228 _ 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 @ @/, a small frame swings. In 
this frame, by the pivots H H’, whose axis is at right angles to G G/, a 
pendulum Pp 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 m Hy the pendulum can only vibrate in the plane 
of © D, and by the pivots G G it can only vibrate in the plane of a B 
at right angles toc 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/, 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= asin (nt—ka) y = B sin (nt — ke + d) 
Hence, = = sin (nt — ke) and yee" 
& +/ a = 008 (nt — ke), 
or expanding y and substituting 
y=6(Zomat [*~Fsina) 
Whence transposing and squaring 
al =~ y2 
P ap 
The equation to an sie which becomes a circle if a = = B and 
d = 90°.— Translator. 
cos d = sin 2d 
