calendarium

călendārĭum, v. kalendarium.

calendārium (kalendārium), ī, n. (calendae), das Schuldregister, Schuldbuch der Geldverleiher, so genannt, weil bei den Alten am ersten Tage des Monats (calendae) die Zinsen abgetragen wurden, Sen. u.a.: auch calendarii liber, Sen. ep. 87, 6: curator kalendariorum rei publicae, Inscr.: cura kalendarii rei publicae Canusinorum, Inscr.: nemo beneficia in calendaria scribit, Sen. – meton. = ein ganzes Vermögen, Tert. de habit. mul. 9 u. de cult. fem. 1, 8. Ps. Cypr. de bono pudic. 12.

călendārĭum (14) (Ka-), ĭī, n. , registre livre de compte : Sen. Ben. 1, 2, 3 ; Ep. 14, 18 || [fig.] la fortune dʼune maison : Tert. Cult. 1, 9 || calendrier : Inscr.

calendarium , ii. n.
利錢單。皇曆。

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CALENDARIUM

CALENDA´RIUMor rather KALENDA´RIUM, is the account-book in which creditors entered the names of their debtors and the sums which they owed. As the interest on borrowed money was due on the Calendae of each month, the name of Calendarium was given to such a book. (Senec. de Benef. 1.2.3; 7.10.3.) The word was subsequently used to indicate a register of the days, weeks, and months, thus corresponding to a modern almanac or calendar.

1. Greek Calendar.

In the earliest times the division of the year into its various seasons appears to have been very simple and rude. Homer speaks of three seasons--ἔαρ, θέρος, and χειμών --coupling with θέρος as a later summer ὀπώρα (Od. 11.191, &c.); and the threefold division seems to have been the most usual as late as the time of Aristophanes [ASTRONOMIA]. Where greater precision was required, it was common to use as determining points the rising or setting of certain stars. Thus Hesiod (Op. et Dies, 381) describes the time of the rising of the Pleiades as the time for harvesting (ἄμητος), and that of their setting as the time for ploughing (ἄροτος); the time at which Arcturus rose in the morning twilight as the proper season for the vintage (l. c. 607), and other phenomena in nature, such as the arrival of birds of passage, the blossoming of certain plants, and the like, indicated the proper seasons for other agricultural occupations; but although they may have continued to be observed for centuries by simple rustics, they never acquired any importance in the scientific division of the year. [ASTRONOMIA]

The moon being that heavenly body whose phases are most easily observed, formed the basis of the Greek calendar, and all the religious festivals were dependent on it. The Greek year was a lunar year of twelve months, but at the same time the course of the sun also was taken into consideration, and the combination of the two (Gemin. Isag. 6; comp. Censorin. de Die Nat. 18; Cic. in Verr. 2.5. 2, § 129) involved the Greeks in great difficulties, which rendered it almost impossible for them to place their chronology on a sure foundation. It seems that in the early times it was believed that twelve revolutions of the moon took place within one of the sun; a calculation which was tolerably correct, and with which people were satisfied. The time during which the moon revolved around her axis was calculated at an average or round number of 30 days, which period was called a month (Gemin. l. c.); but even as early as the time of Solon, it was well known that a lunar month did not contain 30 days, but only 29 1/2 . The error contained in this calculation could not long remain unobserved, and attempts were made to correct it. The principal one was that of creating a cycle of two years, called τριετηρίς, or annus magnus, and containing 25 months, one of the two years consisting of 12 and the other of 13 months. Boeckh (Zur Gesch. des Mondcyclen, p. 10, 63 ff.) regards the τριετηρὶς as wholly fabulous; but his views have been refuted by Mommsen (Röm. Chron. p. 211 ff.). The months themselves, which in the time of Hesiod (Op. et Dies, 770) had been reckoned at 30 days, afterwards alternately contained 30 days (full months, πλήρεις) and 29 days (hollow months, κοῖλοι). According to this arrangement, one year of the cycle contained 354 and the other 384 days, and the two together were about 7 1/2 days more than two tropical or solar years. (Gemin. 6; Censorin. 18.) When this mode of reckoning was introduced, is unknown; but Herodotus (Hdt. 2.4) mentions it as still in use in his own time, although he recognises the superior correctness of the Egyptian method of intercalation. (In 1.32 there is either great carelessness or some corruption of the text.) The 7 1/2 days, in the course of 8 years, made up a month of 30 days, and such a month was accordingly omitted every eighth year. (Censorin. l. c.) But a more usual method of treating the ἐνναετηρίς, or the cycle of 8 years,

The cycle of eight years was called sometimes ἐννεαετηρίς (or more commonly ἐνναετηρίς), sometimes ὀκταετηρίς, according as the inclusive or the exclusive reckoning was adopted.

was the following. The calculation was that as the solar year is reckoned at 365 1/4 days, eight such years contain 2922 days, and eight lunar years 2832 days; that is, 90 days less than eight solar years. Now these 90 days were constituted as three months, and inserted as three intercalary months into three different years of the ἐνναετηρίς, --that is, into the third, fifth, and eighth. (Censorin., Gemin. ll. cc.) It should, however, be observed that Macrobius (Macrob. Sat. 1.13.9) and Solinus (Polyhist. iii.) state that the three intercalary months were all added to the last year of the ennaeteris, which would accordingly have contained 444 days. But this is not very probable. The period of 8 solar years, further, contains 99 revolutions of the moon, which, with the addition of the three intercalary months, make 2923 1/2 days; so that in every eight years there is 1 1/2 day too many, and in fifty years the year would begin not with a new moon, but with a full moon. The ennaeteris, accordingly, again was incorrect. The time at which the cycle of the ennaeteris was introduced is uncertain, but the prominent place which an eight years' cycle has in many legends and ancient customs leads to the belief that it was very ancient. Its inaccuracy called forth a number of other improvements or attempts at establishing chronology on a sound basis, the most celebrated among which is that of Meton. The cycle of Meton consisted of 19 years, in 7 of which there was an intercalated month. The total number of months was therefore 235, amounting to 6940 days. The average year thus was one of 365 5/19 days, i. e. about 30′ 9″ too much. Callippus about a century later, by combining four of Meton's cycles into one and omitting one day, brought the duration of the year to 365 1/4 days, the length afterwards adopted in the Julian Calendar. The slight error which still remained was finally removed about B.C. 126 by Hipparchus of Nicaea, who again combined four of the cycles of Callippus into a period of 304 years, deducting from this one more day, so bringing the total to 111035 days. By this means the greatest attainable accuracy was secured. But this calendar of Hipparchus was never introduced into practice. Meton's new year began probably on the 20th of June B.C. 432: but it has been shown by Boeckh (contrary to the view previously current) that it is erroneous to suppose that it was at this date formally adopted by the Athenian state: it is, indeed, extremely doubtful whether it was ever so adopted (cf. Unger, Zeitrechnung der Griechen und Römer, § 33). Very elaborate calculations have been made to determine the precise equivalence of the Athenian years to those of our own calendar, and many coincidences can now be determined by the aid of inscriptions, but scholars are still at variance on many details, and much has to be left to uncertain conjectures. It seems probable that an eight-year cycle was in use until B.C. 336, although somewhat modified in B.C. 422: then a cycle of 19 years appears to have been in use, but not one identical with that of Meton. There is reason, however, to believe that the eight years' cycle was again adopted, for thus only can we explain the fact, that in the time of the early empire the Attic new year seems to have fallen one month too late. The Athenians were much later than some of the Oriental Greeks in adopting the Roman calendar, with its year based wholly upon the sun, and neglecting the phases of the moon. These circumstances render it almost impossible to reduce any given date in Greek history to the exact date of our calendar.

