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152 THE JEWISH QUARTERLY REVIEW 



BEN MEIR AND THE ORIGIN OF THE JEWISH 
CALENDAR. 

Among the " Egyptian Fragments " which Dr. Neubauer published 
in the October number of the Jewish Qtjaktebly Review (IX, 
pp. 24-38), the most interesting is undoubtedly the portion of a 
letter directed against Ben Meir (pp. 36-38) x . Its writer 2 reports 
that he had heard at Aleppo that Ben Meir wished to declare the 
months Marcheshvan and Kislev defective (D'HDn); whereupon he 
sent letters to Ben Meir and warned him not to do so, as these 
months were plenary (Wu?W). After he had returned to Bagdad, 
he learnt that Ben Meir had, in spite of the warning, proclaimed, 
two months previously,, both Marcheshvan and Ki3lev defective, 
in accordance with his own calculations. To counteract the effect 
of this step, Ben Meir's opponent sent epistles to all congregations, 
including those of the Exilarch and of the heads of the schools 
(probably Sura and Pumbaditha), informing them that the two 
months in question must, according to all authorities, be accepted 
as plenary, and that the coming Passover would therefore commence 
on a Tuesday. Once more he urgently appeals to the community 
to take the necessary measures to save the Jews from being misled 
by Ben Meir's calculation — which made Passover fall on a Sunday — 
into the desecration of that feast by eating leaven on it, and eating, 
drinking, and working on the day of Atonement. 

Concerning the personality of this Ben Meir, his activity and 
the period in which he flourished, some information can be 
obtained from another fragment, published by Dr. Harkavy 8 . From 
this source, as Well as indications in Saadiah's *1?3n "ISD, it appears 

1 This fragment calls for much textual criticism. On p. 37, 1. 3, 
302 1UJ vb is not quite clear : for }nv 29 read J01 w : 1. 5, for Tirm read 
roiroi (cp. the second line from the bottom of the page D'«nn o© ypn 'nrrwi 
TnaN -prn dst'jm DrrnnaN rt«): instead of ds»n read dson' : 1. 7, after 
lYfnrf) add vW>, as in 1. 13 : 1. 8, for usmrrti read wtinVi : last line, for 
mop! read Diinjri. 

* Dr. Neubauer suggests that the writer was Saadiah. See below, 
p. 153, n. 1. 

3 Studien und Mittheilungen, V, 212-221. 



BEN MEIR AND ORIGIN OF JEWISH CALENDAR 153 

that Ben Meir was a scion of the Hillelites, that he was head of 
a school in Palestine, lived at the beginning of the tenth century, 
and strove to re-assert the authority of Palestine in the appointment 
of the New Moons and Festivals. He sought to win converts for 
his views among the communities outside Palestine ; and, with this 
object, sent his son on missions to various places, where he indeed 
seems to have found considerable support. The heads of the schools 
in Babylon feared a schism in Judaism, and commissioned Saadiah, 
who was at that time in Egypt, to issue an Epistle to the congrega- 
tions denouncing Ben Meir's ideas and aims. Saadiah composed 
a charge of this character in the month of Tebeth, 1233 aer. contr. 
(end of 921). Ben Meir replied, in detail, in a letter he sent to the 
congregations in Babylon, and endeavoured afresh to establish the 
authority of Palestine. Saadiah replied to this with his D^yiDD "1DD 1 . 
We may assume with some degree of certainty that the incident 
narrated in Dr. Neubauer's fragment really took place also in 921, and 
it is more than probable that only after Ben Meir had attempted to 
give an emphatic practical expression to his theory by attempting 
to dislocate the Festivals on two days, that the official repre- 
sentatives of the Judaism of those times took alarm, and felt it 
necessary to utter a note of warning. This account of the event 
receives weighty confirmation from the testimony of a Syrian his- 
torian. Elias of Nisibis (obiit post 1046) tells us that the year of 
the Hegira 309 began on Saturday, the 22nd of Ijar, in the year 
1232 of the Greek era; and that, in this year, a schism broke out 
between the Eastern and Western Jews in reference to the dates 
of the Feasts. The Western Hebrews began their year on a Tuesday, 
the Eastern on a Thursday 2 . Here we have clear evidence that 
the Eastern Jews, i. e. those of Babylon, celebrated the New Tear's 
day in 1233 on a Thursday, and consequently the preceding Passover 
must have begun on a Tuesday, which corresponds with the narra- 
tive in the letter against Ben Meir. We see also that the Western 
Jews, i. e. those in Palestine, followed the head of their school and 
kept Passover — and consequently all the other feasts— two days 

