384i Royal Irish Academy. 



been in my possession for nearly six years, before I became aware of 

 their close agreement with my formulae ; but the fact is, that I did 

 not regard them with much interest, because, from the circumstances 

 in which they were made, I did not expect more than a general ac- 

 cordance with theory. And even now I am in no haste to infer the 

 absolute exactitude of the formulae, though they are found to repre- 

 sent the phaenomena so well. It was far more allowable to infer 

 that the formula of Fresnel was exact in the case just mentioned, 

 though it appeared to represent the phaenomena less perfectly. For, 

 to say nothing of the small number of our experiments, the present 

 is a much more complicated case, and the phenomena depend on 

 two constants instead of one, so that the formulae might be slightty 

 altered, and yet perhaps continue to agree very well with rough ex- 

 periments. Where there is only one constant this is not so probable. 

 Again, there is one of the quantities in the preceding formulae which 

 may be greatly altered without producing more than a slight effect 

 on the values of d and /3. This quantity is the ratio of sini to sini', 

 which, according to the value in formula (C), is a number so large 

 as to make the angle V always small, so that its cosine never differs 

 much from unity ; and therefore if the above ratio were taken equal 

 to any other large number, the value of ju. in formula (D.) would re- 

 main nearly the same, and consequently the values of d and |3 would 

 be but slightly changed. 



It is with regard to the value of jtx, as a function of the incidence 

 that I entertain the greatest doubts, and if any defect shall be found 

 in the formulae I think it will be here. The relations (C.) and (D.), 

 from which (* 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 % from the observed values of 6 and j3 at a given 

 incidence, 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 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 vibration. Put <{> for the difference of phase ; 

 and supposing, for simplicity, the incident light to be polarized in 

 an azimuth of 45°, let cr be angle less than 45°, such that tan <r may 

 represent the ratio of the reflected amplitudes respectively perpen- 

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



tand> = - r — i— , cos 2 cr = , J ; .... (H.) 



v' — v v' + v 



from which we may infer that 



