22^ FRESNEL. 



mon polarization of Huygliens. This special double re- 

 fraction, results not from the nature of the crystal, but 

 two branches, on which, by the pivots g g', a smah frame swings. In 



D ii 



this frame, by the pivots h h^, whose axis is at right angles to g g', a 

 pendulum p vibrates. (The upper end is light, and carries a white 

 ball or disk, carried up to such a height as to be conspicuous for lec- 

 ture illustrations.) 



Now, by the pivots h h/ the pendulum can only vibrate in the plane 

 of c D, and by the pivots o gi it can only vibrate in the plane of a b 

 at right angles to c d. If now motion be given it in one of these planes, 

 and at an instant after in the other, the result will be a revolution in 

 the ellipse e e/, which will be a circle if the interval be exactly one 

 fourth of a vibration. 



Or mathematically thus : — 



Let the waves in planes at right angles, with a difference of retarda- 

 tion d, be expressed by 



z = a sin (nt — kx) y = 13 sin (nt — kx -{- d) 



Hence, — = sin (nt — kx) and / \ ^2 



" ■%/ — = cos (n< — kx), 



or expanding ?/ and substituting 



Whence transposing and squaring 



-TT, + ^ — ^ cos rf = sin 2(i 

 /3^ a2 ap 



The equation to an ellipse : which becomes a circle if fl = /3 and 

 d = 90°.— Translator. 



