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In 1678 a committee of Fellows of the Royal Society was appointed to oversee the production of an ‘English Atlas’ in co-operation with the printer Moses Pitt. The new atlas was to be large and grand, published in eleven volumes with hundreds of maps. It was, as the official proposal put it, no less than ‘a new and Accurat description of the World’. However, it was never brought to completion. This article examines unpublished mathematical papers which document John Pell’s attempts to devise a projectional model in accordance with the published proposals for the atlas. Proposals and advertisements for potential collaborators, composed and circulated by the committee, put forward a representation of idealised cartographic practice. However, when it came to calculating the projection, Pell struggled to accommodate these idealised practices. Pell’s mathematical papers, previously unexamined, afford an unusual perspective on the Royal Society’s methods, and suggest that failures, as well as successes, influenced the developing identity of the scientific community. [ABSTRACT FROM PUBLISHER]