382 



there is one of the quantities in the preceding formulfie which 

 may he greatly altered without producing more than a slight 

 effect on the values of 9 and j3. This quantity is the ratio 

 of sin i to sin i', which, according to the value in formula (c), 

 is a number so large as to make the angle i' always small, so 

 that its cosine never differs much from unity ; and therefore 

 if the above ratio were taken equal to any other large num- 

 ber, the value of ju in formula (d) would remain nearly the 

 same, and consequently the values of 9 and j3 would be but 

 slightly changed. 



It is with regard to the value of ju as a function of the 

 incidence that I entertain the greatest doubts, and if any 

 defect shall be found in the formula I think it will be here. 

 The relations (c) and (d), from which fi 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 problem, and seek to determine the constants M 

 and X from the observed values of 9 and /3 at a given inci- 

 dence, the results are rather complicated and involved, 

 though the approximate determination is easy enough. As 

 the formulae are in a great measure 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 

 vibrations be I'esolved in directions parallel and perpendicu- 

 lar 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 formulae which express the diffe- 

 rence of phase after reflexion, and the ratio of the amplitudes 

 of vibration. Put ^ for the difference of phase; and sup- 

 posing, for simplicity, the incident light to be polarized in 

 an azimuth of 45°, let a be angle less than 45°, such that 

 tan (T may represent the ratio of the reflected amplitudes 



