making Experiments upon Elliptic Polarization. 233 



days ago, to try how far they agreed with my formulae ; and the 

 agreement turns out to be so close, that I think myself justified 

 in publishing them. Besides, it will be curious hereafter to 

 compare them with more careful measurements. 



Before we proceed, however, to the details of the experi- 

 ments, it may be well to give the formulae in a state fitted for 

 immediate application. The light incident on the metal being 

 polarized in a certain plane, let a denote the azimuth of this 

 plane, or the angle which it makes with the plane of incidence ; 

 and as the reflected light will be elliptically polarized, or, in 

 other words, will perform its vibrations in ellipses all similar 

 and equal to each other, as well as similarly placed, put for 

 the angle which either axis of any one of these ellipses makes 

 with the plane of incidence, and let ]3 be another angle, such 

 that its tangent may represent the ratio of one axis of the 

 ellipse to the other. Then when the optical constants M and x 

 (of which I suppose the first to be a number greater than unity, 

 and the second an angle less than 90) are known for the par- 

 ticular metal, the angles 9 and ]3 may be computed for any 

 value of a, at any given angle of incidence, by the following 

 formulas : 



(i/ - v) sin 2a 



tan 20 



sin 



2/+ (v' + v) cos2a' 



2g sin 2a 

 v' + v < + 2/cos2a' 



in which /and g are constant quantities given by the expres- 

 sions 



- -^J cos x , ff = (^ f+ jj\ sin X> ( B ) 



and v, i/ are quantities depending on the angle of incidence *, 

 in the following way. Let i' be an angle such that 



sin i M 



~, = 9 ( C ) 



sin \ cos 



