THE DISTANCES OF THE HEAVENLY BODIES. 



By W. S. ElCHELBEEGEE. 



[/. /S. Naval Oiserratory. 



Before any attempt was made by the ancients to determine the 

 distance from the earth of any celestial body we find them arrang- 

 ing these bodies in order of distance very much as we know them 

 to-day, assummg that the more rapid the motion of a body among 

 the stars the less its distance from the earth; the stars, that were 

 supposed to have no relative motions, Avere assumed to be the most 

 distant objects. 



The first attempt to assigii definite relative 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 equiva- 

 lent to saying that, since the sun and the moon have approximately 

 the same apparent diameter, the distance of the sun from the earth 

 is nine times greater than that of the moon. 



A century later, about 275 B. C, Aristarchus of Samos gave a 

 method of determining 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 

 nonilluminated part, and the line from the observer to the center of 

 the moon is perpendicular to the line from the center of the moon 

 to the sun. If at this instant the angular separation of the sun and 

 moon is determined, one of the acute angles of a right-angle tri- 

 angle — 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 it follows that the distance from the earth to the sun is 



I Presidential address before tbe Philosopliieal Society of Washington on Mar. 4, 1916. 



169 



