formula II.
a = J12B + 12) _ J 21828 \ = lfi
The Constant = 20'0955877
a x 1-5542418 = 24'8678688
b x -25 .. = 0-5
45-4634565
B x -003177794 . .. = 5'7772294
39-6862271
The same result as that given by Formula I. is obtained.
230 THE JEWISH CALENDAR
2. Find the Christian date of Nisan 15 in A.M. 5616.
H = 5616. B = H - 3760 = 1856.
f!2H + 17) (67409) , r
19 )>~IT9 \r~
The Constant = 32 "0440932
a x 1-5542418 = 24-8678688
b x -25 .. =
56-9119620
Hx -003177794. ..=17-8464911
39-0654709
March 39 = April 8 ; the Julian Sunday Letter for A.D. 1856 is
G. The day is therefore Sunday, and there is no postponement.
The corresponding Gregorian date is Sunday, April (8 + 12) =
April 20.
By Formula II.
(12B + 12) j 22284 \
~~\ 19 \r~ ( 19 Jr~
b- f?l =| 1856 l -0
~\4\r \~T\r~
The Constant = 20*0955877
a x 1-5542418 = 24 '86 78688
b x -25 .. =
44-9634565
B x -003177794 . .. = 5'8979856
39-0654709
The same result is obtained as that given by Formula I.
Many of the figures in Example 2 are identical with those in
Example 1, for, in both examples, a = 16, and b = 0. It has been
intentionally taken because it affords an opportunity of considering
THE JEWISH CALENDAR 231
the effect produced by the augmentation of the Constant, which is
increased by "25 of a day above the Jewish reckoning.
Suppose that the Constant had not been thus increased ; then, in
Example 1 the computed date would have been determined by
39-6862:271 - "25, or 39'4362271. This, being less than 39'75, would
not have been affected by the rule with respect to 18h. But March 39,
that is, April 8 Julian, April 20 Gregorian, being a Monday, the
Festival would still be postponed by BaDU to Tuesday, April 9 Julian,
April 21 Gregorian.
In Example 2 the computed date would have bean determined by
39-0654709 - '25, or 38'8154709. This is greater than 38'75, and
therefore the day would be postponed to March 39, that is, April 8
Julian, April 20 Gregorian. This is the very day which is found by
the formula. It is a Sunday in A.D. 1856, which is not a forbidden
day for the Passover.
Thus the Example is an illustration of the fact that the result
given by the formula is not affected by the rule respecting the 18h.
3. If the rules of the reformed Jewish Calendar were observed
in A.D. 622 upon which days in that year would the Passover and
Tishri 1 have occurred?
Let H be the Jewish year in which Nisan 15 of the Christian year
622 occurred.
H + 1 will be the Jewish year of which the Tishri 1 occurring in
A.D. 622 was the first day.
H = 622 + 3760 = 4382
(12H
19
(12H + 17) (52601) _ Q
~ ~-
The Constant ............... = 32*0440932
a x 1-5542418 ............ = 13'9881762
b x -25 .. = -50
46-5322694
Hx -003177794.. .. = 13-9250933
3-2-6071761
March 32 = April 1.
232 THE JE WISH CALEND. I K
The Sunday Letter for A.D. 622 is C. April 1 is, therefore, Thurs-
day, and there is no postponement.
Tishri 1, being the first day of A.M. 4383, or of H + 1, corresponds
to March (32 + 163) = March 195. There are 184 days from March 1
to August 31, both inclusive. The day required is Saturday, September
(195 - 184) = September 11.
4. The same result is obtained by the method described in Article
61, p. 115. The Jewish year which commenced in the Autumn of
A.D. 622 was A.M. (622 + 3761) = 4383.
The years elapsed before its commencement are 4382, or 230 com-
plete Cycles + 12 years.
200 Cycles =1387937 22 200
30 = 208120 16 570
First 12 years of next Cycle = 4370 12 724
1600499 3 414
This is the actual time elapsed, by Jewish Astronomical computa-
tion, from the commencement of the Era to the instant of the New
Moon of Tishri, A.M. 4383. The serial number of the day is, therefore,
1600500 ; and because this number = In + 6 the day was a Saturday,
for the Era commenced with a Monday.
To find the corresponding Christian date.
Days elapsed before the Christian Era commenced,
from October 7 to December 31, B.C. 3761... = 86
3760 Julian years =1373340
1373426
But the total number of days to Tishri 1, A.M. 4383, inclusive, is
1600500. Consequently there remain of the Christian Era
227024 days, or 621 Julian years + 254 days.
The Christian date required is, therefore, the 254th daj r of A.D. 622,
that is to say, September 11, which was a Saturday, for the Sunday
Letter is C.
THE JEWISH CALENDAR 233
Nisan 15 is 163 days earlier, or the (254 163) = 91st day
= Thursday, April 1.
The feria for Tishri 1 may, if it be considered necessary, be verified
by the addition of the Molad BeHaRD to the interval of time elapsed
before the occurrence of the New Moon of Tishri, 4888, and rejecting
In days from the sum.
1600499 3 414
BeHaKD . 2 5 204
1600501 8 618, or 7 8 618.
The day is Saturday.
110. Before leaving the subject it may be well to give the full
working for some year.
Find the Christian dates corresponding to Tishri 1 and Nisan 15 in
the Jewish year 5799.
1. 5799 = 19 x 305 + 4 ; it is therefore the fourth year of the
306th Cycle, or 305 complete Cycles + 3 years have elapsed.
BeHaBD =2 5 204
For 800 Cycles add 1 21 300
For 5 6 10 815
For the fourth year 7 15 181
Molad for A.M. 5799 =4 4 420
Feria 4 = Wednesday. Tishri 1 is postponed by ADU to Thursday.
2. In order to know how many days after the commencement
of the year Nisan 15 will occur, the length of the year must be ascer-
tained.
It is a Common year, for it is the fourth in a Cycle.
To the Molad of 5799, which is 4 4 420
add, for a Common year 4 8 876
Molad for 5880 1 13 216
Feria 1 is Sunday. Tishri 1 of 5880 is postponed, by ADU, to Mon-
day. Hence 5799, which commences with a Thursday, terminates
.234 THE JEWISH CALENDAR
with a Sunday, and. being a Common year, is of the form 350 + 4, or
354 days. It is a Regular Common year.
Nisan 15 is therefore the 192nd day of the year, that is to say, 191
days must be added to the date of Tishri 1 when that day is found ;
for in a Regular Common year the number of days in the months are
Tishri 30
Marheshwan 29
Kisle"w 30
Tebeth 29
Schebhat 30
Adhar 29
Nisan 15 15
192
3. To find the corresponding Christian dates ; first, by the method
of " time elapsed " ; second, by the formula of Gauss.
Time elapsed since the commencement of the Jewish Era to the
New Moon of Tishri, 5799.
a. h. ch.
