170 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1916. 



nineteen times that from the earth to the moon. This method of 

 Aristarchus is theoretically correct, but in determining the angle at 

 the earth as being 3° less than a right angle he made an error of 

 about 2° 50'. 



Hipparchus, who lived about 150 B. C. and was called by Delambre 

 the true father of astronomy, attacked the problem of the distances 

 of the sun and moon through a study of ecli]:)ses. Assuming in 

 accordance with the result of Aristarchus that the sun is 19 times 

 as far from the earth as the moon, having determined the diameter 

 of the earth's shadow at the distance of the moon and knowing 

 the angidar diameter of the moon he found 3' as the sun's horizontal 

 parallax. By the sun's parallax is meant the angle at the sun sub- 

 tended by the earth's semidiameter and if a = the semidiameter of 

 the earth, A = the distance to the sun, and 11 = sun's horizontal 

 parallax, the relation between these quantities is expressed by the 

 equation : 



a 

 Sin II = — 



A 



The next attempt to determine the distance of a heavenly body 

 was made about 150 A. D. by Claudius Ptolemy, the last of the 

 ancient astronomers and one whose writings were considered the 

 standard in things astronomical for 15 centuries. To determine 

 the lunar parallax he resorted to direct observations of the zenith 

 distance of the moon on the meridian, comparing the result of his 

 observations with the position obtained from the lunar theory. He 

 determined the j^arallax when the moon was nearest the zenith, and 

 also when it crossed his meridian at its farthest distance from the 

 zenith. From his observations he obtained results varying from less 

 than 50 per cent of the true parallax (57'.0) to more than 150' per 

 cent of that value. According to Houzeau the definitive result of 

 Ptolemy's work is 58'. 7. 



It is thus seen that the astronomers of 2,000 years ago had a 

 fairly accurate knowledge of the distance of the moon from the 

 earth, but an entirely erroneous one of the distance of the sun, the 

 true distance being something like 20 times that assumed by them. 

 This value of the distance of the sun from the earth was accepted for 

 19 centuries from Aristarchus to Kepler, having been deduced anew 

 by such men as Copernicus and Tycho Brahe. 



With the announcement by Kepler, early in the seventeenth cen- 

 tury, of his laws of planetary motion it became possible to deduce 

 from the periodic times of revolution of the planets around the sun 

 their relative distances from that body, and thus to determine the 