1 My exposition is entirely based on Dr. Harkavy's views, in which, how- 
ever, there is much that is uncertain. If Saadiah had really been invited 
to Babylon in the year 921 for the purpose of refuting Ben Meir, he 
might also have visited Aleppo ; and the fragment edited by Dr. Neubauer 
may in fact be by him. Cp. also Zeitschr.f. hebr. Bibliogr., II, 79, note 1. 

2 Fragmente syrischer und arabischer Historiker, edited by Prof. Baethgen, 
text, p. 84, translation, p. 141 (cp. also the Jewish Quarterly Review, II, 
p. 107). Elias of Nisibis always gives his authority, with unfortunately 
this exception (and a few others). 



154 THE JEWISH QUARTERLY REVIEW 

earlier than their Eastern co-religionists. Ben Meir's injunctions had, 
accordingly, been obeyed ; and this it was which threatened a serious 
danger to the religious leaders of the Babylonian communities. 

The events here related we have also rediscovered in a Hebrew 
source, viz. in Sahl b. Mazliach's polemic against Jacob b. Samuel, 
Saadiah's pupil. The former, a Karaite zealot, says that in the 
time of the Fajjumite (Saadiah) a dispute broke out concerning 
the Feasts which the Palestinians kept on different days to the 
Babylonians. The two parties indulged in mutual recriminations 
and excommunications, and even went so far as to charge one 
another with fraud and deception. Several Babylonians, however, 
sided with the Palestinians, and vice versa 1 . Frankl, who subjected 
Sahl's story to a severe critical examination 2 , tried to demonstrate 
that the New Year is here meant, and that the point about which 
the controversy turned was whether the Palestinian Jews were 
to keep New Year two days or only one day— a question which 
engaged the attention of such late authorities as Alfasi and his 
literary antagonist, Zerachiah Hallevi Gerundi. Before Saadiah, 
according to Frankl, the Jews of Palestine only kept Rosh hash- 
shanah on one day; but the G-aon prevailed on many penetrating 
minds in the Holy Land to adopt the Babylonian rule and celebrate 
the beginning of the year on two days. Saadiah believed that this 
would restore uniformity of religious practice, and effectively parry 
the attack of the Karaites who made capital out of the differences 
between Palestinian and Babylonian usages. After Saadiah's death, 
the result of his labours was undone. The Babylonian party in 
Palestine reverted to the prevalent customs, and hence the well- 
known inquiry which Nissim b. Jacob addressed to Hai Gaon as 
to Saadiah's Response to the inhabitants of Kafsa (D3Np) s . Sahl, 
according to Frankl, wrote with a distinct bias and was guilty of 
exaggeration, partiality, and perversion of the truth. 

