ON ASTRONOMY. 115 



it, viz : the size of the earth, was wanting. The instrnraental means 

 known to the ancients were insufficient to furnish the elements of the 

 calculation. 



Aristarchus, of Samos^ in the third century before the Christian era, 

 instituted observations for the purpose of determining the relative 

 distances of the sun and moon from the eartli. He wrote a treatise 

 upon the subject which has come down to modern times. Hismetliod 

 was to observe the angular distance of the moon from the sun at the 

 time when the moon appeared just half illuminated. This method, as 

 a preliminary one, is ingenious, and worthy of a passing notice. 

 Thus, in figure 10, 



when the one-half of the moon is illuminated, the angle EMS will 

 be a right angle. If the angle M B S is accurately measured, the 

 angle at S will be known, and we shall have this proportion : 



E M : E S : : sin. E S M : sin. E M S = 1. 



This was the substance of Aristarchus' method. The lines of the 

 angles are known, and this makes known the relative distances of the 

 sun and moon. 



The measurements of Aristarchus must have been very inaccurate. 

 He concluded that the sun was nineteen times more distant than the 

 moon. We now know the sun to be about four hundred times more 

 distant than the moon, which shows how extremely wide of the truth 

 this ancient determination was ; and yet Ptolemy, four centuries later, 

 adopted the determination of Aristarchus, and, combining it with 

 observations of his own, or more probably those of Hipparchus, com- 

 puted the sun's parallax to be three minutes, which is more than 

 twenty times its true value. The parallax of three minutes would place 

 the sun at only one-twentieth of its real distance. This conclusion of 

 the great Alexandrian astronomer appears to have been adopted down 

 to the time of Kepler, including Copernicus and Tycho Brahc. Kep- 

 ler's researches on the orbit of Mars led him to conclude that the 

 sun was at least three times more remote than Ptolemy had supposed. 



But it is time to explain the method by which modern astronomers 

 have determined the distances of the planetary bodies within narrow 

 limits of error. And here it may be remarked that the relative dis- 

 tances of the planets from the sun were quite accurately known long 