The Greeks, as early as the time of Homer, appear to have been perfectly familiar with the division of the year into the twelve lunar months. mentioned above; but no intercalary month μὴν ἐμβόλιμος) or day is mentioned. Independent of the division of a month into days, it was divided into periods according to the increase and decrease of the moon. Thus, the first day or new moon was called νουμηνία. (Hom. Od. 10.14, 12.325-Z2, 20.156-Z2, 21.258-Z2; Hes. Op. ct Dies, 770.) The period from the νουμηνία until the moon was full was expressed by μηνὸς ἱσταμένου, and the latter part during which the moon decreased by μηνὸς φθίνοντος. (Hom. Od. 14.162.) The 30th day of a month, i. e. the day of the conjunction, was called τριακάς, or, according to a regulation of Solon (Plut. Sol. 25), ἕνη καὶ νέα, because one part of that day belonged to the expiring and the other to the beginning month. The day of the full moon, or the middle of the month, is sometimes called διχομηνία (Inscr. Att. 1.1): cf. Μήνα διχόμηνις (Pind. O. 3.35).

The month in which the year began, as well as the names of the months, differed in the different countries of Greece, and in some parts even no names existed for the months, they being distinguished only numerically, as the first, second, third, fourth month, &c. In order, there-fore, to acquire any satisfactory knowledge of the Greek calendar, the different states must be considered separately.

The Attic year began with the summer solstice, and each month was divided into three decads, from the 1st to the 10th, from the 10th to the 20th, and from the 20th to the 29th or 30th. The first day of a month, or the day after the conjunction, was νουμηνία: and as the first decad was designated as ἱσταμένου μηνός, the days were regularly counted as δευτέρα, τρίτη, τετάρτη, &c., μηρὸς ἱσταμένου. The days of the second decad were distinguished as ἐπὶ δέκα, or μεσοῦτος, and were counted to 20 regularly, as πρώτη, δευτέρα, τρίτη, τετάρτη, &c., ἐπὶ δέκα. The 20th itself was called εἰκάς, and the days from the 20th to the 30th were counted in two different ways, viz. either onwards, as πρώτη, δευτέρα, τρίτη, &c., ἐπὶ εἰκάδι, or backwards from the last day of the month with the addition of (φθίνοντος, παυομένου, λήγοντος, or ἀπιόντος, as ἐννάτη, δεκάτη, &c., φθίνοντος, which, of course, are different dates in hollow and in full months. But this mode of counting backwards seems to have been more commonly used than the other. With regard to the hollow months, it must be observed that the Athenians, generally speaking, counted 29 days, but in the month of Boedromion they counted 30, leaving out the second, because on that day Athena and Poseidon were believed to have disputed about the possession of Attica. (Plut. de Frat. Am. p. 489; Sympos. 9.7.) It is to be noticed also that the 21st day was called δεκάτη φθίνοντος, not, as some have supposed, ἐνάτη, and that there was no δευτέρα φθίνοντος in the hollow months. (Cp. Schol. on Hesiod, Op. et Di. 763.) So in the Rhodian inscription in Newton, Ancient Greek Inscr. 1883, No. 334, τριακὰς follows immediately upon τρίτη φθίνοντος in such cases, προτριακὰς being omitted. (This has been proved by K. F. Hermann against Ideler and Boeckh.) The following table shows the succession of the Attic months, the number of days they contained, and the corresponding months of our year:-- 1.Hecatombaeon (Ἑκατομβαιών) contained 30 days, and corresponds nearly to our July.2.Metageitnion (Μεταγειτνιών) contained 29 days, and corresponds nearly to our August..3.Boedromion (Βοηδρομιών) contained 30 days, and corresponds nearly to our September..4.Pyanepsion (Πυανεψιών) contained 29 days, and corresponds nearly to our October..5.Maimacterion (Μαιμακτηριών) contained 30 days, and corresponds nearly to our November..6.Poseideon (Ποσειδεών) contained 29 days, and corresponds nearly to our December.7.Gamelion (Γαμηλιών) contained 30 days, and corresponds nearly to our January.8.Anthesterion (Ἀνθεστηριών) contained 29 days, and corresponds nearly to our February.9.Elaphebolion (Ἐλαφηβολιών) contained 30 days, and corresponds nearly to our March.10.Munychion (Μουνυχιών) contained 29 days, and corresponds nearly to our April.11.Thargelion (Θαργηλιών) contained 30 days, and corresponds nearly to our May.12.Scirophorion (Σκιροφοριών) contained 29 days, and corresponds nearly to our June.

At the time when the Julian Calendar was adopted by the Athenians, probably about the time of the Emperor Hadrian, the lunar year appears to have been changed into the solar year; and it has further been conjectured, that the beginning of the year was transferred from the summer solstice to the autumnal equinox.

The following lists of months may also be given with some confidence, although there is uncertainty as to the exact place of some of them:--  Delphian. Lacedaemonian. Delian. Boeotian.Corresponding nearly to1.Ἀπελλαῖος 10.Ἡράσιος 7.Ἑκατομβαιών 7.Ἀγριώνιος (?)July.2.Βουκάτιος 11.Καρνεῖος 8.Μεταγειτνιών 8.Ἱπποδρόμιος August.3.Βοαθόος   9.Βουφονιών 9.Πάναμος September.4.Ἡραῖος   10.Ἀπατουριών 10.Παμβοιώτιος October.5.Δᾳδαφόριος   11.Ἀρησιών 11.Δαμάτριος November.6.Ποιτρόπιος   12.Ποσειδεών 12.Ἀλαλκομένιος December.7.Ἀμάλιος   1.Ληναιών 1.Βουκάτιος January.8.Βύσιος   2.Ἱερός 2.Ἑρμαῖος February.9.Θεοξένιος 6.Ἀρτεμίσιος 3.Ταλαιών 3.Προστατήριος March.10.Ἐνδυσποιτρόπιος 7.Γεράστιος 4.Ἀρτεμισιών 4.Θιούιος (?)April.11.Ἡρακλεῖος 8.Ἑκατομβεύς 5.Ταργηλιών 5.Θειλούθιος (?)May.12.Ἰλαῖος 9.Φλιάσιος 6.Πάνημος 6.Ὁμολώιος (?)June.

The intercalated month was probably in all cases a repetition of that which corresponds nearly to our December.

The names of the months at Cyzicus and in Sicily are probably as follows:--  Cyzicene. Sicilian.Answering nearly to1.Boedromion (Βοηδρομιών) 1.Thesmophorius Θεσμοφόριος) October.2.Cyanepsion (Κυανεψιών) 2.Dalius Δάλιος) November.3.Apaturion (Ἀπατουριών) 3.Unknown.December.4.Poseideon (Ποσειδεών) 4.Agrianius (Ἀγριάνιος) January.5.Lenaeon (Ληναιών) 5.Unknown.February.6.Anthesterion (Ἀνθεστηριών) 6.Theudasius (Θευδάσιος) March.7.Artemision (Ἀρτεμισιών) 7.Artamitius (Ἀρταμίτιος) April.8.Calamaeon (Καλαμαιών) 8.Unknown.May.9.Panemus (Πάνημος) 9.Badromius (Βαδρόμιος) June.10.Taureon (Ταυρεών) 10.Hyacinthius (Ὑακίνθιος) July.11 and 12 are unknown.11.Carneius (Καρνεῖος) August.  12.Panamus (Πάναμος) September.

