CALCŬLI, little stones or pebbles, used for various purposes, as, for instance, among the Athenians for voting. Calculi were used in playing a sort of draughts. Subsequently, instead of pebbles, ivory, or silver, or gold, or other men (as we call them) were used; but they still bore the name of calculi. Calculi were also used in reckoning; and hence the phrases calculum ponere, calculum subducere.

CALDĀRĬUM. [[Balneum].]

CĂLENDAE or KĂLENDAE. [[Calendarium].]

CĂLENDĀRĬUM or KĂLENDĀRĬUM, generally signified an account-book, in which were entered the names of a person’s debtors, with the interest which they had to pay, and it was so called because the interest had to be paid on the calends of each month. The word, however, was also used in the signification of a modern calendar or almanac. (1) Greek Calendar. The Greek year was divided into twelve lunar months, depending on the actual changes of the moon. The first day of the month (νουμηνία) was not the day of the conjunction, but the day on the evening of which the new moon appeared; consequently full moon was the middle of the month. The lunar month consists of twenty-nine days and about thirteen hours; accordingly some months were necessarily reckoned at twenty-nine days, and rather more of them at thirty days. The latter were called full months (πληρεῖς), the former hollow months (κοῖλοι). As the twelve lunar months fell short of the solar year, they were obliged every other year to interpolate an intercalary month (μὴν ἐμβολιμαῖος) of thirty or twenty-nine days. The ordinary year consisted of 354 days, and the interpolated year, therefore, of 384 or 383. This interpolated year (τριέτηρις) was seven days and a half too long, and to correct the error, the intercalary month was from time to time omitted. The Attic year began with the summer solstice: the following is the sequence of the Attic months and the number of days in each:—Hecatombaeon (30), Metageitnion (29), Boedromion (30), Pyanepsion (29), Maemacterion (30), Poseideon (29), Gamelion (30), Anthesterion (29), Elaphebolion (30), Munychion (29), Thargelion (30), Scirophorion (29). The intercalary month was a second Poseideon inserted in the middle of the year. Every Athenian month was divided into three decads. The days of the first decad were designated as ἱσταμένου or ἀρχομένου μηνος, and were counted on regularly from one to ten; thus, δευτέρα ἀρχομένου or ἱσταμένου is “the second day of the month.” The days of the second decad were designated as ἐπὶ δέκα or μεσοῦντος, and were counted on regularly from the 11th to the 20th day, which was called εἴκας. There were two ways of counting the days of the last decad; they were either reckoned onwards from the 20th (thus, πρώτη ἐπὶ εἰκάδι was the 21st), or backwards from the last day, with the addition φθίνοντος, παυομένου, λήγοντος, or ἀπίοντος; thus, the twenty-first day of a hollow month was ἐνάτη φθίνοντος; of a full month, δεκάτη φθίνοντος. The last day of the month was called ἕνη καὶ νέα, “the old and new,” because as the lunar month really consisted of more than twenty-nine and less than thirty days, the last day might be considered as belonging equally to the old and new month. Separate years were designated at Athens by the name of the chief archon, hence called archon eponymus (ἄρχων ἐπώνυμος), or “the name giving archon;” at Sparta, by the first of the ephors; at Argos, by the priestess of Juno, &c.—(2) Roman Calendar. The old Roman, frequently called the Romulian year, consisted of only ten months, which were called Martius, Aprilis, Maius, Junius, Quinctilis, Sextilis, September, October, November, December. That March was the first month in the year is implied in the last six names. Of these months, four, namely, Martius, Maius, Quinctilis, and October, consisted of thirty-one days, the other six of thirty. The four former were distinguished in the latest form of the Roman calendar by having their nones two days later than any of the other months. The symmetry of this arrangement will appear by placing the numbers in succession:—31, 30; 31, 30; 31, 30, 30; 31, 30, 30. The Romulian year therefore consisted of 304 days, and contained thirty-eight nundinae or weeks; every eighth day, under the name of nonae, or nundinae, being especially devoted to religious and other public purposes. Hence we find that the number of dies fasti afterwards retained in the Julian calendar tally exactly with these thirty-eight nundines; besides which, it may be observed that a year of 304 days bears to a solar year of 365 days nearly the ratio of five to six, six of the Romulian years containing 1824, five of the solar years 1825 days; and hence we may explain the origin of the well-known quinquennial period called the lustrum, which ancient writers expressly call an annus magnus; that is, in the modern language of chronology, a cycle. It was consequently the period at which the Romulian and solar years coincided. The next division of the Roman year was said to have been made by Numa Pompilius, who instituted a lunar year of 12 months and 355 days. Livy says that Numa so regulated his lunar year of twelve months by the insertion of intercalary months, that at the end of every nineteenth year (vicesimo anno) it again coincided with the same point in the sun’s course from which it started. It is well known that 19 years constitute a most convenient cycle for the junction of a lunar and solar year. It seems certain that the Romans continued to use a lunar year for some time after the establishment of the republic; and it was probably at the time of the decemviral legislation that the lunar year was abandoned. By the change which was then made the year consisted of 12 months, the length of each of which was as follows:—

