Unpublished paper, 'Memoir of the binomial calculus, the Irish calculation' by John Walsh Walsh writes on the definitions of mathematical terms, focusing particularly on the definitions of 'addition' and 'demonstration'. He then presents his own theory of analysis using binomial calculus. A short note at the end of the paper indicates that this is an improvement on a previous paper, and that he had initially submitted the paper to the Institute of France, fearing opposition at the Royal Society and particularly from Dr [John] Brinkley. Subject: Mathematics Written by Walsh at 22 Tuckey Street in Cork [Ireland] and addressed to W T [William Thomas] Brande at 20 Grafton Street, London. 11 November 1823