300 Cycles =2081906 21 300
5 = 34698 10 815
Add for fourth year 1092 15 181
2117697 23 716
That is to say, 2117697 complete days, and 23h. 716ch. of the next day
have elapsed up to the time of New Moon of Tishri 5799. This New
Moon therefore occurs upon the day whose serial number is 2117698,
which is of the form In + 2, and the day is Tuesday, for the Era
commenced with a Monday and the In days terminate with a Sunday ;
the remaining two days are Monday and Tuesday.
On account of the 23h. 716ch. belonging to this Tuesday the
celebration of this New Moon, or Tishri 1, is postponed, by YacH, to
Wednesday, and thence, by ADU, to Thursday, the serial number of
which day will be 2117700.
The total number of Jewish days elapsed before the commence-
ment of the Christian Era is 1373426, so that there remain 744274 days
of that Era to be reckoned.
THE JE WISH CALENDAR 235
This number of days = 2037 Julian years + '260 days of A.D. 2038.
= September 17, A.D. 2038 Julian.
= September 30, ,, Gregorian.
The Sunday Letter for 2038, Gregorian, is C ; September 30 is, there-
fore, Thursday.
For Nisan 15 there are to be added to this date 191 days.
September 17 = day, number 260
191
451
Days in A.D. 2038 365
Day of the year 2039 ... 86
= March 27, Julian.
= April 9, Gregorian.
The Sunday Letter, Gregorian, for 2039 is B ; therefore April 9 is
Saturday.
The required dates are : for Tishri 1, September 30, 2038, Thurs-
day ; for Nisan 15, April 9, 2039, Saturday.
By Formula I. of Gauss
H = 5799. B = 5799 - 3760 = 2039 A.D.
(12a + 17) (69588 + 17) _ Q
~l9~~Jf~r "1ST "Jr."
(5799) _,,
t~T"fr =
The Constant = 32'0440932
a x 1-5542418 = 12-4339344
b x -25 .. = '75
45-2280276
H x -003177794 . .. = 18'4280274
26-8000001
= March 26
236 THE JE WISH CALENDAR
The Christian year is A.D. 2039. The Julian Sunday Letter is C.
March 26 is therefore Friday, and Nisan 15 will be on Saturday,
March 27, Julian, = April 9, Gregorian.
By Formula II.
B = 2039.
(12B
_
19
The Constant = 20'0955877
a x 1-5542418 = 12"4339344
6 x -25 .. = '75
33-2795221
B x -003177794 . .. = 6-4795220
26-8000001
The result is the same as by Formula I. Nisan 15 is postponed
from Friday, March 26, to Saturday, March 27, Julian = April 9,
Gregorian.
For the date of Tishri 1.
It has already been shown that Nisan 15 is the 192nd day of the
year ; therefore 191 days must be subtracted from the date of Nisan 15
to give the date of Tishri 1.
April 9 = January 99, A.D. 2039,
365
= January 464, A.D. 2038,
191
= January 273 = September 30, 2038
THE JEWISH CALENDAR 237
NOTE OX THE FORMULA 6 = "
Neither Dr. Gauss, nor any of his commentators, so far as I am
aware, afford any explanation of the method by which this formula
may be obtained.*
The problem is To find an expression, a function of one variable
n, which has the property of giving for the successive values n =
1, 2, 3, 4, &c., certain integral values fixed in advance, fractions
being neglected, corresponding to the successive values of n.
In seeking such an expression it is, in the first place, clear that,
because the first two years in the Cycle are Common, and the third
is not Common,
e must = 1, when n = 1,
and e must = 2, when n = either 2, or 3.
Again ; before the sixth year is reached, only one Embolismic
year, namely the third, occurs, therefore,
e must = 4 1, or 3, when n = 4,
and e must = 5 1, or 4, when n = either 5, or 6.
In the same way, there are two Embolismic years and five
Common years before the eighth year is reached, therefore,
e must = 7 2, or 5, when n = either 7, or 8.
Proceeding thus, and tabulating the results, we obtain the first and
second columns in the Table which follows.
Now, to find an expression, of which the integral part will give
these required fixed values to e, it is natural to assume for the first
term -j 1Q ;- because in every Cycle of nineteen years there are
twelve which are Common. The question then becomes, What
12 K + 17
' Reno Martin, p. 119, gives a Table for the successive values of - ; (he uses R
-!."
for the H in the formula) ; but he bsgins by assuming that is the correct value
I I /
for c, and only shows, by his Table, that this expression does satisfy the required conditions.
238 THE JE U'ISH CALENDAR
must be the second term? In other words, What increment, ./ .
may be made to the numerator, 12, in order that -
1 1 J )
may give the required known integral values to e, corresponding to
the successive values of n? We must ascertain what is the minimum,.
and what the maximum possible value that can be assigned to jc in
each case.
Thus: For the first year in a Cycle, when n = l, and e must
also = 1, it is necessary to make an increment to VLn of 7, at the
I j \
very least, in order that - Q ;- may = 1 ; for here n = l, and
I j.y )
12+7 is the minimum possible value of the numerator. If the
increment were only 6 we should have - ' Q = 0, whereas
i j.y )
it ought to = 1.
On the other hand, the increment may be increased by any number
greater than 6 up to 25, but the increment must not be more than 25.
/ 1 O.I I rp \
If it were 26, or 27, or 28, &c., -, 1Q j- would have for its numerator
{ iy )
38, or 39. or 40, &c., and this would give 2 for the value of e, whereas
it ought to be not more than 1.
So again, for year 10, that is, when n = 10, and 12;? = 120, the
( 12?i + x i
increment must be at least 13, in order that- - - may = 7, which
i. iy j
is the required value of e, because there are 7 Common years among
the first 10 of the Cycle.
On the other hand, the increment may be any number greater than
13, so long as the maximum does not exceed 31 ; for if the increment
(12 x 10 + 32) .
were 32 we should have \ 1Q , = 8, for the value ot e>
\ J.y i
whereas e must not be more than 7.
In this way the third and fourth columns of the Table are
obtained.
Now from the fifth column it appears that the lowest of all the
maxima increments that can be made is that for the eighth year.
This increment is 17. Also, from the fourth column it appears that
the highest of all the minima increments that can be made is that for
the sixteenth year, and this also is 17. In other words, the
THE JEWISH CALENDAR
*39
increment cannot be less than 17, and cannot be greater than 17 ;:
., -, f 12w + x \ I 12w + 17 )
therefore it must be 17 ; and we have -, - = -
\ -L t/ / _L <7 I
This gives the number of Common years which have occurred in ;i
Cycle when n years of that Cycle have elapsed ; by writing H for >/
we have ] - -yq 1 f or the number of Common years which have
occurred when H years of the Era have elapsed.