Martius,31days.September,29days.
Aprilis,29”October,31”
Maius,31”November,29”
Junius,29”December,29”
Quinctilis,31”Januarius,29”
Sextilis,29”Februarius,28”

The year thus consisted of 355 days, and this was made to correspond with the solar year by the insertion of an intercalary month (mensis intercalaris or intercalarius), called Mercedonius or Mercidonius. This month of 22 or 23 days seems to have been inserted in alternate years. As the festivals of the Romans were for the most part dependent upon the calendar, the regulation of the latter was entrusted to the college of pontifices, who in early times were chosen exclusively from the body of patricians. It was therefore in the power of the college to add to their other means of oppressing the plebeians, by keeping to themselves the knowledge of the days on which justice could be administered, and assemblies of the people could be held. In the year 304 B.C., one Cn. Flavius, a secretary (scriba) of Appius Claudius, is said fraudulently to have made the Fasti public. The other privilege of regulating the year by the insertion of the intercalary month gave the pontiffs great political power, which they were not backward to employ. Every thing connected with the matter of intercalation was left to their unrestrained pleasure; and the majority of them, on personal grounds, added to or took from the year by capricious intercalations, so as to lengthen or shorten the period during which a magistrate remained in office, and seriously to benefit or injure the farmer of the public revenue. The calendar was thus involved in complete confusion, and accordingly we find that in the time of Cicero the year was three months in advance of the real solar year. At length, in the year B.C. 46, Caesar, now master of the Roman world, employed his authority, as pontifex maximus, in the correction of this serious evil. The account of the way in which he effected this is given by Censorinus:—“The confusion was at last carried so far that C. Caesar, the pontifex maximus, in his third consulate, with Lepidus for his colleague, inserted between November and December two intercalary months of 67 days, the month of February having already received an intercalation of 23 days, and thus made the whole year to consist of 445 days. At the same time he provided against a repetition of similar errors, by casting aside the intercalary month, and adapting the year to the sun’s course. Accordingly, to the 355 days of the previously existing year he added ten days, which he so distributed between the seven months having 29 days that January, Sextilis, and December received two each, the others but one; and these additional days he placed at the end of the several months, no doubt with the wish not to remove the various festivals from those positions in the several months which they had so long occupied. Hence in the present calendar, although there are seven months of 31 days, yet the four months, which from the first possessed that number, are still distinguishable by having their nones on the seventh, the rest having them on the fifth of the month. Lastly, in consideration of the quarter of a day, which he regarded as completing the true year, he established the rule that, at the end of every four years, a single day should be intercalated, where the month had been hitherto inserted, that is, immediately after the terminalia; which day is now called the bissextum.” The mode of denoting the days of the month will cause no difficulty, if it be recollected that the kalends always denote the first of the month; that the nones occur on the seventh of the four months of March, May, Quinctilis or July, and October, and on the fifth of the other months; that the ides always fall eight days later than the nones; and lastly, that the intermediate days are in all cases reckoned backwards upon the Roman principle of counting both extremes. For the month of January the notation will be as follows:—