We further know the names of several isolated months of other Greek states; but as it is as yet impossible to determine what place they occupied in the calendar, and with which of our months they correspond, their enumeration here would be of little or no use. We shall therefore confine ourselves to giving some account of the Macedonian months, and of some of the Asiatic cities and islands, which are better known.

On the whole it appears that the Macedonian year agreed with that of the Greeks, and that accordingly it was a lunar year of twelve months, since we find that Macedonian months are described as coincident with those of the Athenians. (See a letter of King Philip in Demosth. de Coron. p. 280; Plut. Camill. 19, Alex. 3, 16.) All chronologers agree as to the order and succession of the Macedonian months; but we are altogether ignorant as to the name and place of the intercalary month, which must have existed in the Macedonian year as well as in that of the Greek states. The order is as follows :--1. Dius (Δῖος), 2. Apellaeus (Ἀπελλαῖος), 3. Audynaeus (Αὐδυναῖος), 4. Peritius(Περίτιος), 5. Dystrus (Δύστρος), 6. Xanthicus (Ξανθικός), 7. Artemisius (Ἀρτεμίσιος), 8. Daesius (Δαίσιος), 9. Panemus (Πάνημος), 10. Lous (Λῶος), 11. Gorpiaeus (Γορπιαῖος), 12. Hyperberetaeus (Ὑπερβερεταῖος). The difficulty is to identify the Macedonian months with those of the Athenians. From Plutarch (Camill. 19, comp. with Alex. 16) we learn that the Macedonian Daesius was identical with the Athenian Thargelion; but while, according to Philip, the Macedonian Lous was the same as the Athenian Boedromion, Plutarch (Plut. Alex. 3) identifies the Lous with the Attic Hecatombaeon. This discrepancy has given rise to various conjectures, some supposing that between the time of Philip and Plutarch a transposition of the names of the months had taken place, and others that Plutarch made a mistake in identifying the Lous with the Hecatombaeon. But the best solution is probably to suppose that by the time of Plutarch the beginning of the Attic year had come to be one month after its true date according to the Roman calendar. We know that the Macedonian year began with the month of Dius, commencing with the autumnal equinox. When Alexander conquered Asia, the Macedonian calendar was spread over many parts of Asia, though it underwent various modifications in the different countries in which it was adopted. When subsequently the Asiatics adopted the Julian Calendar, those modifications also exercised their influence and produced differences in the names of the months, although, generally speaking, the solar year of the Asiatics began with the autumnal equinox. During the time of the Roman emperors, the following calendars occur in the province of Asia:-- 1.Caesarius (Καισάριος) had 30 days, and began on the 24th of September.2.Tiberius (Τιβέριος) had 31 days, and began on the 24th of October.3.Apaturius (Ἀπατούριος) had 31 days, and began on the 24th of November.4.Posidaon (Ποσιδαών) had 30 days, and began on the 25th of December.5.Lenaeus (Λήναιος) had 29 days, and began on the 24th of January.6.Hicrosebastus (Ἱεροσέβαστος) had 30 days, and began on the 22th of February.7.Artemisius (Ἀρτεμίσιος) had 31 days, and began on the 24th of March.8.Evangelius (Εὐαγγέλιος) had 30 days, and began on the 24th of April.9.Stratonicus (Στρατόνικος) had 31 days, and began on the 24th of May.10.Hecatombaeus (Ἑκατόμβαιος) had 31 days, and began on the 24th of June.11.Anteus (Ἄντεος) had 31 days, and began on the 25th of July.12.Laodicius (Λαοδίκιος) had 30 days, and began on the 25th of August.

Among the Ephesians we find the following months:-- 1--4. Unknown.5.Apatureon (Ἀπατουρεών) nearly answers to our November.6.Poseideon (Ποσειδεών) nearly answers to our December.7.Lenaeon (Ληναιών) nearly answers to our January.8.Unknown.9.Artemision (Ἀρτεμισιών) nearly answers to our March.10.Calamaeon (Καλαμαιών) nearly answers to our April.11, 12. Unknown.

At a later time the Ephesians adopted the same names as the Macedonians, and began their year with the month of Dius on the 24th of September.

The following is a list of the Bithynian months:-- 1.Heraeus (Ἡραῖος) contained 31 days, and began on the 23rd of September.2.Hermaeus (Ἕρμαιος) contained 30 days, and began on the 24th of October.3.Metrous (Μητρῷος) contained 31 days, and began on the 23rd of November.4.Dionysius (Διονύσιος) contained 31 days, and began on the 24th of December.5.Heracleius (Ἡράκλειος) contained 28 days, and began on the 24th of January.6.Dius (Δῖος) contained 31 days, and began on the 21st of February.7.Bendidaeus (Βενδιδαῖος) contained 30 days, and began on the 24th of March.8.Strateius (Στράτειος) contained 31 days, and began on the 23rd of April.9.Periepius (Περιέπιος) contained 30 days, and began on the 24th of May.10.Areius (Ἄρειος) contained 31 days, and began on the 23rd of June.11.Aphrodisius (Ἀφροδίσιος) contained 30 days, and began on the 24th of July.12.Demetrius (Δημήτριος) contained 31 days, and began on the 23rd of August.

The following system was adopted by the Cyprians:-- 1.Aphrodisius (Ἀφροδίσιος) contained 31 days, and began on the 23rd of September.2.Apogonicus (Ἀπογονικός) contained 30 days, and began on the 24th of October.3.Aenicus (Ἀἰνικός) contained 31 days, and began on the 23rd of November.4.Julius (Ἰούλιος) contained 31 days, and began on the 24th of December.5.Caesarius (Καισάριος) contained 28 days, and began on the 24th of January.6.Sebastus (Σεβαστός) contained 30 days, and began on the 21st of February.7.Autocratoricus (Αὐτοκρατορικός) contained 31 days, and began on the 23rd of March.8.Demarchexusius (Δημαρχεξούσιος) contained 31 days, and began on the 23rd of April.9.Plethypatus (Πληθύπατος) contained 30 days, and began on the 24th of May.10.Archiereus (Ἀρχιερεύς) contained 31 days, and began on the 23rd of June.11.Esthius (Ἔσθιος) contained 30 days, and began on the 24th of July.12.Romaeus (Ῥωμαῖος contained 31 days, and began on the 23rd of August.

The system of the Cretans was the same as that used by most of then inhabitants of Asia Minor, viz.-- 1.Thesmophorion (Θεσμοφοριών) contained 31 days, and began on the 23rd of September.2.Hermaeus (Ἑρμαῖος) contained 30 days, and began on the 24th of October.3.Eiman (Εἴμαν) contained 31 days, and began on the 23rd of November.4.Metarchius (Μετάρχιος) contained 31 days, and began on the 24th of December.5.Agyius (Ἄγυιος) contained 28 days, and began on the 24th of January.6.Dioscurus (Διόσκουρος) contained 31 days, and began on the 21st of February.7.Theodosius (Θεοδόσιος) contained 30 days, and began on the 23rd of March.8.Pontus (Πόντος) contained 31 days, and began on the 23rd of April.9.Rhabinthius (Παβίνθιος) contained 30 days, and began on the 24th of May.10.Hyperberetus (Ὑπερβέρετος) contained 31 days, and began on the 23rd of June.11.Necysius (Νεκύσιος) contained 30 days, and began on the 24th of July.12.Basilius (Βασίλιος) contained 31 days, and began on the 23rd of August.

