the year that was past, of the former to stimulate their exertions for the future.1

The year of 304 days corresponds with the course neither of the sun nor of the moon, and many hypotheses have been formed with regard to its origin and import. By far the most ingenious and profound of these, so ingenious indeed that it almost carries conviction, is the theory propounded by Niebuhr. He supposes it to have been employed along with a lunar year for the purpose of making the solar and lunar years coincide at certain fixed epochs. He moreover finds traces of it in history at a period long after it is generally believed to have fallen into disuse, and by its aid explains several of the chronological anomalies and contradictions so frequent in the early annals. His calculations are too intricate to be developed here, but well deserve the attention of all interested in such researches.2

13. The year of Romulus was succeeded by a pure lunar year, introduced according to the prevailing tradition by Numa,3 who retained the names of the ten months already in use, and added two more, Januarius from the god Janus, and Februarius from Februus, the deity who presided over expiatory rites.

The true length of a lunar month, that is the interval between two successive New or Full Moons, is 29 days, 12 hours, 44 minutes, 2.87 seconds, and hence twelve lunar months contain 354 days, 8 hours, 48 minutes, 34.386 seconds. The Athenians made their lunar year consist of 354 days, but Numa, influenced it said by the virtue attributed to odd numbers, added another to make up 355.

14. Each month was divided into three periods by the Calenda, Nonæ and Idus. The Calenda marked the first of the month, the day following the evening upon which the slender crescent of the New Moon was first visible in the sky, the Nona the First Quarter, the Idus the Full Moon. The origin of these terms must be explained. Macrobius has preserved the record of the ancient practice, S. I. 15.

Priscis ergo temporibus, antequam fasti a Cn. Flavio scriba invitis patribus in omnium notitiam proderentur, pontifici minori hæc provincia delegabatur, ut novæ lunæ primum observaret adspectum, visamque regi sacrificulo nuntiaret, itaque sacrificio a rege et minore pontifice celebrato, idem pontifex Kalata, id est, vocata in Capitolium plebe iuxta curiam Kalabram, quæ casæ Romuli proxima est, quot numero

1 See Macrob. S. 1. 12. Ov. Fast. III. 135, seqq. Plutarch. Q. R. XIX. 2 Niebuhr's Roman History, Vol. 1. Chapter "On the secular cycle." 3 Censorin. XX. Solin I. Macrob. S. I. 13. On the other hand Junius Gracchanus maintained (Censorin. 1. c.) that this change was introduced by Tarquinius (Priscus.) 4 Thus Virgil E. VIII. 75, "numero deus impare gaudet;" Plin. H. N. XXVIII. 5, "Impares numeros ad omnia vehementiores credimus;" and Festus, "Im. parem numerum antiqui prosperiorem hominibus esse crediderunt."

dies a Kalendis ad Nonas superessent pronuntiabat: et quintanas quidem dicto quinquies verbo xaλã, septimanas repetito septies prædicabat. verbum antem xaλ græcum est, id est, voco. et hunc diem qui ex his diebus qui Kalarentur primus esset, placuit Kalendas vocari. hinc et ipsi curiæ, ad quam vocabantur, Kalabræ nomen datum est. Ideo autem minor pontifex numerum dierum qui ad nonas superessent Kalando prodebat, quod post novam lunam oportebat nonarum die populares qui in agris essent confluere in urbem accepturos causas feriarum a rege sacrorum, scripturosque quid esset eo mense faciendum.

It appears from this that the Kalenda were derived from calo, the same with the Greek xaλã, because immediately after the appearance of the New Moon the people were called together that they might be told on what day the Nones would fall. It must be observed that the New Moon in question was not the astronomical New Moon or period of conjunction, but the first appearance of the crescent in the evening twilight. Now, according to circumstances, the New Moon is visible sometimes on the evening after conjunction, sometimes not for two or three days. Hence the Nones or First Quarter would fall sometimes as early as the fifth of the month, sometimes as late as the seventh, and thus the Ides or Full Moon would fall sometimes as early as the thirteenth, sometimes as late as the fifteenth. The pontiffs appear by ancient custom to have been confined to the extremes, and hence according to the appearance of the New Moon they proclaimed that the Nones would be on the fifth, in which case they were called Quintanæ, or on the seventh Septimanæ. Idus is derived from an Etruscan verb iduare, signifying to divide, because the full moon divides the lunar months; Nona is the plural of nonus "the ninth," because the Nones were always just nine days before the Ides, according to the Roman system of computation explained above.

