Hourglass: An Unpublished Map Projection by John P. Snyder

Hourglass is an equal-area pseudocylindrical map projection developed by John P. Snyder in mid 1940s. It was never published in a detailed way by its author, and only a couple of references exist in the literature since 1991, both of them including a picture but without any mathematical description. In this work, the equations of the projection for the sphere are derived, for both direct and inverse problems, together with a generalization that allow meridians not restricted to straight lines as in the original Snyder version. We prove also that the cylindrical equal-area projection can be derived as a limit case of the generalized Hourglass version. The Hourglass projection was designed only to demonstrate that area preservation in a map projection is a parameter that must never be evaluated in isolation; it is a projection not useful in real applications in surveying nor in cartography, but its formulation, as any other thought of John P. Snyder on map projections, deserves to be known.