It should be observed that several of the Eastern nations, for the purpose of preventing confusion in their calculations with other nations, dropped the names of their months, and merely counted the months, as the first, second, third, &c., month. For further information see Corsini, Fast. Att., which however is very imperfect; Ideler, Handbuch der Mathem. u. technischen Chronol., Berlin, 1826, vol. 1. p. 227, &c.; Clinton, Fast. Hellen. vol. ii. Append. xix.; and more especially K. F. Hermann, Ueber Griechische Monatskunde, Göttingen, 1844, 4to; Th. Bergk, Beiträge zur Griechischen Monatskunde, Giessen, 1845, 8vo; A. Boeckh, Ueber die vierjähriger Sonnenkreise der Alten, Berl., 1863; Mommsen, Chronologie, Leipz., 1883.

[L.S] [A.S.W] 2. Roman Calendar.

The early history of the Roman calendar is a question of great difficulty, and on some of the most important points involved the opinions of scholars are still widely divided, according as they are inclined to attach more or less weight to the statements of ancient authorities. In the following article an attempt is made to state both the traditional views and the criticisms to which they have been recently subjected, especially by Mommsen in his work on Roman Chronology.

I.

Censorinus (de die natali, c. xx.) says: Licinius Macer, and after him Fenestella, maintained that from the first there was at Rome a solar year (annus vertens) of twelve months; but we ought rather to follow Junius Gracchanus, Fulvius, Varro, and Suetonius, in the belief that the year consisted of ten months, as it was with the Albans, from whom the Romans were sprung. These ten months had 304 days, as follows: March 31, April 30, May 31, June 30, Quintilis 31, Sextilis and September 30, October 31, November and December 30; the four longer months being called full (pleni), the other six hollow (cavi). This view is confirmed by Ovid (Ov. Fast. 1.27, 43; 3.99, 119, 151), Gellius (Noct. Att. 3.16), Macrobius (Saturn. 1.12), Solinus (Polyh. i.), and Servius (on Georg. 1.43). The existence of a year of ten months is established in the judgment of Niebuhr by the fact that ten months is a period frequently employed in legal provisions: e.g., for the time of a widow's mourning, for the paying back of a dowry, for the credit allowed for goods not bought for ready money, for the calculation of interest, and apparently for truces. (Hist. Rom. 1.275 if.) He further endeavours to support it by pointing out that 110 solar years correspond to 132 years of 304 days; but inasmuch as the supposed cycle of 110 is merely a figment of a later age, the view obtains no confirmation from this source. Mommsen regards the existence of the ten-month year as proved, not only by the excellent authorities which vouch for it, but still more convincingly by the indications of its legal use; but he regards it as adopted merely for business purposes, in order to avoid the inconvenience arising from the varying lengths of the ordinary years, produced by intercalation. He holds that it was in earlier times composed of ten calendar months, varying thus between 298 and 292 days, but that after the decemviral calendar reforms it was fixed as ten-twelfths of the average year of 365 days. On the other hand, Hartmann sees in it an evidence of the statement of Macrobius, that originally it was only the period between the beginning of spring, when the activities of life recommenced, and mid-winter when they ceased, which was divided into months, while what remained over of the sun's course was left undivided, and unmarked by Kalends, Nones, and Ides. The number of 304, which does not correspond to any number of lunar months, he regards as a late invention.

II.

Mommsen holds that the earliest full Roman year was one which attempted to take account both of the moon and of the sun. That the moon was regarded as especially the measurer of time is proved by the common origin of most of the Indo-European names for month and moon in the root ma, to measure. (Curtius, Principles of Greek Etymology, 1.415.) But the names of the Roman months show that at a very early time the months must have been grouped into a cycle, the length of which was determined by the course of the sun. Names like Aprilis (from aperio), Maius (the month of growth, akin to maior), and Junius (the month of increase, connected with iuvo), could not have been used, except at a time when their place was fixed as falling in the spring and early summer. Now the simplest way of reconciling approximately the lunar and the solar years is that which seems to have been adopted in the Greek trieteris. Taking the average length of a lunation at 29 1/2 days, the months have to be made up of 29 and 30 days alternately. Now, a solar year answers pretty nearly to 12 1/2 of such months: that is to say, a cycle can be framed by taking alternately 12 and 13 months of alternating length (the additional month in every alternate year being in the first instance of 30 days, in the next of 29, and so on), which shall not at first depart very widely from the actual phenomena. Thus:-- The first ordinary year= 6 x 30 + 6 x 29=354 days.The first intercalated year= 6 x 30 + 6 x 29 + 30=384 days.The second ordinary year= 6 x 30 + 6 x 29=354 days.The second intercalated year= 6 x 30 + 6 x 29 + 29=384 days. The period of four years=1475 days. The average of each year=368 3/4 days.

The Romans, it is supposed, having learnt this cycle from the astronomers of Magna Graecia, kept to the total number of days, but re-arranged the months so as to harmonise with that love of odd numbers which marked the Pythagorean system, and produced the following cycle:-- First ordinary year= 4 x 31 + 7 x 29 + 28= 355 days.First intercalated year= 4 x 31 + 8 x 29 + 27= 383 days.Second ordinary year= 4 x 31 + 7 x 29 + 28= 355 days.Second intercalated year= 4 x 31 + 7 x 29 + 28 + 27= 382 days.with the sum total and average as before. This theory represents as close an approximation as is possible to the traditional account, consistently with an intelligible explanation of the origin of the system. The date of the introduction of this cycle cannot be fixed with precision. It must have been long enough before the decemviral legislation to allow the effects of the accumulated error of 3 1/2 days in each year to have become so marked as to call imperatively for reform; but it cannot have been before a considerable Greek influence had been felt in matters of science.

It may be noticed that while the Greek calendar did fairly well follow the phenomena of the moon, the introduction of uneven numbers in the Roman calendar made the divergence very marked; while the slight error in the total length of the year rapidly accumulated so as to produce an almost equally complete divergence from the solar seasons. Hence Mommsen is justified in saying that even at a very early period the Roman calendar went on its own way, tolerably unconcerned about moon and sun.

Mommsen's view of this ante-decemviral cycle has been strongly contested, but it is supported by the elaborate calculations of Matzat.

III.

The year as we find it employed after the decemviral reforms is that which is commonly known as the year of Numa. Censorinus (c. xx.) says expressly that it consisted of 355 days, although the moon appeared to make up 354 days in its course of 12 months. The one additional day, he says, was due either to carelessness, or (and this explanation he prefers) to the superstitious feeling in favour of an unequal number. The diminution in the length of the year was effected by cutting down the number of days assigned to February in an intercalated year to 23 or 24, and by intercalating a period of 27 days, or what comes to the same thing, of intercalating 22 or 23 days in the course of February. Thus the cycle now became-- First ordinary year= 4 x 31 + 7 x 29 + 28=355 days.First intercalated year= 4 x 31 + 7 x 29 + 23 + 27=377 days,Second ordinary year= 4 x 31 + 7 x 29 + 28=355 days.Second intercalated year= 4 x 31 + 7 x 29 + 24 + 27=378 days. Total of four years=1465 days. Average of a year=366 1/4 days.

This is again in excess of the real year by one day; but the inaccuracy of the cycle is no justification for rejecting the positive testimony of good authorities like Censorinus, who must have quoted the statement of Varro about a calendar which he had used all his life. The notion of an intercalated day, based upon a statement by Macrobius, Mommsen rejects altogether, as a transference from the imperial times to those of the republic. Matzat, however (Röm. Chron. 1.47), defends it, and would regard the 23rd of February as the invariable day after which intercalation was made, and the intercalated month as varying between 28 and 27 days. There is no practical difference between these views (Matzat, 1.228-9).