Frankl's arguments will, however, not stand the test of examination. 
Even if Saadiah had succeeded in persuading the Jews of Palestine 
to keep the New Year two days, complete religious unity would 
by no means have been secured, as the same difference with regard 

1 Pinsker, Likkuie Kadmonioth, p. 36 : ct» sirs iitm wvan 'D'a nra <3Bh 
-irw dv lniNro Drrnrw D'aVinm o"baam dv bttrm< \p* >«.•:» i«wi DHSina ipfrm 
an '3 nn« 'm-w px imni wen htrw y-i« 'cj» 'a (soil. D'^aan) -nom 
run ova -iymn too©' yi« >«»» teem nw ana ltort i"?« ran ltort ito« Wipi wsn 
yiN 'jaifflo d'bw s;'i ntort nto* D'aian vm (r. -vm) -inn ova vimws taa '«n*« 

.to*-uB» p« »«m nrm tttoi rim psa d'btoti oji o"baan nrw n'rrm tow 

2 Honalsschrift, XX, (1871), pp. 355-360. 

3 Responses of the Geonim, ed. Lyck, no. I. 



BEN MEIR AND ORIGIN OP JEWISH CALENDAR 155 

to the other Feasts would continue to divide Palestine from the 
rest of the world. Saadiah, moreover, does not condemn the differ- 
ence of practice, as fostering disunion ; for he asserts that Grod had, 
from the beginning, commanded Moses that the Feasts should, in 
Palestine, be kept one day, and outside it two days '—a view which 
he maintains against the Karaites. Finally, Sahl would not have 
said that the Palestinians celebrated the Festival — precisely the 
Festivals— on one day, and the Babylonians on another, or on the 
morrow 2 , but that the former keep the Feast on a certain day and 
the Babylonians kept it on the morrow also. Again, what is the 
meaning of the statement that some of the Babylonians followed 
the practice of Palestine ? The former in any case kept two days. 
I, therefore, do not doubt that Sahl had in mind the affair with Ben 
Meir, and we learn that a portion of the Palestinians, at least, refused 
to follow the lead of the head of their school, while, on the other 
hand, he counted many Babylonians among his adherents. The last 
circumstance appears from several passages in Ben Meir's epistle 
to the Babylonian communities which Dr. Harkavy has published s . 
Frankl has cast suspicion upon Sahl's account as tainted with a pro- 
nounced bias. His reason is that, if accepted, it would involve the 
assumption that the Rabbanites were still disputing about the dates 
of the Festivals as late as the tenth century, and that, even in the 
time of Saadiah, the rules of the Calendar had not yet been unalter- 
ably fixed. This, says Frankl, is impossible. But what appeared to 
him, in 187 1, an impossibility, has been proved by Dr. Harkavy 's and 
Dr. Neubauer's publications to have been a plain fact. As late as the 
tenth century there were differences of opinion as to the institution of 
a fixed and constant Calendar. And this presents an opportunity 
for a word concerning the time and place in which the present 
fixed Calendar originated. Though this theme has had the benefit 
of frequent and varied treatment, yet it will be generally admitted 
that several complicated questions still await solution, and that 
much of what has hitherto been advanced is hypothetical 4 . 

1 Ibidem : ra n'a'pn sbs mjrso ?ed ps 1WTTB3 ins Vi rms>D un o • • • 
pi oi3> Km Virai irw or oni nw y-im torwrt on') ion sim vn» two ns 
'131 J'W tone to dV»o rm. 

2 Sahl says of the Babylonians in the first passage ins ov inwtw, and 
the second time -inn ova im»u» . Frankl would read in the first passage 
-ffro or. According to my opinion, it is more correct to read in both 
cases nn« av. 

3 See especially Dr. Harkavy, p. 215. 

4 Herr Epstein (DHimn nvjimpo, p.17), for example, counts six periods in 
the evolution of the Jewish Calendar. His demonstrations, particularly in 
regard to the earliest period, are mostly hypothetical. 



