However accurate an instrument for the mensuration of time may be, it would be of little use for close observation unless we have some standard by which to test its performance. We look to Astronomy to furnish us with this desideratum, nor do we look in vain. The mean sidereal day, measured by the time elapsed between any two consecutive transits of any star at the same meridian, and the mean sidereal year—which is the time included between two consecutive returns of the sun to the same star—are immutable units with which all great periods of time are compared; the oscillations of an isochronous pendulum affording us a means of correctly dividing the intermediate space into hours and days.
We must premise that the whole theory of taking time by sidereal observations is based on angular motion, the mensuration of one of the angles of motion giving a measurement of space, so that to say space, or distance, is equivalent to saying time. From noon of one day to noon of another is the whole problem to be solved by correct division. The astronomical day begins at noon, but in civil law the day is dated from midnight. So in the year the astronomical day is dated December 31, while in common reckoning the 1st of January is the initial point. This day is divided into twenty-four hours, counted in England, America, and the most of the Continental nations of Europe, by twelve and twelve. The French astronomers, however, adopted the decimal system, for ease in the computation. Thus they divided the day into ten hours, the hour into one hundred minutes, and the minute into one hundred seconds. This plan was in conformity with the French system of decimal weights and measures. Again, in Italy, the day was divided into twenty-four hours, but counting from one to twenty-four o’clock. The French system presents some features well worthy of adoption, as it gives results so much more easy in computation—a facility unattainable in the common division; yet it did not come into general use in other countries, and although some French astronomers still hold to the system, it is gradually dying out.
At one time during the Revolution in France a clock in the gardens of the Tuileries was regulated to show time by the decimal system.
For the Horologist the mean length of the day is sufficient to show the rate of his instrument for that particular day, but the astronomical and civil division requires a much longer period of observation. This is obtained by the position of the mean annual equinoxes or solstices, and is estimated from the winter solstice, the middle of the long annual night under the North Pole; and the period between this solstice and its return is a natural cycle, peculiarly suited for a standard of measurement.
Even with such a standard as the civil year of 365d. 5h. 48m. 49.7s., the incommensurability that exists between the length of the day and the real place of the sun makes it very difficult to adjust the ratio of both in whole numbers. Were we to return to the point in the earth’s orbit in exactly 365 days, we would have precisely the same number of days in each year, and the sun would be at the same point on the ecliptic at the same second at the beginning and end of the year. There is, however, a fraction of a day, so that a solar year and civil are not of equal duration.
It is thus we have our bissextile year, from the fact that the inequality amounts to nearly a quarter of a day, so that in four years we have a whole day’s gain; but not exactly, because a fraction still remains to be accounted for. Now, if we should suppress the one day of leap-year once at the end of each three out of four centuries, the civil would be within a very small fraction equal to the solar year, as given by observation; this small fraction would be almost entirely eliminated, provided we suppressed the bissextile at the end of every four thousand years. Were this fraction neglected, the beginning of the new civil year would precede the tropical by just that much, so that in the course of 1507 years the whole day’s difference would obtain.
The Egyptian year was dated from the heliacal rising of the star Sirius; it contained only 365 days. By easy computation it can be shown that in every 1461 years a whole year was lost; this cycle was called the Sothaic period, in which the heliacal rising of Sirius passed through the whole year and took place again on the same day. The commencement of that cycle took place 1322 years before Christ. The year by the Roman calendar was dated by Julius Cæsar the 1st of January, that being the day of the new moon immediately following the winter solstice in the 707th year of Rome. Christ’s nativity is dated on the 25th of December, in Cæsar’s 45th year, and the 46th year of the Julian calendar is assumed to be the 1st year of our era. The preceding year is designated by chronologists the 1st year before Christ, the dates thence running backward the same as they run forward subsequent to that period.
Astronomically, that year is registered 0; the astronomical year begins at noon on the 31st of December, and the date of any observation expresses the number of days and hours which have actually elapsed since that time, the 31st of December—Year 0.
The year is divided into months by old and almost universal consent, but the period of seven days is by far the most permanent division of a rotation of the earth around the sun. It was the division long before the historic period. The Brahmins in India used it with the same denominations as at the present day the Jews, Arabs, Egyptians, and Assyrians. “It has survived the fall of empires, and has existed among all successive generations, a proof of their common origin.”