ers 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 deg.)--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. 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 Fortunatae
Insulae, 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,