THE • 



LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



JULY 1856. 



I. On the Demonstration of FresnePs Formulas for Reflected and 

 Refracted Light ; and their Applications. By the Rev. Baden 

 Powell, M.A., F.R.S, ^c, Savilian Professor of Geometry in 

 the University of Oxford^. 



1. A QUESTION between two fundamentally different views 

 --lTL of the theory of polarization, which has been long 

 agitated among inquirers into the undulatory theory, viz. as to 

 the direction of the plane of vibrations in relation to that of 

 polarization, has of late excited more peculiar interest, partly 

 from the announcement, a few years ago, of a remarkable crucial 

 experiment by Professor Stokes, and partly from several subse- 

 quent investigations, especially the recent elaborate discussion of 

 the general bearing of the experimental evidence by M. Haidinger, 

 The revival of this question recalls the attention of the student 

 to the very unsatisfactory condition in which the elementary de- 

 monstration of those parts of the theory on which it depends has 

 long been left, and from which recent speculations have done 

 little to deliver it. 



2. The well-known and remarkable formulas originally given 

 by Fresnel to express the amplitudes of the vibrations, and thence 

 the intensities, of reflected and refracted rays of polarized light 

 (for singly-refracting media), which are found to represent so 

 beautifully all the observed changes, — in fact including the whole 

 doctrine of plane polarization, and thus invaluable as inductive 

 laws, — yet long remained confessedly defective as to their system- 

 atic deduction from theory. 



3. Fresnel, indeed, with that marvellous sagacity for which 

 he was so conspicuous, satisfied himself of their truth by reason- 



* Communicated by the Author. 

 Phil Mag. S. 4. Vol. 13. No. 76. July 1856. B 



