2 fin

think we should read Caesii: cp. Q. Fr. iii. 1. Omnino spero paucis mensibus opus Diphili perfectum fore: curat enim diligentissime Caesius qui tum erat mecum. From the last words we gather that Caesius does not appear to have been continually overseeing the repairs at the Arcanum of Q. Cicero.

ON THE FIXED ALEXANDRINE YEAR.

THE

HE date of the introduction of the fixed Alexandrine year has given rise to a considerable amount of discussion, and has been placed by some authorities in 30 B.C. with 26 B.C. for the first intercalary year: by others in 26 B.C., with 22 B.C. for the first intercalary year: Ideler maintained the earlier date, Boeckh left the question undecided, and more modern writers incline to accept the later date. The present condition of opinion on the subject may be gathered from the following quotations :

Kubitschek, in Pauly-Wissowa, 1. 617, s. v. Aera 9:-Die Streitfrage (s. Ideler 1. 153ff. Lepsius Berl. Monatsb. 1858, 531ff. Boeckh, Studien, 94 ff. Sonnenkreise, 260 ff. Mommsen, Röm. Chronologie, 258 ff. E. Müller, PRE I 1068 ff. Soltau, Chronologie, 170 ff.) ist zu keinem befriedigenden Resultate geführt worden; nur ist wahrscheinlich geworden, dass die Ordnung des Alexandrinischen Kalenders erst 26 v. Chr. erfolgte, die Aerenepoche aber auf dem 30 August 30 v. Chr. zuruckgeschoben wurde.

Strack, Rhein. Mus. 1898, p. 425-Im 5. Jahre des Augustus ägyptischer Zählung d. h. im Jahre 26/5 ist vermuthlich diese Kalenderänderung beschlossen; im Jahre 23/2 in dem die überschüssigen im Wandeljahr ausser Rechnung bleibenden Vierteltage einen ganzen Tag ausmachen ist jedenfalls zuerst geschaltet.

An examination of the evidence of the papyri, which were unknown to previous investigators, leads decisively to the conclusion that the first year, in which an intercalary day was inserted, was 22 B.C. The passages on which this

conclusion is based are as follows:

1. Ox. Pap. I. xlv. 15: [ ιδ Αὐτοκράτορος Καίσαρος Δομιτιανοῦ Σεβαστοῦ Γερμανικοῦ, μη(νὸς) Καισαρείου ἐπαγομένων) 5.

2. An inscription from Abydos, quoted by Wilcken, Ostraca, I. Ρ. 793 : L ιζ Τιβερίου Καίσαρος Σεβαστοῦ Τύβηι ιη (= 13 Jan. 30 A.D.), accompanied by a Demotic note, thus translated by Brugsch: "Geschrieben im Jahre 17 des Tiberius Caesar des (oben genannten), zur Zeit des 18. Tybi des Ioniers, welches entspricht dem 1. Mechir des Aegypters."

3. Brit. Mus. Pap. cxxx. 37 : ἔτους τρίτου θεοῦ Τίτου Φαρμούθι τῇ ἐπιφωσκούσῃ ἕκτηι ἐπὶ τρίτης τῆς νυκτὸς ὥρας, ὡς δὲ Ρωμαῖοι ἄγουσι καλάνδαις Απριλίαις, κατ ̓ ἀρχαίους δὲ Παχὼν νεομηνίᾳ εἰς τὴν δευτέραν. 4. P. Paris. 19. 7: αἱ ̓Αντωνίνου Καίσαρος τοῦ κυρίου μηνὸς Αδρια[νού η κατὰ τῶν Ἑλλήνων, κατὰ δὲ τοὺς Αἰγυπτίους Τύβι ιη. 5. P. Paris 19bis 3 = Brit. Mus. Pap. cx. 2: Lā 'AvTwvívov Kaíoaρος τοῦ κυρίου μηνός Αδριανοῦ η, κατὰ δὲ τοὺς ἀρχαίους) Τύβι ιη.

It may be assumed here, without question, that in the fixed Alexandrine calendar the intercalary day was inserted at the end of each period of four years, immediately before the first of Thouth of the following year. We learn from (1) that there was an intercalary day in the year 95 A.D., and deduce that there was such a day in the year 3 A.D.: 95 = 3 + (4 × 23). Now let y denote the difference in days between the fixed and variable calendars in the years 3/4, 4/5, 5/6, 6/7, then y +x will be the difference in years expressed in the form 3 + 4x/4 + 4x, 4 + 4x/5 + 4x, 5 + 4x/6 + 4x, 6 + 4x 7 + 4x.

