i. 'The Year of Romulus,' of ten months and 304 days. ii. 'The Year of Numa,' a pure lunar year of twelve lunar months and 355 days, with suitable intercalations. iii. The Year of the Decemviri,' nominally a lunar year like the former, but which from the intercalations employed, ceased to correspond with the phases of the moon. 18. We have not yet mentioned the distribution of the days among the twelve months of the year of 355 days. It was as follow:1 This arrangement, which remained in force until the Julian reform, is usually referred to the time of Numa; but as the number of days in the different months is inconsistent with a lunar calendar, it can scarcely have been introduced until the intercalary months of twenty-two and twenty-three days were employed. The position of the Calends, Nones and Ides, was the same as in the year of Caesar, the Calends always marked the first of every month, the Nones and Ides the fifth and thirteenth, except in March, May, July, and October, when they fell upon the seventh and fifteenth. All dates in works written before 45 B. C. must of course be calculated by the above table. Thus when Cicero, in a letter written 51 B. C., says that he arrived at the camp in Lycaonia ‘VII. Kal. Sept.' we must not translate this 'the 26th of August,' as we should do had it been written after the beginning of 45 B. C., but 'the 24th of August,' because Sextilis at that time had twentynine days only. 19. Plutarch names the intercalary month twice; in the life of Numa he calls it Mepkidivos; in the life of Caesar Μερκηδόνιος. It is remarkable that this term is not to be found in any Roman writer; the expressions ‘mensis intercalaris,' and 'mensis intercalarius,' being alone employed by them. The intercalations took place in the month of February, between the 'Terminalia' and the 'Regifugium;' that is, between the twenty-third and the twenty-fourth, at least such was the rule, although it may have been violated at times. The remaining five days belonging to February were added 1 Macrob. 1. 14, Censorin. 20. after the intercalary month, probably from some superstition; but all the calculations of time in intercalary years were founded upon the supposition that in such years February contained twenty-three days only. Thus in ordinary years the day after the Ides of February was 'A. D. XVI. Kal. Mart.,' but in intercalary years 'A. D. XI. Kalendas Intercalares.' The Terminalia' in ordinary years fell 'A. D. VII. Kal. Mart.,' in intercalary years, ‘Pridie Kalendas Intercalares.' The intercalary month had its own Calends, Nones, and Ides, with the addition of the epithet 'intercalares,' the day after the Ides would be 'A. D. XV. or A. D. XVI. Kal. Mart.,' according as the month contained twenty-two or twenty-three days, and the five remaining days of February being added, in either case the 'Regifugium' would always stand as 'A. D. VI. Kal. Mart.' As examples of what has just been said, we find in the Fasti Capitolini 'C. DUILLIUS COS. PRIMUS NAVALEM DE SICUL. ET CLASSE POENICA EGIT AN. CDXCIII. K. INTERKALAR.' and again, 'L. CORNELIUS LENTULUS CAUDINUS COS. DE LIGURIBUS IDIB. INTER. AN. DXVI.' To which we may add Livy 37. 59, speaking of L. Scipio'Trumphavit mense intercalario, pridie Kalendas Martias,' and Cicero pro Quinct. 25 'Dic, Naevi, diem. Ante V. Kalend. intercalares. Bene agis. Quam longe est hinc in saltum vestrum Gallicanum? Naevi, te rogo. DCC millia passuum. Optime. De saltu deiicitur Quintius. Quo die?-Quid taces?-Deiicitur de saltu, C. Aquilli, pridie Kalend. intercalares, biduo post, aut ut statim de iure aliquis concurrerit, non toto triduo DCC millia passuum conficiuntur.' 20. We have seen that the whole management of the Calendar was originally in the hands of the Pontifices, and even after Cn. Flavius had divulged the secrets of the Fasti, they retained the privilege of adjusting the intercalations 1. This trust they shamefully betrayed, and to gratify their private animosities, or show favour to their friends, in order that a magistrate might remain in office for a period shorter or longer than the law permitted, that a farmer of the taxes might be defrauded of his just right, or obtain an unfair advantage, they curtailed or drew out the year at pleasure, 1 Pontificum Arbitrio intercalandi ratio permissa' Censorin, 20. until the whole Calendar was involved in a degree of uncertainty and confusion, to which we can find no parallel in the history of a civilized people1. The ignorance which prevailed with regard to the years in which the intercalations ought to take place, and the mystery observed by the priests, is well illustrated by the expressions of Cicero. Thus in Ep. ad Att. 5. 21, we find 'Cum scies Romae intercalatum sit, necne, velim ad me scribas;' again in Ep. ad Fam, 7. 2 'Quotidie vota facimus ne intercaletur, ut quam primum te videre possimus;' and in Ep. ad Att. 6. 1, we find 'Accepi tuas literas. A. D. quintum Terminalia;' that is, on the 19th of February, this singular method of fixing the date being employed to prevent ambiguity, since the day would be 'A. D. XI. Kal. Mart.' in a common year, and A. D. VI. Kal. Intercal.' in an intercalary year, and Cicero knew not when he wrote whether an intercalation had or had not taken place. 21. Accordingly, when Caesar became dictator, the year was about two months in advance of the seasons; the spring festivals happened in what were nominally the summer months, and those of summer in autumn. To take a single example. Cicero, in one of his Epistles to Atticus (10. 