On the Laws of the Double Refraction of Quartz. 67 



a wave in air. The resultant rectilinear vibration will bisect this 

 angle ; and therefore ^, the angle of rotation, will be equal to 



y-. Hence, substituting for S its value, and observing that /, 

 the length of a wave in quartz, is equal to #A, we find 



2- 2 C6 

 p " a*\* ; 



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 (7, 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 k when and 

 / are given. Now it happens that Mr. Airy,* by a very inge- 

 nious method of observation, has determined the values of k in 

 red light for two different values of <f> ; and of course we must 

 compare these observed values of k 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 Fraun- 

 hofer. For this ray, Fraunhofer has given the length A, which, 

 expressed in parts of an English inch, is equal to '0000258 ; and 

 M. Eudberg has found a = '64859, b = 64481. Moreover, from 

 the experiments of M. Biot, we may collect that the arc of rota- 

 tion, produced by the thickness of a millimetre, is something 

 more than 19 degrees for the ray we have chosen ; so that the 

 fraction % may be taken to express nearly the length of that 



* Transactions of the Cambridge Philosophical Society, Vol. iv., p. 205. 



