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 , 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 d, be expressed by 



z = a sin (nt lex) y = j3 sin (nt lex + d) 



/T^_ 



V 2 ~ 



or expanding y and substituting 



cos d -f- 

 Whence transposing and squaring 



Hence, ^ = sin (nt Tex) and 



y - ft I -|- 



p^ at a/3 



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

 d = 90. Translator. 



