476 



SCIENCE 



[N. S. Vol. XLIII. No. 1110 



The first attempt to assign definite rela- 

 tive distances to any two of the bodies was 

 probably that of Eudoxus of Cnidus who, 

 about 370 B.C., supposed, according to 

 Archimedes, that the diameter of the sun 

 was nine times greater than that of the 

 moon, which is equivalent to saying, since 

 the sun and the moon have approximately 

 the same apparent diameter, that the dis- 

 tance of the sun from the earth is nine 

 times greater than that of the moon. 



A century later, about 275 B.C., Aris- 

 tarchus of Samos gave a method of deter- 

 mining the relative distances of the sun and 

 moon from the earth as follows : When the 

 moon is at the phase, first quarter or last 

 quarter, the earth is in the plane of the 

 circle which separates the portion of the 

 moon illuminated by the sun from the non- 

 illuminated part, and the line from the ob- 

 server to the center of the moon is per- 

 pendicular to the line from the center of 

 the moon to the sun. (Diagram shown.) 

 If, at this instant, the angular separation 

 of the sun and moon is determined, one of 

 the acute angles of a right-angle triangle — 

 sun, moon and earth — is known, from 

 which can be deduced the ratio of any two 

 of the sides, as, for instance, the ratio of 

 the distance from the earth to the moon to 

 that from the earth to the sun. Aristarchus 

 gives the value of this angle as differing 

 from a right angle by only one thirtieth of 

 that angle, i. e., it is an angle of 87°, from 

 which follows that the distance from the 

 earth to the sun is 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 dis- 

 tances of the sun and moon through a study 

 of eclipses. Assuming in accordance with 



the result of Aristarchus that the sun is 

 nineteen 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 angular diameter of 

 the moon, he found 3' as the sun's hori- 

 zontal parallax. By the sun's parallax is 

 meant the angle at the sun subtended by 

 the earth's semi-diameter and if a^^the 

 semi-diameter of the earth, A = the dis- 

 tance to the sun, and 7r = sun's horizontal 

 parallax, the relation between these quan- 

 tities is expressed by the equation (dia- 

 gram shown). 



Sin TT = o/A. 



The next attempt to determine the dis- 

 tance of a heavenly body was made about 

 A.D. 150 by Claudius Ptolemy, the last of 

 the ancient astronomers, and one whose 

 writings were considered the standard in 

 things astronomical for fifteen centuries. 

 To determine the lunar parallax, he re- 

 sorted to direct observations of the zenith 

 distance of the moon on the meridian, com- 

 paring the result of his observations with 

 the position obtained from the lunar theory. 

 He determined the parallax when the moon 

 was nearest the zenith, and also when it 

 crossed his meridian at its farthest dis- 

 tance from the zenith. From his observa- 

 tions 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 

 two thousand years ago had a fairly accu- 

 rate knowledge of the distance of the moon 

 from the earth, but an entirely erroneous 

 one of the distance of the sun, the true dis- 

 tance being something like twenty times 

 that assumed by them. This value of the 

 distance of the sun from the earth was ac- 

 cepted for nineteen centuries, from Aris- 

 tarchus to Kepler, having been deduced 



