1/2 MATHEMATICAL GEOGRAPHY. [CHAP. circle of the earth must be 250,000 stadia, or 25,000 geographical miles1. This calculation involved two minor errors. One of these arose from the belief that the earth was a perfect ^criticism of Sphere) instead of being flattened at the poles—a mistake which was unavoidable according to the knowledge of that time. The other was caused by Syene being regarded as lying directly under the tropic, whereas in reality it was 37 miles to the northward of it. This slight inaccuracy was caused by the imperfection of the methods of observation then employed, for the position of the tropic was calculated partly from the sun being seen from the bottom of a well at the summer solstice, and therefore being considered vertical, and partly from the gnomon casting no shadow at that time8. A more consider- able error proceeded from the distance between Syene and Alexandria being overestimated, for the number of stadia assumed for this by Eratosthenes is in excess by more than one- fifth. Still, after all deductions have been made, the general accuracy of the .result is very striking; for whereas the real cir- cumference of the earth at the equator is 25,000 English miles, Eratosthenes estimates the great circle of the meridian at 25,000 geographical miles, which is about one-seventh part in excess. By the ancients it was regarded as an extraordinary achievement of science, and immense importance was attached to it8. Eratosthenes also endeavoured to estimate the dimensions of the habitable world. For this attempt the increased Eratosthenes' . . . . ., Measurement acquaintance with the surface of the globe which •MeWcSd.*" had arisen since ^ time of Aristotle afforded especial facilities, and it had already been essayed 1 This account of Eratosthenes' measurement is given by Cleomedes, De Motu Circulari Corporum Caekstium, i. 10, pp. 95—101, ed. Ziegler. 3 Strabo, 17. i. 48; h & rj? Swjvfl Kctl TO 0p&p Arri TO dmffijfjLaufW TO.S Qcptvas Tpoiras, 8i6*Tt T<£ Tpoiruc$ KVK\(# vwoKetvTai ol TdVot ovTot* carb yap TUP , X^-yw 8£ TWV 'EAXa&Jtwv, vpo'Covw &rl n)i> jMffiqtLpptcur frravQa -tfXws Kwrb Kopwfrijv faur yberai /cai iroia TOUS ytHapoiw ourictovs Karat, jf & KO.TO, Kopv/te?s re xal Ta tpvypara. rwv Qpe&rtav icaTeffjrwcwrrau 8 Banbury, Hist. ofAnc. Gcogr., i. pp. 621—625.