156 THE JEWISH QUAETERLY EEVIEW 

A well-known Response of Hai Gaon, preserved for us by Abraham 
b. Chija, is extant, which states that our present Calendar was fixed 
by the patriarch Hillel II in Palestine, in the year 670 (=368 or 
369 c. E.) 1 . This is accepted by most authorities, e.g. Zerachiah 
Gerundi 2 , Nachmanides 3 , &c. ; Isaac Israeli 4 alone asserts that 
this Hillel belonged to the last Talmudic period, and lived about 
500 c. E. ; an obvious error, for nothing is known of a patriarch of 
that name in that era ; his statement, moreover, is uncorroborated 
by any other authority. Hai's account bristles, however, with 
difficulties. On the question of date, Slonimski 5 has rightly pointed 
out that several passages in the Talmud show that even in the 
days of the last Amoraim, the new moon was fixed by observation, 
though since Gamliel II, astronomical rules were also brought into 
requisition— a view which is accepted by no less an authority than 
Dr. Steinschneider, who differs from Graetz and Pineles. As to the 
place of origin, M. Theodore Reinach 6 has drawn attention to a fact 
which makes it improbable that our Calendar was fixed in Palestine. 
In that country, he points out, the Greek eight-year cycle (Oktaeteris) 
at first in vogue, was succeeded by the solar cycle under the Roman 
rule. Sextus Julius Africanus (beginning of the third century) also 
notes that the Greeks as well as the Jews observe the Oktaeteris, 
i. e. in every eight years they have three leap years 7 . The Book 
of Enoch, § 74, vv. 13-16, likewise refers to an eight-year cycle". 
The Metonic nineteen years' cycle was used in Babylon. Reinach 
accordingly assumes that Babylon is the original home of our 
Calendar. He ascribes the authorship, on the ground of his astro- 
nomical knowledge, to the Amora Samuel. Though this is a mistake, 
Samuel's era being far too early a date, yet Reinach's hypothesis 
as regards the place of origin must command assent. It may be 
added that Mahler, in a series of investigations, has shown that 
the ancient Babylonians already had the nineteen years' cycle; 
and he also therefore believes that our Calendar is of Babylonian 

1 Y03CT "IDD, p. 97. a TWa on Eosh hash-slianah, I. 

3 rvrann 'd to nwen, § 153. According to Maimonides (n"np rvoV?, V, 2) 
it was an 'rcn rrcob robn that, as soon as the Synhedrion ceases to exist, 
the new moons and festivals were to be fixed according to the present 
Calendar. This view is impugned already by Nachmanides and others. 

* dnv lie, IV, 9. 5 ram, p. 4, &c. ; toot hid 1 , § 29, &c. 

' Revue des Etudes Jukes, XVIII, 90, &q. 

7 Africanus' remarks are found in Georgius Syncellus' Chronography, 
p. 611 (cited by Reinach, I.e.), and read as follows : Sid rovro *ai "EAAj/m? 
ual 'lovSatoi rpus tajvas i/j0oAi/iovs irtaiv 6kt$> irafitii0&K\ov<nv. 

8 Cp. Eev. E. Charles, The Booh of Enoch, pp. 201-202. 



BEN MEIB AND ORIGIN OF JEWISH CALENDAR I57 

origin 1 . It does not necessarily follow that it was first adopted by 
the Jews resident in Babylon ; they might have learnt it and brought 
the knowledge with them to Palestine, as indeed was the case with 
the names of the months. The Babylonian cycle does not follow 
quite the same order as ours. Its mnemonic would be not DrtN riij 
but tifts nfa. Instead of the seventeenth, the sixteenth year of 
the cycle is embolismic. Such a variation might easily, however, 
have developed in the course of centuries, nay millenniums 2 . It is 
curious that Alberuni, who wrote about the year 1000, and who is 
the earliest authority for the systematic exposition of our Calendar, 
reports a difference between the Palestinian and Babylonian Jews in 
regard to the sequence of leap years 8 . He says that there are three 
series of intercalation (or dines inlercalationis), viz. : — 

(1) liii'irn, i. e. the second, fifth, seventh, tenth, thirteenth, six- 
teenth, and eighteenth years. 

(2) frQDnN, i.e. the first, fourth, sixth, ninth, twelfth, fifteenth, 
and seventeenth years. 

