GEOGRAPHICAL LATITUDE. 767 



shadow at the first point was the lougest), gave the position of the 

 equator, or the middle distance between the poles. So there was one 

 point on the earth, viz, that of the Tropic of Cancer, apparently fixed,' 

 and a relation was established between the position of the sun at two 

 other points, and the length of shadows cast on the earth. This may be 

 called the first foundation stone of scientific geography ; for without 

 such a sure grounding in nature itself, the science is impossible. Pre- 

 supposing that the rays of the sun come to ns parallel to each other, it 

 happens from the nature of a sphere that the ratio between the length 

 of a shadow at noon, cast by an object perpendicular to the plane of 

 the horizon to the object itself, is equal to the ratio of the distance 

 between the place of observation and the point where the sun casts no 

 shadow. Having thought out this principle, the earliest astronomers 

 waited for noon at the summer solstice to make their observations, and 

 somewhat later came to use also the winter solstice and the equinoxes 

 therefor. But the position thus gained was not absolute and unchange- 

 able, as the ancients supposed. 



In the first place, accuracy of observation was not possible, owing to 

 defective instruments ; they supposed the position of the tropic marked 

 by the position of the upper edge of the sun at the summer solstice, 

 instead of by its center. And in the second place, they could not sus- 

 pect that the ecliptic plane is itself subject to a secular variation of 

 between one and two degrees in about ten thousand years; as a result 

 of which — during the historical period — the earth's axis has been 

 slowly becoming more perpendicular to the plane of its course around 

 the sun. The obliquity is now 24' less than it was 2,000 years ago. 

 This causes a slight approach of the troj)ics toward the equator and of 

 the ijolar circles toward the poles. Syene, whose i)Osition was accepted 

 as marking that of the tropic, lay in 24° 5' 32" north latitude, and ac- 

 cording to modern calculations was under the edge of the sun at the 

 summer solstice about 700 b. c, when the obliquity of the Ecliptic 

 was probably 23° 51'.^ Though Eratosthenes determined with a fair 

 degree of accuracy the obliquity at 23° 51' 19".5, the ancients gen- 

 erally accepted the round sum of 24 degrees. Later classical authors 

 made no improvement on this, and these figures passed with the remain- 

 der of Greek learning to the Arabs. Though the latter added little or 

 nothing to the theory of the Greeks, they were much better observers.^ 

 Accordingly we find Albateguius in the second half of the ninth cen- 

 tury observing with carefully divided parallactic rules the distance 

 between the sun and the zenith at the solstices. The diiference he 

 found to be 47^ 10', from which he determined the oblicpiity of the 

 Ecliptic to be 23° 35'. Delambre names this "the most trustworthy 

 ancient observation," and comparing the result with that of his own 



' Later it will be seen that this point is not stationary, but slightly movable. 



* Neglected to note anthor. 



^Pelambie, Astron. du xviii""^ siecle, p. 6. 



