The only child of Richard and Catherine Elrington of Dublin, he was born near that city on 18 December 1760. He entered Trinity College Dublin, on 1 May 1775 as a pensioner, under the tutorship of the Rev. Dr. Drought, and was elected a Scholar in 1778. He graduated B.A. in 1780, M.A. in 1785, and B.D. and D.D. in 1795. In 1781 he was elected a fellow of his college. He was Donegall Lecturer of Mathematics, and in 1794 he was the first to hold the office of Donnellan Divinity Lecturer. In 1795 he was appointed Archbishop King's Lecturer in Divinity, succeeded to a senior fellowship, and also became the third Erasmus Smith's Professor of Mathematics. In 1799 he exchanged the Erasmus Smith's professorship of mathematics for that of natural philosophy. In 1789, he published the mathematical treatise Euclidis Elementorum Sex Libri Priores, Cum Notis, whose 10th edition appeared in 1833. On resigning his fellowship in 1806 Elrinton was presented by his college to the rectory of Ardtrea, in the diocese of Armagh, which he held until December 1811. He resigned, having been appointed to the provostship of Trinity College. During his tenure of this office he was the acting manager of almost every public board, and a supporter of charitable institutions. Elrington was advanced on 25 September 1820 to the bishopric of Limerick, and on 21 December 1822 he was translated to Leighlin and Ferns. While on his way to attend Parliament duties in London he died of paralysis at Liverpool on 12 July 1835. He was buried under the chapel of Trinity College Dublin, in which there was a monument with a Latin inscription to his memory. Another monument was erected by his clergy in the cathedral church of Ferns. Elrington was an active member of the Royal Irish Academy, and of other literary and scientific societies. The Elrington theological essay prize was instituted in Trinity College in 1837. A portrait of the bishop was painted in 1820 for his brother, Major Elrington, by Thomas Foster; engraved by William Ward, it was published in 1836 by Graves & Co. There was a marble bust in the library of Trinity College.
Works
His works are:
'Refutation of the Arguments in Dr. Butler's Letter to Lord Kenmare,' 1787.
'Reply to the Third Section of Mr. O'Leary's Defence,' 1787.
'Thoughts on the Principles of Civil Government, and their Foundation in the Law of Nature, by S.N.' , 1793.
'Enquiry into the Consistency of Dr. Troy's Pastoral Instruction,' 1793.
'Sermon on the Death of Matthew Young, D.D., Bishop of Clonfert; with some Anecdotes of his Life', 1800.
'The Vindication of Dr. Troy Refuted,' 1804.
'The Clergy of the Church of England truly Ordained, in reply to Ward's Controversy of Ordination; with an Appendix,' 1808.
'Letters on Tythes, first published in the "Dublin Journal"', 1808.
'Reflections on the Appointment of Dr. Milner as the Political Agent of the Roman Catholic Clergy of Ireland,' 1809.
'Remarks occasioned by the Supplement and Postscript to the second edition of Dr. Milner's Tour in Ireland,' 1809.
'Letter to the Right Hon. W. W. Pole on the Proposal for a Commutation of Tythes in Ireland,' 1810.
'The Validity of English Ordination Established, in answer to the Rev. P. Gandolphy's Sermon on John x. 1,' 1818.
'Inquiry whether the Disturbances in Ireland have originated in Tythes,' 1822; second edition, with an Appendix, 1823.
'Observations on J.K.L.'s Letter to the Marquess Wellesley; on Tracts and Topics by E. Barton; and on the Letter to Mr. Abercrombie,' 1824.
'Review of the Correspondence between the Earl of Mountcashell and the Bishop of Ferns, with the Letters,' 1830.
'Reply to John Search's Considerations on the Law of Libel as relating to Publications on the subject of Religion,' 1834.
Elrington also published sermons and charges, and edited, for the use of Trinity College, 'Euclid's Elements, the first Six Books,' 1788 ; 'Locke on Government, with Notes,' 1798; and 'Juvenalis et Persius, edito expurgata,' 1808.
