54 PROFESSOR KELLAND ON THE POLARIZATION OF LIGHT 



and equation (VI) gives 



,, , sin 6 cos </>. sin d> , cos O'cosch'sin d> n 



(a' + 6f) cos d> p c - - r V - J-p'd- iJn -- -*-=0 . . (VI) 



sin (p, sin <p 



Now it will be convenient to alter the notation slightly, since the notation I 

 for the incident vibration is more intelligible to the eye than a. Let us then de- 

 note the incident vibration by I, or, which is the same thing, multiply every part 

 of our expressions by cos (fy + c t) : then our equations are (I), (II), (III), which 

 remain unaltered ; 

 and (1 -p) T cos <, cos 6 - (1 -p'} T' cos <' sin & = ..... (IV) 



'^'sina'-R. + .T^O (V) 



' 



. 

 sm(p sm(/>, 



' S 0' = (VI") 



sin sin (>, sin (>' 



together with (e B -2D)R, + (c 9 -2D,)T,=0 ..... (VII) 



or (see previous Memoir) R,+T,=0 ....... (VII') 



SECTION II. APPLICATION TO ORDINARY REFRACTION. 



The first application we propose to make of our formulae is the determination 

 of the intensity of light reflected and refracted at the surface of a non-crystallized 

 medium. This problem differs from that which we solved in the memoir on 

 FRESNEL'S formulae, in this respect, that in that case the incident light was sup- 

 posed to be light polarized in two planes at right angles to each other. We now 

 suppose common light to be composed of light whose plane of polarization conti- 

 nually shifts its position. 



Our equations at once answer this hypothesis by making <p,=(f>', and .-. />=/>'. 

 Now equation (IV") is, in this case, 



(1-p) (T cos 6- T' sin <9') cos </>,=<). 

 Either, therefore, 1-^=0, or T cos 6= T sin &. 



If the latter be the case, equations (I), (II), and (V"), that is, all the equations de- 

 pending on the plane of incidence are independent of T and T', or of the trans- 

 mitted ray. But this can never be conceived to exist, except perhaps in metals ; 

 we must, therefore, adopt the other solution 1 p=Q. 

 Also =1 ; /. our equations become 



T / . (1) 



. . . (2) 

 (3) 



-- .T. (4) 



sin <p sm (p sm <p 



