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160 abandon the said opinion," which the Cardinal did. Immediately afterwards a decree was issued condemning the opinions in question and placing on the well-known Index of Prohibited Books three books containing Coppernican views, of which the De Revolutionibus of Coppernicus and another were only suspended "until they should be corrected," while the third was altogether prohibited. The necessary corrections to the De Revolutionibus were officially published in 1620, and consisted only of a few alterations which tended to make the essential principles of the book appear as mere mathematical hypotheses, convenient for calculation. Galilei seems to have been on the whole well satisfied with the issue of the inquiry, as far as he was personally concerned, and after obtaining from Cardinal Bellarmine a certificate that he had neither abjured his opinions nor done penance for them, stayed on in Rome for some months to shew that he was in good repute there.

127. During the next few years Galilei, who was now more than fifty, suffered a good deal from ill-health and was comparatively inactive. He carried on, however, a correspondence with the Spanish court on a method of ascertaining the longitude at sea by means of Jupiter's satellites. The essential problem in finding the longitude is to obtain the time as given by the sun at the required place and also that at some place the longitude of which is known. If, for example, midday at Rome occurs an hour earlier than in London, the sun takes an hour to travel from the meridian of Rome to that of London, and the longitude of Rome is 15° east of that of London. At sea it is easy to ascertain the local time, e.g. by observing when the sun is highest in the sky, but the great difficulty, felt in Galilei's time and long afterwards (chapter, §§ 197, 226), was that of ascertaining the time at some standard place. Clocks were then, and long afterwards, not to be relied upon to keep time accurately during