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He was the son of Edward Rudge, a merchant and alderman of Salisbury, who possessed a large portion of the abbey estate at Evesham. He matriculated from Queen's College, Oxford, on 11 October 1781, but took no degree. His attention was early turned to botany, through the influence of his uncle, Samuel Rudge (died 1817), a retired barrister, who formed an herbarium, which passed to his nephew. His uncle's encouragement and the purchase of a fine series of plants from The Guianas, collected by Joseph Martin, led Rudge to study the flora of that country, and to publish between 1805 and 1807 "Plantarum Guianæ rariorum icones et descriptiones hactenus ineditæ," fol. London.