of this interpretation; and if he meant, as his words seem to imply, that philosophers of his day had a tolerably precise idea of the globe, we must assume that this idea was based upon some sort of measurement. The recorded size, 400,000 stadia, is a sufficient approximation to the truth to suggest something more than a mere unsupported guess. Now, since Aristotle died more than fifty years before Eratosthenes was born, his report as to the alleged size of the earth certainly has a suggestiveness that cannot be overlooked; but it arouses speculations without giving an inkling as to their solution. If Eratosthenes had a precursor as an earth-measurer, no hint or rumor has come down to us that would enable us to guess who that precursor may have been. His personality is as deeply enveloped in the mists of the past as are the personalities of the great prehistoric discoverers. For the purpose of the historian, Eratosthenes must stand as the inventor of the method with which his name is associated, and as the first man of whom we can say with certainty that he measured the size of the earth. Right worthily, then, had the Alexandrian philosopher won his proud title of "surveyor of the world."
HIPPARCHUS, "THE LOVER OF TRUTH"
Eratosthenes outlived most of his great contemporaries. He saw the turning of that first and greatest century of Alexandrian science, the third century before our era. He died in the year 196 B.C., having, it is said, starved himself to death to escape the miseries of blindness;—to the measurer of shadows, life without light seemed not worth the living. Eratosthenes left no immediate successor. A generation later, however, another great figure appeared in the astronomical world in the person of Hipparchus, a man who, as a technical observer, had perhaps no peer in the ancient world: one who set so high a value upon accuracy of observation as to earn the title of "the lover of truth." Hipparchus was born at Nicaea, in Bithynia, in the year 160 B.C. His life, all too short for the interests of science, ended in the year 125 B.C. The observations of the great astronomer were made chiefly, perhaps entirely, at Rhodes. A misinterpretation of Ptolemy's writings led to the idea that Hipparchus, performed his chief labors in Alexandria, but it is now admitted that there is no evidence for this. Delambre doubted, and most subsequent writers follow him here, whether Hipparchus ever so much as visited Alexandria. In any event there seems to be no question that Rhodes may claim the honor of being the chief site of his activities.
It was Hipparchus whose somewhat equivocal comment on the work of Eratosthenes we have already noted. No counter-charge in kind could be made against the critic himself; he was an astronomer pure and simple. His gift was the gift of accurate observation rather than the gift of imagination. No scientific progress is possible without scientific guessing, but Hipparchus belonged to that class of observers with whom hypothesis is held rigidly subservient to fact. It was not to be expected that his mind would be attracted by the heliocentric theory of Aristarchus. He used the facts and observations gathered by his great predecessor of Samos, but he declined to accept his theories. For him the world was central; his problem was to explain, if he could, the irregularities of motion which sun, moon, and planets showed in their seeming circuits about the earth. Hipparchus had the gnomon of Eratosthenes—doubtless in a perfected form—to aid him, and he soon proved himself a master in its use. For him, as we have said, accuracy was everything; this was the one element that led to all his great successes.
Perhaps his greatest feat was to demonstrate the eccentricity of the sun's seeming orbit. We of to-day, thanks to Keppler and his followers, know that the earth and the other planetary bodies in their circuit about the sun describe an ellipse and not a circle. But in the day of Hipparchus, though the ellipse was recognized as a geometrical figure (it had been described and named along with the parabola and hyperbola by Apollonius of Perga, the pupil of Euclid), yet it would have been the rankest heresy to suggest an elliptical course for any heavenly body. A metaphysical theory, as propounded perhaps by the Pythagoreans but ardently supported by Aristotle, declared that the circle is the perfect figure, and pronounced it inconceivable that the motions of the spheres should be other than circular. This thought dominated the mind of Hipparchus, and so when his careful measurements led him to the discovery that the northward and southward journeyings of the sun did not divide the year into four equal parts, there was nothing open to him but to either assume that the earth does not lie precisely at the centre of the sun's circular orbit or to find some alternative hypothesis.
In point of fact, the sun (reversing the point of view in accordance with modern discoveries) does lie at one focus of the earth's elliptical orbit, and therefore away from the physical centre of that orbit; in other words, the observations of Hipparchus were absolutely accurate. He was quite correct in finding that the sun spends more time on one side of the equator than on the other. When, therefore, he estimated the relative distance of the earth from the geometrical centre of the sun's supposed circular orbit, and spoke of this as the measure of the sun's eccentricity, he propounded a theory in which true data of observation were curiously mingled with a positively inverted theory. That the theory of Hipparchus was absolutely consistent with all the facts of this particular observation is the best evidence that could be given of the difficulties that stood in the way of a true explanation of the mechanism of the heavens.
But it is not merely the sun which was observed to vary in the speed of its orbital progress; the moon and the planets also show curious accelerations and retardations of motion. The moon in particular received most careful attention from Hipparchus. Dominated by his conception of the perfect spheres, he could find but one explanation of the anomalous motions which he observed, and this was to assume that the various heavenly bodies do not fly on in an unvarying arc in their circuit about the earth, but describe minor circles as they go which can be likened to nothing so tangibly as to a light attached to the rim of a wagon-wheel in motion. If such an invisible wheel be imagined as carrying the sun, for example, on its rim, while its invisible hub follows unswervingly the circle of the sun's mean orbit (this wheel, be it understood, lying in the plane of the orbit, not at right-angles to it), then it must be obvious that while the hub remains always at the same distance from the earth, the circling rim will carry the sun nearer the earth, then farther away, and that while it is traversing that portion of the are which brings it towards the earth, the actual forward progress of the sun will be retarded notwithstanding the uniform motion of the hub, just as it will be accelerated in the opposite arc. Now, if we suppose our sun-bearing wheel to turn so slowly that the sun revolves but once about its imaginary hub while the wheel itself is making the entire circuit of the orbit, we shall have accounted for the observed fact that the sun passes more quickly through one-half of the orbit than through the other. Moreover, if we can visualize the process and imagine the sun to have left a visible line of fire behind him throughout the course, we shall see that in reality the two circular motions involved have really resulted in producing an elliptical orbit.
The idea is perhaps made clearer if we picture the actual progress of the lantern attached to the rim of an ordinary cart-wheel. When the cart is drawn forward the lantern is made to revolve in a circle as regards the hub of the wheel, but since that hub is constantly going forward, the actual path described by the lantern is not a circle at all but a waving line. It is precisely the same with the imagined course of the sun in its orbit, only that we view these lines just as we should view the lantern on the wheel if we looked at it from directly above and not from the side. The proof that the sun is describing this waving line, and therefore must be considered as attached to an imaginary wheel, is furnished, as it seemed to Hipparchus, by the observed fact of the sun's varying speed.
That is one way of looking at the matter. It is an hypothesis that explains the observed facts—after a fashion, and indeed a very remarkable fashion. The idea of such an explanation did not originate with Hipparchus. The germs of the thought were as old as the Pythagorean doctrine that the earth revolves about a centre that we cannot see. Eudoxus gave the conception greater tangibility, and may be considered as the father of this doctrine of wheels—epicycles, as they came to be called. Two centuries before the time of Hipparchus he conceived a doctrine of spheres which Aristotle found most interesting, and which served to explain, along the lines we have just followed, the observed motions of the heavenly bodies. Calippus, the reformer of the calendar, is said to have carried an account of this theory to Aristotle. As new irregularities of motion of the sun, moon, and planetary bodies were