It hardly admits of doubt that the origin of this reform in the calendar is to be sought in the Greek octaeteris. In this, as has been shown above, three months of 30 days each were intercalated in the course of eight years; and it cannot be by accident that the intercalation of 22 + 23 days every four years exactly corresponds to this. Of the date of the change we have no positive evidence: but Macrobius tells us (1.13, 21), on the authority of Tuditanus and of Cassius, that the decemvirs, who added two tables to the ten, brought a proposal before the people for intercalation. As so much of the decemviral legislation was based upon the Athenian jurisprudence, it is natural to suppose that the same reformers made an attempt to incorporate in their own calendar the period then current at Athens: and it may well have been the case that one of the additional tables was really a calendar, with directions for intercalation. Varro indeed (quoted by Macrobius, 1.13, 21) shows that there was intercalation in the consulship of Pinarius and Furius, B.C. 472, twenty years before their time; but this statement may naturally have referred to the earlier system. Dionysius (Dionys. 10.59) intimates that the decemvirs brought the calendar into harmony with the phenomena of the moon's course again:: and though this statement is erroneous as it stands, it points in the same direction as the other evidence. Ovid, too (Fast. 2.47), states that before the decemvirs January was the first month of the year and February the last, so that the order was January, March, &c., December, February--a statement which, though rejected by Mommsen and many other scholars, seems strongly confirmed by the nature of the festivals held in these two months. In any case this points to an alteration made by the decemvirs in the treatment of February. We may therefore safely ascribe to the decemvirs a change in the calendar, which entirely deprived it of its connexion with the phases of the moon--a connexion which, however, had long ceased to be more than nominal.

It remains now to consider how it was possible that in this reform an average length should have been assigned to the year exceeding its true length by a whole day. It is impossible to suppose that this was mere error. The true length of the solar year was known to the Greeks at least as early as the introduction of the octaeteris. It is evident that the Greek advisers of the decemvirs must have had some reason for this inaccuracy. Mommsen's explanation, which is at least plausible, is as follows. They started from the assumption that the Roman calendar was essentially the same as that of Athens before the octaeteris, and must be set right in the same way, by reducing the average intercalation from 14 3/4 to 11 1/4 days, and that it was a matter of indifference how the previous intercalation was reduced in each four years by 4 x 3 1/2 days. It would evidently have been the simplest thing to reconstruct the whole system, but the strongly conservative religious feelings of the Romans made this impossible. Hence they did not venture to attack either the ordinary year, or the alternation of intercalated and ordinary years, or the four-year period of intercalation, or the intercalated month of 27 days. The only course left was to shorten the month of February, which preceded the intercalated month. Now, if they had reduced this month to 22 and 21 days in the alternate years of intercalation, all would have been well, and the cycle would have been 1461 days, instead of 1475. Other considerations may have contributed to hinder them from doing this, but probably the main difficulty lay in the fact that the festival of Terminus fell on February 23. The obstinate god, who had refused to yield his shrine even when required for a temple to Jupiter Optimus Maximus (Liv. 1.55), would not have surrendered his ancient feast-day for all the mathematics in the world. That the intercalation was not always after the 23rd, which would have lessened the mischief by one-half, but in alternate years after the 24th, was probably due to the love for lucky odd numbers, which had already been the source of confusion.

The first attempt. to reform the system of intercalation of which we have any indication was made by a lex Acilia of B.C. 191 (Censor. 20.6). This law empowered the pontiffs to deal with intercalation at their discretion ( pontificibus datum negotium, eorumque arbitrio intercalandi ratio permissa). But, as Censorinus informs us, this only made matters much worse, for most of them, either from hatred or from favour, to cut short or to extend the tenure of office, or that a farmer of the public revenue might gain or lose by the length of the year, by intercalating more or less at their pleasure, deliberately made worse what had been entrusted to them to set right. This statement is supported by what Cicero says in Legg. 2.12, 29. We find in fact that great irregularity prevails, and that the years known to us from Livy and the Fasti Triumphales to have been intercalated cannot be brought into any system.

Similar to this is the language employed by Macrobius (1.4), Ammianus (26.1), Solinus (c. i.), Plutarch (Plut. Caes. 100.59); and their assertions are confirmed by the letters of Cicero, written during his proconsulate in Cilicia, the constant burthen of which is a request that the pontifices will not add to his year of government by intercalation.

In consequence of this licence, says Suetonius (Caes, 40), neither the festivals of the harvest coincided with the summer, nor those of the vintage with the autumn. But we cannot desire a better proof of the confusion than a comparison of three short passages in the third book of Caesar's Bell. Civ.(100.6), Pridie nonas Januarias navis solvit --(100.9), jamque hiems adpropinquabat --(100.25) multi jam menses transierant et hiems jam praecipitaverat.

Livy (Liv. 1.19, 6) asserts that Numa established a year to suit the revolutions of the moon (ad carsus lunae), which, because the moon does not complete thirty days in each month, and some days are lacking to the complete solar year (even if it did), he arranged by inserting intercalary months, so as to agree at the end of nineteen years (vicesimo anno) with the solar year. It seems to be generally admitted that this statement of Livy's is a mere invention of some late authority (perhaps one of the pontiffs) who was acquainted with the Metonic cycle, and who wished to ascribe the credit of it to the traditional founder of the Roman year, and the confusion into which the calendar after-wards fell, to the neglect of the original provision. Cicero (de Leg. 2.12, 29) has probably the same tradition in his mind when he writes: diligenter habenda ratio intercalandi est; quod institutum perite a Numa posteriorum pontificum neglegentia dissolutum est. But there is no reason to believe that this cycle was ever really the guide for intercalation at Rome. Macrobius (Macrob. Sat. 1.13, 13) talks of a cycle of twenty-four years (tertio quoque octennio) by which the errors of the decemviral system had been removed; and some have wished to bring Livy's statement into harmony with this by inserting quarto after vicesimo (l. c.). But Mommsen has acutely seen that this, too, only represents a suggestion put forward by some reforming pontiff. He points out that, assuming that the years are to be of one of the three normal lengths--355, 377, or 378 days--there are two cycles by which these can be made to coincide with the number of days in the (Julian) solar year. Either 20 x 365 1/4 = 7305 = 11 x 355 + 2 x 377 + 7 x 378, or 24 x 365 1/4 = 8766 = 13 x 355 + 7 x 377 + 4 x 378.

The former is the shortest possible cycle; and if it is adopted, one intercalated month of twenty-two days is omitted, and two of twenty-two days are lengthened into two of twenty-three days. In the latter, one intercalated month of twenty-three days is omitted, and a second of the same length is shortened by one day. Hence the longer cycle has a slight advantage in the way of simplicity.

It is extremely difficult, or rather quite impossible, to determine the actual dates, which correspond to the nominal dates of any events before the Julian reform of the calendar, especially after the irregularities introduced by the lex Acilia. The eclipse of the sun, mentioned by Ennius (apud Cic. de Rep. 1.1. 6) as happening on June 5th in the year after the foundation of Rome 351, must have been that which took place on the Julian June 21st, B.C. 400: the eclipse of July 11th, in Varro's year 564 (Liv. 37.4), was that of the Julian March 14th, B.C. 190. But to deduce any other correspondences from these ascertained facts requires very elaborate and (in part) very untrustworthy calculations.

Year of Julius Caesar.

