126 M. Holzmann on the Vibration of Polarized Light 



and the horizontal projection falling on the plane of the grating 

 is equal to 



s sin a. 



For a diffracted ray which forms with the continuation of the 

 incident ray the angle yS, the angle of diffraction, the vibration, 

 which is given by s sin a, decomposes into one, in the direction 

 of the diffracted ray, for which the distance of the aether particle 

 from its position of rest is 



s sin a sin /8 ; 



and into a vibration normal to the diffracted ray, which is given 

 by the distance 



s sin a cos /3. 



This last vibration gives with the vertical s cos a. the transverse 



vibration, which propagates itself in the direction of the diffracted 



ray ; and this vibration occurs under an angle a, with the vertical, 



for which we have 



ssinacosyS , „ ,,. 



tana,= = tan « cos p. . . (1) 



' scosa 



This formula agrees with that which Stokes, in his large 

 memoir on the Dynamical Theory of Diffraction, has found in 

 another manner. 



2. The consideration of the preceding paragraph can be used 

 in two ways to determine the direction of vibration of polarized 

 light. Either we can measure the angle which the plane of po- 

 larization of the incident ray forms with the vertical, — let it be y, 

 — and also the angle of the plane of polarization of the diffracted 

 ray with the vertical, which shall be 7,. Then if 7^ be greater 

 than 7, the light vibrates normally to the plane of polarization ; ■ 

 or if 7^ be smaller than 7, the light vibrates in the plane of po- 

 larization ; one of these two positions of the direction of vibra- 

 tion must take place, and the direction of vibration must be 

 steeper in diffracted light, or nearer to the vertical, than in inci- 

 dent light. 



A second method of investigation is as follows : — If we let the 

 diffracted light pass through a double-refracting prism, which is 

 so placed that the two images seen through it stand vertical over 

 one another, then the one will be produced by the horizontal, 

 and the other by the vertical vibrations of the diffracted light, at 

 least by the method by which double-refracting prisms are usually 

 constructed. The first will thus be formed by the vibrations 



s sin a cos /3, 

 and that with the vertical vibrations by 



