By Water & Blood

Book 1, Chapter 13: Numa's Calendar and Intercalation

"But Numa following, as much as in a rude and still unpolished age he could grasp with genius alone as teacher, or because he was perhaps instructed by the observation of the Greeks, added fifty days, so that the year might be extended to the three hundred and fifty-four days in which he believed twelve courses of the moon were completed. And to these fifty days added by himself he joined six others withdrawn from those six months which had thirty days—that is, one from each—and divided the fifty-six days thus made into two new months by equal reckoning. And of the two he named the former January and wished it to be the first of the year, as the month of the two-headed god, looking back and looking forward to the end of the year past and the beginnings of the future; the second he dedicated to the god Februus, who is believed powerful over purifications. But it was necessary that the city be purified in that month in which he established that due rites be paid to the Manes.

The neighboring peoples soon followed Numa's arrangement and began to compute their year with as many days and as many months as pleased Pompilius; but they differed in this alone, that they alternated months of twenty-nine and thirty in number. A little later Numa, in honor of the odd number—this secret which nature was bringing to birth even before Pythagoras—added one day, which he gave to January, so that both in the year and in the individual months, except for February alone, an odd number might be preserved. For because twelve months, if each were reckoned either with an even or with an odd number, would make an even sum, one instituted with an even number made the whole reckoning odd. January therefore, April, June, Sextilis, September, November, December were counted at twenty-nine days and had Nones on the fifth, and after the Ides in all of them reckoning was made to the seventeenth day before the Kalends. But March, May, Quintilis, and October possessed thirty-one days. In these the Nones were on the seventh, and likewise after the Ides seventeen days in each were reckoned up to the following Kalends; but February alone retained twenty-eight days, as though both diminution and an even number suited the underworld gods.

When therefore the Romans from this distribution of Pompilius computed their own year according to the course of the moon as the Greeks did, they necessarily also instituted an intercalary month after the custom of the Greeks. For the Greeks too, when they perceived that they had rashly arranged the year at three hundred and fifty-four days, since it appeared from the course of the sun, which completes the zodiac in three hundred and sixty-five days and a quarter, that eleven days and a quarter were lacking to their year, invented intercalaries by a fixed reckoning, so that in every eighth year they intercalated ninety days, from which they composed three months of thirty days each. The Greeks did this because it was laborious and difficult to intercalate eleven days and a quarter every year. And so they preferred to multiply this number eight times and to insert the ninety days which arise if the quarter with eleven days is composed eight times, to be distributed into three months, as we have said. These days they called hyperbainontes, but the months embolimoi.

This order therefore it pleased the Romans also to imitate, but in vain, since it escaped them that one day, as we have reminded above, had been added by them to the Greek number in honor of the odd number. For this reason through an eight-year period the number and order could not agree. But this error not yet having been discovered, through eight years they computed ninety days as though to be carried over after the Greek example, and expended them in intercalations four times, intercalating in alternate years twenty-two and in alternate years twenty-three. But in every eighth year eight intercalary days flowed in from the individual days by which we have already said the number of the turning year among the Romans had exceeded the Greek. This error too having now been recognized, this form of correction was introduced. In every third eight-year period they so dispensed the days to be intercalated that they intercalated not ninety but sixty-six, twenty-four days having been compensated for those which through as many years had grown above the Greek number.

But to every intercalation the month of February was assigned, since it was the last of the year—which very thing they also did from imitation of the Greeks. For they too inserted the superfluous days in the last month of their year, as Glaucippus reports, who wrote on the sacred rites of the Athenians. But in one matter they differed from the Greeks. For those, when the last month was finished, intercalated; the Romans intercalated not when February was finished but after its twenty-third day, the Terminalia of course having already been completed. Then they joined the remaining days of the month of February, which were five, after the intercalation—I believe by the ancient custom of their religion, that March should in every way follow February.

But since it often happened that the market-day (nundinae) fell now on the first day of the year, now on the Nones—and either was thought destructive to the state—a remedy by which this might be averted was devised, which we shall open if we have first shown why the market-days were guarded against either on the first Kalends or on all the Nones. For whenever at the beginning of the year a day began which was assigned to the market-days, that whole year was mournful with unlucky mishaps, and this opinion was especially confirmed by the Lepidian tumult. But on the Nones a gathering of the whole multitude was thought to be avoided, since the Roman people, even after the kings had been driven out, especially celebrated this day of the Nones which it thought the birthday of Servius Tullius; because though it was uncertain in what month Servius Tullius had been born, yet it was agreed that he had been born on the Nones, they frequented all the Nones with celebratory notice; those therefore who were in charge of the days, fearing lest the whole body collected on market-days innovate something out of longing for a king, took care that the Nones be separated from the market-days. Whence that day by which we have said the year abounds was left to the judgment of those who were in charge of the Fasti, that it might be intercalated when they wished, provided they so placed it in the middle of the Terminalia or of the intercalary month as to turn the celebration of the market-days away from the suspected day. And this is what certain of the ancients have related: that among the Romans there was not only an intercalary month but also an intercalary day.

But when intercalation first took place is variously reported. And Licinius Macer indeed assigns the origin of this matter to Romulus; Antias in his second book contends that Numa Pompilius invented it for the sake of the sacred rites; Junius records that King Servius Tullius first intercalated, by whom also Varro holds that the market-days were instituted. Tuditanus in the third book of his Magistrates reports that the decemvirs who added two to the Ten Tables put a bill to the people concerning intercalation. Cassius writes that the same were the authors; but Fulvius says that Manius Acilius the consul did it in the five hundred and sixty-second year from the founding of the city, soon after the Aetolian war had been begun. But Varro refutes this by writing that there was a most ancient law cut on a bronze column by the consuls Lucius Pinarius and Publius Furius, to which an intercalary month is ascribed. Let these things related concerning the beginning of intercalation be enough."