464 Mr. MacCutracu on the Laws of 
\ is the length of a wave in air. The resultant rectilinear vibration will bisect this 
; j 8 «Wie 
angle; and therefore p, the angle of rotation, will be equal to = Hence, substituting 
for 8 its value, and observing that /, the length of a wave in quartz, is equal to a, 
we find 
2n°CO 
rd Seat 12. 
a‘? Med 
which gives the experimental law of M. Biot, that the angle of rotation is directly as 
the thickness of the crystal, and inversely as the square of the length of a wave for any 
particular colour. By changing the sign of C, we should have an equal rotation in 
the opposite direction. And here we may remark, that C may be made negative in 
all the preceding equations, its magnitude remaining. There are two kinds of quartz, 
the right-handed and left-handed, distinguished by the sign of C. 
The angle of rotation, for a given colour and thickness, is known from M. Biot’s 
experiments. We can therefore find the value of C by means of the last formula ; 
and substituting this value in equation (8.), we shall be able to compute & when ¢ and 
lare given. Now it happens that Mr. Airy *, by a very ingenious method of observ- 
ation, has determined the values of & in red light for two different values of ¢; and 
of course we must compare these observed values of & with the independent results of 
theory. As Mr. Airy’s experiments were made upon red light, we shall select, for 
the object of our calculations, the red ray which is marked by the letter C in the 
spectrum of Fraunhofer. For this ray, Fraunhofer has given the length \, which, 
- expressed in parts of an English inch, is equal to .0000258; and M. Rudberg has 
found a= .64859, b= .64481. Moreover, from the experiments of M. Biot, we may 
collect, that the arc of rotation, produced by the thickness of a millimetre, is some- 
thing more than 19 degrees for the ray we have chosen; so that the fraction } may 
be taken to express nearly the length of that arc in a circle whose radius is unity. 
We have, therefore, 8=.03937 inch, and p=.333, Substituting these values in the 
formula 
derived from (12.), we find 
l 
from which it appears that C is about twenty thousand times less than the millionth 
part of an inch. 
* Transactions of the Cambridge Philosophical Society, vol. iv. p. 205. 
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