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1727, and senior fellow, 11 June 1739. He took pupils at Cambridge, was master of mechanics to George II, and held the post of mathematical preceptor to William, duke of Cumberland, from June 1739 to July 1740. Smith, like his cousin Cotes, was throughout life the ‘decided partizan’ of Richard Bentley, the master of Trinity, in his struggles with the fellows.

On 16 July 1716 Smith was elected to succeed Cotes as Plumian professor of astronomy, and on 21 May 1718 he was admitted F.R.S. Early in 1739 the observatory over the great gate of Trinity College, for the use of the professor, was completed under his direction (Bentley, Correspondence, ii. 448, 451, 786). The telescope in the library, which is described in Smith's work on ‘Opticks,’ and is shown to strangers as Sir Isaac Newton's telescope, was made for him. He retained the professorship until 1760.

Smith was literary executor to Cotes, and communicated notes for the memoir of him in the ‘General Biographical Dictionary’ of Lockman and others (1736, iv. 441–5). In 1722 he edited and augmented with some of his own theorems Cotes's ‘Harmonia Mensurarum et alia opuscula Mathematica,’ and in 1738 he edited, with notes, his cousin's ‘Hydrostatical and Pneumatical Lectures’ of Cotes. The first work was dedicated to Dr. Mead, the second (which was republished in 1747 and 1775, and translated into French by Le Monnier in 1720) to the Duke of Cumberland. He projected, but did not proceed with, the publication of others of his cousin's works. The monument to Cotes's memory, with the epitaph by Bentley, was erected at the cost of Smith, and he presented to the library of the college in 1758 a marble bust of his cousin by P. Scheemakers.

At Bentley's death Smith was appointed, on 20 July 1742, master of Trinity College, and he also acted in 1742–3 as vice-chancellor of the university. As master his ‘equitable and judicious conduct healed all wounds and conciliated all parties’ (Monk, Life of Bentley, ii. 420). His acts of kindness were numerous, and his influence in the university was considerable. He recommended John Colson [q. v.] to come to Cambridge, and obtained for him in 1739 the Lucasian chair. He advised Richard Cumberland to apply himself to mathematics, and supported his claims to a fellowship. His encouragement gave Bishop Watson, when an undergraduate, ‘a spur to his industry and wings to his ambition,’ for which the bishop always revered Smith's memory. Israel Lyons, the younger, was aided by him in his studies, and in return dedicated to Smith his ‘Treatise of Fluxions,’ 1758. At the contest between Lords Hardwicke and Sandwich for the post of high steward of the university of Cambridge, he was a supporter of Sandwich. He was consequently introduced by Churchill into the poem of the ‘Candidate’ (lines 615–620) as

    Black Smith of Trinity; on Christian ground
    For faith in mysteries none more renowned.

A recluse and a student, Smith, whose health was for many years precarious, lived in the lodge with an unmarried sister, Elizmar (1683–1758), who was buried in the ante-chapel at Trinity, and with a niece. He was fond of music, and played the violoncello. Smith died in the lodge on 2 Feb. 1768, and was buried on the south side of the communion table in the college chapel, where he is commemorated by a Latin epitaph. A funeral oration in Latin on his death was delivered by the Rev. Thomas Zouch in the chapel on 8 Feb. (Zouch, Works, 1820, i. 438–43).

Richard Cumberland records that he was thin in frame, with an aquiline nose, a penetrating eye, and shrill nasal voice. A bust of Smith by P. Scheemakers was placed in the library of the college in 1758, with the inscription ‘Præsenti tibi maturos largimur honores.’ A portrait of him, painted by Vanderbank in 1730, and given by Thomas Riddell, one of the fellows, in 1827, hangs in the lodge; another, painted by J. Freeman in 1783, and said to have been given by the Rev. Edward Howkins in 1779, is in the hall. It was probably paid for by moneys bequeathed by Howkins for that purpose.

Smith's benefactions to the university and to Trinity College were munificent. To the former he left by will the sum of 3,500l. South Sea stock, part of the interest to be applied in a dinner to the trustees, and of the remainder, half to the Plumian professor, and half between two junior B.A.s who have made the greatest progress in mathematics and natural philosophy. The Smith's prizes, which now amount to about 23l. each, ‘proved productive of the best results, and at a later time enabled the university to encourage some of the higher branches of mathematics.’ The college, to which during his lifetime he had presented many pictures and sculptures, obtained under the will the sum of 2,000l. of the same stock, which was ordered to be sold on 15 Dec. 1770, and applied towards the new combination-room in the great court, and the painted window, containing nearly 140 square feet of glass, at the south end of the library. The grotesque design (by Cipriani) for the window, which was completed by 1775, represented George III