- f7H + 1
A similar formula, E
-, may be obtained in like manner
for the number of Embolismic years which have occurred when H
years of the Era have elapsed.
Years of the Cycle.
i =
No. of
Common
years in n.
e =
1271.
Increments that may be made
to 12 H.
Least.
Greatest.
1
1
12
7
25
2
2
24
10
32
3 Emb.
2
36
2
20
4
3
48
9
27
5
4
60
ir>
34
6 Emb.
4
72
4
22
7
5
84
11
29
8 Emb.
&
96
17
'.) 6
108
6
24
10
7
120
13
31
11 Emb.
7
132
1
19
12
8
144
8
26
13
9
156
15
33
14 Emb.
9
168 3
21
15
10
180
10
28
10
11
192
17
25
17 Emb.
11
204
5
23
18
12
216 12
30
19 Emb.
12
228
18
CHAPTEE IX
MEGILLATH TA'ANITH
111. The following account of the Megillath Ta'anith, or Scroll of
Fasting, is derived from a paper read by M. Moise Schwab at the
eleventh International Congress of Orientalists, held in Paris, 1897. It
was published in the following year among the Transactions of that
Society.*
Under the title Megillath Ta'anith there is given a list of com-
memorative days, or anniversaries to be observed, extending from the
commencement of the fourth century before the Christian Era to the
time of the Emperor Antoninus Pius, A.D. 138. The text itself has a
literary interest, for though not so old as the Bible itself, it is anterior
to the Talmudic compositions.
M. Joseph Derenbourg t points out a curious fact connected with
the title, for this short Chronicle, instead of giving a list of Fasts, does
actually enumerate the days which are celebrated as Festivals, or
semi-festivals, upon which it is forbidden to Fast. In this connection
Ewald says : t " The title of the work should be ' List of the Festivals' ;
but a late anonymous elucidator designated it ' Book of Fasts,' because
he appended to it of his own accord a list of the numerous Fast days
to which the Rabbis in the Middle Ages had given the force of law ;
besides, in the* Mishna, Ta'anith iv. 4 sqq., an enumeration of the
Festival days was really begun. The author of the little Festival
book is described by the interpreter at the close of his work as the
* Actes du onzierae congres International cles Orientalistes ; Quatrieme Section, 1897,
pp. 199-259.
t " Essai sur 1'histoire de la Palestine," p. 439.
I "History of Israel," vol. v., f.n. 3, p. 381.
240
THE JEWISH CALENDAR 241
' School of Eleazar, son of Haninah, son of Hezekiah, son of
Garon.' '
M. Schwab says : "Or rather, as is well expressed elsewhere, the
ancient Doctors, disciples of Schamma'i and of Hillel, wrote it in the
chamber of Eleazar when they went to visit him."
Ewald continues : " This very uncertain expression is to some
extent appropriate, for the work could not have been completed in its
ultimate form till the time of the Koman wars, for some of its festivals
are actually derived from them. But even this late and unhistorical
interpreter, who probably did not write till the time of Islam, had still
an obscure feeling that the book first arose in the Asmonean-Greek
age, and looks there for an explanation of everything which he could
not explain from the Old Testament."
It was at the house of the Eleazar here mentioned that meetings
were held, a short time before the destruction of the Temple, for the
purpose of discussing what measures could be taken to prevent any
intercourse with the heathen. The essential plan of this treatise may,
therefore, be referred to that period. Additions have certainly been
made to it in later times, for there are two days commemorative of
events which occurred after the destruction of Jerusalem and the end
of the Jewish state of independence Adhar 12, the Day of Trajan, and
Adhar 28, the revocation by Antoninus Pius of the decrees of Hadrian
against the Jews, A.D. 139 or 140.
There are but few MSS. of this Chronicle ; these are chiefly to be
found in the Bodleian Library.* Only a few editions of the text
have been printed.!
The Chronicle is composed of three distinct parts :
1. The original text.
2. The Scholia, or additions.
3. The Explanations.
The two last parts are sometimes blended together. They form that
which is hereafter called the Commentary. They are the parts that are
* M. Schwab gives the numbers of the MSS. in the Bodleian 641, 3; 867,2; 882;
902; and 2421, Wit.
Of these, 867, 2, and 902 are entire ; the rest are only fragments.
t The best edition is that of Hambourg, with notes by Jacob Israel Emden, 1757.
An edition was published by Ambroise Froben at Bale in 1580. The text, with a Latin
version, is given by I. Meyer, at the end of his " De Temporibus," Amsterdam, 1724. More
recently it has been printed in " Anecdota Oxoniensia," Semitic Series vol. i. part vi.,
pp. 3 to 26.
17
242 THE JE WISH CALENDAR
of more recent date than the original text ; the language in which they
are written is a mixture of Hebrew and Aramaic, like that of the
Talmud. The original text is in the Aramaic dialect.
At the end of the work a certain number of days are enumerated
upon which it is recommended to fast. This series appears to be a
still later addition ; it has no commentary attached. The language is
pure Hebrew.
The memorable days recorded in the Chronicle are thirty-five in
number. They are not given in chronological order, but follow the
order of the months, that is to say, they are given according to the order
of days as they stand in the Calendar.
With respect to the "Commentary and Historical Notices" here-
with the former is that given in the treatise itself as rendered by
M. Schwab ; the Historical Notices are derived partly from Schwab,
but chiefly from " The History of the Jews," by Graetz,* from
Josephus, and from the books of the Maccabees. The quotations from
Graetz are not literal transcripts from that author, but are, as a rule,
much abbreviated.
112. COMMEMORATIVE DAYS.
1. Nisan 1 to 8. The expenses of the daily sacrifices ought to be
defrayed by the Temple.
Mourning is forbidden.
2. Nisan 8 to 22. Restoration of the Feast of Weeks to the fiftieth
day.
Mourning is forbidden.
3. lyar 7. Inauguration of the wall of Jerusalem.
Mourning is forbidden.
4. lyar 14. Day for the sacrifice of the Paschal Lamb. [This is
the Second Passover, Numbers xi. 1.]
Mourning is forbidden.
5. lyar 23. The defenders of Acra have to leave Jerusalem.
(5. lyar 27. The crown taxes revoked for Judaea and Jerusalem.
7. Siwan 15, 16. The dwellers in Bethshean and the Plain are
exiled.
* The references are to the English translation by Miss Bella Lowy, Nutt., London,
1891.
243
8. Siwan 17. The fortress of Bethsura is taken.
9. Si wan 25. The [Eoman] tax-gatherers are withdrawn from
Judah and Jerusalem.
10. Tammuz 14. The Book of Decisions is abrogated.
Mourning is forbidden.
11. Abh 15. Day for the offering of wood to the priests.
Mourning is forbidden.
12. Abh 24. Keturn to the Law.
13. 'Elul 7. Inauguration of the wall of Jerusalem.
Mourning is forbidden.
