Copies of the sentence on Galilei and of his abjuration were at once circulated in Italy and in Roman Catholic circles elsewhere, and a decree of the Congregation of the Index was also issued adding the _Dialogue_ to the three Coppernican books condemned in 1616, and to Kepler’s _Epitome_ of the Coppernican Astronomy (chapter VII., § 145), which had been put on the _Index_ shortly afterwards. It may be of interest to note that these five books still remained in the edition of the _Index of Prohibited Books_ which was issued in 1819 (with appendices dated as late as 1821), but disappeared from the next edition, that of 1835. 133. The rest of Galilei’s life may be described very briefly. With the exception of a few months, during which he was allowed to be at Florence for the sake of medical treatment, he remained continuously at Arcetri, evidently pretty closely watched by the agents of the Holy Office, much restricted in his intercourse with his friends, and prevented from carrying on his studies in the directions which he liked best. He was moreover very infirm, and he was afflicted by domestic troubles, especially by the death in 1634 of his favourite child, a nun in a neighbouring convent. But his spirit was not broken, and he went on with several important pieces of work, which he had begun earlier in his career. He carried a little further the study of his beloved Medicean Planets and of the method of finding longitude based on their movements (§ 127), and negotiated on the subject with the Dutch government. He made also a further discovery relating to the moon, of sufficient importance to deserve a few words of explanation. [Illustration: FIG. 58.—The daily libration of the moon.]