Page:Harper's New Monthly Magazine - v109.djvu/1025

951 when compared with ancient observations of the Babylonian astronomers, as made accessible through the efforts of followers of Alexander the Great, proved that the apparent plane of the ecliptic shifts gradually—a phenomenon ever since familiar as the precession of the equinoxes.

Two other examples of remarkable measurements made by the astronomers of the Alexandrian epoch must be cited. Both were made by the famous Alexandrian, Eratosthenes. One consisted of the accurate measurement of the obliquity of the ecliptic, that is to say, of the angular tip of the earth's axis; the other, of which mention has already been made, was the relatively accurate determination of the actual size of the earth. Both these measurements were made with the aid of the same simple instrument.

This instrument was nothing more complex than a perpendicular post attached to a scale for measuring the angle of its shadow. The instrument was called an armillary sphere. It introduced no new principle, having been used from the earliest time by the Egyptian astronomers. Eratosthenes perfected it as to details. In determining the obliquity of the ecliptic he measured the sun's angular height on the day of the winter solstice, and again six months later, on the day of the summer solstice. Half the difference between these angles gives the angle of the ecliptic. This is readily comprehensible, and indeed involved no new idea, as a similar measurement had probably been made in a cruder way many times before; but the measurement of the earth, although almost equally simple in principle and practice, was a stroke of inventive genius, as any one must admit who will reflect that the known habitable world at that time comprised but a tiny fraction of the earth's surface. The principle which Eratosthenes hit upon was to measure an arc of the earth's circumference, it being of course assumed that the earth is round.

Eratosthenes knew that certain two cities in Egypt, Alexandria and Syene, namely, were situated almost exactly on the same meridian, and that the distance between these cities was about five thousand stadia. Here then was a measured arc of the earth's circumference. If a means could be devised to determine the number of degrees of arc represented by this distance, a simple multiplication would of course solve the problem. But how determine this all-important number? The answer came through reflection on the relations of concentric circles. If you draw any number of circles, of whatever size, about a given centre, a pair of radii drawn from that centre will cut arcs of the same relative size from all the circles. One circle may be so small that the actual arc subtended by the radii in a given case may be but an inch in length, while another circle is so large that its corresponding arc is measured in miles; but in each case the same number of so-called degrees will represent the relation of each arc to its circumference. Now Eratosthenes knew that the sun, when on the meridian on the day of the summer solstice, was directly over the town of Syene, since on that day it was reported that the gnomon cast no shadow, while a deep well was illuminated to the bottom. This meant that, at that moment, a radius of the earth projected from Syene would point directly toward the sun. Meanwhile of course the zenith would represent the projection of the radius of the earth passing through Alexandria. All that was required then was to measure, at Alexandria, the angular distance of the sun from the zenith to secure an approximate measurement of the arc of the sun's circumference, corresponding to the arc of the earth's surface represented by the measured distance between Alexandria and Syene.

The reader will observe that the measurement could not be absolutely accurate because it is made from the surface of the earth, and not from the earth's centre, but the size of the earth is so insignificant in comparison with the distance of the sun, that this slight discrepancy could be disregarded. Eratosthenes found that the angle in question represented an arc of one-fiftieth of the entire circle; therefore, multiplying five thousand stadia by fifty, he had the answer, two hundred and fifty thousand stadia, for the circumference of the earth. Unfortunately, we do not know the precise length of the stadium used by Eratosthenes as his unit measure, but the best conjectures make it probable that the