He studied law, and in 1834 took his degree of LL.B., hut did not practise. He assisted his father in his literary work, and was for some years chairman of the council of the Society of Arts, besides taking a prominent part in the affairs of the Royal Horticultural Society and other bodies. He was one of the most zealous promoters of the Great Exhibition (1851), and a member of the executive committee. At the close of the exhibition he was honoured by foreign sovereigns, and the queen offered him knighthood, which, however, he did not accept; he also declined a large remuneration offered by the royal commission. In 1853 Duke was one of the English commissioners at the New York Industrial Exhibition, and prepared a report on it. He again declined to receive any money reward for his services.
He was appointed one of the five royal commissioners for the Great Exhibition of 1862; and soon after the death of the prince consort he was created a baronet. In 1865 he entered parliament as member for Wallingford. In 1869 he was sent to Russia as representative of England at the horticultural exhibition held at St Petersburg. His health, however, had been for some time failing, and he died suddenly in that city, on the 10th of May 1869. A selection from his writings, Papers of a Critic (2 vols., 1875), contains a biographical sketch by his son.
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