Holzapfel[3620] argues, further, that Matzat’s theory, according to which the calendar, as reformed by Augustus, was inaugurated on the 1st of January, 757 (A.D. 4), rests upon the assumption that the first day of the intercalary cycle coincided with the first day of the civil year, whereas it was really the day after the Terminalia, that is to say, the sixth day before the Kalends of March. This, he maintains, is proved (a) by the place which Caesar gave to his intercalary day; (b) by the fact that the two months intercalated between November and December of 708 were called respectively mensis intercalaris prior and mensis intercalaris posterior, and also by the fact that, according to Dion Cassius, the number of days intercalated in that year was only 67, whereas the number of days intercalated in the civil year 708 was 90; (c) by the fact that, according to Macrobius and Solinus, Caesar ordained that the intercalary day [which followed the 23rd of February] should be inserted at the end of the fourth and before the fifth year of the Julian calendar.[3621]

Matzat[3622] summarily replies to these arguments. Referring to Macrobius,[3623] he observes (a) that the place which Caesar gave to the intercalary day was identical with the place which the intercalary day, whenever it occurred, had occupied before his reform; and (b) that the two intercalary months known as mensis intercalaris prior and mensis intercalaris posterior were added to the year 708 in order that the calendar year 709 might begin on the Kalends of January, and thus coincide with the consular year. If it be asked why they were called prior and posterior although another intercalary month had preceded them, the answer is easy: the other month ought in any case to have been intercalated in that year, whereas the prior and posterior were extraordinarily intercalated. The passages in Macrobius and Solinus on which Holzapfel relies have been already explained; and it has been shown that they do not necessarily bear the meaning which he ascribes to them. One fact alone appears to me to dispose of his contention, that the Julian calendar did not come into operation until the sixth day before the Kalends of March, 709: if it did not, why did January in that year contain 31 days, whereas in every previous year it had contained only 29?

Holzapfel also invokes the support of Böckh,[3624] who remarked that it would have been unnatural for a reformer to correct the error caused by the difference of a quarter of a day between the civil and the solar year until the error required correction. The conclusion appears to Holzapfel inevitable that Caesar intended to make his first intercalation as soon as, and not before, the error should have amounted to one day, that is to say, in 713. Matzat,[3625] on the contrary, maintains that logically the proper place for the intercalary day would have been immediately after the second year of the quadriennial cycle. But he does not believe that Caesar cared for such academic considerations. He undoubtedly fixed the place of the intercalary day in the year not on astronomical grounds, but according to usage. Why, then, asks Matzat, should it be considered improbable that he fixed the place of the intercalary year in the quadriennial cycle on the same principle?

3. Holzapfel[3626] holds, as we have just seen, that the Caesarian cycle began on the day after the Terminalia of 709, that is to say, on the sixth day before the Kalends of March; that Caesar intended that the first intercalation should take place in 713; that the pontiffs, misunderstanding his directions, made the first intercalation at the beginning of the fourth year, that is to say, in 712; that, as Dion says, a day was extraordinarily intercalated in 713; that, to compensate for this extraordinary intercalation, a day was omitted in 714, which accordingly comprised 364 days only; that the pontiffs thenceforth intercalated every three years, namely in 715, 718, 721 ... 745; that, to compensate for the three superfluous days which had been intercalated in consequence of the misunderstanding of Caesar’s regulations, the intercalations which ought to have occurred in 749, 753, and 757, were omitted; and that the first intercalation after the reform of Augustus took place in 761.

This theory, as the reader will have already seen, cannot stand unless the evidence of Dion Cassius is to be rejected. Indeed it cannot stand even then. Holzapfel is not justified in assuming that in order to compensate for the extraordinary intercalation of 713, a day was omitted in 714; for, on his own theory, 714 was an ordinary year. Matzat[3627] points out that, in the passage in which Dion[3628] describes the omission of a day to compensate for the extraordinary intercalation—καὶ δῆλον ὅτι ἀνθυφῃρέθη αὖθις, ὅπως ὁ χρόνος κατὰ τὰ τῷ Καίσαρι τῷ προτέρῳ δόξαντα συμβῇ—the words ἡμέρα ἐμβόλιμος (an intercalary day) must necessarily be supplied, as the subject of the verb ἀνθυφῃρέθη, from the preceding sentence. Holzapfel retorts that his view does not involve the assumption of a change of subject. ‘One can very well translate,’ he says, ‘“an intercalary day was inserted, and self-evidently in turn omitted”’ (Man kann sehr wohl übersetzen: ‘es wurde ein Schalttag eingelegt und selbstverständlich wiederum in Abzug gebracht’[3629]). This is not a satisfactory answer; for, on Holzapfel’s own showing, the omitted day was not an intercalary day. There is no evidence that a day was ever withdrawn from an ordinary year in the Roman calendar; and, as Matzat[3630] points out, the best proof that such a proceeding would have been regarded as out of the question is supplied by the procedure of Augustus. Instead of correcting the error of the pontiffs by withdrawing three days from one ordinary year, he omitted three intercalary days in three intercalary years, thus taking twelve years to accomplish a reform which, according to modern notions, might have been accomplished in one. If Dion’s words are interpreted in their natural sense, they evidently mean that the next intercalary day which would have occurred, according to Caesar’s regulations, was omitted. Thenceforth, accordingly, if the first intercalation occurred in 710, the intercalary years were 716, 719, 722 ... 743. Or if, as Holzapfel insists, Dion’s words, παρὰ τὰ καθεστηκότα, mean ‘contrary to the regulations as erroneously interpreted by the pontiffs’, and if, as he also insists, the year in which they first intercalated was 712, then the next year in which they would naturally have intercalated was 715: the extraordinary intercalation of 713 must have been compensated for by the omission of an intercalary day in 715; and the following series of intercalary years must have been 718, 721, 724 ... 745.