(3) Ubii (properly MJJiiJ), i. e. the third, fifth (3 + 2 = 5), eighth, 
eleventh, fourteenth, sixteenth, and nineteenth years. 

The first two series, Alberuni tells us, were adopted by the Syrian 
Jews; the last, by their co-religionists generally, who preferred 
it to the others, because it was invented by the Babylonians. The 
first two series are identical with DH& nii. The first need only 
be increased by the numeral one, the second series by two, and the 
identity will become apparent. The third, however, DHN flrii, differs 
from the ancient Babylonian series as well as from our system ; 
and yet AlbSruni testifies that it was the most widely disseminated 
among the Jews, by which last term he refers, of course, to the 

1 See Zeitschrift fur Assyriologie, VI, 457-464 ; IX, 42-61 ; XI, 41-46 ; 
Sitzungsberichte d. Wiener Akademie, Mathem.-naturw, Classe, 1892 ; Transactions 
ofihelJCCongr. of Oriental., II, 209-217. Strassmaier and Oppert, however, 
refuted the opinion of Mahler, see Zeitschr.f. Assyriol., VIII, 173-178; X, 
64-69 ; Zeitschr. d. Deutsch. Morgeri. Gesettsch., L, 138-165. 

2 Another difference was that the Babylonians had, besides the inter- 
calary Adar, an intercalary Ellul. Mahler has, however, shown that 
the latter was only introduced after Babylon had come under Syrian 
domination, when the year began, as in the Graeco-Syrian calendar, with 
autumn instead of spring. According to Anan, the embolismic month 
must be intercalated after Shebat, for which, in my opinion, there is no 
analogy. See Qirqisani's Kitdb al- Anwar, I, 13 (ed. Harkavy, p. 313, 
line 7) ; Alberuni' s Chronology of Ancient Nations, edited by Sachau, text, 
p. 59, translation, p. 69. 

8 Loc. cit., text, p. 56, translation, pp. 64-65. 



158 THE JEWISH QUARTERLY REVIEW 

Babylonian Jews, who are contrasted with their Syrian brethren 
and of whom Alberuni, living in the same country with them, was 
in a position to obtain accurate knowledge \ However that may be, 
Hai's account is certainly inadmissible. 

I think I am justified in supposing that our Calendar was finally 
fixed after the close of the Talmud in the sixth or seventh centuries, 
and in the Babylonian schools. Palestine was not, indeed, the scene 
for an event of such moment. Spiritual life in that country had 
been strangled by terrible persecutions. The Jews of Babylon, 
on the other hand, particularly after the rise of Islam, enjoyed 
comparative rest, and were endowed with the requisite spirit and 
courage for so incisive a reform. That no account of the origin 
of the Calendar has come down to us need not occasion surprise. 
The origin of the system of Punctuation is similarly wrapped in 
impenetrable obscurity 2 . The authority of the Babylonian schools 
was so great that they were able to secure universal acceptance 
for their Calendar, even in the Holy Land. And thus not only was 
Judaism emancipated, in regard to its almanac, from dependence 
on Palestine, an object which Gamliel's contemporaries already 
strove to attain*; but the relation between the two countries was 
reversed. Babylon now became the authority to which the Holy 
Land had to bow. In the latter country they never forgot that 
the Calendar had not originated in their midst, and that it had 
been fixed at a late period. Hence we see in the tenth century 
an attempt to overthrow its authority, an attempt which is partly 
successful in and also outside Palestine. If it had been generally 
believed that the Calendar was fixed by Hillel II, it would have 
been not merely idle and futile, but positively foolish on the part 
of Ben Meir, who, rightly or wrongly, styled himself a descendant 
of the Patriarch, to revolt against the Calendar, of which his own 
ancestor had been the author, and in regard to which Palestine had 
laid down the law for all Israel. 

