of the solar year, he supplied the defect by adding to every second year an intercalary month, which he called Mercedonius, consisting of twenty-two and twenty-three days alternately. This month was thrown in at the end of February in each year, and by this plan four years contained 1465 days, making an average annual excess of one day. This was corrected by reducing the number of days in the intercalarated month in every third "6. octennium," or period of eight years, by which means, in a cycle of twenty-four years, the Calendar was reduced to the same state as if every year had consisted of 365 days and a quarter.

The direction of the intercalations was left with the Pontifices, and it is supposed that they frequently lengthened or shortened the year at their own option, for the benefit or detriment of the Consuls and other public officers, and the farmers of the revenue, according as they were friendly or hostile to them.

These abuses, and the fact, that, as the fixed part of the year of Numa was not adapted to the sun's revolution, while the intercalary part did not observe the phases of the moon, the places of the seasons on the calendar were not exactly the same in any two consecutive years, influenced Julius Cæsar, when Pontifex Maximus, to reform the Calendar, as by virtue of his office he was empowered to do. This was the more necessary, when we consider that the first of January had at that time retrograded nearly to the Autumnal equinox. To bring that day to its proper place, he made the current year to consist of 445 days, by adding two intercalary months of sixty-seven days to the usual intercalary month Mercedonius. This year is generally called "the year of confusion." His chief alteration was, the abolition of the month Mercedonius, and the distribution of the ten days, which thereby became wanting, among some of the other months; and by this means the months became of their present length. As, however, this year was still too short by about a quarter of a day, he provided for the deficiency by the insertion, every fourth year, of an extra day immediately after the 23rd of February, which was to be esteemed as a duplicate of the 24th of February, or, as the Romans called it, the sixth of the Calends of March. It is this double day which gave the name of "Bissextile" to the Leap year. The months, which had

previously been called Quintilis and Sextilis, then received the names of Julius and Augustus, in honour of the first two emperors. The Pontifices, soon after, mistook the proper method of intercalation, by making it every third year; but Augustus finally corrected the results of this error by omitting the intercalary day during twelve years.

The Romans did not, as we do, count the days of the month in a regular numerical succession, but reckoned them with reference to three principal points of time-the Calends, the Nones, and Ides. The first day of every month was entitled its Calends. In March, May, July, and October the Nones were the seventh, and the Ides the fifteenth of the month; in all the other months the Nones were the fifth and the Ides the thirteenth; and thus the Nones were always eight days before the Ides. After passing over one of these points, the Romans counted forward to the next, calling the day after the Calends so many days before the Nones, the day after the Nones so many days before the Ides, and the day after the Ides so many days before the Calends of the next month. The days were accordingly entitled with reference to the number backwards from each point to the preceding one; thus the thirty-first of January was "Pridie Calendas Februarias," or "the day before the Calends of February;" the day before that was reckoned as the third day before the Calends of February (as the Romans included both extremes in counting), and was called "Tertio Calendas Februarias," or "Calendarum Februariarum," which we translate "the third of the Calends of February." though it really means "the third day before the Calends of February." Pursuing this mode of enumeration, we find the fourteenth of January (the day after the Ides) to be the nineteenth "before," or, as we say, "of the Calends of February." So the day before the Ides of January was "Pridie Idus Januarias," and so on backwards to the Nones, the day before which was "Pridie Nonas," and the day before that was "Tertio Nonas Januarias." It should be remembered that the space between the Nones and Ides was the same in all the months; while those between the Calends and Nones and the Ides and Calends varied. The Calends were originally the day of the new moon, which received its name from the fact that on that day the Pontifex addressed the moon in presence of the people, in the words "Calo te,

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The

Jana Novella," "I call upon thee, new moon,' which was repeated as many times as intimated to his hearers the number of days before the arrival of the Nones. The Nones were so called from being always nine days before the Ides (including in the enumeration, according to the Roman custom, both the day of the Nones and the day of the Ides). Ides derived their appellation from the Etrurian verb “iduare,' "to divide," their place being in the middle of the month; and they originally represented the day about which the moon was full. In Cæsar's Calendar the year was divided into eight periods; the points which marked them were thus named:—

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The civil day began at midnight. The artificial day was from sunrise to sunset, and was divided into twelve parts, called “horæ,” which, though usually translated by our word hours," really varied with the seasons. The night (from sunset to sunrise) was divided into four watches, of three hora" each.

