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IV. Researches towards establishing a Theory of the Dispersion of Light. No. IV. 

 By the Rev. Baden Powell, M.A. F.R.S. F.G.S., Savilian Professor of Geometry 

 in the University of Oxford. 



Received January 11, — Read February 8, 1838. 



Introductory Remarks. 



In my last communication I laid before the Royal Society a comparison of the re- 

 sults of observation and of theory, with respect to the dispersion of light, in the in- 

 stances 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 suffi- 

 ciently close for the lower cases, but displayed an increasing discrepancy as we ad- 

 vanced 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 investi- 

 gation 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 Math^matiques, 

 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. 



I therefore commenced with a trial of the method proposed in the memoir of 

 Mr. Kelland =*, applying it of course in the first instance to the case of the most 

 highly dispersive substance, oil of cassia, in which the greatest discrepancy had be- 

 fore appeared. Owing to an obscurity in the statement of an important part of the 

 process in the paper referred to, I was led to communicate with the author, and 



* Cambridge Transactions, vol. vi. Part I. • 



K 2 



