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EFORE the end of the fifteenth century, European seamen had ceased to be mere unscientific gropers in darkness. They knew how Eratosthenes had calculated the obliquity of the ecliptic by means of the armillæ, or great copper circles, fixed in the square porch of the Alexandrian Museum, and how he had determined the circumference of the earth. He had heard that deep wells in Syene were enlightened to the bottom on the day of the summer solstice, and he therefore reasoned that Syene must be on the tropic. He had ascertained the latitude of Alexandria by observation, and he assumed that the two places were on the same meridian. The arc thus measured enabled him to calculate the proportion it bore to the whole circumference of the earth, and his result was a fair approximation to the truth.

Then again, the fifteenth-century seamen had the catalogue of the stars and constellations, the system of mapping by degrees of latitude and longitude, and the theory of the precession of the