Ptolemy commences with laying down the undoubted truth that the shape of the earth is globular.  The proofs which he gives of this fundamental fact are quite satisfactory; they are indeed the same proofs as we give today.  There is, first of all, the well-known circumstance of which our books on geography remind us, that when an object is viewed at a distance across the sea, the lower part of the object appears cut off by the interposing curved mass of water.

The sagacity of Ptolemy enabled him to adduce another argument, which, though not quite so obvious as that just mentioned, demonstrates the curvature of the earth in a very impressive manner to anyone who will take the trouble to understand it.  Ptolemy mentions that travellers who went to the south reported, that, as they did so, the appearance of the heavens at night underwent a gradual change.  Stars that they were familiar with in the northern skies gradually sank lower in the heavens.  The constellation of the Great Bear, which in our skies never sets during its revolution round the pole, did set and rise when a sufficient southern latitude had been attained.  On the other hand, constellations new to the inhabitants of northern climes were seen to rise above the southern horizon.  These circumstances would be quite incompatible with the supposition that the earth was a flat surface.  Had this been so, a little reflection will show that no such changes in the apparent movements of the stars would be the consequence of a voyage to the south.  Ptolemy set forth with much insight the significance of this reasoning, and even now, with the resources of modern discoveries to help us, we can hardly improve upon his arguments.

Ptolemy, like a true philosopher disclosing a new truth to the world, illustrated and enforced his subject by a variety of happy demonstrations.  I must add one of them, not only on account of its striking nature, but also because it exemplifies Ptolemy’s acuteness.  If the earth were flat, said this ingenious reasoner, sunset must necessarily take place at the same instant, no matter in what country the observer may happen to be placed.  Ptolemy, however, proved that the time of sunset did vary greatly as the observer’s longitude was altered.  To us, of course, this is quite obvious; everybody knows that the hour of sunset may have been reached in Great Britain while it is still noon on the western coast of America.  Ptolemy had, however, few of those sources of knowledge which are now accessible.  How was he to show that the sun actually did set earlier at Alexandria than it would in a city which lay a hundred miles to the west?  There was no telegraph wire by which astronomers at the two Places could communicate.  There was no chronometer or watch which could be transported from place to place; there was not any other reliable contrivance for the keeping of time.  Ptolemy’s ingenuity, however, pointed out a thoroughly satisfactory method