plausibility of the heliocentric theory which, had he applied it, must have seemed almost demonstrative. This new scientific weapon consisted of the knowledge gained by Hipparchus through study of the moon in eclipse as to the actual distance of the moon from the earth. Hipparchus found this distance to equal fifty-nine radii of the earth, a measurement which, as corrected by modern observers, is found to vary from the truth by less than two radii. But in the time of Hipparchus, thanks to a wonderful measurement to which we shall refer more at length in a moment, the actual length of the earth's radius was approximately known; hence, as just mentioned, the measurement of Hipparchus determined the actual distance of the moon. But this distance, it will be recalled, represents one side of the right-angled triangle of Aristarchus. Had Hipparchus now remeasured this triangle, with his perfected means of observation, he might perhaps have come nearer the truth as to the relative distance of the sun. He might then have learned that the sun, instead of being merely three hundred times as large as the earth, as Aristarchus supposed, in reality bears some such relation to the earth as a hand-ball bears to a tiny shot. Granted this knowledge, Hipparchus might well have felt, as Aristarchus did, the absurdity of supposing that so gigantic a body could revolve about, and as it were be held in thraldom by, what in comparison was but a mere speck of matter. But unfortunately Hipparchus either did not make the measurement, or failed to make it with increased accuracy, and so his verdict was given for the old false doctrine and against the new, correct one. His verdict, as expounded in detail by Ptolemy, completely dominated scientific thought until the time of Copernicus.
But however Hipparchus erred in regard to this vastly important matter, he is to be credited with several discoveries that show how great were his merits as an investigator. One of the most remarkable of these was his demonstration that the earth does not lie at the centre of the sun's apparent path. He was led to this discovery by the careful measurement of the time occupied by the sun in passing from equinox to equinox. He found that the equinoxes did not divide the year into precisely equal parts. The explanation of this, as we now know, thanks to Kepler, is that the earth's path about the sun is elliptical, and not circular. But in the time of Hipparchus, and for many generations thereafter, it would have been rank heresy to suggest an elliptical orbit for any heavenly body. According to the ancient conception, which had the approval of Aristotle, the circle is the perfect figure, and therefore the figure to which all motions of the heavenly bodies must conform. It never occurred to Hipparchus to doubt the truth of this metaphysical conception. Instead of assuming therefore that the sun's path is not circular, he assumed that the earth lies a little distance from the centre of the circle. Even this supposition did not altogether account for the observed anomalies of motion of the sun. To explain the observed retardation and acceleration of motion, it became necessary to invent another hypothesis, according to which the sun, as it revolves about the earth, performs also a secondary revolution about an imaginary centre. This secondary orbit was spoken of as an epicycle, and the fact that the earth does not lie at the centre of the orbit was described by the phrase "eccentricity of the sun's orbit." It being discovered that similar anomalies pertained to the motions of the moon and the planets, the imaginary mechanism of the heavens came to involve an elaborate series of eccentrics and epicycles vastly more complicated than the actual mechanism of the heavens as we know it. It must be recalled, however, that this theory, though false as to its chief assumptions, nevertheless sufficed to explain the observed motions of the heavenly bodies. The system was promulgated later on by Ptolemy, and it continued the stock doctrine of astronomy until the time of Copernicus. As it was a false doctrine, it was not in a proper sense an anticipation of modern science, yet it was based upon measurements of marvellous accuracy. Another measurement of Hipparchus was that which determined the precise length of the year. In making this really difficult measurement, Hipparchus differed from the exact truth by less than six minutes. Yet other measurements of Hipparchus,