1. Kal. Jan.
2. a. d. IV. Non. Jan.
3. a. d. III. Non. Jan.
4. Prid. Non. Jan.
5. Non. Jan.
6. a. d. VIII. Id. Jan.
7. a. d. VII. Id. Jan.
8. a. d. VI. Id. Jan.
9. a. d. V. Id. Jan.
10. a. d. IV. Id. Jan.
11. a. d. III. Id. Jan.
12. Prid. Id. Jan.
13. Id. Jan.
14. a. d. XIX. Kal. Feb.
15. a. d. XVIII. Kal. Feb.
16. a. d. XVII. Kal. Feb.
17. a. d. XVI. Kal. Feb.
18. a. d. XV. Kal. Feb.
19. a. d. XIV. Kal. Feb.
20. a. d. XIII. Kal. Feb.
21. a. d. XII. Kal. Feb.
22. a. d. XI. Kal. Feb.
23. a. d. X. Kal. Feb.
24. a. d. IX. Kal. Feb.
25. a. d. VIII. Kal. Feb.
26. a. d. VII. Kal. Feb.
27. a. d. VI. Kal. Feb.
28. a. d. V. Kal. Feb.
29. a. d. IV. Kal. Feb.
30. a. d. III. Kal. Feb.
31. Prid. Kal. Feb.

The letters a d are often, through error, written together, and so confounded with the preposition ad which would have a different meaning, for ad kalendas would signify by, i.e. on or before the kalends. The letters are in fact an abridgment of ante diem, and the full phrase for “on the second of January,” would be ante diem quartum nonas Januarias. The word ante in this expression seems really to belong in sense to nonas, and to be the cause why nonas is an accusative. Whether the phrase kalendae Januarii was ever used by the best writers is doubtful. The words are commonly abbreviated; and those passages where Aprilis, Decembris, &c. occur are of no avail, as they are probably accusatives. The ante may be omitted, in which case the phrase will be die quarto nonarum. In the leap year (to use a modern phrase), the last days of February were called,—

Feb. 23. a. d. VII. Kal. Mart.
Feb. 24. a. d. VI. Kal. Mart. posteriorem.
Feb. 25. a. d. VI. Kal. Mart. priorem.
Feb. 26. a. d. V. Kal. Mart.
Feb. 27. a. d. IV. Kal. Mart.
Feb. 28. a. d. III. Kal. Mart.
Feb. 29. Prid. Kal. Mart.

In which the words prior and posterior are used in reference to the retrograde direction of the reckoning. From the fact that the intercalated year has two days called ante diem sextum, the name bissextile has been applied to it. The term annus bissextilis, however, does not occur in any classical writer, but in place of it the phrase annus bissextus.—The names of two of the months were changed in honour of Julius Caesar and Augustus. Julius was substituted for Quinctilis, the month in which Caesar was born, in the second Julian year, that is, the year of the dictator’s death, for the first Julian year was the first year of the corrected Julian calendar, that is, B.C. 45. The name Augustus in place of Sextilis was introduced by the emperor himself in B.C. 27. The month of September in like manner received the name of Germanicus from the general so called, and the appellation appears to have existed even in the time of Macrobius. Domitian, too, conferred his name upon October; but the old word was restored upon the death of the tyrant.—The Julian calendar supposes the mean tropical year to be 365 d. 6 h.; but this exceeds the real amount by 11′ 12″, the accumulation of which, year after year, caused at last considerable inconvenience. Accordingly, in the year 1582, Pope Gregory XIII. again reformed the calendar. The ten days by which the year had been unduly retarded were struck out by a regulation that the day after the fourth of October in that year should be called the fifteenth; and it was ordered that whereas hitherto an intercalary day had been inserted every four years, for the future three such intercalations in the course of four hundred years should be omitted, viz., in those years which are divisible without remainder by 100, but not by 400. Thus, according to the Julian calendar, the years 1600, 1700, 1800, 1900, 2000, were to be bissextile as before. The bull which effected this change was issued Feb. 24th, 1582. The Protestant parts of Europe resisted what they called a papistical invention for more than a century. In England the Gregorian calendar was first adopted in 1752. In Russia, and those countries which belonged to the Greek church, the Julian year, or old style, as it is called, still prevails. In the ancient calendars the letters A, B, C, D, E, F, G, H, were used for the purpose of fixing the nundines in the week of eight days; precisely in the same way in which the first seven letters are still employed in ecclesiastical calendars, to mark the days of the Christian week.