ALEXANDRIAN OR HELLENISTIC PERIOD 



sun. We have seen that, in the study of the heavenly 

 bodies, much depends on the measurement of angles. 

 Now the easiest way in which angles can be meas- 

 ured, when solar angles are in question, is to pay atten- 

 tion, not to the sun itself, but to the shadow that it 

 casts. We saw that Thales made some remarkable 

 measurements with the aid of shadows, and we have 

 more than once referred to the gnomon, which is the 

 most primitive, but which long remained the most im- 

 portant, of astronomical instruments. It is believed 

 that Eratosthenes invented an important modifica- 

 tion of the gnomon which was elaborated afterwards 

 by Hipparchus and called an armillary sphere. This 

 consists essentially of a small gnomon, or perpendicular 

 post, attached to a plane representing the earth's 

 equator and a hemisphere in imitation of the earth's 

 surface. With the aid of this, the shadow cast by the 

 sun could be very accurately measured. It involves 

 no new principle. Every perpendicular post or ob- 

 ject of any kind placed in the sunlight casts a shadow 

 from which the angles now in question could be roughly 

 measured. The province of the armillary sphere was 

 to make these measurements extremely accurate. 



With the aid of this implement, Eratosthenes care- 

 fully noted the longest and the shortest shadows cast 

 by the gnomon that is to say, the shadows cast on the 

 days of the solstices. He found that the distance be- 

 tween the tropics thus measured represented 47 42' 39" 

 of arc. One-half of this, or 23 51' 19.5", represented 

 the obliquity of the ecliptic that is to say, the angle 

 by which the earth's axis dipped from the perpendicu- 

 lar with reference to its orbit. This was a most im- 



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