For the measurement of time the most important units furnished by natural phenomena are the Day and the Year. In regard of both, it is convenient and usual to speak of the apparent movements of the sun and stars as if they were real, and not occasioned by the rotation and revolution of the earth.

The Day is the interval between two successive passages of the sun across the meridian of any place. It is commonly computed from the midnight passage across the inferior meridian on the opposite side of the globe; but by astronomers from the passage at the noon following. The Civil Day is thus twelve hours in advance of the Astronomical.

The Solar Day, which is what we always mean by this term day, is longer by about four minutes of time than the Sidereal, or the successive passages of a fixed star across the same meridian; for, owing to the revolution of the earth in its orbit from west to east, the sun appears to travel annually in a path (the ecliptic), likewise from west to east, among the stars round the entire heavens. The belt of constellations through which it appears to proceed is styled the zodiac. During half the year (March to September) the ecliptic lies to the north of the celestial equator; during the other half (September to March) to the south. The points where ecliptic and equator intersect are called the equinoxes. In the northern hemisphere the March equinox (or "first point of Aries") is called the vernal equinox; the September equinox ("first point of Libra"), the autumnal.

The Year (Tropical Year) is the period in which the sun makes a complete circuit of the heavens and returns to the point in the zodiac whence it started, and the problem to be solved by those who construct calendars is to find the exact measure of this yearly period in terms of days, for the number of these occupied by the sun's annual journey is not exact. Taking the vernal equinox as a convenient starting-point, it is found that before the sun arrives there again, 365 days and something more have passed. These are, of course, solar days; of sidereal days, each shorter by four minutes, there are 366. The first attempt to find a practical solution of this problem was made by Julius Cæsar, who introduced the Julian Calendar. With the assistance of the astronomers of Alexandria, he determined the true length of the year to be 365 days and 6 hours, or a quarter of a day. From this it followed that the reckoning of the civil year began too soon, i.e. six hours before the sun had reached the point whence it started its annual cycle. In four years, therefore, the year would begin an entire day too soon. To remedy this Cæsar instituted leap-years, a 366th day being introduced in every fourth year, to cover the fractional portions of a day thus accumulated. This extra day was assigned to February, the 24th and 25th day of which were styled in leap-year the sixth before the calends (or first) of March. Hence the name Bissextile given to these years.

Cæsar's reform, which was introduced in the year 46 B.C., would have been perfect had the calculation on which it was based been accurate. In reality, however, the portion of a day to be dealt with, over and above the complete 365, is not quite six hours, but 11 minutes and 14 seconds less. To add a day every fourth year was, therefore, almost three quarters of an hour too much, the following new year commencing 44 minutes and 52 seconds after the sun had passed the equinox. At the end of a century these accumulated errors amounted to about three-quarters of a day, and at the end of four centuries to three entire days. The practical inconveniences of this defect in the system were not slow in making themselves felt, the more so as, Cæsar being murdered soon after (44 B.C.), leap-year, by a misunderstanding of his play, occurred every third year, instead of every fourth. At the time of the Julian reform the sun passed the vernal equinox on 25 March, but by the time of the Council of Nicæa (A.D. 325) this had been changed For the 21st, which was then fixed upon as the proper date of the equinox—a date of great importance for the calculation of Easter, and therefore of all the moveable feasts throughout the year.

But the error, of course, continued to operate and disturb such arrangements. In the thirteenth century the year was seven days behind the Nicæan computation. By the sixteenth it was ten days in arrear, so that the vernal equinox fell on 11 March, and the autumnal on 11 September; the shortest day was 11 December, and the longest 11 June, the feast of St. Barnabas, whence-the old rhyme:

Such alterations were too obvious to be ignored, and throughout the Middle Ages many observers both pointed them out and endeavoured to devise a remedy. For this purpose it was necessary, however, not only to determine with accuracy the exact amount of the Julian error, but also to discover a practical means of correcting it. It was this latter problem that chiefly stood in the way of reform, for the amount of error was ascertained almost exactly as early as the thirteenth century. The necessity of a reform was continually urged, especially by Church authorities, who felt the need in connexion with the ecclesiastical calendar. It was accordingly strongly pressed upon the attention of the pope by the councils of Constance, Basle, Lateran (A.D. 1511), and finally by Trent, in its last session (A.D. 1563).

Nineteen years later the work was accomplished by Pope Gregory XIII (from whom the Gregorian reform takes its name) with the aid chiefly of Lilius, Clavius, and Chacon or Chaconius. There were two main objects to be attained: first, the error of ten days, already mentioned, which had crept in, had to be got rid of; second, its recurrence had to be prevented for the future. The first was attained by the omission from the calendar of the ten superfluous days, so as to bring things back to their proper position. To obviate the recurrence of the same convenience, it was decided to omit three leap years in every four centuries, and thus eliminate the three superfluous days, which, as we have seen, would be introduced in that period under the Julian system. To effect this, only those Centurial years were retained as leap years the first two figures of which are exact multiples of 4—as 1600, 2000, 2400—other centurial years 1700, 1800, 1900, 2100, etc.—becoming common years of 365 days each. By this comparatively simple device an approximation to perfect accuracy was effected, which for all practical purposes is amply sufficient; for, although the length of the Gregorian year exceeds the true astronomical measurement by twenty-six seconds, it will be about thirty-five centuries before the result will be an error of a day, and, as Lord Grimthorpe truly says, before that time arrives mankind will have abundant time to devise a mode of correction. For the actual introduction of the Gregorian Calendar or New Style, throughout Christendom, see CHRONOLOGY.

John Gerard.