In the year 46 B.C. Caesar, now master of the Roman world, crowned his other great services to his country by employing his authority, as pontifex maximus, in the correction of this serious evil. For this purpose he availed himself of the services of Sosigenes, the peripatetic, and a scriba named M. Flavius,

The existence of this M. Flavius, who is mentioned only by Macrobius (1.14, 2), has been recently denied by Hartmann (Röm. Kal., pp. 120-123), who believes that his name is due only to a confusion with Cn. Flavius.

though he himself too, we are told, was well acquainted with astronomy, and indeed was the author of a work of some merit upon the subject, which was still extant in the time of Pliny. The chief authorities upon the subject of the Julian reformation are Plutarch (Plut. Caes. 100.59), Dio Cassius (Dio Cass. 43.26), Appian (de Bell. Civ. ii. ad extr.), Ovid (Fasti, 3.155), Suetonius (Suet. Jul. 100.40), Pliny (Plin. Nat.18.211), Censorinus (c. xx.), Macrobius (Macrob. Sat. 1.14), Ammianus Marcellinus (Ammian. 26.1), Solinus (Solin. 1.45). Of these Censorinus is the most precise: The confusion was at last, says he, carried so far that C. Caesar, the pontifex maximus, in his third consulate, with Lepidus for his colleague, inserted between November and December two intercalary months of 67 days, the month of February having already received an intercalation of 23 days, and thus made the whole year to consist of 445 days. At the same time he provided against a repetition of similar errors by casting aside the intercalary month, and adapting the year to the sun's course. Accordingly to the 355 days of the previously existing year he added ten days, which he so distributed between the seven months having 29 days, that January, Sextilis, and December received two each, the others but one; and these additional days he placed at the end of the several months, no doubt with the wish not to remove the various festivals from those positions in the several months which they had so long occupied. Hence in the present calendar, although there are seven months of 31 days, yet the four months, which from the first possessed that number, are still distinguishable by having their nones on the seventh, the remaining three having them on the fifth of the month. Lastly, in consideration of the quarter of a day, which he considered as completing the true year, he established the rule that, at the end of every four years, a single day should be intercalated, where the month had been hitherto inserted, that is, immediately after the Terminalia; which day is now called the Bisextum.

This year of 445 days is commonly called by chronologists the year of confusion; but by Macrobius, more fitly, the last year of confusion. The kalends of January, of the year 708 A.U.C., fell on the 13th of October, 47 B.C. of the Julian Calendar; the kalends of March, 708 A.U.C., on the 1st of January, 46 B.C.; and lastly, the kalends of January, 709 A.U.C., on the 1st of January, 45 B.C. Of the second of the two intercalary months inserted in this year after November, mention is made in Cicero's letters (ad Fam. 6.14).

It was probably the original intention of Caesar to commence the year with the shortest day. The winter solstice at Rome, in the year 46 B.C., occurred on the 24th of December of the Julian Calendar. His motive for delaying the commencement for seven days longer, instead of taking the following day, was probably the desire to gratify the superstition of the Romans, by causing the first year of the reformed calendar to fall on the day of the new moon. Accordingly it is found that the mean new moon occurred at Rome on the 1st of January. 45 B.C., at 6h. 16′ P.M. In this way alone can be explained the phrase used by Macrobius: Annum civilem Caesar, habitis ad lunam dimensionibus constitutum, edicto palam proposito publicavit. This edict is also mentioned by Plutarch (Cacs. 59), where he gives the anecdote of Cicero, who, on being told by some one that the constellation Lyra would rise the next morning, observed, Yes, no doubt, in obedience to the edict.

The mode of denoting the days of the month will cause no difficulty, if it be recollected that the kalends always denote the first of the month, that the nones occur on the seventh of the four months March, May, Quinctilis or July, and October, and on the fifth of the other months; that the ides always fall eight days later than the nones; and lastly, that the intermediate days are in all cases reckoned backwards upon the Roman principle of counting both extremes.

For the month of January the notation will be as follows:-- 1Kal. Jan.2a. d. IV. Non. Jan.3a. d. III. Non. Jan.4Prid. Non. Jan.5Non. Jan.6a. d. VIII. Id. Jan.7a. d. VII. Id. Jan.8a. d. VI. Id. Jan.9a. d. V. Id. Jan.10a. d. IV. Id. Jan.11a. d. III. Id. Jan.12Prid. Id. Jan..13Id. Jan.14a. d. XIX. Kal. Feb.15a. d. XVIII. Kal. Feb.16a. d. XVII. Kal. Feb.17a. d. XVI. Kal. Feb.18a. d. XV. Kal. Feb.19a. d. XIV. Kal. Feb.20a. d. XIII. Kal. Feb.21a. d. XII. Kal. Feb.22a. d. XI. Kal. Feb.23a. d. X. Kal. Feb.24a. d. IX. Kal. Feb.25a. d. VIII. Kal. Feb.26a. d. VII. Kal. Feb.27a. d. VI. Kal. Feb.28a. d. V. Kal. Feb.29a. d. IV. Kal. Feb.30a. d. III. Kal. Feb.31Prid. Kal. Feb.

The letters a. d. are an abridgment of ante diem, and the full phrase for on the second of January would be ante diem quartum nonas Januarias. The word ante in this expression seems really to belong in sense to nonas, and to be the cause why nonas is an accusative. Hence occur such phrases as (Cic. Phil. 3.8, 20) in ante diem quartum Kal. Decembris distulit,he put it off to the fourth day before the kalends of December, (Caes. Bell. Gall. 1.6) Is dies erat ante diem V. Kal. Apr., and (Caes. Bell. Civ. 1.11) ante quem diem iturus sit, for quo die. The same confusion exists in the phrase pest paucos dies, which means a few days after, and is equivalent to paucis post diebus. Whether the phrase Kalendae Januarii was ever used by the best writers is doubtful. The words are, commonly abbreviated; and those passages where Aprilis, Decembris, &c. occur, are of no avail, as they are probably accusatives. The ante may be omitted, in which case the phrase will be die quarto nonarum. In the leap year (to use a modern phrase), the last days of February were called-- Feb. 23 = a. d.VII.Kal. Mart.Feb. 24 = a. d.VI.Kal. Mart. posteriorem.Feb. 25 = a. d.VI.Kal. Mart. priorem.Feb. 26 = a. d.V.Kal. Mart.Feb. 27 = a. d.IV.Kal. Mart.Feb. 28 = a. d.III.Kal. Mart.Feb. 29 = Prid. Kal. Mart.

In which the words prior and posterior are used in reference to the retrograde direction of the reckoning. Such at least is the opinion of Ideler, who refers to Celsus in the Digest (Dig. 50, tit. 16, s. 98).

From the fact that the intercalated year has two days called ante diem sextum, the name of bissextile has been applied to it. The term annus bissextilis, however, does not occur in any writer prior to Beda, but in place of it the phrase annus bisextus.

It was the intention of Caesar that the bisextum should be inserted peracto quadriennii circuitu, as Censorinus says, or quinto quoque incipiente anno, to use the words of Macrobius. The phrase, however, which Caesar used seems to have been quarto quoque anno, which was interpreted by the priests to mean every third year. The consequence was, that in the year 8 B.C. the Emperor Augustus, finding that three more intercalations had been made than was the intention of the law, gave directions that for the next twelve years there should be no bissextile (Plin. Nat.18.211).

