26 



vibrations travellins^ in the positive direction of tlie axis of z. Let 

 Uq be the amplitude of each of the original linear vibrations takino; 

 place in the plane z = 0, By passag-e throuj^h the medium the 

 amplitudes of the components are reduced and become 



(1) a, = «o Pxp ( — 27ix^ Zj?.) ; a., = a^ exp (' — 2ny.2zlX) 



where X is the wave-lenu;th in vacuo and Xj. x^ are the values 

 which the coefficient of extinction of the medium assumes for the 

 two circular vibrations. These values, /.^ und Xg, being- unequal, the 

 emergent vibration will be an elliptical one. 



In conformity with the notati(m i)reviously used we shall adopt 

 suffix 1 when dealing with the right-handed circularly polarized 

 wave and suffix 2 when dealing with the left-handed circularly 

 polarized wave. The angle ^ which the major axis of the resultant 

 ellipse makes with the direction of the original linear vibrations is 



c, and c.y being the velocities of propagation of the two components 

 and n the frequency of vibrations in the wave. The angle ip is to 

 be taken positive when the rotation, about the positive direction 

 of the axis of z. of the major axis of the ellipse (reckoned from 

 the original direction of the major axis to its given direction) takes 

 j)lace in the positive sense. 



It is important to bear in mind that in deducing equation (2) 

 we have assumed no condition respecting the amplitudes a^. a^ or 

 the coefficients x^, H2 that would limit the generality of our result. 

 Hence equati<m (2) is valid w^hatever value the difference x, — x., 

 has, or whatever values the coefficients x^, x.,. taken separately^ 

 have; e. g. it will huld true in the case when 



(3) >ii == , x,= 



which is the particular case usually considered. 



4:} 3. At this point I am sorry to find myself in disagreement 

 with § 24 of Professor W. Voigt's recently published, valuable 



namique et la Theorie yUcanique de la Lumihe Paris 1903 (p. 625. footnote). 

 1 regret that 1 overlooked these two Notes when writing iny first Coniiiiunicatiou 

 on the present sabject. 