January and February having been added to the ten months of the old year, a question arises as to the order of succession then or subsequently established.

That February was in the first instance the last month of the year seems scarcely to admit of doubt, thus Cicero de legg. II. 21.

Venio nunc ad Manium iura, quæ maiores nostri et sapientissime instituerunt et religiosissime coluerunt. Februario antem mense, qui tunc extremus anni mensis erat, mortuis parentari voluerunt.

and Varro,

Terminalia, quod is dies anni extremus constitutus. Duodecimus enim mensis fuit Februarius.1

See also Festus v. Februarius and Servius on Virg. G. I. 43. Macrobius S 1. 12, 13, asserts that January and February were placed by Numa as the first and

We have no satisfactory evidence to determine the epoch at which January and February became the first and second months. Plutarch supposes them to have been from the first the eleventh and twelfth. According to Ovid, who supposes them to have been added by Numa, January was placed at the beginning of the year, February at the end, and the new arrangement, by which February was placed second, was introduced by the Decemvirs. It is perfectly clear, however, from the various ceremonies described above, that March must have been looked upon as the commencement of the year at the time when these rites were established. Januarius, therefore, was called after Janus, the deity presiding over the beginning of all things, not because it was the first month of the sacred or of the civil year, but because it was the month which immediately followed the winter solstice, when the sun may be said to resume his career.2 We know that from B. C. 153 the consuls always entered upon their office on the first January, but we cannot positively assert that this day was considered the first of the civil year before that time, although it undoubtedly was looked upon as such ever after.

(15.) The lunar year of the Greeks consisted of 354 days, that of the Romans of 355, while the length of the solar year, upon which depends the return of the seasons, is 365 days nearly. Hence almost all nations who have adopted a lunar year have had recourse to intercalations, that is, to the insertion of additional days or months from time to time, which, if managed skilfully, will insure a correspondence between the civil and natural year at fixed periods, and prevent the dislocation of the seasons. The insertion of a day every fourth year in the Julian Calendar, which has no reference to the moon, is also an intercalation, the object being to compensate for the error arising from making the Solar year consist of an exact number (365) of days, instead of 3654, and we shall see how it became afterwards necessary to modify this intercalation to compensate for the error arising from supposing the solar year to be exactly 365.25 days in length, instead of 365.242264, &c., as it really is.

(16.) If we reckon the lunar month at 29 days, and the solar year at 365 days, and the earliest astronomers did not arrive at greater accuracy, then twelve lunar months or 354 days will fall short of a solar year by 114 days, which in eight lunar years will amount to 90 days. If, therefore, in the space of eight lunar years we add three lunar

second months of the year, and in the last quoted chapter contradicts himself downright, "Omni intercalationi mensis Februarius deputatus est, quoniam is ultimus anni erat."

1 Fast. II. 49. See Extract, p. 86, v. 29, and notes.

2 Bruma novi prima est, veterisque novissima solis:

Principium capiunt Phoebus et annus idem.-Fast. 1. 163.

month, or, in other words, make three lunar years out of every eight consist of thirteen lunar months instead of twelve, then at the end of eight years there will a difference of only one day and a half between the solar and lunar years. This correction was at one time employed by the Athenians, the intercalary months were added at the end of the third, fifth, and eighth years, and the period, or to use the technical phrase, the Cycle of eight years was termed ixraɛrngis.

With the progress of science a more convenient correction was introduced. According to the most accurate calculations,

19 Solar years contain.....

235 Lunar months

..6939.603016 days.

or, 19 Lunar years and 7 months contain {6939.68718 days.

