making Experiments upon Elliptic Polarization. 237 



same, and consequently the values of and j3 would be but 

 slightly changed. 



It is with regard to the value of p as a function of the inci- 

 dence that I entertain the greatest doubts, and if any defect 

 shall be found in the formulae I think it will be here. The re- 

 lations (c) and (D), from which p. may be deduced in terms of i, 

 were not indeed adopted without strong reasons ; but I am not 

 entirely satisfied with them ; because, when we reverse the prob- 

 lem, and seek to determine the constants M and ^ from the ob- 

 served values of and ft at a given incidence, the results are 

 rather complicated and involved, though the approximate deter- 

 mination is easy enough. As the formulae are in a great mea- 

 sure built upon conjecture, we must not be disposed to receive 

 them without the strongest experimental proofs ; and it will 

 certainly require experiments of no ordinary accuracy to decide 

 some of the questions which may be raised respecting them. 



When plane-polarized light is incident on a metal, if its vi- 

 brations be resolved in directions parallel and perpendicular to 

 the plane of incidence, the effect of the reflexion is to change 

 unequally the phases of the resolved vibrations ; and it may be 

 useful to have the formulas which express the difference of 

 phase after reflexion, and the ratio of the amplitudes of vibra- 

 tion. Put ^ for the difference of phase ; and supposing, for 

 simplicity, the incident light to be polarized in an azimuth of 

 45, let a be an angle less than 45, such that tan <r may represent 

 the ratio of the reflected amplitudes respectively perpendicular 

 and parallel to the plane of incidence ; then we shall have 



2a 2f 



tn A = -r^ t cos 2<r = , ; (H) 



v v v + v 



from which we may infer that 



sin <f> tan 2<r = -, (i) 



or that the product on the left side of the last equation is inde- 

 pendent of the angle of incidence. It is to be observed that the 



