EXPLANATION OF ROTATORY POLARIZATION. 



581 



The velocities V' and V correspond to two different lengths 

 A/ and A", and the values of U and of #, which are introduced into 

 the second term of the equation (4), refer to the propagation of the 

 vibrations of these two lengths of wave in the medium in the natural 

 state. Hence, restricting ourselves to terms of the first order, we 

 may write 



(5)' 



n' = 



dn lX K 



^A A^ 



dn 

 dX 



it follows from this that 



AT 

 (9) -i 



A 



We have, moreover, 



7^'-^ 



^"-A); 



i dn 



_(r-V) . 



aX^A J 



A" V 



I+aX + - (A"- A) 

 ^ /2 A 



which gives, to the same degree of approximation, 



A" -A' / \dn\ 



= -A( i- - ) = -A. 



7 



The magnetic rotation then becomes 

 (10) 



=a ^,_x-). 



d\ 



We see that the result, independent of the dispersion, must be 



multiplied by the factor (i --- ) . 



n d\ 



The coefficient a is itself a function of the wave length. To 

 agree with the formula of (595) which best satisfies the experiments, 



the coefficient must be proportional to . We shall see from what 



A 



considerations this formula may be theoretically deduced. 



