This Ivory demonstrates in the volume for 1838 of the 'Philosophical Transactions.' The volumes in 1823 and 1838, contain Ivory's two papers on the 'Theory of Atmospheric Refraction,' a subject which, next to the Theory of Attractions, engaged most seriously his attention on account of its great importance in astronomy and the curious mathematical difficulties which its investigation presents. For each of these papers he was awarded the Royal medal by the Society. Of all his contributions to the 'Transactions,' only one is purely mathematical; this is contained in the volume for 1831, and is entitled, 'On the Theory of Elliptic Transcendants.' Besides these contributions to the Royal Society, Ivory wrote several papers in the Philosophical Magazine of 1821-27; in Maseres's 'Scriptores Logarithmici;' in Leybourne's 'Mathematical Repository;' and in the Supplement to the sixth edition of the Encyclopædia Britannica. In the beginning of 1819 Ivory, finding that his health began to decline under the great exertions which he made in carrying on his scientific researches, and performing his duties as professor, resigned his professorship at Sandhurst and retired into private life. In consideration, however, of his great merit, the pension due for the full period of service required by the regulations was granted to him, although that period had not been completed. After his retirement, Ivory devoted himself entirely to his scientific researches, living in or near London until his death. In 1814 he had received the Copley medal for his communications to the Royal Society; in 1815 he became a Fellow of the same society. He was also an honorary fellow of the Royal Society of Edinburgh; an honorary member of the Royal Irish Academy and of the Cambridge Philosophical Society; a corresponding member of the Institute of France, of the Royal Academy of Sciences at Berlin, and of the Royal Society of Göttingen. In the year 1831, in consideration of the great talent displayed in his investigations, Ivory was recommended by Lord Brougham, whom he had known in early life, to the notice of the King (Wm. IV.), who, with the Hanoverian Guelphic Order of Knighthood, gave him an annual pension of 300_l._, which he enjoyed during the rest of his life; and in 1839 he received the degree of Doctor in Laws from the University of St. Andrews.