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The Romans had no week of seven days like ours; but from the recurrence of the "Nundina," or market-day, every eighth day, on which the citizens in the neighbouring country repaired to the city, they may be considered to have had a week of eight days. The "Nundina" were sacred to Jupiter, and originally no legal business could be despatched on them; but the necessity, from the increase of numbers, of enlarging the "dies fasti," which alone were originally devoted to litigation, and a wish to promote the convenience of the residents in the country, induced the Consul, Hortensius, to make these days "fasti," or days of sitting in judgment for the Prætor. The days were distinguished into " fasti," nefasti," and "endotercisi" or "intercisi," which were marked in the Calendars with the letters F. N. and EN. The "dies fasti" were those on which the courts sat, and the Prætor, who was the

chief judge, gave his decisions, which contained three words which were essential to his power of adjudication, "do,” “I give," or "appoint," judges and the form of the writ; "dico," "I pronounce" sentence; "addico," "I adjudge❞ the property in dispute. On the "dies nefasti," these words were not allowed to be uttered; the prætor was consequently forbidden to adjudicate, and the courts of law were closed. These were the days set apart for religious ceremonials. The word "fasti" is derived from "for," or from the old Greek verb páw, both signifying "to speak;" consequently the "dies fasti" were literally "the speaking days," and the "dies nefasti" the "non-speaking days," in allusion to the restrictions put upon the judgments of the Prætor.

The "dies intercisi," or "endotercisi," ("endo" being an old form for "in,") were certain days, partly "fasti" and partly "nefasti," on only a part of which the courts might sit and justice be administered. Thus, some days were "nefasti," while the victim was being killed; "fasti," from the minute of its death until the laying out of the entrails on the altar; and "nefasti," while the victim was being consumed.

The Romans had three kinds of public "Feriæ," or "holydays," which all belonged to the "dies nefasti," and were observed by the whole nation. These were the "Feriæ stativæ," "conceptivæ," and "imperativa." The first were held regularly, and on stated days, marked in the Calendar. To these belonged the "Lupercalia," "Carmentalia," and "Agonalia." The "Feriæ conceptivæ," or "conceptæ,' were moveable feasts, held at certain seasons every year, but not on fixed days; the time being annually appointed by the magistrates or priests. Among these we find the "Feriæ Latina," the "Sementivæ," the "Paganalia," and the "Compitalia." The "Feriæ imperativa" were appointed on certain emergencies by the order of the Consuls, Prætors, or Dictator; and were mostly held, either to avert national calamities, or to celebrate great victories.

In reckoning longer periods than a year, the Romans used a measure of time called a "lustrum," which signified the period intervening between each Census or review of the people by the Censors. This interval averaged about five years, which was, consequently, the usual measure of a "lustrum." Sometimes, however, as in the Fasti (Book iii.

1. 165), a "lustrum" denotes only four years, and sometimes an indefinite number of years. Twenty-two "lustra" made а seculum" of 110 years, the largest measure of time existing among the Romans.

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ÓN THE RISING AND SETTING OF THE STARS. BEFORE the age of Thales, the astronomer, only the settings and risings of the stars, as they were visible to the naked eye, were the subject of observation. Ever since that period, however, astronomers have divided these phænomena, with reference to the sun, into three classes. They are termed the cosmical, acronychal, and heliacal risings and settings. The cosmical rising or setting is the true one in the morning; the acronychal, the true one in the evening; and the heliacal the apparent rising in the morning or setting in the evening. A star or Constellation is said to rise cosmically when it rises at the same time with the sun; and to set cosmically, when it sets in the west, as the sun rises in the east. It rises or sets acronychally when it rises or sets at sunset. When it rises heliacally it emerges to the sight from the lustre of the sun's rays, where before it was hidden, and it arrives to such a distance from him as to be seen in the morning before the sun's rising; and when it sets heliacally, approaching the sun, it is lost sight of in his superior brightness. The heliacal rising of a star takes place from twelve to fifteen days after the cosmical rising, and the heliacal setting the same time before the acronychal setting. From the time of its heliacal setting to its heliacal rising, the star is over the horizon by daylight only, and is therefore invisible.

Thus we find that there are three risings and as many settings of a star, two of each of which are real and one apparent, namely: