of pontiffs, or general religious overseers.  The Roman year consisted of three hundred and fifty-five days; and in the time of Caesar the calendar was in great confusion, being ninety days in advance, so that January was an autumn month.  He inserted the regular intercalary month of twenty-three days, and two additional ones of sixty-seven days.  These, together with ninety days, were added to three hundred and sixty-five days, making a year of transition of four hundred and forty-five days, by which January was brought back to the first month in the year after the winter solstice; and to prevent the repetition of the error, he directed that in future the year should consist of three hundred and sixty-five and one-quarter days, which he effected by adding one day to the months of April, June, September, and November, and two days to the months of January, Sextilis, and December, making an addition of ten days to the old year of three hundred and fifty-five.  And he provided for a uniform intercalation of one day in every fourth year, which accounted for the remaining quarter of a day.

Caesar was a student of astronomy, and always found time for its contemplation.  He is said even to have written a treatise on the motion of the stars.  He was assisted in his reform of the calendar by Sosigines, an Alexandrian astronomer.  He took it out of the hands of the priests, and made it a matter of pure civil regulation.  The year was defined by the sun, and not as before by the moon.

Thus the Romans were the first to bring the scientific knowledge of the Greeks into practical use; but while they measured the year with a great approximation to accuracy, they still used sun-dials and water-clocks to measure diurnal time.  Yet even these were not constructed as they should have been.  The hour-marks on the sun-dial were all made equal, instead of varying with the periods of the day,—­so that the length of the hour varied with the length of the day.  The illuminated interval was divided into twelve equal parts; so that if the sun rose at five A.M., and set at eight P.M., each hour was equal to eighty minutes.  And this rude method of measurement of diurnal time remained in use till the sixth century.  Clocks, with wheels and weights, were not invented till the twelfth century.

The last great light among the ancients in astronomical science was Ptolemy, who lived from 100 to 170 A.D., in Alexandria.  He was acquainted with the writings of all the previous astronomers, but accepted Hipparchus as his guide.  He held that the heaven is spherical and revolves upon its axis; that the earth is a sphere, and is situated within the celestial sphere, and nearly at its centre; that it is a mere point in reference to the distance and magnitude of the fixed stars, and that it has no motion.  He adopted the views of the ancient astronomers, who placed Saturn, Jupiter, and Mars next under the sphere of the fixed stars, then the sun above Venus and Mercury, and lastly the moon next to the earth.  But he differed from Aristotle, who conceived that the earth revolves in an orbit around the centre of the planetary system, and turns upon its axis,—­two ideas in common with the doctrines which Copernicus afterward unfolded.  But even Ptolemy did not conceive the heliocentric theory,—­the sun the centre of our system.  Archimedes and Hipparchus both rejected this theory.