Again, Holzapfel’s theory compels him to disregard silently the testimony of Solinus, on whose authority he lays such stress. Solinus[3631] says that twelve days were intercalated in the first thirty-six years of the Julian calendar: according to Holzapfel, thirteen were intercalated.

Lastly, if we accept Holzapfel’s view, that the first day of the Julian calendar was the sixth day before the Kalends of March, 709, we find that a day was intercalated immediately after the end of the fourth year of the cycle, namely, after the Terminalia of 713. But Holzapfel assures us that, according to Macrobius and Solinus, this was not the case.

But I am not arguing against Holzapfel’s theory as regards the first intercalary year of the Julian calendar; and what appears to tell most strongly in favour of it, besides the probability that the Lepidianus tumultus occurred in 711,[3632] is the statement of Macrobius,[3633] that Augustus enacted that the intercalation should take place ‘every fifth year’ (quinto quoque anno), that is to say, according to our reckoning, every four years. These words seem to imply that the pontiffs had actually misunderstood Caesar’s regulation. On Matzat’s theory, however, the pontiffs who intercalated παρὰ τὰ καθεστηκότα in 713 deliberately set that regulation aside in order to avoid the dreaded coincidence of the Kalends of January with a market-day. But, says Matzat, every three years this troublesome necessity recurred; and thus ultimately, as he suggests, the erroneous view might prevail that Caesar had himself intended to intercalate every three years ([anno] quarto non peracto sed incipiente[3634]). But what right have we to assume that after 713 the pontiffs took any account of the nundinal superstition? At all events, if Holzapfel is right in maintaining that the first intercalary year of the reformed calendar was 712, there can be no doubt that the subsequent intercalary years were 713, 718 ... 745; and it is therefore impossible for him to reconcile his view, that the first intercalation under the reform of Augustus occurred in 761, with the statement that Augustus allowed twelve years to pass without any intercalation. Augustus’s first intercalation undoubtedly took place in 757; for in that year, if Caesar’s regulation had been observed, the twelfth intercalation would have occurred.

Opinions may differ as to whether Matzat’s theory or the modification of Holzapfel’s which I have just suggested is the more probable. As, according to the latter, the series of intercalary years must have been 712, 713, 718, 721, 724, 727, 730, 733, 736, 739, 742, 745, it implies that after 713 the pontiffs thought it safe to disregard the nundinal superstition. So far my suggestion may be objectionable. On the other hand, it fits in with all the statements of the ancient writers, except that one remark of Dion Cassius which, as Holzapfel suggests, he may have made on erroneous information;[3635] and particularly it fits in, as no other series which has been suggested does, with the statements that twelve days were intercalated in the first thirty-six years of the Julian calendar,[3636] and that Augustus allowed the next twelve years to pass without any intercalation. However, the difference between Matzat’s theory and mine (which is purely tentative) is unimportant; for they agree in the main point,—that the Kalends of January, 709, corresponded with the 1st of January, 45 B.C.

V. We have now gained the knowledge which will enable us to investigate the chronology of Caesar’s second invasion of Britain. We have ascertained that the Kalends of January, 709, fell on the 1st of January, 45 B.C.; that 90 days were intercalated in 708, which accordingly consisted of 445 days; that a month of 23 days was intercalated in 702, which accordingly comprised 378 days; and that 701, 703, 704, 705, 706, and 707 were ordinary years, each comprising 355 days. It follows that the last day of 700, the year in which Caesar made his second expedition to Britain, corresponded with the 30th of November, 54 B.C., and that the sixth day before the Kalends of October, the day on which he wrote to tell Cicero that he was on the point of bringing back his army from Britain to Gaul, corresponded with the 29th of August. From these data it will be easy to ascertain the correspondence of any date in the year 700 which we find in our authorities with the Julian calendar.