22$ FRESNEL. 



mon polarization of Huyghens. This special double re- 

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

 two branches, on which, by the pivots G G', a small frame swings. In 



this frame, by the pivots H H X , 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 G G/ 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 c?, be expressed by 



z = a sin (nt Toe) y = ft sin (nt kx + d) 



Hence, = sin (nt lex) and 



or expanding y and substituting 



"( 



Whence transposing and squaring 



/3 2 02 aft 



The equation to an ellipse : which becomes a circle if a = ft and 

 d= 90. Translator. 