1 A Boraitha cited by Israeli (loe. cit., IV, 2) contains the following 
passage: nn ©b© en© ©V© vfw ©■>© D'n© ©">© "rwn re© mm »n 'd 
en© ©">© ©S© -ctm j"t ©to en© ©to ©to en© ©V© ©to *»"3m -m?' 1 ?** S 
'131 D'mo ©to ©to ©to. Thus we have here, too, three systems of 
intercalation. The first is iii» linj , and corresponds to Alberuni's third 
series ; the second is ©iix mi, like the Babylonian ; the third is ffiiiH liij, 
which is identical with the one at present in use. Cp. Dr. Steinschneider, 
in rovn, pp. 28, 29. 

' Here, too, Babylon takes precedence over Palestine, the Babylonian 
system of punctuation being older than that of Tiberias. See Prof. Bacher's 
Lie Anfange der hebriiischen GrammaHk, p. 15 et sqq. 

3 See Berachoth, 63, concerning the nephew of R. Joshua b. Chananja. 



BEN MEIR AND ORIGIN OF JEWISH CALENDAR 159 

The consciousness, however, that the Calendar was of com- 
paratively late origin induced not only the Karaites, hut also 
the other sects, to reject and denounce it. Characteristic is the 
following narrative of al-Qirqisani, one of Saadiah's contempora- 
ries 1 : "I once said to the Palestinian, Jacob b. Ephraim *, ' You 
have intercourse with the Isawites (i. e. followers of Isa or Obadiah 
al Isfahani), you even intermarry with them. But they acknow- 
ledge as prophets those whom you do not recognize 8 .' The reply 
was "They have not seceded from us (the Rabbanites) in regard 
to the Feasts.' This shows that the Rabbanites tolerated open 
unbelief rather than a schism in the dates of the Feasts which 
they themselves permanently fixed." The Sectaries, especially the 
Karaites, by their attacks on the Calendar, misled so illustrious 
a genius as Saadiah into anachronisms, logical fallacies, and 
egregious blunders. The Gaon claims that the Calendar is of 
Sinaitic origin, and that its rules existed in the days of Moses. 
It was easy for his opponent to demonstrate the utter absurdity 
of this contention. And Hai Gaon had to admit that Saadiah did 
not really intend the assertion to be taken seriously. His object 
was to snatch a momentary triumph in the verbal combat*. 

Thus we observe seething among the Jews in the tenth century 
an agitation that was far from superficial, but, on the contrary, 
stirred men's minds to their depths. The Karaites sought their 
profit in this ferment, and won many waverers over to their camp. 
Possibly to this dispute about the Calendar we may trace the fact 
recorded by Sahl, that some Rabbanites in Palestine kept two days 
of the Festival— one, according to the observation of the moon ; 
and one according to the fixed Calendar, and that many of them 
renounced the latter (and thus were converted to Karaism) 5 . The 
last statement may be merely an unwarranted, idle rumour. 

These suggestions I have here offered are, of course, purely hypo- 
thetical. It would be a subject for congratulation if this publica- 

1 Loc. cit., I, 11 (ed. Harkavy, p. 312). 

' Concerning this Jacob b. Efraim, who is undoubtedly identical with 
the one cited by Salmon b. Jerucham (Pinsker, p. 14), see my Essay 
in the Sttinsckneider-Festschrift, pp. 201-202. 

3 This sectary had asserted that Jesus and Muhammed were prophets 
sent by God, not to the Jews but to the Gentiles. 

* Responses of the Geonim, 1. c. : NOT m? V't v"-\ arO» DmQW m 'D 13W "p 
mvw rw rrrro. Abraham b. Chija naively says (yasn ncD, p. 94) : 
rovcnn jtoo in: cramVi avan raven 'ri Dm S"i (iihsd '1 Sic) v-in dh Yjn 
'131 Dmn m "ovb hvto -h nwve miem S31 Drr? varh '«tm o-iwb. 

