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Rh allowed so much to be spent in such ways, but that he felt bound to take his father's place, whatever the cost. It was in 1601 that he began to earn additional fees by undertaking the tuition during the holidays, which he usually spent at Florence, of the Grand Duke's son, Cosmo, both of whose parents held Galileo in high esteem, the Grand Duke regarding him as the greatest mathematician in Christendom, while the Grand Duchess Cristina believed him the greatest of astrologers. In spite of the vogue of this pseudo-science, it is difficult to suppose that Galileo had any real faith in astrology, though he did not refuse to cast horoscopes, just as he lectured on Ptolemy's system after he became a convinced Copernican.

In 1602 Galileo invented his air-thermometer which was not perfected until some years after his death. Two years later the sudden appearance of a bright new star in Ophiuchus provided him with a new interest, and he lectured on it in the great hall of the University. The ordinary lecture rooms were frequently unable to hold the large numbers of students who flocked to hear the new ideas propounded by Galileo, and it is said that sometimes even the great hall was insufficient, so that he had to lecture in the open air. Galileo's conclusions about the new star, though not now acceptable, included at any rate the fact that it was as distant as other stars and not an atmospheric phenomenon. The suggestion that it belonged to the region regarded by the Aristotelians as perfect and unchangeable led to direct conflict, and Galileo openly argued in favour of the theory of Copernicus against that of Ptolemy, who had followed Aristotle. His third term of six years began in 1604, but there was as before delay on the part of the Venetian Council. Once more, in spite of the objections urged by some, among which his irregular household was not forgotten,