14. 'Elul 17. The Romans retreat from Judaea and Jerusalem.
15. 'Elul 22. We proceed to kill the Apostates.
16. Tishri 3. The Divine Name removed from Deeds and Docu-
ments.
17. Marheshwan 23. The stones of the altar [which had been defiled],
are buried in the court of the Temple.
18. Marheshwan 25. Samaria was taken.
19. Marheshwan 27. Renewal of the offering of loaves of wheat-flour
on the altar.
20. Kislew 3. The stones of the heathen images removed from the
court of the Temple.
21. Kislew 7. A Festival day.
22. Kislew 21. Day of Mount Gerizim.
Mourning is forbidden.
23. Kislew 25. Commencement of the eight days of the Purification
of the Temple [Chanukka] .
Mourning is forbidden.
24. Tebeth 28. The Synhedrion re-established according to the
Law.
25. Schebhat 2. A Festival day.
Mourning is forbidden.
J'J. Schebhat 22. Counteraction of the work which the enemy had
ordered to be done in the Temple.
Mourning is forbidden.
244 THE JE WISH CALENDAR
27. Schebhat 28. King Antiochus was taken away from Jerusalem.
28. Adhar 8, 9. Days of rejoicing for rain.
29. Adhar 12. The Day of Trajan.
30. Adhar 13. The Day of Nicanor.
31. Adhar 14, 15. Days of Purim.
Mourning is forbidden.
32. Adhar 16. Kebuilding of the walls of Jerusalem is commenced.
Mourning is forbidden.
33. Adhar 17. Israel delivered, when the heathen rose against the
Doctors of the Law, in the Province of Seleucia and in
Beth-Zebedee.
34. Adhar 20. The people fasted to obtain rain, and the rain fell.
35. Adhar 28. The Jews receive the good news that they are no
longer to be prevented from following the ordinances of
their Law.
Mourning is forbidden.
Nevertheless, every one who had previously made a vow r to fast is
bound by his prayer.
These, then, are the thirty-five commemorative days for rejoicing,
to be observed as minor, or semi-festivals. They may be arranged
chonologically in six divisions, as follows :
Division A. In this division there is but one day, lyar 14. This alone
of the minor Festivals recalls any of the Mosaical ordinances.
Division B, contains three days : anniversaries instituted previous to
the time of the Hasmouaeans.
'Elul 7. Rebuilding the walls of Jerusalem by Nehemiah.
Adhar 14, 15. The Feast of Purim.
Abh 3. The Festival of the Wood-offering.
Division C, contains fifteen days, instituted as anniversaries in the
time of the Hasmonaeans. Some of these recall the victories over
the Syrians and Greeks ; others are in remembrance of happy
events which followed in consequence of those victories. All these
days are within the time of the Hasmonaean princes, Judas
Maccabaeus, Jonathan, Simon, and Johanan Hyrcanus.
THE JE WISH CALENDAR
245
Division D, contains ten days ; eight of these commemorate events
in the reign of Queen Salome Alexandra, B.C. 79-70 ; two refer to
the reigns of Aristobulus and Hyrcanus II.
Division E. Time of the Roman domination, four days ; previous to
the destruction of the Temple and to the end of the Jewish state
of independence.
Division F. Two days, instituted as anniversaries at a later period,
Adhar 12, and Adhar 28.
The following Index will facilitate reference from the list of Com-
memorative Days arranged in monthly order to the Historical Notices,
which are in chronological order.
The first column contains the numbers attached to the days in
the former list ; the second has the day of the month ; the third, the
division under which the day is placed ; and the fourth gives the
numbers of the days as arranged in the Historical Notices.
1
Nisan 1-8
D
XXIV.
20
KislSw 3
C
V.
2
8-22
D
XXV.
21
7
D
XXI.
3
lyar 7
C
XIX.
22
21
C
XIV.
4
14
A
I.
23
25
C
VI.
5
23
C
X.
24
Tebeth 28
D
XX.
6
27
C
XIII.
25
Schebhat 2
E
XXX.
7
Siwan 15, 16
C
XVI.
26
22
E
XXXI.
8
17
C
XI.
27
28
C
vn.
9
25
E
XXXII.
28
Adhar 8, 9
D
XXIX.
10
Tammuz 14
D
XXII.
29
12
F
xxxrv.
11
Abb. 15
B
IV.
30
13
C
VIII.
12
24
D
XXIII.
31
14, 15
B
III.
13
'Elul 7
B
II.
32
16
C
xvm.
14
17
E
XXXIII.
33
17
D
xxvu.
15
22
C
XII.
34
20
D
XXVIII.
16
Tishri 3
C
XVII.
35
28
F
XXXV.
17
Marheshwan 23
C
IX.
18
25
C
XV.
19
27
D
XXVI.
246 THE JE WISH CALENDAR
113. COMMENTABY AND HISTOEICAL NOTICES.
DIVISION A.
Mosaical Ordinance.
DAY I.
lyar 14. This refers to the secondary observance of the Passover
on the " fourteenth day of the second month," permitted to those who
had been prevented by any material cause from celebrating the Feast
on the fourteenth day of the first month. Numbers ix. 9-11, "And
the LORD spake unto Moses, saying, Speak unto the children of
Israel, saying, If any man of you, or of your posterity shall be
unclean by reason of a dead body, or be in a journey afar off, yet
he shall keep the Passover unto the LORD. The fourteenth day of
the second month at even they shall keep it, and eat it with unleavened
bread and bitter herbs."
DIVISION B.
Anterior to the time of the Hasmonceans.
DAY II.
'Elul 7. [Restoration of the walls of Jerusalem by Neheniiah. The
commentator adds, " The walls of Jerusalem had been thrown down
by the Syrians. When Israel again obtained supremacy they were
rebuilt, as it is said, ' the wall is finished.' '
Nehemiah vi. 15. " So the wall was finished in the twenty and
fifth day of the month 'Elul, in fifty and two days."
M. Schwab says with respect to this, that 'Elul 25 is definitely
fixed for the date, but without doubt the reconstruction of the wall
was well advanced by 'Elul 7.
DAY III.
Adhar 14 and 15. The Feast of Purim.
" After the death of Moses there was no prophet who had
prescribed to the Israelites a new commandment, with this exception
to observe the feast of Purim. There is only one distinction
THE JEWISH CALENDAR 247
between the feasts prescribed by Moses and this feast. The de-
liverance from Egypt was celebrated for example during seven days,
while the feast of Mordecai and Esther had only one day. If we
celebrate as a feast the escape from Egypt, where the lives of our
children alone were in peril, how much more reason is there for
us to be joyful on the anniversary of the day when the miracle was
wrought under Mordecai and Esther which delivered from danger men
and women, children and aged persons."
DAY IV.
Abh 15. The wood-offering. [Xylophoria.]
