In 1833 Mr Gregory’s name was entered at Trinity College, Cambridge, and shortly afterwards he went to reside there. He took with him a most unusual amount of knowledge on almost all scientific subjects, in fact many men said that it was the diffuseness of his learning that prevented him from taking the first place in the mathematical honours in that university; for when the tripos came he was only fifth wrangler. A few months after his arrival in Cambridge he agreed to act as assistant to the Professor of Chemistry, and he was one of the founders of the Chemical Society, and occasionally gave very charming lectures in their rooms. His other pursuits were botany, natural philosophy, and astronomy, but his most serious study was of course mathematics. After taking his degree of B.A. in 1837, he felt himself more at liberty to follow original speculation, and turned his attention to the general theory of the combination of symbols. His studies in this subject appeared from time to time in the _Cambridge Mathematical Journal_, of which Duncan Farquharson Gregory was editor, with only an interval of a few months, from its first appearance till shortly before his death. Mr Gregory was in 1840 elected a Fellow of Trinity College, and he took his M.A. degree in the following year. In that year, too, he was appointed to fill the office of moderator in the Mathematical Tripos. This position, which is regarded as one of the most honourable of those to which the younger members of the university may aspire, was filled by him with great success. His most considerable book (though possibly less well known than his lucid work on solid geometry), appeared about this time. It is entitled _Collection of Examples of the Processes of the Differential and Integral Calculus_, and was thoughtful and original. At first his plan had been to edit a second edition of a work with a similar title, which twenty-five years before had come from the pens of Herschel, Peacocke, and Babbage, but as he considered this, he discovered what immense strides had been made in the general aspect of mathematics. The mathematical theories of heat, light, electricity, and magnetism were all new, and they required a fresh treatment. Thus he undertook the book which brought him so much honour. Gregory had an absolute passion for mathematics. ‘All these things seem to me,’ he said once, while turning over the pages of Fourier’s great work on heat, ‘to be a kind of mathematical paradise,’ and the enjoyment comes out all through his book. He contested unsuccessfully with Professor Kelland the Chair of Mathematics in the University of Edinburgh, and in 1841 was offered the corresponding chair in Toronto, which, however, he declined; and it was well that he did so, for in the following year he had the first attack of the illness which was to end fatally for him. In the spring he left Cambridge never to return again.