Of course at this early period the reference of any particular phenomenon to true time was out of the question. The ancients at the period we are considering used twelve hours to represent a day, irrespective of the time of the year—the day always being reckoned as the time between sunrise and sunset. So that in summer the hours were long and in winter they were short. The idea of equal hours did not occur to them till later; but no observations are closer than an hour, and the smallest division of space of which they took notice was something like equal to a quarter or half of the moon’s diameter. When we come down, however, to three centuries before Christ, we find that a different state of things is coming about. The magnificent museum at Alexandria was beginning to be built, and astronomical observations were among the most important things to be done in that vast establishment. The first astronomical workers there seem to have been Timocharis and Aristillus, who began about 295 B.C., and worked for twenty-six years. We are told that they made a catalogue of stars, giving their positions with reference to the sun’s path or ecliptic. It was soon after this that the gnomon gave way to the invention of the Scarphie. It is really a little gnomon on the summit of which is a spherical segment. An arc of a circle passing out of the foot of the style was divided into parts, and we thus had the angle which the solar ray formed with the vertical. Nevertheless the scarphie was subject to the same inconveniences, and it required the same corrections, as the gnomon; in short, it was less accurate than it. That did not, however, hinder Eratosthenes from making use of it to measure the size of the earth and the inclination of the ecliptic to the equator. The method Eratosthenes followed in ascertaining the size of the earth was to measure the arc between Syene and Alexandria by observing the altitude of the sun at each place. He found it to be 1/50 of the circumference and 5,000 stadia, so that if 1/50 of the circumference of the earth is 5,000 stadia, the whole circumference must be 50 times 5,000, or 250,000 stadia.[5] [Illustration: FIG. 6.—The First Meridian Circle. ] And now still another instrument is introduced, and we begin to find the horizon altogether disregarded in favour of observations made on the meridian. The instrument in question was probably the invention of Eratosthenes. It consisted of two circles of nearly the same size crossing each other at right angles, (Fig. 6); one circle represented the equator and the other the meridian, and it was employed as follows:—