SEQUEL TO THE EPOCH OF HIPPARCHUS. 215 



be divided into 60 minutes, the minute into 60 

 seconds, and so on. But in practice it was impos- 

 sible to divide the limb of the instrument into 

 parts so small. The armils of Alexandria were 

 divided into no parts smaller than sixths of degrees, 

 or divisions of 10 minutes. 



The angles, observed by means of these divi- 

 sions, were expressed as a fraction of the circum- 

 ference. Thus Eratosthenes stated the interval 

 between the tropics to be J- of the circumference 9 . 



It was soon remarked that the whole circum- 

 ference of the circle was not wanted for such 

 observations. Ptolemy 10 says, that he found it more 

 convenient to observe altitudes by means of a 

 square flat piece of stone or wood, with a quadrant 

 of a circle described on one of its flat faces, about 

 a center near one of the angles. A peg was 

 placed at the center, and one of the extreme radii 

 of the quadrant being perpendicular to the horizon, 

 the elevation of the sun above the horizon was 

 determined by observing the point of the arc of 

 the quadrant on which the shadow of the peg fell. 



As the necessity of accuracy in the observations 

 was more and more felt, various adjustments of 

 such instruments were practised. The instruments 

 were placed in the meridian by means of a meridian 



9 Delambre, A. A. i. 87. It is probable that his observation 



rp, , ,. 47 143 11-18 11 

 gave him 4/| degrees. The fraction m = j^j - -^ = 



1 1 * 



which is very nearly gn 



10 Synt. i. 1. 



