If we contrast ancient with modern scientific theories we find that the chief distinguishing characteristic of the former is that they employ principles drawn from other branches of knowledge or speculation. It would be, perhaps, rash to say that modern science, in all its branches, is yet completely autonomous; sometimes, for instance, it seems to make assumptions which are the result of an uncritical philosophy, but even the grossest of these examples, compared with many celebrated early scientific theories, shows how great is the purification that has been effected. The chief error of the old speculators consisted in imagining that the world is a more obvious unity than we have now any reason to suppose. Hence they were always willing to argue by “analogy,” comparing terms between which we cannot now find the slightest resemblance. The method was not only illegitimate, but sometimes led to quite unnecessary complexities of explanation. The Ptolemaic system of astronomy, for instance, conceived as the theory that the heavenly bodies revolve round the earth, was a perfectly reasonable and satisfactory theory. It was capable of explaining all the observed planetary motions, except a few minute irregularities requiring precise measurements for their detection. Its proper development required, of course, complete docility in face of the facts. But in its actual development it was forced to accommodate itself to quite other considerations. It had to take into account the venerable principle that, the celestial bodies being obviously sublime, incorrupt and perfect, their orbits must be perfect and described with uniform velocities. The only possible perfect orbit was as obviously a circle. Hence the Ptolemaic theory was loaded with the task of explaining the observed heavenly motions on two grounds: first, that the earth was stationary and at the centre of the system, and second, that the planetary orbits were circular and described with unvarying velocities. Alternative hypotheses were not only stupid but impious. The task thus set to the early astronomers was one of considerable difficulty.