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 busily occupied in tutorial and literary work until 1803, when he accepted the college living of Derryvullane in the diocese of Clogher, In 1796 he delivered, but did not publish, a course of lectures on the Donnellan foundation 'On the Causes which impeded the further Progress of Christianity.' In 1797 he published a critical edition of Dionysius Longinus 'De Sublimitate,' Dublin, 8vo, 2nd edit. 1820. In 1799 appeared his 'Elements' Natural Philosophy,' Dublin, 8vo, 2nd edit. 1820. An enthusiastic member of the historical society founded by Grattan, he held from 1799 until 1803 the post of assistant professor of modern history, and from 1803 to 1811 that of lecturer on the same subject in the university. His lectures at first attracted but little attention, but grew steadily in popularity, and were afterwards published under the title 'Lectures on the Philosophy of Modern History delivered in the University of Dublin,' Dublin, 1816-28, 8 vols. 8vo. Though hardly justifying their somewhat pretentious title, they are characterised by width of reading, grasp of principle, and methodical arrangement. A free and carefully revised abridgment, entitled 'History Philosophically Illustrated from the Fall of the Roman Empire to the French Revolution,' appeared in 1832, London, 4 vols. 8vo, reprinted 1848-9 and 1852, ed. Bohn.

In 1817 Miller had been appointed head-master of the Royal School, Armagh, a post which he held until shortly before his death. Miller began life an Arian in theology and a liberal in politics, but was gradually converted to strongly orthodox protestant church and state principles. In 1825 he published an ingenious pamphlet entitled 'Observations on the Doctrines of Christianity in reference to Arianism, illustrating the Moderation of the Established Church, and on the Athanasian Creed, purporting to prove that it is not damnatory, nor metaphysical, nor contradictory,' London, 1825, 8vo; and in 1826 'The Athanasian Creed: with Explanatory Observations,' Dublin, 8vo. In the latter year the celebrated 'Dissertation' by (1789-1882) [q. v.] 'On the Use and Importance of Unauthoritative Tradition,' which heralded the rise of the tractarian movement (cf., Apologia, chap, i.), was met by Miller with a learned and ably reasoned defence of the principles of the reformation, entitled 'An Historical Review of the Plea of Tradition as maintained in the Church of Rome: with Strictures on Hawkins's Dissertation,' London, 8vo. He also issued a manifesto against the emancipation of the Roman catholics, entitled 'The Policy of the Roman Catholic Question discussed in a Letter to the Right Hon. W. C. Plunket,' London, 1826, 8vo. In October 1840 he published a trenchant 'Letter to the Rev. E. B. Pusey, D.D., in reference to his Letter to the Lord Bishop of Oxford' (London, 8vo), which perhaps helped to elicit Newman's celebrated 'Tract XC.,' to which he virtually replied in 'A Second Letter to the Rev. E. B. Pusey in reference to his Letter to the Rev. R. W. Jelf, D.D., Canon of Christ Church,' London, September 1841, 8vo (cf. the correspondence between Miller and Professor Sewell in the Irish Ecclesiastical Journal, November 1840 et seq.) In 1843 Miller was appointed vicar-general of the diocese of Armagh, of which he had for some time previously been surrogate. His judgments in this capacity were marked by ability and settled some important points on the law of marriage and divorce, lie died in Armagh on 6 Oct. 1848, and was buried in St. Mark's churchyard. For the last forty years of his life he had been a strict vegetarian.

Miller was a member of the Royal Irish Academy, in the 'Transactions' of which learned society will be found three papers by him, viz.: 'On the Nature and Limits of Certainty and Probability,' and 'On the Origin and Nature of our Idea of the Sublime,' both in vol. v. (1793), and 'Observations on the Theory of Electric Attraction and Repulsion' (1799). To the 'British Critic,' January 1828, he contributed an article on 'The Irish Reformation of 1826 and 1827;' to Blackwood's 'Edinburgh Magazine,' November 1829, 'Considerations on the Law of Divorce.' He was also a contributor to the 'Irish Ecclesiastical Journal,' 1840-6, and the 'British Magazine,' 1845-6. Besides the treatises and pamphlets above mentioned, Miller published various sermons and the following miscellanea: 'An Examination of the Charters and Statutes of Trinity College, Dublin, in regard to the supposed distinction between the College and the University,' Dublin, 1804, 8vo. 'A Lecture on the Origin and Influences of the Wars of the French Revolution,' Dublin, 1811, 8vo. 'A Letter to the Lord Primate of Ireland on the manner in which Christianity was taught by our Saviour and his Apostles,' London, 1822, 8vo. 'The Temptations of Jesus Christ in the Wilderness explained as symbolically representing the Trials of the Christian Church,' London, 1826, 8vo. 'The Question of the Change of the Sabbath examined, in reference to the Jewish Scriptures, for obviating the inferences both of Jews and of Roman Catholics,' London, 1829, 8vo. 'Examination of the Act to amend the Representation