}

so that if seven lunar months are intercalated during nineteen lunar years, or if, in other words, seven out of every nineteen lunar years are made to consist of thirteen lunar months instead of twelve, then the difference between the solar and lunar years at the end of that period will amount to only .084164 of a day, and the error would be less than one day in two hundred years. This weadexarng's or cycle of nineteen years is usually named, from its inventor, the Cycle of Meton, and came into use at Athens on the 16th of July, B.C. 432. It was afterwards corrected by Calippus of Cyzicus, who invented a cycle of seventy-six years, which in its turn was corrected by Hipparchus, who invented a cycle of three hundred and four years.

17. It seems to be certain that the Romans for a considerable period made use of a pure lunar year, the introduction of which, as we have seen above, was usually ascribed to Numa, and it can scarcely be doubted that intercalations were employed resembling some of those described above, in order to bring about a correspondence with the solar or natural year. On this subject, however, the ancient writers are silent, with the exception of Livy, (I. 19.) but unfortunately his language is extremely obscure and the text of the passage disputed.

The intercalations which we do find described by Macrobius, Censorinus, and Plutarch, and which were certainly in use at the time of the Julian reform, belong to a system essentially different. The scheme which they describe is the following. The year of Numa consisted of 355 days. The Romans having become acquainted with the Grecian Octaeteris, according to which 90 days were to be intercalated in a cycle of eight years, applied it thus. They intercalated at the end of every two years a month, which consisted alternately of twenty-two and twenty-three days, thus making up the sum of 90 days at the end of eight years.' It was soon discovered, however, that

1 So Censorinus (XX) and Macrob. S. I. 18. Plutarch, on the other hand, says that Numia doubled the difference between the solar and lunar year, and thus

the year of the Greeks contained 354 days only, while their own had 355, and hence it followed that in the cycle of eight years there was an excess of eight days. To remedy this a new cycle was invented of twenty-four years, and in the last eight years of this twenty-four days were omitted, sixty only being intercalated instead of 90, thus compensating for the excess which would have taken place in the whole period had the full number been employed.

At what time this (or any other) system of intercalation was brought into use we cannot tell. The Roman antiquaries themselves were at variance. Some referred the introduction of intercalations to Romulus, some to Numa, some to Servius, some to the Decemvirs, while some brought it down as low as the consulship of Manius Acilius Glabrio in the Ætolian war, B.C. 191. Whatever opinion we may adopt on this matter it is important to attend to the following consideration.

So long as we make use of a year the months of which are regulated by the phases of the Moon, it is evident that all intercalations employed to produce a correspondence with the solar year must be in the form of entire lunar months. As soon as a period is inserted either longer or shorter than one lunar month, or an exact number of entire lunar months, from that time forward all regular connection between the phases of the moon and the commencement of the months and years is destroyed. Hence as soon as the Romans began to employ the intercalary months of twenty-two and twenty-three days, from that moment they virtually abandoned the lunar year and adopted a solar cycle, the same in substance as that afterwards perfected by Julius Cæsar, but less accurate and less convenient. The old names of Calends, Nones, and Ides were retained, but these would no longer answer to the first appearance of the New Moon, to the First Quarter, and to Full Moon, more than the first, fifth, and thirteenth of any month at the present time. Ideler believes the change from the pure lunar year to have taken place during the sway of the Decemvirs, an opinion of which we find some trace in Macrobius.2 Hence he supposes that the Roman Calendar assumed three different shapes before the Julian Reform. These he distinguishes as

I. The Year of Romulus of 10 months and 304 days.

II. The Year of Numa, a pure lunar year of 12 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.

made a month of 22 days, which was intercalated every alternate year, but makes no allusion to the month of 23 days. 1 Macrob. S. 1. 13. See also Cic. de legg. 11. 12. Macrob. S. I. 13. It is clear from Ov. Fast. II. 54, (see p. 85,) that there was a tradition that the Decemvirs had made some changes in the Calendar.