According to the Commentary, " this anniversary had for its origin
the return from the Babylonish Captivity. By order of the Doctors
of the Law the Israelites, when freed, brought wood for the burnt
sacrifices. The day was instituted as a commemorative festival
because the enemies of Palestine had in vain endeavoured to prevent
this from being done."
Nehemiah x. 34. "We cast lots among the priests, the Levites,
and the people for the wood-offering, to bring it into the house of our
God, after the houses of our fathers, at times appointed year by year,
to burn upon the altar of the LORD our God, as it is written in the
law."
Josephus, "Wars of the Jews," bk. ii. ch. xvii. . 6, speaks of this
day as a Festival in the time when Florus was governor. See post,
under 'Elul 17, Day xxxiii.
It appears that after the return from the Captivity the number
of Levites, part of whose duty it was to provide wood for the altar,
was so reduced that a regular supply could not be maintained. Kene
Martin * states that the accounts of these Festivals as given by Selden,
De Zach, and Le Boyer are not in accord, but he obtained from the
chief Kabbi the following information : " The Xylophoria were nine in
number, Ntsan 1, Tammuz 20, Abh 5, 7, 10, 15, 20, 'Elul 20, and
TSbeth 1. The privilege of providing wood for the Temple on the
appointed days was accorded to certain families, and the festival
celebrated on these occasions was for the family whose turn had
arrived."
* " Memoire sur le Calendrier Hebralque," p. 371.
248 THE JE WISH CALENDAR
DIVISION C.
In the time of the Hasmonccans.
DAY V.
Kislew 3. The Simot, or large stones of the heathen images, are
cast out of the Temple. B.C. 165.
The Greeks had erected statues and idols in the outer court, or
public precinct of the Temple. Twenty-two days before the re-
consecration of the Temple (which Josephus, " Antiq.," xii. vii. 6, says
took place on Kislew 25) the Hasmonaeans threw down these idols.
The account is given in 1 Maccabees iv. 42, 43, where we are told
that Judas Maccabaeus " chose priests of blameless conversation, such
as had pleasure in the law : who cleansed the sanctuary and bare out
the denied stones into an unclean place."
These were the large stones, Simot, either of the idols themselves
or upon which the images had been placed. The author of the Book
of Maccabees makes a distinction between these and the smaller
stones, Sorega, with which the altar was built. The latter were
not removed to an unclean place, but were buried in the court of
the Temple. See post, Marheshwan 23, Day ix.
With respect to the defilement of the Temple, Graetz, vol. i.
ch. xxii. p. 470, gives the following history : " Antiochus Epiphanes
had issued a decree, which was sent forth to all the towns of Judaea,
commanding the people to renounce the laws of their God, and to
offer sacrifice only to the Greek gods. In order to strike an effectual
blow at Judaism he ordained that unclean animals, particularly swine,
should be used at the sacrifices. He forbade, under severe penalty,
the three religious rites which outwardly distinguished the Judaeans
from the heathen, namely, circumcision, the keeping of the Sabbath,
and the abstinence from unclean food. . . . The Temple was first
desecrated, and Antiochus sent a noble there to dedicate the Sanctuary
to Jupiter. A swine was sacrificed on the altar in the fore-court, and
its blood was sprinkled in the Holy of Holies on the stone which
Antiochus had imagined to be Moses' statue ; the flesh was cooked,
and the melted grease spilt over the leaves of the Holy Scriptures.
. . . The roll of the Law, which was found in the Temple, was not
only bespattered, but burnt, because, though it taught purity and
morality, Antiochus maintained that it inculcated hatred of mankind.
THE JE WISH CALENDAR 249
. . . The statue of Jupiter was placed on the altar, ' the abomination
of destruction,' to which sacrifices are now to be offered." This
occurred in B.C. 168, on Kislew 15, according to 1 Maccabees i. 54.
According to M. Derenbourg,* as quoted by M. Schwab, the words
Simot and Sirouga, or Sorega, are of uncertain signification. It can,
however, be gathered that they indicate two different objects in stone,
of which one commanded respect, while the other was cast aside
without hesitation.
Josephus gives the account of the actions of Antiochus in
" Antiquities," xii. v. 4, and of the cleansing of the Temple in xii. vii. 6.
DAY VI.
Kislew 25. Keconsecration of the Temple. B.C. 165.
2 Maccabees x. 5-8. " Upon the same day that the strangers
profaned the Temple, on the very same day it was cleansed again, even
the five and twentieth day of the same month, which is Casleu. And
they kept eight days with gladness, as in the feast of the tabernacles,
remembering that not long afore they had held the feast of the
tabernacles, when as they wandered in the mountains and dens like
beasts. . . . They ordained also by a common statute and decree,
That every year those days should be kept of the whole nation of
the Jews."
Josephus, ' Antiq.," xii. vii. 7, says that this Festival, Channitkka,
was called the Feast of Lights.
Graetz, vol. i. ch. xxiii. p. 488. " All the people from every town
of Juda3a took part in the festival, and the inhabitants of Jerusalem
lit bright lamps in front of their houses as a symbol of the Law,
called ' Light ' by the poets. The Hasrnonsean brothers and the other
members of the Great Council decided that in future the week
beginning on Kislew 25 should be held as a joyous festival, to com-
memorate the consecration of the Temple. Year after year the
members of the House of Israel were to be reminded of the victory
of a small body of men over a large army, and of the re-establishment
of the Sanctuary. This decree was conscientiously carried out. For
two thousand years these days have been celebrated as ' the days
of Consecration ' (Channukka), and lamps have been lighted in every
household in Israel. The days derived their name of ' Feast of
Lights ' from this custom."
* " Essai sur 1'histoire de la Palestine," p. 60.
250 THE JEWISH CALENDAR
M. Schwab says that this is the historical basis for the tradition
concerning a miraculous supply of pure oil. He says nothing more
about this tradition, but it is given by Dr. Bannister in his book,
" The Temples of the Hebrews," p. 391 : " When they were employed
in cleansing the Temple, after it had been profaned by the Greeks,
they found there only one small phial of oil, sealed up by the High
Priest, which would hardly suffice to keep in the lamps so much
as one night ; but God permitted that it should last several days, till
they had time to make more : in memory of which the Jews lighted up
several lamps in their synagogues and at the doors of their houses."
DAY VII.
Schebhat 28. Anniversary of the death of Antiochus Epiphanes.
B.C. 164.
Graetz, vol. i. ch. xxiii. p. 493. " Suddenly important news came
to Palestine concerning Antiochus Epiphanes. The progress of that
monarch through Parthia had not been signalised by any military
success ; nor had he been able to refill his treasury. Driven by want
of money he undertook an expedition to the city of Susa in Elymais,
to plunder the temple of the goddess Anaitis ; but the inhabitants
resisted the invader and forced him to retreat. He fell sick in the
Persian city of Tabae, and expired in frenzy."
