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William Dempsey entered the Dublin Society's School of Drawing in Architecture on 5 June 1788 and won a second-class prize on 7 April 1791. He was awarded one of two first-class prizes on 15 March 1792. Another William Dempsey entered the School on 17 Dec 1818. William Dempsey was one of a number of persons of the same surname who attended the school during the latter half of the eighteenth century. Luke Dempsey was admitted on 11 May 1769, Langton Dempsey on 5 Dec 1776, Richard Dempsey on 26 Jul 1787 and Edward Dempsey on 3 Mar 1791.
William Dempsy (sic), builder, signed a plan, elevation and estimate for an Erasmus Smith school at Gortin, Co. Tyrone, dated 1813, which is in the Erasmus Smith Schools drawings collection at the High School, Rathgar, Dublin.