34 Mr. Mac Cullagh on the Laws of 



reflexion for ordinary media, afford only three conditions. We will state his 

 hypotheses at length : — 



1st. The vibrations of polarised light are in the plane of the wave, and 

 perpendicular to the plane of polarisation. 



2nd. The density of the ether is inversely as the square of the refractive 

 index of the medium. 



3rd. The vis viva is preserved. 



4th. The vibrations parallel to the separating surface of two media are 

 equivalent ; that is, the refracted vibration parallel to the surface is the resultant 

 of the incident and reflected vibrations parallel to the same. 



We see that the fourth hypothesis gives two conditions, and the law of vis 

 viva gives a third. 



Let us now take the more general principle of equivalent vibrations, in place 

 of the fourth hypothesis of Fresnel, altering the first hypothesis in the way 

 that we have shown to be necessary 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 polarised light are in the plane of the wave, and 

 parallel to the plane of polarisation ; which may be expressed in a word, by 

 saying that the vibrations are transversal, 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 coordinates ; 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 em- 

 ployed 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, T obtained formulae which represented such expe- 



