32 2 POPULAR SCIENCE MONTHLY. 



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 sim- 

 ple 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 ob- 

 servation. 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 dis- 

 coveries 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. 



* Our constellation figures are those designed by Albrecht Diirer on the 

 star maps of StoeflBer and Heinfogel from the descriptions of Ptolemy. 



