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R. L. Ellis was born at Bath on 25 August 1817 and entered Trinity College in 1836, graduating Senior Wrangler and First Smith's Prizeman in 1840. He was elected to a Trinity Fellowship in the same year, and whilst at Cambridge he conducted research into a variety of subjects, publishing, amongst other works, papers on Roman aqueducts, George Boole's Laws of Thought, the compilation of a Chinese dictionary and the formation of bees' cells and vegetable spirals. During this period he also worked on an edition of the works of Francis Bacon, in collaboration with Douglas Denon Heath and James Spedding. For several years he was editor of the Cambridge Mathematical Journal.
Persistent ill-health, however, eventually forced Ellis to leave Cambridge, and he resigned his Trinity Fellowship in 1849. Moving to the continent, he suffered an attack of rheumatic fever which left him further weakened, and he returned to England the following year in broken health and spirits. His last years were spent near Cambridge at Anstey Hall in Trumpington, where he was able to enjoy the company of old friends and to pursue his studies in spite of recurrent illness. He died on 12 May 1859 at the age of forty-one and was buried at Trumpington.
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