94 JAMIN ON METALLIC REFLEXION. 



It has appeared to me useful to point out the theoretical 

 meaning of these two determinations, which define completely 

 the elliptical movement of the ethereal particles after metallic 

 reflexion. It would have been still more interesting to compare 

 the theory with experiments ; unfortunately, these do not appear 

 to be sufficiently accurate, practical difficulties, which M. de 

 Senarmont has himself recognised, impairing the observations 

 and rendering them often impossible. 



IV. Phcsnomena presented by multiplied reflexions. 



Although I have already spoken of multiplied reflexions whilst 

 treating of difference of phase, it remains nevertheless to be 

 shown, that all the circumstances of these experiments are easily 

 foreseen and calculated : this I shall do, commencing with the 

 case in which the reflecting surfaces are parallel. 



It will be remembered that several reflexions, even or uneven in 

 number, are capable at certain incidences of restoring plane po- 

 larization ; it will also be recollected that if the incident ray is 

 polarized in a certain azimuth, to the left of the plane of inci- 

 dence, for example, the reflected ray regains its polarization, 

 sometimes to the right, sometimes to the left of this plane ; and 

 lastly, it is also known that the azimuth of the restored ray is 

 always less than that of the incident ray. There are then, as 

 will Jbe seen, three points to be examined in this pheenomenon ; 

 namely, 



1st. The incidence for which the polarization is restored ; 



2nd. The direction of the azimuth of the restored ray ; 



3rd. The absolute value of this azimuth. 



We shall pass these successively under review. 



1st. We may always calculate the angles for which, after a 

 single reflexion, the differences of phases are 



TT 2 7r Stt (»t — 1) tt m^r 



u, , , , .... , . 



m m m m m 



In fact, the formulae for the difference of phases being 



4. i 4. n ■ 4. UcOSi 



tan 6 = tan 2 w sin u, tan w = — ^o^j 



sm^ ^ 



if we replace successively (8) by the (m + l) preceding values 

 in these equations, they will make known the (m + 1) values of 

 (i), of which the first is 0°, the last 90°, for which the difference 

 of phase is equal to the preceding quantities. By reflecting 



