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XII. Remarks on the Theory of the Dispersion of Light, as connected with Polariaia- 

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

 Geometry in the University of Oxford. 



Received May 10,— Read May 31, 1838. 



Introductory Observations. 



(1.) In the course of four successive papers, I have laid before the Royal Society the 

 comparison of observations of the refractive indices for the standard rays in various 

 media, with the results calculated from the formula of theory, as deduced upon the 

 most improved views of the hypothesis of undulations ; the cases discussed including 

 the greatest range of data which experiment has yet furnished. 



The degree of accordance thus exhibited between observation and theory, even in 

 the most extreme case, I believe will now be considered sufficient to warrant the con- 

 clusion, that the theory at least affords a very satisfactory approximation to the ex- 

 pression and explanation of the actual law of nature ; and this in the instance of a 

 class of phenomena which it had long been the reproach of that theory to be sup- 

 posed incapable of accounting for, if they were not absolutely contradictory to it. 

 At any rate, if, in the instances referred to, the discrepancies should by any be thought 

 still too great, or if it should be contended that other cases may yet arise in which 

 theory may be put to a severer test, yet, with so strong a presumption in its favour, 

 the only fair inference would be, that further examination was required of the prin- 

 ciples on which any extension or modification of the theory might be pursued. 



(2.) The investigation, then, having advanced thus far, it seemed desirable, as a se- 

 quel to my former papers, to devote the present to some remarks connected with the 

 theory which has been thus applied. 



The facts of interference, on which the undulatory theory was originally based by 

 Dr. Young, obliged us to adopt some idea of an alternating motion, as well as a motion 

 of translation^ in our conception of light. And this, with all the accessions it has re- 

 ceived, especially from the investigations of Fresnel, has at the present day been con- 

 nected by the labours of M. Cauchy and others with general dynamical principles, 

 which regulate the propagation of vibratory motions through an elastic medium. 



(3.) More precisely, from such dynamical principles certain differential equations 

 of motion have been deduced ; the integration of which gives tiie well-known expres- 

 sion for a wave, involving the relation between the velocity and the wave-length which 

 explains the dispersion. The direct and complete integration of these forms, effected. 



