212 THE GREEK ASTRONOMY. 



adopted the method of making visual coincidences 

 of the objects with the instruments, either by means 

 of shadows or of sights. 



Probably the oldest and most obvious measure- 

 ments of the positions of the heavenly bodies were 

 those in which the elevation of the sun was deter- 

 mined by comparing the length of the shadow of 

 an upright staff or gnomon, with the length of the 

 staff itself. It appears 5 , from a memoir of Gautil, 

 first printed in the Connaissance des Temps for 

 1809, that, at the lower town of Loyang, now called 

 Hon-anfou, Tchon-kong found the length of the 

 shadow of the gnomon, at the summer solstice, 

 equal to one foot and a half, the gnomon itself 

 being eight feet in length. This was about 1100 

 B.C. The Greeks, at an early period, used the 

 same method. Strabo says 6 that " Byzantium and 

 Marseilles are on the same parallel of latitude, 

 because the shadows at those places have the same 

 proportion to the gnomon, according to the state- 

 ment of Hipparchus, who follows Pytheas." 



But the relations of position which astronomy 

 considers, are, for the most part, angular distances ; 

 and these are most simply expressed by the inter- 

 cepted portion of a circumference described about 

 the angular point. The use of the gnomon might 

 lead to the determination of the angle by the 

 graphical methods of geometry ; but the numerical 

 expression of the circumference required some pro- 

 6 Lib. U. K. Hist. Ast. p. 5. Del. A. A. i. 257. 