17), says that at the time when he was writing his journey was delayed by the Equinox. The date affixed to this letter is XVII. Kal. Iun., i.e. 16th of May. In order to remedy these defects, it was found necessary to add sixty-seven days to the year 46 B.C., which were divided into two intercalary months, and inserted between November and December. In this year the ordinary intercalations of twenty-three days took place in February, so that it contained in all, Ordinary length of year Intercalary month Two additional intercalary months Total 355 days. 23 Such was the year 46 B.C., which among modern chronologers has received the name of Annus Confusionis,' although, as Ideler observes, Macrobius has more correctly termed it 'Annus confusionis ultimus.' Censorinus says that ninety days were added to the year, Dion Cassius sixty-seven; but there is no contradiction here, for the former includes the ordinary intercalation of twenty 1 See Censorin. 20, Macrob. I. 14, Plutarch. Vit. Caes. 59, Ammianus Marcellinus 26, Solinus I. three days in February, which is not taken into account by the latter'. The two additional months seem to have been called 'Mensis intercalaris prior' and 'Mensis intercalaris posterior,' for we find in Cic. Ep. ad Fam. 6. 14 'Ego idem tamen cum A. D. V. Kalendas Intercalares priores rogatu fratrum tuorum venissem mane ad Caesarem,' &c. 22. The Julian Calendar was founded upon the supposition that the length of the solar or tropical year was exactly 365 days, 6 hours, or 365.25 days. Therefore The length of the Julian Year being 365d. 6h. But the true length of the Solar Year being 365d. 5h. 48m. 51s. It follows that the Julian Year is too long by This excess in 10 years will amount to IIM. 8 s. 1h. 51m. 25S. 18h. 34m. IOS. 7d. 17h. 41m. 40s. To correct this accumulating error, Pope Gregory XIII. published a bull in 1582, by which it was ordained that common years should consist of 365 days, and that a day should be added every fourth year as formerly, with this difference, that the intercalation was to be omitted in the last year of those centuries not divisible by four; that is, that ninety-seven days instead of 100 should be inserted in 400 years 2. The Gregorian Calendar was almost immediately adopted in all Roman Catholic countries, and to compensate for the error already incurred, ten days were dropped. The change was not admitted into England until 1752, when eleven days were dropped between the 2nd and 14th of September, from which arose the distinction between Old and New Style. Russia and other countries which follow the Greek church still retain the original Julian Calendar, and hence their dates are now twelve days behind those of the rest of Europe. According to the Gregorian scheme by which three leap years are omitted in 400 years— 1 See Censorin. 15, Dion Cassius 43. 26, Macrob. S. 1. 16, Pliny H. N. 18. 17, Ammian. Macrob. 26. 1, Suet. Caesar 40, Ov. Fast. 3. 155, Appian. B. C. 2. 2 Thus no intercalation takes place in the years 1900, 2100, 2200, 2300, 2500, all of which, according to the old system, would have been leap years. A a Length of the Gregorian Year being 365d. 5h. 49m. 12s. True length of the Solar Year being 365d. 5h. 48m. 51s. Therefore the Gregorian Year is too long by 20 S. An excess which will not amount to one day in 4500 years. If the insertion of a day be omitted each 4000th yearLength of year according to cycle of 4000 years365d. 5h. 48m. 50s. which is too short by one second-a deficiency which will not amount to a day in 70,000 years. 23. We may now say a few words with regard to the longer divisions of time, the 'Lustrum' and the 'Saeculum.' The word 'Lustrum' (see p. 331), derived from 'luo,' signified properly the expiatory sacrifice offered up for the sins of the whole people by the Censors at the end of every five years, the period during which these magistrates originally held office. Hence 'lustrum' was used to denote 'a space of five years,' and the Censors in performing the sacrifice were said, 'condere lustrum,' to bring the 'lustrum' to a close. Varro, in explaining the term, derives it from 'luere,' in the sense of 'to pay' 'Lustrum nominatum tempus quinquennale a luendo, id est, solvendo, quod quinto quoque anno vectigalia et ultro tributa per censores persolvebantur' L. L. 6. 2. It is to be observed here that 'quinto quoque anno,' according to the Roman method of computation, might mean 'every fourth year,' and 'quinquennale tempus,' a term of 'four years,' just as Cicero (De Orat. 3. 32) calls the Olympic games 'maxima illa quinquennalis celebritas ludorum;' but since we know from other sources that the Censors originally held office for five years, and that the taxes were farmed out upon five years' leases, the interpretation of the above passage is not open to doubt. We may add, that wherever the word 'lustrum' occurs in the older writers, it is always in connection with the duties of the Censors. When we come down to the age of Ovid, a confusion seems to have arisen, and the meaning of ‘lustrum' was no longer definite; in Amor. 3. 6, 27 'Nondum Troia fuit lustris obsessa duobus,' it unquestionably stands for five years, and also in Fast. 3. 119, where the ten-month year of Romulus is described, 'Ergo animi indociles et adhuc ratione carentes, |