Reflexion and Refraction. 9 1 



the first hypothesis in the way that we have shown to be neces- 

 sary in order to suit that principle, and making the ethereal 

 density constant. Then, if we retain the law of vis viva, our 

 new hypotheses will be these : 



1st. The vibrations of polarized light are in the plane of the 

 wave, and parallel to the plane of polarization ; which may be 

 expressed in a word, by saying that the vibrations are transver- 

 sal, according to the peculiar sense in which I use the term. 



2nd. The density of the ether is the same in all bodies as in 

 vacuo. 



3rd. The vis viva is preserved. 



4th. The vibrations in two contiguous media are equivalent ; 

 that is, the resultant of the incident and reflected vibrations is 

 the same, both in length and direction, as the resultant of the 

 refracted vibrations. 



It is evident that the last hypothesis affords three equations, 

 by resolving the vibrations parallel to three axes of co-ordinates ; 

 and the law of vis viva supplies a fourth equation. Thus we 

 have the requisite number of conditions. 



The hypotheses that we have last enumerated are those 

 which will be employed in the present Paper. They have been 

 made to include the law of vis viva, because I lately found that 

 this law must necessarily accompany the rest ; but at first I 

 neglected it, and even made considerable progress without it; 

 for, by the help of another hypothesis, I obtained formulae 

 which represented such experiments as I was aware of at the 

 time. This other hypothesis I took up from reading an article 

 by M. Cauchy in the Bulletin des Sciences Mathematiques* in 

 which he arrives, by a peculiar process, at the formulae of 

 Fresnel for the case of ordinary reflexion. The hypotheses 



* " Sur la Refraction et la Beflexion de la Lumiere," Bulletin des Sci. Math., 

 Juillet, 1830. In this Paper the vibrations of polarized light must be supposed 

 perpendicular to the plane of polarization, though the Paper was published im- 

 mediately after the author had promulged the contrary opinion. The latter 

 opinion, which I adopted from him because it harmonized with my analogy 

 before mentioned, he has formally renounced of late, and has returned to the 



