the Double Refraction of Quartz. 4.67 
negative. For, if C be positive, &, will be negative, and formule (4) will become, 
by exhibiting the sign of k,, 
=p cos} Fiet—2yh, n= —k, psin§ F(st-)t, (15.) 
for the ordinary vibration ; and 
7) 
b= F0 cos f Fst —2)t, n=q sin} Fost—2) b, (16.) 
- : : : 2 : 
for the extraordinary vibration. Now if we suppose the are 7 (st =z) either to va- 
nish, or to be a multiple of the circumference, the molecule will be at the east point 
of its vibration; and upon increasing the time a little, the value of » 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 vibration takes place in the direction NES, 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 negative, the ordinary and extraordinary vibrations are in the direc- 
tions SEN and NES, 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 po- 
larization will be turned in the direction of the ordinary vibration, because this vibra- 
tion, 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, and the agreement of our 
results with experiment proves that this supposition is at least very nearly true in the 
neighbourhood of the axis. It is probable, however, not only that C varies with 9, 
but that it becomes different in equations (1.) and (2.) ; that is to say, it is probable 
that the following equations 
PE —Aavé +C dn 
d@ dz dz (17) 
dn —-péa oc @é UG 
de dz de 
in which C’ is a little different from C, would be more correct than those which we 
have assumed. Indeed Mr. Airy’s experiments seem to indicate that C’ is greater 
than C; for he found, as we haye already said, that the ratio of the axes of the little 
VOL. XVII. 40N 