This account is derived from 1 Maccabees vi. 1-16 ; another history
of his dishonour in Persia, his terrible disease, and his death, with
fuller details is recorded in 2 Maccabees ix.
Josephus, "Antiq.," xii. ix. 1, is somew r hat brief in his account.
Driven away from the siege of Susa in Elymais, " he fled as far as
Babylon, and lost a great many of his army. And when he was
grieving for this disappointment, some persons told him of the defeat
of his commanders whom he had left behind him to fight against
Judaea ; ... he was confounded, and by the anxiety he was in,
fell into a distemper, which, as it lasted a great while, and as his
pains increased upon him, so he at length perceived he should die
in a little time ; so he called his friends to him, and told them that
his distemper was severe upon him for the miseries he had brought
on the .Jewish nation, while he plundered their Temple and con-
demned their God; and when he had said this, he gave up the
ghost."
THE JEWISH CALENDAR 251
DAY VIII.
Adhar 13. Commemorative of the defeat and death of the Syrian
general Nicanor at the battle of Adarsa. B.C. 160.
This day is mentioned as one to be observed in both the Books
of the Maccabees ; I. vii. 49, " Moreover, they ordained to keep yearly
this day, being the thirteenth of Adhar; " and, II. xv. 36, "And they
ordered all with a common decree in no case to let that day pass-
without solemnity, but to celebrate the thirteenth day of the twelfth
month, which in the Syrian tongue is called Adhar."
Demetrius, surnamed Soter, son of Seleucus Philopator, had been
sent when a child to Eome, as a hostage, by his father. He remained
there during the reign of Antiochus Epiphanes ; but after the death
of that king he demanded his liberty. This was refused by the Senate,
and he fled secretly from Rome, accompanied by his friend Nicanor.
He went to Syria, where he was well received. The young king
Antiochus Eupator, son of Epiphanes, was put to death by his own
guards ; and Demetrius obtained from the Eomans the recognition of
himself as king. Shortly afterwards he sent Nicanor against Judas
Maccabseus, and " on the thirteenth day of the month Adhar the hosts
joined battle, but Nicanor's host was discomfited, and he himself was
first slain in the battle " (1 Maccabees vii. 43).
Graetz, vol. i. ch. xxiii. p. 501. Nicanor marched out from
Jerusalem at the head of an immense army, pitching his camp at
Bethoron, whilst Judas, surrounded by 3,000 of his bravest followers,
took up his post at Adarsa. Judaean valour was once more triumphant
over the superior numbers of the Syrians. Nicanor fell on the battle-
field, and his army fled in utter confusion. . . . The battle of Adarsa
was of so decisive a character that its anniversary was celebrated in
years to come under the name of the Day of Nicanor.
The head and one of the arms of Nicanor were cut off, and hung as
trophies upon the walls of Jerusalem. 2 Maccabees xv. 32, 35.
DAY IX.
Marheshwan 23. Restoration of a partition wall in the Temple
which had been cast down by the High Priest Alcimus.
With respect to this day the text says, " They buried the Sorega in
the court of the Temple in order to hide them " : it is so rendered by
M. Derenbourg, p. 61.
252 THE JEWISH CALENDAR
M. Schwab states that the Commentator has not understood the
subject upon which he was engaged, and has confused this date with
that of Nisan 1 (? Kislew 3). The heathen, says the Commentator,
had erected in the court a construction for which they had used some
of the stones of the sacred edifice (a laquelle ils avaient aussi employe
de bonnes pier res). It was decided that these stones should be
allowed to remain until the arrival of the prophet Elias, in order that
he might decide which of them were pure, and which were impure.
Accordingly M. Derenbourg renders the original text as above. In
support of this he adds the following argument : "It is sufficient to
compare the passages in the Chronicle with those in the First Book of
Maccabees, in order to recognise the fact that the Sorega must have
been a part of the altar of burnt offerings which had been defiled, or a
collection of stones erected above the altar upon which the heathen
had offered sacrifice. There was an uncertainty about these stones :
some of them might have been holy originally, some might have
formed a part of the material brought from outside, and erected upon
the altar. The decision which was reached is described alike in the
First Book of Maccabees, and in the Megillath Ta'anith. Moreover,
there is an indication in the Mishna (Tr. Middoth, i. 6), that the
Hasmonaeans buried the stones of the altar which the Greek kings had
defiled."
M. Schwab says that this explanation is too plausible to be refused
admission. Nevertheless, he describes this day as. commemorative of
the restoration of the wall which Alcimus pulled down, or proposed to
pull down. This wall consisted of a wooden partition between the
courts of the Gentiles and of the women. It was called Soreg because
made of laths superimposed in the way of grill- work. In 1 Maccabees
ix. 54 it is called " the wall of the inner hall of the Sanctuary," TO
Tti\oq rfig uAjc TMV aytuv rJjc lawrtpag, and is said to have been the
Work of the prophets, ipya TMV Trpo^rjrwv.
Josephus, "Antiq.," xii. x. 6. "As the High Priest Alcimus was
resolving to pull down the wall of the Sanctuary, which had been
there of old time, and had been built by the holy prophets, he was
smitten suddenly by God and fell down . . . and undergoing torments
for many days he at length died."
Alcimus was the Greek name of Jakim, a priest who was nephew
to Jose one of the teachers of the Law. He was made High Priest by
Demetrius, and was devoted to the interests of. the Syrian court. It
THE JEWISH CALENDAR 253.
was through his accusations against the Hasmonaeans that Nicanor
was sent against them. When Judas Maccabaeus fell at the battle of
Eleasa, B.C. 160, Alcimus obtained full possession of the Temple and
the Holy City.
With respect to the particular act in question Graetz says, i. xxiii.
p. 509, " The offence with which he was reproached appears, on closer
examination, hardly to have been a sin aimed against the religion of
the Judaeans. It appears that between the inner and outer courts of
the Temple was a kind of screen, named, on account of its fragility,
' Soreg.' This screen, the work of the prophets, as it was called, was
used as a boundary, which no heathen might pass to penetrate into
the Temple. But Alcimus gave orders for the destruction of this
partition,, probably with the intention of admitting the heathen within
the sacred precincts. The pious Judaeans were justly incensed, and
when Alcimus was seized, directly after this command, with paralysis
of speech and of body, from which he never recovered, they attributed
his fatal illness to Heaven's wrath."
DAY X.
lyar 23. Capture of the Fortress Acra, and expulsion of the
Syrians. B.C. 142.
In the text we read, " The sons of Acra retire from Jerusalem."
The expression " Sons" for Defenders occurs also in 1 Maccabees iv. 2,
where the English, version has, " And the men of the fortress were his
guides " ; the Greek is " KOI ol vioi TJJC aicpac; i]aav awrtjJ bSriyoi."