5 Pinsker, loc cit, p. 33. 



l6o THE JEWISH QUARTERLY REVIEW 

tion stimulated experts and specialists to contribute, out of their 
rich stores, to the discussion and elucidation of the vexed question 
in this little known but absorbing branch of science. 

Samuel Poznanskx 
Berlin, November, 1896. 



Postscript. 

My learned friend, Herr H. Bornstein of Warsaw, has pointed out 
to me that the report quoted by Elias of Nisibis needs correction. 
First, the year of the Hegira 309 began on the 12th, and not on the 
22nd of Ijar, 1233. Secondly, Ben Meir's contradiction related to 
Marcheshvan and Kislev, 1233, not 1232, so that the difference of two 
days affected the Passover of 1233, and, consequently, the New Year 
of 1234 (not 1233). This may also be deduced from the following 
passage in the fragment in Harkavy (p. 218, 1. 13 sqq.) : — 

nw w i "bh rran fa&rb Vann ruea nswi iiw yae . . . 
nxan nxm , . . 'i*Dn ownm n ova wn mm 'pbn hbphh 
K»ri nw to i Wa *ii>u Nin ntai^a man fawb •him iw nw 

/i3i piDa 'innt j i?un mm 'pbn 

Ben Meir further maintains that in the year 853, after the destruc- 
tion of the second Temple (=1233 of the era of contracts), the New 
Year should have fallen on a Thursday, and the months Marcheshvan 
and Kislev should have been defective (D'HDn), and that New Year's 
day of the following year, 854=1234 era of contracts, ought to be 
a Tuesday. Consequently, the Passover of 1233 fell, according to 
Ben Meir on a Sunday, but according to the common reckoning on 
a Tuesday, and the New Year of 1234 on a Thursday. In fact, the 
Molad of the year 1233 was 3?p)iri N1 i, and the formula (ni^np) was 
JtWI (according to Ben Meir, Nlin). The letter published by Neubauer 
shows the conflict to have arisen in the summer, i.e. in 1232., The 
informant of Elias of Nisibis knew that in 1232 there had been a 
conflict between the eastern and western Jews about the fixing of 
the New Year's day, and related it erroneously to the New Year 
of 1233, instead of to that of 1234. 

The same friend further points out that the third formula of 
intercalation of Albenini (J3D3J) can also be reduced to our formula 

1 So correctly in the Oxford MS. The St. Petersburg MS. has wrongly 

rain. 



BEN MEIR AND ORIGIN OP JEWISH CALENDAR l6l 

(tins tiii), if we begin to reckon the intercalary years from the 
third year of the cycle, for then we arrive at the series J33M3J. 
Hai Gaon also mentions, in Responsum cited by Abraham b. Chija 
(pp. 97, 98 ; cf. DTiy TlD 1 " iv, 14), the same three formulae of inter- 
calation as Albgruni, namely f\M Mrii, TnioVlK, and ifuijii, and his 
words show that all three are identical. Vide also Steinschneider, 
1. c, pp. 34, 35- 

Finally, the discrepancy between the Babylonian and the Jewish 
series of the intercalary years by no means proves the impossibility 
of the latter having originated from the former, for our nineteen 
years' cycle is supposed to have been borrowed from the Metonic, but 
even in the latter, the sequence of the intercalary years has not been 
satisfactorily established. The sequence was, according to Dodwell, 
Ideler, Boeckh, in the Metonic system, 3. 5. 8. 11. 13. 16. 19; and in 
that of Kallipos, 1. 4. 7. 10. 12. 15. 18. On the other hand, according 
to Scaliger, Em. Miiller, and Aug. Mommsen, in both systems, 2. 5. 8. 
10. 13. 16. 18. Cf. Unger, Die Chronologie d. Grieehen u. R6mer, in 
Iwan Mflller's Handbuch d. Mass. Alterthums-Wissenschaften, I. 

S. P. 

Warsaw, January, 1897. 



VOL. X. M