The services which Caesar and Augustus had conferred upon their country by the reformation of the year seems to have been the immediate causes of the compliments paid to them by the insertion of their names in the calendar. Julius was substituted for Quinctilis, the month in which Caesar was born, in the second Julian year, that is, the year of the dictator's death (Censorinus, c. xxii.); for the first Julian year was the first year of the corrected Julian Calendar, that is, 45 B.C. The name Augustus, in place of Sextilis, was introduced by the emperor himself, at the time when he rectified the error in the mode of intercalating (Suet. Aug. 100.31), anno Augustano xx. The first year of the Augustan era was 27 B.C., viz. that in which he first took the name of Augustus, se vii. et M. Vipsanio Agrippa coss. He was born in Sep. tember; but gave the preference to the preceding month, for reasons stated in the senatus consultum, preserved by Macrobius (1.12): Whereas the Emperor Augustus Caesar, in the month of Sextilis, was first admitted to the consulate, and thrice entered the city in triumph, and in the same month the legions, from the Janiculum, placed themselves under his auspices, and in the same month Egypt was brought under the authority of the Roman people, and in the same month an end was brought to the civil wars; and whereas for these reasons the said month is, and has been, most fortunate to this empire, it is hereby decreed by the senate that the said month shall be called Augustus. A plebiscitum, to the same effect, was passed on the motion of Sextus Pacuvius, tribune of the plebs.

Domitian gave to the month of September the name of Germanicus from his own surname, and to the month of October the name of Domitianus; but these names fell into disuse after the death of the tyrant. Our days of the Month.March, May, July, October, have 31 days.January, August, December, have 31 days.April, June, September, November, have 30 days.February has 28 days, and in Leap Year 29.1.KALENDIS. KALENDIS. KALENDIS. KALENDIS. 2VI.ante Nonas.IV.ante Nonas.IV.ante Nonas.IV.ante Nonas.3.V.III.III.III.4.IV.Pridie Nonas.Pridie Nonas.Pridie Nonas.5.III.NONIS. NONIS. NONIS. 6.Pridie Nonas.VIII.ante Idus.VIII.ante Idus.VIII. 7.NONIS. VII.VII.VII. 8.VIII.an te Indus.VI.VI.VI. 9.VII.V.V.V. 10.VI.IV.IV.IV. 11.V.III.III.III. 12.IV.Pridie Idus.Pridie Idus.Pridie Idus.13.III.IDIBUS. IDIBUS. IDIBUS. 14.Pridie Idus.XIX.Ante Kalendas (of the month following)XVIII.Ante Kalendas (of the month following).XVI.Ante Kalendas Martias.15.IDIBUS. XVIII.XVII.XV.16.XVII.Ante Kalendas (of the month following).XVII.XVI.XIV.17.XVI.XVI.XV.XIII.18.XV.XV.XIV.XII.19.XIV.XIV.XIII.XI.20.XIII.XIII.XII.X.21.XII.XII.XI.IX.22.XI.XI.X.VIII.23.X.X.IX.VII.24.IX.IX.VIII.VI.25.VIII.VIII.VII.V.26.VII.VII.VI.IV.27.VI.VI.V.III.28.V.V.IV.Pridie Kalendas Martias29.IV.IVIII.30.III.III.Pridie Kalendas (of the month following).  31.Pridie Kalendas (of the month following).Pridie Kalendas (of the month following).  

The Fasti of Caesar have not come down to us in any one table, in their entire form. Such fragments as exist may be seen in the Corpus Inscriptionum Latinarum, vol. i. (Berlin, 1863), edited with the most minute accuracy, and with very valuable notes, by Mommsen. They are nineteen in number, and by combining them the Fasti can be completely reconstructed. Three others have been discovered since, and published in the Ephemeris Epigraphica.

The official year before the Julian reforms, with its frequent and irregular intercalations, could not have at all met the practical requirements of an agricultural population; and there is reason to believe that the farmers' year was that which had been adopted with slight modifications from the Egyptian sages of Heliopolis by Eudoxus. This gave up altogether the attempt to take notice of the phases of the moon, and was a purely solar year. The cycle was made up of four years,--the first of 366, the others of 365 days,--thus corresponding exactly with the reformed Julian system. There was no division into months, but the subdivisions were marked by the entrance of the sun into the various signs of the zodiac, and by the tropics and equinoxes. Spring began when the sun was in Aquarius, summer when it was in Taurus, autumn when it was in Leo, and winter when it was in Scorpio. (Varro, de R. R. 1.28.) The new year began when the sun entered Leo and the dog-star rose.

The Gregorian Year.

The Julian Calendar supposes the mean tropical year to be 365 d. 6 h.; but this exceeds the real amount by 11′ 12″, the accumulation of which, year after year, caused at last considerable inconvenience. Accordingly, in the year 1582, Pope Gregory XIII., assisted by Aloysius, Lilius, Christoph. Clavius, Petrus Ciacconius, and others again reformed the calendar. The ten days by which the year had been unduly retarded were struck out by a regulation that the day after the fourth of October in that year should be called the fifteenth; and it was ordered that, whereas hitherto an intercalary day had been inserted every four years, for the future three such intercalations in the course of four hundred years should be omitted, viz. in those years which are divisible without remainder by 100, but not by 400. Thus, according to the Julian Calendar, the years 1600, 1700, 1800, 1900, and 2000 were to have been bissextile; but, by the regulation of Gregory, the years 1700, 1800, and 1900 were to receive no intercalation, while the years 1600 and 2000 were to be bissextile, as before. The bull which effected this change was issued Feb. 24, 1582. The fullest account of this correction is to be found in the work of Clavius, entitled Romani Calendarii a Gregorio XIII. P. M. restituti Explicatio. As the Gregorian Calendar has only 97 leap-years in a period of 400 years, the mean Gregorian year is (303 x 365 + 97 x 366) / 400; that is, 365 d. 5 h. 49′ 12″, or only 24″ more than the mean tropical year. This difference in 60 years would amount to 24′, and in 60 times 60, or 3600 years, to 24 hours, or a day. Hence the French astronomer, Delambre, has proposed that the years 3600, 7200, 10,800, and all multiples of 3600 should not be leap years. The Gregorian Calendar was introduced in the greater part of Italy, as well as in Spain and Portugal, on the day named in the bull. In France, two months after, by an edict of Henry III., the 9th of December was followed by the 20th. The Catholic parts of Switzerland, Germany, and the Low Countries adopted the correction in 1583, Poland in 1586, Hungary in 1587. The Protestant parts of Europe resisted what they called a Papistical invention for more than a century. At last, in 1700, Protestant Germany, as well as Denmark and Holland, allowed reason to prevail over prejudice; and the Protestant cantons of Switzerland copied their example the following year.

In England the Gregorian Calendar was first adopted in 1752, and in Sweden in 1753. In Russia, and those countries which belong to the Greek Church, the Julian year, or old style as it is called, still prevails.

In this article free use has been made of Ideler's work Lehrbuch der Chronologie(2 vols. Berlin, 1826). Cf. also Mommsen, Die Römische Chronologie, Berlin, 1858; and Matzat, Röm. Chronologie, 2 vols., Berlin, 1883. For other information connected with the Roman measurement of time, see ASTRONOMIA; DIES; HOROLOGIUM; LUSTRUM; NUNDINAE; SAECULUM.

[T.H.K] [A.S.W]

Calendarium

(more properly Kalendarium). Originally the account-book in which debts were entered. As these debts fell due on the Kalends, the name got its first signification from that fact; coming later to mean a register of the days, weeks, and months. The Greek terms are ἡμερολόγιον and ἐφημερίς.

