162 THE GREEK ASTROXOMY. 



But nothing like accurate measurements of any portions of the sky 

 were obtained, till astronomers adopted the method of making visual 

 coincidences of the objects with the instruments, either by means of 

 shadozos or of sights. 



Probably the oldest and most obvious measurements of the positions 

 of the heavenly bodies were those in which the elevation of the sun 

 was determined 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 statement 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 intercepted portion of a circumference described about the angular 

 point. The use of the gnomon might lead to the determination of he 

 angle by the graphical methods of geometry ; but the numerical ex- 

 pression of the circumference required some progress in trigonometry ; 

 for instance, a table of the tangents of angles. 



Instruments were soon invented for measuring angles, by means of 

 circles, which had a border or limb, divided into equal parts. The 

 whole circumference was divided into 360 degrees : perhaps because 

 the circles, first so divided, were those which represented the sun's 

 annual path ; one such degree would be the sun's daily advance, more 

 nearly than any other convenient aliquot part which could be taken. The 

 position of the sun was determined by means of the shadow of one part 

 of the instrument upon the other. The most ancient instrument of 

 this kind appears to be the Hemisphere of Berosus. A hollow hemi- 

 sphere was placed with its rim horizontal, and a style was erected in 

 such a manner that the extremity of the style was exactly at the centre 

 of the sphere. The shadow of this extremity, on the concave surface, 

 had the same position with regard to the lowest point of the sphere 

 which the sun had with regard to the highest point of the heavens. 



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



