Ptolemy's errors of calculation would not have been so extensive but that he adopted a method of measurement which made them accumulative. If he had chosen Alexandria for the point of departure in measuring longitude, the errors he made when reckoning westward would have been counterbalanced by those reckoning eastward, and would not have resulted in any serious distortion of the truth; but instead of this, he adopted as his point of departure the Fortunatæ Insulæ, or Canary Islands, and every degree measured to the east of these was one-fifth too great, since he assumed that it was only fifty miles in length. I may mention that so great has been the influence of Ptolemy on geography, that, up to the middle of the last century, Ferro, in the Canary Islands, was still retained as the zero-point of the meridians of longitude. Another point in which Ptolemy's system strongly influenced modern opinion was his departure from the previous assumption that the world was surrounded by the ocean, derived from Homer. Instead of Africa being thus cut through the middle by the ocean, Ptolemy assumed, possibly from vague traditional knowledge, that Africa extended an unknown length to the south, and joined on to an equally unknown continent far to the east, which, in the Latinised versions of his astronomical work, was termed "terra australis incognita," or "the unknown south land." As, by his error with regard to the breadth of the earth, Ptolemy led to Columbus; so, by his mistaken notions as to the "great south land," he prepared the way for the discoveries of Captain Cook. But notwithstanding these errors, which were due partly to the roughness of the materials which he had to deal with, and partly to scientific caution, Ptolemy's work is one of the great monuments of human industry and knowledge. For the Old World it remained the basis of all geographical knowledge up to the beginning of the last century, just as his astronomical work was only finally abolished by the work of Newton. Ptolemy has thus the rare distinction of being the greatest authority on two important departments of human knowledge--astronomy and geography--for over fifteen hundred years. Into the details of his description of the world it is unnecessary to go. The map will indicate how near he came to the main outlines of the Mediterranean, of Northwest Europe, of Arabia, and of the Black Sea. Beyond these regions he could only depend upon the rough indications and guesses of untutored merchants. But it is worth while referring to his method of determining latitude, as it was followed up by most succeeding geographers. Between the equator and the most northerly point known to him, he divides up the earth into horizontal strips, called by him "climates," and determined by the average length of the longest day in each. This is a very rough method of determining latitude, but it was probably, in most cases, all that Ptolemy had to depend upon, since the measurement of angles would be a