both stars and planets to be "quite round". From that point forward, he continued to report that telescopes showed the roundness of stars, and that stars seen through the telescope measured a few seconds of arc in diameter. He also devised a method for measuring the apparent size of a star without a telescope. As described in his Dialogue Concerning the Two Chief World Systems, his method was to hang a thin rope in his line of sight to the star and measure the maximum distance from which it would wholly obscure the star. From his measurements of this distance and of the width of the rope, he could calculate the angle subtended by the star at his viewing point. In his Dialogue, he reported that he had found the apparent diameter of a star of first magnitude to be no more than 5 arcseconds, and that of one of sixth magnitude to be about 5/6 arcseconds. Like most astronomers of his day, Galileo did not recognise that the apparent sizes of stars that he measured were spurious, caused by diffraction and atmospheric distortion, and did not represent the true sizes of stars. However, Galileo's values were much smaller than previous estimates of the apparent sizes of the brightest stars, such as those made by Brahe, and enabled Galileo to counter anti-Copernican arguments such as those made by Tycho that these stars would have to be absurdly large for their annual parallaxes to be undetectable. Other astronomers such as Simon Marius, Giovanni Battista Riccioli, and Martinus Hortensius made similar measurements of stars, and Marius and Riccioli concluded the smaller sizes were not small enough to answer Tycho's argument. Theory of tides Cardinal Bellarmine had written in 1615 that the Copernican system could not be defended without "a true physical demonstration that the sun does not circle the earth but the earth circles the sun". Galileo considered his theory of the tides to provide such evidence. This theory was so important to him that he originally intended to call his Dialogue Concerning the Two Chief World Systems the Dialogue on the Ebb and Flow of the Sea. The reference to tides was removed from the title by order of the Inquisition. For Galileo, the tides were caused by the sloshing back and forth of water in the seas as a point on the Earth's surface sped up and slowed down because