The date of (2) is 13 Jan. 30 A.D.; it is therefore in the year 29/30; but 29 5 + (4 × 6); .. x = 6.

=

The difference in days is 13, .'. y + x = 13 ; ·'. y = 7.

The date of (3) is 1 April 81 A.D.; it is therefore in the year 80/81, but 80 = 4+ (4 × 19); .. x = 19.

Pharmouthi 6 corresponds to Pachon 2; hence the difference in days is 26; ..y + x 26; .. y = 7.

=

The date of (4) and (5) is 4 Dec., 137 A.D.; it is there. fore in the year 137/8, but 137 = 5 + (4 × 33); .'. x = 33.

Hadrianus (= Choiak) 8 corresponds to Tybi 18; hence

the difference in days is 40; .. y × x = 40 ; .'. y' = 7.

These three dates accordingly give a consistent result; and we learn that in the year 3/4 and the three following years the difference between the fixed and variable calendars was seven days. Calculating backwards from this we find that the first intercalary day was inserted in the year 22 B.C., and that the fixed Alexandrine year was instituted at the beginning of the year 26/25 B.C.

The statement made above that, in (3), Pharmouthi 6 corresponds to Pachon 2, and not to Pachon 1, requires justification. The dates of all events recorded as having taken place at night present a certain amount of difficulty, owing to the uncertainty as to the time at which the day began. The Greeks counted their 24-hour day from sunset to sunset, the Romans from midnight to midnight (see Unger, Philologus, 1892, vol. 51, pp. 14, 212), but at the same time there was everywhere a popular method of regarding the day as lasting from sunrise to sunset, and leaving the night undated: in this article two days are said to correspond whose periods of daylight correspond. Now in (3) the expression ἡ ἐπιφώσκουσα ἕκτη must denote some hour near the beginning of the 6th, whether counted from sunset or midnight' hence in this case the supposition, that both the day began at midnight and the hours of the night were counted from sunset, is excluded, because, under these circumstances, the third hour of the night would be very near the end of the day; for the same reason Pharmouthi 6 cannot have begun at sunrise. If then Pharmouthi 6 began, Roman fashion, at midnight, it coincided completely with April 1, and the following noon must correspond to the noon of Pachon 2; if it began, according to the Greek

1 The word επιφώσκουσα does not necessarily imply that the time was near dawn, because mipavoke and ἐπιφώσκειν are used of the moon well as of the sun (e.g. Job xxv. 5):

as

in

Luke xxiii. 54, καὶ σάββατον ἐπέφωσκε, and the sabbath drew on,' the time indicated is evening; so also Epiphanius, Haeres. 70. 11, èπipwσкOVONS TĤS κυριακῆς ἑσπέρας.

style, at sunset, then Pharmouthi 6 extended from sunset on March 31 to sunset on April 1, and, in this case also, the following noon is that of Pachon 2. In both cases, the words ἐπὶ τρίτης τῆς νυκτὸς ὥρας must be equivalent to ἐπὶ τρίτης τοῦ μεσονυκτίου ὥρας in the first case, because, as we have seen, the hour of birth must have been near the beginning of the day; in the second case, because the only part of the night common to Pharmouthi 6 and April 1 was the period after midnight.

If this reasoning be considered inconclusive, the argument can be reversed. Independently of this papyrus, the other instances are sufficient to establish the fact, that in the year 3/4 the difference between the two calendars was seven days, and consequently in the year 80/81 the difference must have been twenty-six days; hence Pharmouthi 6 corresponded to Pachon 2.

From the preceding argument the following rules may be deduced:

1. If the difference in days between the fixed and variable calendars be known, and be greater than 6, the date is after A.D., and may lie in one of four years, the earliest of which is determined (a) if the day lie between Thouth and December 31 by subtracting 7 from the difference, multiplying the result by 4 and adding 3; or, more simply, by multiplying the difference by 4 and subtracting 25; (b) if the day lie between January 1 and the end of the Alexandrine year, by multiplying the difference by 4 and subtracting 24.

2. If the year A.D. be known, the difference in days between the fixed and variable calendars can be determined by reducing the year to one of the forms 3 + 4x/4 + 4x, 4 + 4x/5 + 4x, 5 + 4x/6 + 4x, 6 + 4x/7 + 4x, and adding 7 to the value of x thus obtained.

The same result may be deduced from the works of Ptolemy and Theon :-Ptolemy, Synt. Math., III., p. 256,