He gave evidence before commissions, and was on the council of the Decimal Association formed in 1854. A commission finally decided against the measure in 1859, and the agitation dropped.
De Morgan's energy, however, was chiefly absorbed by his voluminous writings upon mathematical, philosophical, and antiquarian points. The most important controversy in which he was engaged arose from a tract ‘On the Structure of the Syllogism,’ read before the Cambridge Philosophical Society 9 Nov. 1846, and his work upon ‘Formal Logic,’ published in 1847. De Morgan had consulted Sir William Hamilton upon the history of the Aristotelian theory. Hamilton gave some information, and afterwards accused De Morgan of unfairly appropriating his doctrine of the ‘quantification of the predicate.’ He returned a copy of the ‘Formal Logic’ presented to him by the author uncut. The value of the doctrine itself may be disputed, but De Morgan's claim to independence is unimpeachable. In 1852 some courtesies were exchanged between the disputants, and Hamilton must have been pacified (Mrs. De Morgan, p. 161). Some of De Morgan's later speculations upon this subject were published in the Transactions of the Cambridge Philosophical Society. His logical writings are not easy reading, and have perhaps attracted less attention than they deserve. They have been in a great degree superseded by the investigations of Boole.
In 1866 the chair of mental philosophy and logic at University College became vacant. A discussion arose as to the true interpretation of the principle of religious neutrality avowedly adopted by the college. One party held that it should include Mr. James Martineau, who, as a unitarian minister, was pledged to maintain the creed of a particular sect. De Morgan, on the other hand, held that any consideration of a candidate's ecclesiastical position or religious creed was inconsistent with the principle. He thought that the refusal to appoint Mr. Martineau was in reality an act of intolerance dictated by a dislike to the candidate's religious philosophy. De Morgan had always been exceedingly sensitive upon this question of religious neutrality, and had thought of resigning his post in 1853, when the college accepted a legacy of books (from Dr. W. G. Peene), which were to be selected by members of the church of England. He now resigned his office in a letter dated 10 Nov. 1866. Some of his old pupils begged him to allow his picture to be taken for the library of ‘our old college.’ He objected on principle to testimonials, and replied that ‘our old college no longer exists.’ It lived only so long as it refused all religious disqualifications. Though no personal bitterness was produced, De Morgan felt the blow so keenly that it injured his health. The last important work which he undertook was a calculation for the Alliance Assurance Company.
In October 1867 he was saddened by the loss of his son George Campbell, a youth of great promise, who had been a founder and secretary of the Mathematical Society. His father was the first president, and gave an inaugural lecture on 16 Jan. 1865. The son became mathematical master in University College school in 1866, and at the time of his death was vice-principal of University Hall, Gordon Square. In 1868 De Morgan had himself a sharp attack of congestion of the brain. He afterwards was able to arrange his own books on moving to a new house. He read the Greek testament carefully, and was interested in a proposed ‘Free Christian Union.’ The death of his daughter Helen Christiana in August 1870 gave a fresh shock to his nerves, and he afterwards sank gradually and died 18 March 1871. A year before his death an annuity of 100l. was obtained from the government and accepted with some reluctance.
De Morgan's library consisted at the end of his life of about three thousand volumes. He was a genuine book-hunter, though his means compelled him to limit himself to occasional treasures from bookstalls. He made many quaint marginal and learned annotations, and turned his bibliographical researches to good account in his writings. His library was bought after his death by Lord Overstone and presented to the university of London.
De Morgan was a man of great simplicity and vivacity of character, of affectionate disposition, and entire freedom from all sordid self-interest. He had a love of puns, and all ingenious puzzles and paradoxes, which makes some of his books, especially his ‘Budget of Paradoxes’ (1872, reprinted from the ‘Athenæum’), as amusing as they are learned. He held to his principles with a certain mathematical rigidity which excluded all possibility of compromise and gave ground for the charge of crotchetiness on some important occasions. But this was at worst the excess of a lofty sense of honour. His mathematical writings include valuable text-books, and many speculations of great interest upon the logic of mathematical reasoning. ‘His “double algebra” was the forerunner of quaternions, and contained the complete geometrical interpretation of the √-1’ (Monthly Notices). Sir W. Rowan Hamilton acknow-
