On the Laws of the Double Refraction of Quartz. 7 i 



also downwards, and the plane of the wave moving parallel, as 

 before, to the plane of xy. ' Then the crystal will be right-handed 

 or left-handed, according as C is positive or negative. For, if C 

 be positive, k will be negative, and formulae (4) will become, by 

 exhibiting the sign of , 



y I^TT /-,-) . (2?T , . ) /i /*\ 



g-jooB {_--(* -sUj i = -A j9Bin (stf-s) , (15) 

 l * ; I . J 



for the ordinary vibration ; and 



= />? cos -y (s# - s) [, jj = q sin |-^ (s# - s) j , (16) 

 I ' ; ' * ; 



for the extraordinary vibration. Now if we suppose the arc 



'2w 



(st - s) either to vanish, or to be a multiple of the circum- 



' 



ference, the molecule will be at the east point of its vibration ; 

 and upon increasing the time a little, the value of rj will become 

 negative in (15), and positive in (16), so that the movement will 

 be towards the south in the first case, and towards the north in 

 the second. Therefore, when C is positive, the ordinary vibra- 

 tion takes place in the direction NJES, or from left to right, and 

 the extraordinary in the direction SEN, or from right to left, 

 supposing a spectator to look in the direction of the progress of 

 the light. It may be shown, in like manner, that when C is ne- 

 gative, the ordinary and extraordinary vibrations are in the 

 directions SEN and NJ2S, or from right to left and from left to 

 right respectively. Now if a plane-polarized ray be transmitted 

 along the axis of the crystal, the plane of polarization will be 

 turned in the direction of the ordinary vibration, because this 

 vibration, being propagated more quickly, will be in advance of 

 the other, upon emerging from the crystal. Hence, the rotation 

 is from left to right when C is positive, and from right to left 

 when C is negative ; and the crystal is called right-handed in 

 the first case, and left-handed in the second. 



We have all along supposed that C is a constant quantity, 

 nnd the agreement of our results with experiment proves that 



