SEQUEL TO THE EPOCH OF HIPPAKCHUS. 163 



But this instrument was in fact used rather for dividing the day into 

 portions of time than for determining position. 



Eratosthenes 7 observed the amount of the obliquity of the sun's 

 path to the equator : we are not informed what instruments he used 

 for this purpose ; but he is said to have obtained, from the munificence 

 of Ptolemy Euergetes, two Ar?nils, or instruments composed of circles, 

 which were placed in the portico at Alexandria, and long used for ob- 

 servations. If a circular rim or hoop were placed so as to coincide 

 with the plane of the equator, the inner concave edge would be en- 

 lightened by the sun's rays which came under the front edge, when 

 the sun was south of the equator, and by the rays which came over 

 the front edge, when the sun was north of the equator : the moment 

 of the transition would be the time of the equinox. Such an instru- 

 ment appears to be referred to by Hipparchus, as quoted by Ptolemy. 8 

 "The circle of copper, which stands at Alexandria in what is called 

 the Square Porch, appears to mark, as the day of the equinox, that on 

 which the concave surface begins to be enlightened from the other 

 side." Such an instrument was called an equinoctial armil. 



A solstitial armil is described by Ptolemy, consisting of two cir- 

 cular rims, one sliding round within the other, and the inner one fur- 

 nished with two pegs standing out from its surface at right angles, and 

 diametrically opposite to each other. These circles being fixed in the 

 plane of the meridian, and the inner one turned, till, at noon, the 

 shadow of the peg in front falls upon the peg behind, the position of 

 the sun at noon would be determined by the degrees on the outer 

 circle. 



In calculation, the degree was conceived to be divided into 60 

 minutes, the minute into 60 seconds, and so on. But in practice it 

 was impossible 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 divisions, were expressed as 

 a fraction of the circumference. Thus Eratosthenes stated the interval 

 between the tropics to be |^ of the circumference. 9 



It was soon remarked that the whole circumference of the circle 



7 Delambre, A. A. i. 86. 8 Ptol. Synt. iii. 2. 



» Delambre, A. A. i. 87. It is probable that his observation gave him 47% 



„,, . • 47 2 / 3 143 11-13 11 , . , . ,11 



degrees. The fraction — - = — — = -7--— == , which is very nearly — 



8 360 1080 1080 83'/i3, 83. 



