sun is daily seen to rise in the east, to travel across the sky, and to set in the west. But the points of the horizon at which it rises and sets, its height in the sky at midday, and the duration of daylight, all go through a series of changes which are accompanied by changes in weather and vegetation which we call the seasons, and which recur after a certain period of time. Thus we have a third unit of time, the year. Both Chaldeans and Egyptians seem to have known that the year consisted of about 365 days, and one of the functions of Greek astronomers was the proper regulation of the calendar.

The Greek calendar was based on the moon, and at an early period the year was made to consist of twelve months of thirty days. By the fifth century B.C. various adjustments had reduced the length of the year to 365 days, but a preference for beginning the month when the new moon was first visible caused arbitrary alterations and much confusion.

In early times the Roman calendar was even more confused than the Greek. It was known to be inaccurate, and so the priests were supposed to correct it from time to time to make it agree with the sun and moon. They, however, allowed it to fall into such chaos that the first day of each month had to be proclaimed by crier. A reformed calendar was produced by Julius Cæsar under the advice of an astronomer of Alexandria named Sosigenes. The year was calculated independently of the moon, an ordinary year consisting of 365 days, and every fourth, by the addition of a day to February, of 366, so that the average length of the year would be 365 days.

The Julian Calendar, which began in the year 45 B.C., and is still in use over the civilized world, has undergone only one reform of any importance. The difference

between the average length of the year as fixed by Julius Cæsar and the true year amounts to about one day in 128 years. In 1582 Pope Gregory XIII arranged that ten days should be omitted from that year and three leap years in each four centuries. The Gregorian Calendar was not adopted in England till 1752, when 11 days had to be omitted, and it has not yet been adopted in Russia and Greece.

The history of Greek astronomy extends over eight centuries, from the sixth century B.C. to the second A.D. The Greeks, unlike their Eastern predecessors, were much more interested in framing theories of the universe than in making observations, a considerable number of which they had, moreover, inherited. These theories were at first mainly fanciful, but later Greek astronomers followed a truly scientific method. They framed a provisional theory to account for facts observed, deduced the mathematical consequences, and tested the truth of the theory by comparing these consequences with the actual facts. Many such theories appeared, of course, to stand the test of facts and afterward were proved false. That is no argument against what is called the inductive method, but merely proves that insufficient facts have been available.

Of the early Greek astronomers the best known is Pythagoras, who lived in the sixth century B.C., chiefly famous for his doctrine of the transmigration of souls. He taught that the earth, in common with the heavenly bodies, was a sphere, resting without support in the middle of the universe. The stars, he held, were attached to a crystal sphere which revolved daily on an axis through the earth, and each of the seven planets (including the sun and moon) moved on a sphere of its own, producing a music audible to the finest ears.

This doctrine of the music of the spheres affected the imaginations of men, and Shakespeare has alluded to it in The Merchant of Venice:

There's not the smallest orb which thou behold'st,

But in his motion like an angel sings,

Still quiring to the young-ey'd cherubins.

One of the followers of Pythagoras who lived about a century later than his master grasped for the first time the idea that the earth was in motion. He appears to have regarded it as revolving, together with the sun, moon, and five planets, round some central fire, the earth rotating on its axis as it revolved.. It is clear that several other Pythagoreans also believed in the rotation of the earth.

The great philosopher Plato makes several references to astronomy in his writings. In the Republic he describes the sun, moon, planets, and fixed stars as revolving on eight concentric spheres round an axis passing through the earth. He also states that the moon shines by reflected light received from the sun. One of his disciples, Eudoxus of Cnidus, went further in a similar attempt to explain the motions of the heavenly bodies. He is the first Greek recorded to have had an observatory, and he produced the first systematic description of the constellations.

Aristotle (384-322 B.C.) in his astronomical writings set forth the best knowledge of his day, but did not contribute anything original of great importance. He discussed and rejected the possibility of the earth's revolving round the sun. He was far from regarding the knowledge that he possessed as final, but so great was his authority that his works actually retarded the advance of astronomy, because, even as late as the

Renaissance, his name was invoked by unintelligent disciples to defend theories which later research had shown to be unworkable.

After the time of Aristotle Alexandria, founded in

From "In Feudal Times," Tappan (Harrap)

332 B.C. by Alexander the Great, who was for a time a pupil of Aristotle's, became the centre of Greek learning. During five centuries all the astronomers and mathematicians of importance, with one great exception, belonged to Alexandria, where the Ptolemies, whose capital it was, had founded the great museum, containing an observatory and a splendid library. To summarize briefly the achievements the results of

lifetimes of toil of the early Alexandrian school, the best-known member of which is Euclid, they investigated the comparative distances of the sun and moon from the earth; discovered that the diameter of the moon was about one-third that of the earth (a result very near that obtained by modern scientists); discovered also that the fixed stars were immeasurably distant as compared with the sun; made the first real star catalogues; constructed improved sundials (first made in Babylon); divided the earth into zones according to the seasons; and made scientific and successful estimates of the circumference of the earth.

Ranking far above these discoverers, however, and among the greatest astronomers of all time, was Hipparchus, who lived in the second century B.C., and who was not, as far as we know, a member of the Alexandrian school. He invented trigonometry, a branch of mathematics of great service in astronomy, made a valuable series of observations, taken with all the care that his instruments permitted, and compared old observations with later ones so as to discover astronomical changes too slow to be apparent within a single lifetime. He improved the theories of the motions of the sun and moon, invented a new geometric representation of their motions, and was thus enabled to predict much more successfully than his predecessors eclipses of the sun and moon. Though superstitious terror was long caused by eclipses, it was known by Greek astronomers at least as early as Aristotle (in the fourth century B.C.) that eclipses of the moon were caused by the passage of the earth between the sun and moon, and eclipses of the sun by the passage of the moon between the sun and the observer. From the time of Hipparchus eclipses of the moon