The Acra, or Acropolis, was a fortress on the north-west of the
Temple which had been erected by the Syrians, and was held by a
strong garrison: but Simon, the High Priest, " took the citadel of
Jerusalem by siege, and cast it down to the ground, that it might not
be any more a place of refuge to their enemies when they took it, to
do them a mischief, as it had been till now." Josephus, "Antiq.,"
xiii. vi. 7.
The casting of the citadel to the ground is not mentioned in
1 Maccabees xiii. 49-52, and is apparently an erroneous statement,
founded however on circumstances which are narrated by Graetz,
i. ch. xxiv. p. 543, " The newly recovered Acra underwent various
changes at the hands of the Hasmonaeans. The wrath of the people
had been too much excited against this fortress to allow of its standing
intact ... it overtopped the Temple-capped Mount itself, and thin
254 THE JEWISH CALENDAR
was not to be. According to the prophecies of Isaiah, in the last days
the Mount, on which the Temple stood should rise above all other
mountains, and be higher than all other heights. This was literally
explained to mean that no mount or building should soar above the
Temple, and Simon, if even unconvinced himself, was obliged to bow
to that belief. ... In dealing with it a middle course was hit upon.
The towers and bastions were taken down ; the walls, courts, and
halls were left standing, but the hated name of Acra was no longer
used, but changed for that of Birah. In this transformed edifice the
Jewish soldiers were quartered, and there they kept their weapons.
Simon himself dwelt in the Birah in the midst of his soldiers."
M. Schwab says that the expression " Sons of Acra " has given
rise to an etymological error. The Commentator has substituted
41 Karaites" for the original word Acra. This is a serious anachronism.
The Karaites were the followers of Anan, who was recognised as the
legitimate " prince of the captivity " by many Jews about the year 765
of the Christian Era.*
Dr. Bannister has followed the Commentator, and fallen into this
error ; " Temples of the Hebrews," p. 394. In speaking of lyar 23, he
says, " A feast for the expulsion of the Karaites out of Jerusalem, by
the Maccabees; according to the Calendar of Sigonius." In describing
the Jewish sects, he says of the Karaites, p. 377, " This sect was an
offshoot from the Zadikim " [i.e., "the righteous," who adhered to
the written Law of Moses strictly, and who came into existence after
the return from Babylon], "but the precise time of its origin is
unknown."
DAY XI.
Siwan 17. Fortress of Bethsur taken. B.C. 142.
This was one of the fortresses taken by Simon from the Syrians
and Hellenistic apostates. Its capture is mentioned only incidentally
in 1 Maccabees xiv. 33, where it is said that Simon "fortified the
cities of Judaea, together with Bethsura that lieth upon the borders of
Judaea, where the armour of the enemies had been before." At the
same time he took Gazara and Joppa.
* Schaff-Herzog, "Religious Encyclopaedia," vol. ii. p. 1225. Graetz, vol. iii. ch. v.
p. 136 of the English edition. Vol. v" p. 174 of the 2nd German edition. Al-Biruni, p. 68,
who, however, gives the date more than one hundred years too late, making it 110 years
(about) before he wrote his book in A.D. 1000.
THE JEWISH CALENDAR 255
DAY XII.
'Elul 22. Extermination of the renegades, or Hellenistic apostates.
The Commentator says that so Jong as they remained under the
rule of the heathen [the Syrians] , the Jews took no action against
these impious persons ; but when they attained their freedom they
warned the unbelievers, and allowed them three days for reflection and
repentance. As no account was taken of this warning, the people
rose up and exterminated them.
An indication in 1 Maccabees xiii. 50 seems to contradict this, for
it is there narrated that " they of the tower in Jerusalem being in
great distress for want of victuals, cried to Simon beseeching him to
be at one with them : which thing he granted them." M. Schwab
assumes that Simon granted to these people a free passage; but points
out that from 1 Maccabees xiv. 14, we may conclude that at least a
part of them were annihilated, " Every contemner of the law, and
wicked person he took away."
Graetz, i. xxiv. p. 543, says, "It is related that 'Elul 22 was set
apart among the days of victory, because it saw the death of those
idolaters who had allowed the respite of three days to elapse without
returning to their faith."
DAY XIII.
lyar 27. Cessation of the crown taxes collected for the Syrians.
B.C. 142.
1 Maccabees xiii. 36, 39-41. " King Demetrius unto Simon the
High Priest and friend of kings, as also unto the elders and nation of
the Jews, sendeth greeting : ... As for any oversight or fault com-
mitted unto this day, we forgive it, and the crown tax also, which ye
owe us : and if there were any other tribute paid in Jerusalem, it shall
no more be paid. . . . Thus the yoke of the heathen was taken away
from Israel in the hundred and seventieth year."
Graetz, i. ch. xxiv. p. 541. "The people looked upon these conces-
sions of Demetrius as the inauguration of their independence, and
from that epoch the customary manner of counting time according to
the years of the reigning King of Syria was discontinued. Thus, in all
public documents in the year 142 B.C. we read, ' In the first year of
the High Priest Commander of the army, and Prince of the nation,
Simon.'"
256 THE JE WISH CALENDAR
So, also, 1 Maccabees xiv. 42. "Then the people of Israel began
to write in their instruments and contracts, ' In the first year of Simon
the High Priest, the governor and leader of the Jews."
DAY XIV.
Kislew 21. Destruction of the Samaritan Temple on Mount
Gerizim. B.C. (circa) 120.
The Samaritan Temple was built in the tune of Alexander the
Great (Josephus, "Antiq.," xiii. iii. 4). This would be after the march
of Alexander into Palestine in B.C. 332. Graetz, i. ch. xx. p. 402,
assigns an earlier date, " Thus on the summit of the fruitful Mount
Gerizim, at the foot of Shechem, in the very heart of the land of
Palestine, Sanballat built his temple, probably after the death of
Artaxerxes (420).
About the year 120 B.C. John Hyrcanus, the fourth of the Has-
nionaean princes, conquered the Samaritans and utterly demolished
their Temple. Graetz, ii. ch. i. 8, says, " The anniversary of the
destruction of this temple was to be kept with great rejoicing, as the
commemoration of a peculiarly happy event, and no fasting or mourn-
ing was ever to mar the brightness of the festival. From this time
forth, the glory of the Samaritans waned."
DAY XV.
Marheshwan 25. Destruction of Samaria, B.C. 109. Samaria
capitulated to Hyrcanus and was given up to him after he had besieged
it for a whole year. He caused it to be entirely destroyed, and the
ground on which it stood to be intersected by ditches and canals so
that not a trace of it should remain. Josephus, "Antiq.," xiii. x. 3.
Graetz, ii. ch. i. p. 11.
The day of its surrender was added to the days of thanksgiving.
DAY XVI.
Siwan 15, 16. Recovery of the city of Bethshean (Scy thopolis) ,.
and of the valley of Jezreel. B.C. 109.
