Penultimate version of published chapter: J.A. Schuster, “‘Waterworld’: Descartes’ Vortical Celestial Mechanics–A Gambit in the Natural Philosophical Contest of the Early Seventeenth Century”, pp.35-79 in Peter Anstey and John Schuster (eds.) The Science of Nature in the Seventeenth Century: Patterns of Change in Early Modern Natural Philosophy (Springer, 2005) (pages in published version entered in brackets)