To restore, therefore, the equality of the year of Numa to the Julian or Solar, tertio quoque octennio, says Macrobius, ita intercalandos dispensabant dies, ut non nonaginta, sed (90-24) sexaginta sex intercalarent. I understand this to mean that for the last eight years of every 24, they introduced three intercalary months of 22 days; two at the end of three years, and one at the end of two*. On this principle, between two successive intercalations, (as for instance, B. C. 170 and B. C. 167.) there might be periodically, that is, every 24 years, three years', and not two years' interval. This could not, however, have been the case, at the period of the battle of Pharsalia; because U. C. 704, before it, and U. C. 708, after it, were, as we have seen, intercalated years.

A still more recent example of an intercalary year was U. C. 671, two years before U. C. 673, when Cicero's Oration pro P. Quintio was pronounced ". On this principle, U. C. 703, just 32 years afterwards, it might be said, would be intercalary. But two intercalations only might take place in six years. U. C. 671

* And this was more agreeable to the usage of the Greeks, who intercalated thrice in the octaeteric cycle; in the third, the fifth, and the eighth years, respectively: τοὺς ἐμβολίμους μῆνας ἔταξαν ἄγεσθαι ἐν τῷ τρίτῳ ἔτει, καὶ πέμπτῳ, καὶ ὀγδόῳ δύο μὲν μῆνας, μεταξὺ δύο ἐτῶν πιπτόντων, that is, two complete years; viz. between the eighth and third, and the fifth and eighth: ἕνα δὲ, μετ ταξὺ ἑνὸς ἐνιαυτοῦ ἀγομένου, viz. that between the third and fifth. Geminus, cap. vi. Uranologion, 35.C.D. Epiphanius' account of the octaeteric cycle, in his time,

a Cf. Livy, i. 19.

differs from this; for he speaks
of ninety days as being to be
distributed over the cycle, in
three intercalary months of full
thirty days each; κατὰ τρία ἔτη
μὴν εἷς, καὶ κατὰ δύο τὰ ὕστερα ἔτη
rà
un eis: that is, every three
years one month, which means
two months in the first six
years, and every two last years
of the cycle one month: Ope-
rum i. 825. C. Audiani xiii. On
this principle, the intercalated
years were the third, the sixth,
and the eighth; which Geminus
supposed to be the third, the
fifth, and the eighth.

b Capp. 6. 8. 12. 18. 25. Aulus Gellius, xv. 28.

might be one of those; and U. C. 674 the next: and U. C. 676 might be the end of that cycle of 24 years. Hence U. C. 676 +24 or U. C. 700, would be the end of the next and U. C. 702, U. C. 704, U. C. 706, U. C. 708, would be the first eight years of the next cycle, and all intercalary of course.

The implicit testimony of Cicero respecting the date of the vernal equinox, U. C. 705, before the correction of the calendar, derives some confirmation from Dionysius of Halicarnassus, where he speaks of certain ceremonies as performed on the Ides or at the middle of May, oσov TI MIKpòv after the vernal equinox. Dionysius, it is true, was writing his history between U. C. 725 and U. C. 747, and therefore after the correction of the calendar in U. C. 708, when the vernal equinox had been fixed to March 25. But he can scarcely mean here the vernal equinox, as it had been recently fixed; he must mean it as it had been before for he would not have called the Ides of May ὅσον τι μικρὸν after March 25.*

But the most decisive criterion of the difference between the civil year and the solar, at particular periods before the redressing of the calendar, is supplied by the dates of eclipses, which are mentioned in the Roman historians, and specified according to the old style. Thus, there was a solar eclipse, B. C. 190, v Ides of Quintilise. This must be the eclipse, mentioned in Pingrè for that year, on March 14, and vi

sible all over Europe. Between March 14 and v Ides of Quintilis (July 11) in the year of Numa, the difference would be 115 days in all f.

There was an eclipse of the moon, the night before Pridie Nonas Septembres *, Sept. 35. old style, B. C. 168, the night before the battle of Pydna; which

f Macrobius, i. 13. g Cicero, De Repub. i. circa principium. Livy, xliv. 37. Valerius Maximus, viii. xi. 1. Pliny, H. N. ii. 9. Justin, xxxiii. 1. Zonaras, ix. 23.458. A. Cf. 24. 459. D. Polybius, xxix. 6. and Suidas, in Пoλλà κerÀ TOÙ TOXÉPOV.

Pingrè exhibits on the 21st of June. The difference between June 21, and September 3 in the year of Numa, would be seventy-one days in all. But if B. C. 170 and B. C. 167 were intercalated, as we have seen, we may presume that neither B. C. 169 nor B. C. 168 was so. In this case, and making allowance for the excess produced by the mere absence of the usual intercalation, the true difference between the civil and the solar year would be only 71-26 days at most, Sept. 3, B. C. 168: or not more than forty-five days; which is the exact amount of the difference between the solar and lunar year, U. C. 708. B. C. 45.

A solar eclipse is also specified B. C. 188, for which Pingrè has none except on July 17, whereas this appears to be mentioned soon after the Ides of March".

In Cæsar, De Bello Africano, a remarkable storm is specified as occurring at the time of the setting of the Pleiads, Virgiliarum signo confecto, which setting took place, for the meridian of Utica, where Cæsar was, somewhere about vi Kal. Feb. U. C. 708, according to the old style. The day, it is true, is not precisely stated; and, therefore, no decisive argument can be founded on the coincidence. In the rectified year, the date of the Virgiliarum occasus was iii Idus Novembres and modern astronomical calculations have shewn that this setting happened, for the meridian in question, U. C. 707, November 10 or 11. From this latter date, to vi Kal. Feb. old style, the interval would be 72 days, or 27 more than 45, our supposed excess, U. C. 708. But of these 27, twenty-two or twentythree would be accounted for by the lapse of two years complete, since the last intercalation U. C. 706. And as the writer is not exact that the storm in question happened critically on vi Kal. Feb. but merely about

that period, it might have happened two or three days earlier, which would explain the remaining difference.

That two years had certainly elapsed since the nominal January, U. C. 706, is unquestionable. The rest of that year, after the battle of Pharsalia, and all U.C. 707, until the very end of the year, were spent by Cæsar in the east. His victory over Juba, which the calendars place on April 6 or 8k, was evidently gained on or about the Nones of April, (old style,) April 5 in this year1; and he himself having set out from Utica on the Ides of June, (old style,) June 13, arrived at Rome, 28 days after; having left Caralis in Sardinia iii Kal. Quinctiles ".

m

The date of the battle of Munda, as exhibited by two ancient calendars, (the Maffæan and Amiternine,) is remarkable for an anomaly just the reverse of that of the battle of Pharsalia. The author of the work De Bello Hispanico, after mentioning xi Kal. March, and ad d. iii Non. Martias, says at last", that the victory was won ipsis Liberalibus; with regard to which fact he is supported by Plutarch: to whom we may add Dio, who tells us the news of the victory was received at Rome, the day before the Palilia, April 20P. As the date of the Liberalia was xvi Kal. Apriles, March 17, there was nothing impossible in this; for examples in abundance have been produced elsewhere, to shew that a month might elapse before tidings could reach Rome from Spain. Cæsar himself was twenty-seven days the same year in travelling from Rome to Obulco, not far from the scene of the action in that country; though no general of antiquity travelled with such expedition.

* Cf. Ovid, Fasti, iv. 377.380. xliii. 14. m 98. n 19. 27. 31. q Strabo, iii. 4. 429, 430.

1 De Bello Africano, 79. 75. 82. Cf. Dio, o Julius Cæsar, 56. P Dio, xliii. 42.