The Syrian king, Antiochus Cyzicenus, manifested a fierce hatred
against Hyrcanus. His generals invaded Judaea, took several
fortresses near the sea-coast, and placed a garrison in Joppa.
Hyrcanus sent five ambassadors to Rome to complain to the Senate,
THE JEWISH CALENDAR 257
and a decree was promulgated forbidding Antiochus to molest the
Judaeans, and commanding him to restore the fortresses and territories
he had seized. He called to his help the co-regent of Egypt,
Ptolemy VIII., called Lathurus, who sent auxiliary troops. These
were placed under the command of two generals, Callimandrus and
Epicrates ; the first lost his life in battle : the second yielded to
bribery, and delivered into the hands of the two sons of Hyrcanus the
town of Bethshean, with all its environs, and other places in the plain
of Jezreel, extending as far as Mount Carmel that is, the whole
valley of Jezreel. Schwab, p. 227. Graetz, ii. i. p. 10.
The anniversaries of the recovery of Bethshean and of the Plain,
and their incorporation in the territory of Judaea, were added to the
days of Victory.
DAY XVII.
Tishri 3. The mention of the Divine Name is suppressed on
official documents.
The Commentator. says, "After their victories the Hasmonaeans
adopted the custom of placing the Divine Name* on their documents
and contracts ; as for an example of their method of writing ' in
such a year of the High Priest Jochanan, who served the Supreme
Being.' The Doctors of the Law disapproved of this practice, for they
said that many a memorandum of indebtedness might be torn up after-
payment had been made, and the pieces be cast upon the ground.
To avoid the risk of this profanation the usage was suppressed, and
the day upon which this was done was observed as a Festival."
M. Schwab considers that this gloss is badly founded. He says :
" It is inadmissible to suppose that they would think it necessary to
glorify a rule of so little importance, made to provide against an
exceptional mischance." But surely the strict Jews would not consider
this a matter of little importance. A piece of parchment, or other
material, with the sacred name written upon it might, if cast upon the
ground, be trodden upon. This would be profanation, and would be a
thing to be avoided. Schwab, however, gives the following as a more
probable reason for the observance of this anniversary : Under the
rule of Simon the enforced use of the Era of the Seleucidae was
suppressed. This Era, called by the Jews the Era of. Contracts,
because used for all deeds and articles of agreement, was imposed on
* The Tetragrammaton, or Tetragram JHWH.
18
258 THE JE U'lSH CALENDAR
them by the Syrians. It was odious to them ; and their rejoicing at
its suppression is explained. He says that Ewald wrongly supposes
that in spite of the introduction of a method of computing according
to the regnal years of the Hasmonaean princes,* the Era of the
Seleucidae was maintained by the Jews in their ordinary life up to the
Middle Ages. This, he says, is incorrect, for neither during the
existence of the Temple at Jerusalem, nor under the Roman rule, did
the Jews of Palestine employ this Era. On the contrary, its employ-
ment annulled any act of divorce which bore such a date ; and the
use of the Era can only be attributed to the Babylonian Jews, the
Middle Ages offering a few scattered examples. He refers to Tr.
Guittin, f. 80a, and the Seder 'olam rabba, towards its end.
DAYS XVIII. AND XIX.
Adhar 16 and lyar 7. Restoration of the walls of Jerusalem.
The repair of the walls in the time of the Maccabees was com-
menced on Adhar 16, and completed on lyar 7. It is not known
under which of the Hasmonaean princes these days were appointed as
commemorative, for the restoration occupied the whole period of
Judas, Jonathan, Simon, and Hyrcanus.
The Commentator has referred this restoration erroneously to that
which was done in the time of Nehemiah.
DIVISION D.
After the independence of Judaea had been assured there com-
menced a long series of disputes between the two sects of the
Pharisees and the Sadducees. This was kept up until after the death
of Alexander Jannaeus, in B.C. 79. Graetz says that the bitter
rivalry of the two kingdoms of Judah and Israel, in the days of
Rehoboam and Jeroboam, was repeated in the history of the strife
between the Pharisees and Sadducees.
Under the reign of Queen Salome Alexandra, B.C. 79-70, who was
devoted to the Pharisees, the chief of that sect obtained the ascendancy,
and the Pharisees celebrated all the days upon which they had been
especially successful against their adversaries.
* See above, Day XIII., lyar 27. Ewald's observation is in vol. v. p. 335, f.n. 1.
THE JEWISH CALENDAR 259
DAY XX.
Tebeth 28. Reorganisation of the Synhedrion in conformity with
the Law.
In order that the question herein involved may be understood it
will be necessary to give some historical details.
The unfriendly relations between the Pharisees and the Sadducees
-did not exist, to any extent, in the time of Hyrcanus. He made
use of both parties according to their capabilities ; the Sadducees
:as soldiers and diplomatists ; the Pharisees as teachers of the Law,
judges, and functionaries in civil affairs. The former honoured
Hyrcanus as the head of the state, the latter as the pious High
Priest. In point of fact Hyrcanus was personally in favour of the
Pharisees, but as Prince he could not quarrel with the Sadducees,
whose leader, Jonathan, was his devoted friend. Until he was over-
taken by old age Hyrcanus managed to solve the difficult problem
of keeping in a state of amity two parties who were always on the
verge of quarrelling ; but in the last years of his life he went quite over
to the Sadducees. He had been bitterly offended by a certain Eleazar
ben Poira, who had stated that his mother had been taken prisoner by
the Syrians, and that it was not fitting for the son of a prisoner to be
a priest much less a High Priest. Hyrcanus then deposed the
Pharisees from the various important posts that they had filled ; and
the offices belonging to the Temple, to the courts of law, and to the
High Council were given to the followers of the Sadducees.
Hyrcanus died in B.C. 106, a short time only after these events.
He had proclaimed his wife to be Queen, and his eldest son Judah,
better known by his Greek name Aristobulus, to be High Priest.
Aristobulus supplanted his mother on the throne, and put her in prison,
together with three of his four brothers. He died after a reign of one
year, in B.C. 105.
He was succeeded by his brother Alexander Jannseus, the third son
of Hyrcanus. He reigned for twenty-seven years. During his reign
the Pharisees were again allowed to appear at Court. Simon ben
Shetach was constantly in the king's presence. He was the brother
of Salome Alexandra, the wife of Jannaeus, who was a warm partisan
of the Pharisees, among whom her brother was a chief leader.
Ever since the secession of Hyrcanus from Pharisaism the Great
Council had been composed entirely of Sadducees, but Jannaeus was
disposed to bring about some kind of equality between the two
260 THE JEWISH CALENDAR
parties by dividing between them the offices of state. The Pharisees
positively refused to act with their opponents. Simon ben Shetach
alone allowed himself to be elected as a member of the Council.
After a time, 
