globe’s surface was known to civilized man. It is no discredit to approach astronomy as a geographer and geography as an astronomer if the results are such as these. What Eratosthenes really did was to approach both astronomy and geography from two seemingly divergent points of attack–namely, from the stand-point of the geometer and also from that of the poet. Perhaps no man in any age has brought a better combination of observing and imaginative faculties to the aid of science.
Nearly all the discoveries of Eratosthenes are associated with observations of the shadows cast by the sun. We have seen that, in the study of the heavenly bodies, much depends on the measurement of angles. Now the easiest way in which angles can be measured, when solar angles are in question, is to pay attention, not to the sun itself, but to the shadow that it casts. We saw that Thales made some remarkable measurements with the aid of shadows, and we have more than once referred to the gnomon, which is the most primitive, but which long remained the most important, of astronomical instruments. It is believed that Eratosthenes invented an important modification of the gnomon which was elaborated afterwards by Hipparchus and called an armillary sphere. This consists essentially of a small gnomon, or perpendicular post, attached to a plane representing the earth’s equator and a hemisphere in imitation of the earth’s surface.
With the aid of this, the shadow cast by the sun could be very accurately measured. It involves no new principle. Every perpendicular post or object of any kind placed in the sunlight casts a shadow from which the angles now in question could be roughly measured. The province of the armillary sphere was to make these measurements extremely accurate.
With the aid of this implement, Eratosthenes carefully noted the longest and the shortest shadows cast by the gnomon–that is to say, the shadows cast on the days of the solstices. He found that the distance between the tropics thus measured represented 47
degrees 42′ 39″ of arc. One-half of this, or 23 degrees 5,’
19.5″, represented the obliquity of the ecliptic–that is to say, the angle by which the earth’s axis dipped from the perpendicular with reference to its orbit. This was a most important observation, and because of its accuracy it has served modern astronomers well for comparison in measuring the trifling change due to our earth’s slow, swinging wobble. For the earth, be it understood, like a great top spinning through space, holds its position with relative but not quite absolute fixity. It must not be supposed, however, that the experiment in question was quite new with Eratosthenes. His merit consists rather in the accuracy with which he made his observation than in the novelty of the conception; for it is recorded that Eudoxus, a full century earlier, had remarked the obliquity of the ecliptic. That observer had said that the obliquity corresponded to the side of a pentadecagon, or fifteen-sided figure, which is equivalent in modern phraseology to twenty- four degrees of arc. But so little is known regarding the way in which Eudoxus reached his estimate that the measurement of Eratosthenes is usually spoken of as if it were the first effort of the kind.
Much more striking, at least in its appeal to the popular
imagination, was that other great feat which Eratosthenes performed with the aid of his perfected gnomon–the measurement of the earth itself. When we reflect that at this period the portion of the earth open to observation extended only from the Straits of Gibraltar on the west to India on the east, and from the North Sea to Upper Egypt, it certainly seems enigmatical–at first thought almost miraculous–that an observer should have been able to measure the entire globe. That he should have accomplished this through observation of nothing more than a tiny bit of Egyptian territory and a glimpse of the sun’s shadow makes it seem but the more wonderful. Yet the method of Eratosthenes, like many another enigma, seems simple enough once it is explained. It required but the application of a very elementary knowledge of the geometry of circles, combined with the use of a fact or two from local geography–which detracts nothing from the genius of the man who could reason from such simple premises to so wonderful a conclusion.