eichelberger: distances of heavenly bodies 163 



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 horizontal 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 

 distance to the Sun, and n = Sun's horizontal parallax, the 

 relation (diagram shown) between these quantities is expressed 

 by the equation: 



a 



Sinn = - 

 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 con- 

 sidered the standard in things astronomical for fifteen centuries. 

 To determine the lunar parallax he resorted to direct obser- 

 vations 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 merid- 

 ian at its farthest distance from the zenith. From his obser- 

 vations 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 i- 

 58'7. 



It is thus seen that the astronomers of two thousand 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 twenty times that 

 assumed by them. This value of the distance of the Sun from 

 the Earth was accepted for nineteen centuries from Aristarchu> 

 to Kepler, having been deduced anew by such men as Copernicu- 

 and Tycho Brahe. 



W ith the announcement by Kepler, early in the seventeenth 

 century, of his laws of planetary motion, it became possible to 

 deduce from the periodic times of revolution of the planets around 



