The real arguments for the rotation of the earth were not then known. There were no direct proofs for the progressive revolution of the earth around the sun. _Galileo_ advanced three main arguments for his theory. First, he advanced the argument from the phenomenon of the tides, which, he said, could not be accounted for but by the rotation of the earth: an argument rejected as futile even at that time. Next he argued from certain observations of the spots on the sun: another worthless argument, which others, like _Scheiner_, looked upon as proof of the older theory. The third argument was that the new theory simplified the explanation of certain celestial phenomena; but the scope of this argument, valid though it was in the abstract, could not be expressed or grasped at the time, especially since the corrections of _Tycho de Brahe_ had removed the greatest objections to the Ptolemaic system. The Copernican theory could not be considered certain till the end of the seventeenth century, after _Newton’s_ work on gravitation. Then there were difficulties, the greatest of which was probably the old idea of inertia, which at that time meant only that all bodies tend to a state of rest; hence it seemed impossible that the earth could ceaselessly execute two movements at the same time, around the sun and around its own axis. This notion of inertia had not been doubted in 1616; even _Kepler_ adhered to it. Later on _Galileo_ came very near to the new idea of inertia: that bodies tended to retain their state of repose or motion. But this new notion, like everything else new, gained ground but slowly. Then it was only with great difficulty that he could dispose of the objection that were the earth to speed through space, as the new theory claimed, the atmosphere would take a stormlike motion. Lastly, the philosophical objection had to be met: the sun and other celestial bodies, as far as we can know by observation, are moving; if they do not move, then we must admit that we can know nothing by observation.