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 30 had been accumulating from the time of Erastosthenes to his own day, which we may fix at about 150 A.D. He took all the information he could find in the writings of the preceding four hundred years, and reduced it all to one uniform scale; for it is to him that we owe the invention of the method and the names of latitude and longitude. Previous writers had been content to say that the distance between one point and another was so many stadia, but he reduced all this rough reckoning to so many degrees of latitude and longitude, from fixed lines as starting-points. But, unfortunately, all these reckonings were rough calculations, which are almost invariably beyond the truth; and Ptolemy, though the greatest of ancient astronomers, still further distorted his results by assuming that a degree was 500 stadia, or 50 geographical miles. Thus when he found in any of his authorities that the distance between one port and another was 500 stadia, he assumed, in the first place, that this was accurate, and, in the second, that the distance between the two places was equal to a degree of latitude or longitude, as the case might be. Accordingly he arrived at the result that the breadth of the habitable globe was, as he put it, twelve hours of longitude (corresponding to 180°)—nearly one-third as much again as the real dimensions from Spain to China. The consequence of this was that the distance from Spain to China westward was correspondingly diminished by sixty degrees (or nearly 4000 miles), and it was this error that ultimately encouraged Columbus to attempt his epoch-making voyage.

Ptolemy's errors of calculation would not have been so extensive but that he adopted a method of measurement which made them accumulative.