252 FRESNEL. 



hesitate to say, if we admit no dependence between the 

 motions of the different luminous molecules (and I know 



plane, thus differing essentially from the former. See Professor Mac- 

 cullagh's paper " On the Laws of Crystalline Refraction," Transac- 

 tions of the Irish Academy, vol. xviii. ; and Dr. Lloyd's Lectures on 

 the Wave Theory, part ii. p. 30. The whole subject has been fully 

 discussed by the Translator in three papers in the Philosophical Mag- 

 azine for July, August, and October, 1856. 



The demonstration in either case is grounded on the assumption of 

 the law of vis viva ; viz : 



And Fresnel's formulas would be directly deduced if we had also 

 the relations 

 h + h' = hj for vibrations perpendicular to the plane of incidence, 



and h h' = fij - - .... parallel to the plane of incidence. 



The difficulty is, that these formulas are not both deducible from 

 the principle of equivalent vibrations as laid down by Professor 

 Maccullagh. Another mode of deduction, on a different assumption, 

 is pointed out in the Philosophical Magazine for Oct. 1855, by means 

 of the geometrical construction above given. 



The theory of Fresnel, it will be easily seen, is equivalent to the 

 assertion that " the plane of vibration is perpendicular to the plane of 

 polarization," whereas in that of Maccullagh they are coincident. 



Several classes of experiments have been now shown to necessitate 

 the adoption of the former view : for an account of which the reader 

 is referred to the Philosophical Magazine for Aug. 1856, before cited. 



To procee'd to the applications of these formulas : we may consider 

 common light as consisting of two portions of equal intensity, polar- 

 ized at right angles to each other. If the intensity of the incident 

 light be 1, that of each of these components will be . At reflexion 

 each component gives a reflected and a refracted ray polarized re- 

 spectively at right angles. In the reflected ray the intensity of the 

 portion polarized in the plane of incidence (i) will be = i 7i' 2 . That 

 in the plane perpendicular to (K) will be = fc/ 2 , and it is easily seen, 

 from the nature of the fractions, that of these quantities the first will 

 always be the greater; and thus in their sum or the total intensity 

 there will be an excess of light polarized in the plane of incidence, or 

 the light is at all incidences partially polarized in the plane of inci- 

 dence. The difference of the two expressions gives the quantity of 

 light so polarized. 



