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In 1792, on the death of his uncle, he returned to Edinburgh, and was much grieved by the loss of his books at sea. He entered the university at Edinburgh, and studied logic under Dr. Finlayson. In 1793 he spent part of the vacation at Liverpool. Here he made the acquaintance of Dr. Currie, the biographer of Burns, who put into his hands the recently published first volume of Dugald Stewart's ‘Elements.’ Next winter he attended Stewart's lectures, and attracted the professor's notice by submitting to him an acute criticism. If, as Stewart held, memory depends upon voluntary attention, how, asked Brown, do we remember dreams? The same objection had been urged in a letter which Stewart had just received from Prevost of Geneva (1755–1819), afterwards professor at Montauban. (Prevost's letter is given in Stewart's ‘Works,’ ii. 491.) Darwin's ‘Zoonomia’ was at this time attracting attention, and Brown wrote some remarks upon it, which, by Stewart's advice, he communicated to Darwin. A correspondence took place (October 1796 to January 1797), in which Darwin showed some annoyance at the sharp treatment of his theories. The remarks were put together by the boyish critic, and published in 1798. They were highly praised by the critics in the literary circles of Edinburgh. Brown had become intimate with young men of promise. He joined the Literary Society in 1796, and a smaller society, formed by some of the members in 1797, which called itself the Academy of Physics, and included Brougham, Jeffrey, Horner, Sydney Smith, Leyden, and others. It flourished for about three years, and helped to bring together the founders of the ‘Edinburgh Review.’ Brown was one of the first reviewers. He wrote an article upon Kant in the second number, which is at least a proof of courage, as it is founded entirely upon Villiers's French account of Kant. Some editorial interference with an article in the third number led him to withdraw from the review. He never afterwards wrote in a periodical. He began to study law in 1796, but finding that it did not suit his health became a medical student from 1798 to 1803. His thesis upon taking his degree, entitled ‘De Somno,’ is praised for the purity of the Latin, in which language, it is said, he could talk as fluently as in English.

In 1804 he published poems in two volumes, and in the same year took part in a famous controversy. The claims of Leslie to the mathematical chair at Edinburgh had been opposed on the ground that he had spoken favourably of Hume's theory of causation. Brown undertook to prove that Hume's theory did not lead to the sceptical consequences ascribed to it. He published ‘Observations on the Nature and Tendency of the Doctrine of Mr. Hume concerning the Relation of Cause and Effect’ in 1804; a second and enlarged edition of which appeared in 1806; and a third, called ‘An Inquiry into the Relation of Cause and Effect,’ in 1818. In 1806 Brown became a partner of Dr. Gregory. In spite of fair professional prospects, his tastes were still philosophical. Attempts had been made in 1799 to obtain his appointment to the chair of rhetoric, and in 1808 to the chair of logic. The tory and church interest was too strong for him. Dugald Stewart's health was now declining, and he obtained the assistance of Brown in lecturing the moral philosophy class in the winter of 1808–9. In the next winter Brown acted for a longer time as Stewart's substitute. His lectures attracted the attendance of professors as well as students, and a committee was formed upon Stewart's reappearance to congratulate him and express admiration for his assistant. In the following May (1810), after an earnest canvass by Stewart himself, and many letters from eminent men, Brown was elected by the town council as Stewart's colleague. He held this position for the rest of his life. His lectures were written at high pressure. He began to write each on the evening before its delivery, sat up late—several times all night in the first winter—and did not finish till the clock struck twelve, the hour of lecturing. Three volumes were thus written in his first session, and the fourth in the second. He lived quietly with his mother and sisters, hospitably entertaining visitors to Edinburgh. His chief amusement was walking, and he had a passion for hill climbing. He also found time to compose a quantity of indifferent poetry, which he alone preferred to his philosophy. In 1814 he finished and published anonymously his ‘Paradise of Coquettes,’ begun six years before. In 1815 he published the ‘Wanderer in Norway,’ an elaboration of some verses in his first volumes, suggested by Mary Wollstonecraft's ‘Letters from Norway.’ In 1816 he published the ‘Warfiend,’ in 1817 the ‘Bower of Spring,’ in 1818 ‘Agnes,’ and in 1819 ‘Emily.’ A collected edition in 1820, in four volumes, includes these and a second edition of a poem called the ‘Renovation of India,’ originally written for a college prize, and published when, after three years, no award was made. He was much grieved by the death, in 1817, of his mother, to whom he had been most tenderly attached. In 1819 he began to prepare a text-book of his lectures. He fell ill, and