really identical with the sun's orbit. It would seem that these very obvious laws could not escape a geometer of the caliber of Ptolemy. It appears that he never attempted the generalization; nor did his successors till the time of Copernicus. Each case was treated separately. When each was solved the explanation was complete. It required fourteen hundred years to make a generalization which is, in reality, simple, almost obvious.
Ptolemy's explanation of the system of the world accounted for all the facts known to him. As time went on, those assiduous observers, the Arabians, discovered other irregularities in the lunar and planetary motions unknown to Ptolemy. Every new irregularity required a new epicycle to explain it and in time the commentators of Ptolemy had added cycle on cycle, orb on orb until more than sixty spheres were necessary. The system lost its simplicity as more and more facts had to be explained and became a tangle of single instances, a web of particularities. It was never refuted. It broke of its own weight. The heliocentric hypothesis of Copernicus explained all these matters so simply, so convincingly, that it was soon adopted by all competent persons who examined it. The simplicity of a hypothesis is, of course, no evidence of its truth. Many modern theories are complex to a degree, but this is no proof that they are not true.
A layman seldom understands the attitude of a man of science towards 'theories,' as they are often half-contemptuously termed. Theory is popularly used as a synonym of opinion. 'His theory' is thought of as merely 'his opinion.' When, let us ask, is a science perfect? It is perfect when the circumstances of a phenomenon that is to occur in the future can be as accurately predicted now, as they can subsequently be observed when the actual phenomenon occurs. The 'theory' of transits of Venus over the sun's disc is practically perfect. We can predict the conditions of the next transit in A. D. 2004 almost as well as the astronomers of that day can observe it. The theory of Neptune's motion is so well known that the position of the planet in 1999 can be now predicted almost as accurately as it can be observed in that year. The theory of the circulation of the sap in plants is, on the other hand, far from perfect. We understand its general laws very well, but it is quite impossible to predict the circumstances for any particular plant in any particular season. The theories of hail, of lightning, of auroras and many others are in the same state.
It is obvious that if our own methods and instruments of observation are greatly improved at any particular epoch the science to which they belong will cease to be perfect even if it were a perfect science in the first instance. Tycho Brahe observed the longitudes of the stars by the naked eye. It is impossible, as we now know, to fix a longitude by such observations within one minute of arc (1′). This depends on the very constitution of the eye. When the telescope was
