Ptolemy correctly argued that the earth itself is a sphere that is curved from east to west, and from north to south as well, clinching his argument, as we do to-day, by the visibility of objects at sea, the lower portions of which are at first concealed from our view by the curved surface of the water which intervenes. To Ptolemy also the earth is at the center of the celestial sphere, and it has no motion of translation from that point; but his argument fails to prove this. Truth and error, indeed, are so deftly intermingled that one is led to wonder why the keen intelligence of this great philosopher permitted him to reject the simple doctrine of the earth's rotation on its axis. But if we reflect that there was then no science of natural philosophy or physics proper, and that the age was wholly undeveloped along the lines of practical mechanics, we shall see why the astronomers of Ptolemy's time and subsequent centuries were content to accept the doctrines of the heavens as formulated by him. When it came to explaining the movements of the "wandering stars," or planets, as we term them, the Ptolemaic theory was very happy in so far as accuracy was concerned, but very unhappy when it had to account for the actual mechanics of the cosmos in space. Sun and moon were the only bodies that went steadily onward, easterly: whereas all the others, Mercury, Venus, Mars, Jupiter, Saturn, although they moved easterly most of the time, nevertheless would at intervals slow down to stationary points, where for a time they did not move at all, and then actually go backward to the west, or retrograde, then become stationary again, finally resuming their regular onward motion to the east. To help out of this difficulty, the worst possible mechanical scheme was invented, that known as the epicycle. Each of the five planets was supposed to have a fictitious "double," which traveled eastward with uniformity, attached to the end of a huge but mechanically impossible bar. The earth-centered circle in which this traveled round was called the "deferent." What this bar was made of, what stresses it would be subjected to, or what its size would have to be in order to keep from breaking--none of these questions seems to have agitated the ancient and medieval astronomers, any more than the flat-earth astronomy of the Hindu is troubled by the necessity of something to hold up the tortoise that holds up the elephant that holds up the earth.