The skilled mariners of ancient days determined their latitude by means still in use, but their instruments were very inferior. The gnomon, in some form or other, was their most common instrument for measuring the length of the sun’s shadow at noon on different days and in different places. We know from Herodotus,[50] that this instrument was of great antiquity—indeed, he ascribes the invention of it to the Babylonians; but the report of Arrian to the Emperor Hadrian[51] of his shipwreck implies that there were other instruments besides this on board. Pytheas, the first known navigator of the North Sea, is said to have determined the summer solstice at Marseilles by observing the proportion of the shadow of the gnomon.[52] Further, Eratosthenes drew a parallel of latitude through Gibraltar, Rhodes, and Lycia to India; while Hipparchus made the first map, on the principle of “Mercator’s Projection,” by transferring the celestial latitudes and longitudes to the terrestrial globe. On the other hand, Ptolemy erred so far in his calculation of the longitude, that he placed China 60° nearer Europe than it really is, and thus led Columbus to fancy the distance he had to traverse to the New World was just so much less. It must not, however, be forgotten that Aristotle, centuries before him, when reasoning from the assumed sphericity of the earth, was really the first to point out that the west coast of Spain was the fittest point of departure for India. The latitudes were reckoned in _stadia_ from the Equator to Syracuse, the stadium being about two hundred and one yards and one foot. The determination of the longitude was, however, a far more difficult problem; as the only phenomena whereby men could readily determine the distance between any two places, viz. eclipses of the moon, would have been of no practical value in calculating a ship’s position at sea; moreover, it would not be easy to secure certainty in such observations, nor could they easily be repeated. Hence the ancients were led to depend either on actual survey, or on the vague information obtainable from the reckonings of sailors, or on the itineraries of travellers. We need not, therefore, be surprised when we see how Ptolemy and the greatest of ancient geographers have erred, owing to the impossibility of fixing with even tolerable accuracy the longitudes of different places. It is likely that their practice of constantly landing might have in some degree supplied their deficiency in this particular; but we have now no record of any astronomical observations which were made at sea, by even the most skilful of ancient navigators. A sort of dead-reckoning—an observation of the position of the sun during the day, or of certain stars during night—was the haphazard mode by which their positions at sea were chiefly ascertained. If they had been accustomed to steer a direct course instead of following the coast line, or if they had been acquainted with the properties of the