Page:Popular Science Monthly Volume 64.djvu/326

322 come down to us only slightly changed. Hipparchus' catalogue stood unique for a thousand years.

An instance of his practical tact as an observer may be quoted. If a straight ruler be held up against the starry sky there will, now and again, be instances where its edge passes through three stars at the same time. Many such cases are recorded by Hipparchus. No one of the three stars can change its situation without detection. A simple observation of the same sort at any subsequent time will at once exhibit any change that may have taken place in the interval between the two observations.

The work of Hipparchus as a theoretical astronomer is as remarkable as his observing skill. The positions of the heavenly bodies are calculated by solving triangles, both plane and spherical. The doctrine of such solutions—trigonometry—was perhaps invented by him; at all events it was greatly developed and improved. Observations give the celestial longitudes and latitudes of planets at the instant of observation. Their positions at past epochs, a month or a year ago, are given by preceding observations of the same sort. Where will Jupiter or Saturn be found in the future—a month or a year hence? It is necessary to invent a geometry of planetary motion that will account for all past and future motions; and this problem was elaborately developed by Hipparchus. We must recollect that his vast activity was exercised under conditions of the most discouraging kind. His best instruments were but rude; all sightings were made with the eye unaided by telescopes; he had only clepsydras (sand or water-clocks) to measure intervals of time; the Greek system of arithmetic in which his calculations were made was cumbrous in the extreme. What he accomplished is little less than astounding.

From his theory of Epicycles Hipparchus was able to construct his tables of the sun and moon. The tables gave the particulars of the motion of these bodies and enabled predictions to be made of coming solar and lunar eclipses. It was sufficient for the purposes of the time to assert that an eclipse would occur on a certain day, about a certain hour of the morning or afternoon, and the tables were adequate to such predictions. His theory was sufficient; it fulfilled all the tests applied to it. The motion of the moon was more complex than that of the sun, but it, too, was reduced to a sufficient order and important discoveries made. The elements of the motions of these bodies were not derived, as we to-day derive them, from continuous observations, but rather from observations made at certain critical times. For the sun the observations were made at the equinoxes and solstices. Six eclipses of the moon sufficed to give him the elements of the lunar orbit and the rate at which they were changing.