Summary Descartes's model for the invisible world has long seemed confined to explanations of known phenomena, with little if anything to offer concerning the empirical investigation of novel processes. Although he did perform experiments, the links between them and the Cartesian model remain difficult to pin down, not least because there are so very few. Indeed, the only account that Descartes ever developed which invokes his model in relation to both quantitative implications and to experiments is the one that he (...) provided for the rainbow. There he described in considerable detail the appearances of colours generated by means of prisms in specific circumstances. We have reproduced these experiments with careful attention to Descartes's requirements. The results provide considerable insight into the otherwise fractured character of his printed discovery narrative. By combining reproduction with attention to the rhetorical structure of Descartes's presentation, we can show that he worked his model in conjunction with experiments to reach a fully quantitative account of the rainbow, including its colours as well as its geometry. In this one instance at least, Descartes produced just the sort of explanatory novelties that the young Newton later did in optics. That Descartes's results in respect to colour are in hindsight specious is of course irrelevant. (shrink)