Experiment and mathematics in Newton's theory of color

On 18 January 1672 Isaac Newton wrote Henry Oldenburg, Secretary of the Royal Society, that he would send him a paper that he modestly described as “being in my Judgment the oddest if not the most considerable detection $wch$ hath hitherto beene made in the operations of Nature.” Newton was not referring to his theory of gravitation—that was still more than a dozen years away—but rather to his new theory of the nature of white light and color. He had discovered that rays of different color have different degrees of refrangibility—or, as we would put it, that the index of refraction varies with wavelength—and that white light and, in particular, sunlight consist of a mixture of innumerable colors. Less than three weeks later, as Newton promised, he sent to the Royal Society his famous paper, “A New theory about light and colors,” which was published at once in the Philosophical Transactions. In the “New theory” he boldly proclaims: “A naturalist would scearce expect to see $ye$ science of [colours] become mathematicall, & yet I dare affirm that there is as much certainty in it as in any other part of Opticks. For what I shall tell concerning them is not an Hypothesis but most rigid consequence, not conjectured by barely inferring ‘tis thus because not otherwise or because it satisfies all phaenomena (the Philosophers universall Topick), but evinced by $ye$ mediation of experiments concluding directly & $wth$out any suspicion of doubt.”