• DOI:10.1086/349399
• Corpus ID: 145493641

Descartes and the Radius of the Rainbow

@article{Boyer1952DescartesAT,
  title={Descartes and the Radius of the Rainbow},
  author={Carl B. Boyer},
  journal={Isis},
  year={1952},
  volume={43},
  pages={95 - 98}
}

• C. Boyer
• Published 1 July 1952
• History
• Isis

EW scientists have been subjected to charges of plagiarism more frequently than Descartes (I596-I650). In particular, each of the appendices to the Discours de la methode has been questioned. La dioptrique long was believed to have been derived from work of Snell;' Les meteores once was regarded as inspired by the ideas of Kepler and De Dominis ;2 and in La geometrie some critics thought they saw unacknowledged indebtedness to Harriot and Oresme.3 None of these charges has been substantiated; yet in each case Descartes was neither so original nor so definitive as he had presumed. In each of the appendices he had been anticipated by some, corrected by others, on at least one essential point. Thus, as is now well known, the Cartesian theory of the rainbow had been given in qualitative form by Theodoric of Freiburg (as well as by Muslim scholars) in the fourteenth century,4 and in the eighteenth century it was superseded by the theory of Young and Airy.5 It is the purpose of this note to call attention to an overlooked detail in his work on the rainbow in which Descartes failed adequately to appreciate his relationship to his predecessors and successors. Descartes believed, mistakenly, that he was the first one to study the rainbow through experiments with a large spherical globe of water which served as a magnified raindrop. On the basis of observations and calculations of the paths of a great number of rays (Descartes reports that he studied io,ooo!) striking the upper half of the globe, he found that the radius of the rainbow is about 420.6 More accurately, he placed the greatest radius at 41?47' and the smallest at about 40?. Descartes was justifiably proud of this achievement, but he carried his boast too far. He claims to have been aware of but one earlier estimate of the size of the bow, a value of 450 given "par la creance commune" and which he ascribed to Maurolycus.7 On the basis of this impression Descartes remarked, "Ce qui monstre le peu de foy qu'on doit adiouster aux observations qui ne sont pas accompagnees de la vraye raison." 8 Yet Maurolycus himself had queried, following his purported demonstration that the radius is 450, "But how does it happen, you ask, that the altitude of the rainbow is not exactly 450, but a little less as ascertained by observation? I do not know how to answer this or what reason I may offer, unless it be that the falling drops are somewhat elongated or somewhat flattened, and thus, varying from the spherical form, change the angle of reflection and hence also the straightness of the ray which in the case of a perfect sphere comes back at an angle of forty-five degrees." 9 Hence, either Maurolycus himself had made a more careful measurement or else he was aware of an older and more accurate determination. That the latter probably was the case is indicated by the fact that closer approximations were given by his contemDoraries. In