IV. Researches towards establishing a theory of the dispersion of light. No. IV

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Abstract
Introductory Remarks . In my last communication I laid before the Royal Society a comparison of the results of observation and of theory, with respect to the dispersion of light, in the instances of the refractive indices for the standard rays in fifteen different cases of transparent media (some being the same medium at different temperatures), including those which exhibit the greatest range, and the highest numbers, of any yet subjected to this kind of observation. The agreement with the theory was found to be sufficiently close for the lower cases, but displayed an increasing discrepancy as we advanced towards the higher. The theoretical formula employed was one derived from the undulatory hypothesis, by a process involving some limitations, which rendered it only approximative; and, in conclusion, I remarked that by pursuing the investigation to a greater degree of development, or by adopting methods of a more precise character, it was still reasonably to be hoped that a more close coincidence might be found. I alluded specifically to the methods of M. Cauchy and of Mr. Kelland, as those to which we might look for the means of following up the inquiry with good prospect of success. Of the former (delivered in the Nouveaux Exercices de Mathématiques, Prague, 1835-6, and extending through livraisons 1 to 8 inclusive), I can only say that the investigations are of so extremely elaborate a character, that I was glad, in the first instance at least, to try any other method which might seem to promise results without involving calculations of such overwhelming extent as those by which the distinguished author establishes the exact agreement with theory of all the indices observed by Fraunhofer.

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