(1) Greek. The Greek year consisted of twelve months—some “full,” i.e. of 30 days each; the others, “hollow” or incomplete, of 29 days each. This made up a lunar year of 354 days, 11 days short of the solar year. To maintain some correspondence between the lunar and the solar years, and to provide at least for the festivals of the seasons always occurring at the right time of year, the Athenians early resorted to the method of intercalation. A space of time was taken which included as many days as would exactly make up eight solar years, and could easily be distributed among the same number of lunar years. This space of time was called a “great year.” Then in every third, sixth, and eighth year, a month of 29 or 30 days was inserted, so that the years in question consisted each of 383 or 384 days. This system was introduced at Athens by Solon. The period of eight years was sometimes called ἐνναετηρίς, or a period of nine years, because it began again with every ninth year; sometimes ὀκταετηρίς, or space of eight years. For this the astronomers, of whom Meton (q.v.) in the Periclean Age may be taken as a representative, substituted a more accurate system, which was afterwards adopted in Athens and other cities as a correction of the old calendar. This was the ἐννεακαιδεκαετηρίς of nineteen years. The alternate “full” and “hollow” months were divided into three decades, consisting of 10 or 9 days each, as the case might be. The days of the last decade were counted from more to less to correspond with the waning of the moon. Thus the 21st of the month was called the 10th of the waning moon, the 22d the 9th, the 23d the 8th, and so on. The reckoning of the year, with the order and names of the months, differed more or less in different States, the only common point being the names of the months, which were almost without exception taken from the chief festivals celebrated in them. The Athenians and the other Ionian peoples began their year with the first new moon after the summer solstice, the Dorians with the autumnal equinox, the Boeotians and other Aeolians with the winter solstice. The table given below shows the succession of the Attic months, the number of days they contained, and the corresponding months of our year.

At the time when the Calendar Julian was adopted by the Athenians, probably about the time of the emperor Hadrian, the lunar year appears to have been changed into the solar year; and it has further been conjectured that the beginning of the year was transferred from the summer solstice to the autumnal equinox. The intercalary month was a second Poseideon inserted in the middle of the year. The official system of numbering the years differed also very much in the various States. The years received their names from the magistrates, sometimes secular, sometimes spiritual. (See Eponymus.) Historical chronology was first computed according to Olympiads, or periods of four years, beginning B.C. 776, by the historian Timaeus in the third century B.C.

(2) Roman. The Roman year was supposed to have consisted, under Romulus, of 10 months— four “full” ones of 31 days (March, May, July, and October) and six “hollow” of 30 days (April, June, August, September, November, December). But, as a space of 304 days makes up neither a solar nor a lunar year, it is difficult to understand the so-called “year of Romulus.” King Numa was popularly supposed to have introduced the year of 12 months by adding January and February at the end; for the Roman year, it must be remembered, began originally with March. By this system every month except February had an odd number of days: March 31, April 29, May 31, June 29, Quintilis 31, Sextilis 29, September 29, October 31, November 29, December 29, January 29, February 28. Numa is also credited with the attempt to square this lunar year of 355 days with the solar year of 365; but how he did it is not certainly known. The Decemviri in B.C. 450 probably introduced the system of adjustment afterwards in use. According to this, a cycle of four years was taken, in the second year of which an intercalary month (mensis mercedonius) of 23 days was inserted between the 24th and 25th of February, and in the fourth year a month of 22 days between the 23d and 24th of February. Thus the period of four years amounted to 1465 days. But this gave the year an average of 366 1/4 days, or one day too many, so that a special rectification was necessary from time to time. This was probably carried out by the omission of an intercalary month. It was the business of the pontifices to keep the calendar in order by regular intercalation; but, partly from carelessness, partly from political motives, they made insertions and omissions so incorrectly as to bring the calendar into complete confusion, and destroy the correspondence between the months and the seasons. The mischief was finally remedied by Iulius Caesar, with the assistance of the mathematician Sosigenes. To bring the calendar into correspondence with the seasons, the year B.C. 46 was lengthened so as to consist of 15 months, or 415 days, and the calendar known as the Julian was introduced on the 1st of January, B.C. 45. This calendar is founded simply on the solar year, which is well known to be a discovery of the Egyptians. Caesar fixed this year at 365 1/4 days, which is correct within a few minutes. After this, the ordinary year consisted of 365 days, divided into 12 months, with the names still in use. Every fourth year had 366 days, a day being inserted at the end of February. The Julian Calendar maintained its ground till 1582, when Pope Gregory XIII. corrected the trifling error which still attached to it. The old names of the months were retained with two exceptions—that of Quintilis, which, in honour of Iulius Caesar, was called Iulius, and that of Sextilis, which in B.C. 8 was called Augustus, in honour of the emperor. The old divisions of the lunar month were also retained for convenience of dating. These were (a) the Kalendae, marking the first appearance of the new moon; (b) the Nonae, marking the first quarter; (c) the Idus, marking the full moon. Kalendae means properly the day of summoning, from calare, to summon. The pontifex was bound to observe the first phase, and to make his announcement to the Rex Sacrorum, who then summoned the people to the Capitol, in front of the Curia Calabra, so called from calare. Here he offered sacrifice, and announced that the first quarter would begin on the fifth or seventh day (inclusive) as the case might be. This day was called Nonae, as (according to Roman calculation) the ninth day before the full moon, and fell in March, May, July, and October on the 7th, in the other months on the 5th. The appearance of the full moon was called Idus (probably connected with the Etruscan word iduare, “to divide”), because it divided the month in the middle. The days of the month were counted backwards, in the first half of the month from the Nones and Ides, in the last half from the Kalends of the following month. The Romans also had a week called internundinum, or the interval between two nundinae. It consisted of eight days, and, like our weeks, could be divided between two months or two years. See Fasti.

After the establishment of the Republic the Romans named their years after the consuls, a custom which was maintained down to the reign of Justinian (A.D. 541). After the time of Augustus it became the practice in literature to date events from the foundation of Rome, which took place, according to Varro, in B.C. 753; according to Cato , in 751.

The Day.—The Greeks reckoned the civil day from sunset to sunset, the Romans (like ourselves) from midnight to midnight. The natural day was reckoned by both as lasting from sunrise to sunset. The divisions of the day were for a long time made on no common principle. It was for military purposes that the Romans first devised such a principle, dividing the night during service into four equal watches (vigiliae). Corresponding to this we find another division (probably calculated immediately for the courts of justice) into mane (sunrise to 9 or 10), forenoon (ad meridiem), afternoon (de meridie) until 3 or 4, and evening (suprema) from thence till sunset. After the introduction of sundials and waterclocks, the day and night were divided each into twelve hours; but the division was founded on the varying length of the day, so that each hour of the day was longer, and conversely each hour of the night shorter, in summer than in winter.

It should be observed that several of the Eastern nations, for the purpose of preventing confusion in their calculations with other nations, dropped the names of their months, and merely counted the months, as the first, second, third, etc., month. For extended information see Corsini, Fast. Att., which, however, is very imperfect; Ideler, Handbuch der mathem. u. technischen Chronol. (Berlin, 1826); Clinton, Fast. Hellen. vol. ii. Append. xix.; and more especially K. F. Hermann, Ueber griechische Monatskunde (Göttingen, 1844); Bergk, Beiträge zur griechischen Monatskunde (Giessen, 1845); Boeckh, Ueber die vierjährigen Sonnenkreise der Alten (Berlin, 1863); Mommsen, Chronologie (Leipzig, 1883); Ideler's work, Lehrbuch der Chronologie, 2 vols. (Berlin, 1826); Mommsen, Die römische Chronologie (Berlin, 1858); and Matzat, Rö. Chronologie, 2 vols. (Berlin, 1883). For further information connected with the ancient measurement of time see the articles Astronomia; Dies; Horologium; Lustrum; Nundinae; Saeculum; Vigiliae.