Optical Activity of Isotropic Media. 471] 



If we adopt this form for F then we deduce from above 

 that 



P=(2^)(E + »c„rlE) 



= aJZ + bi curlE. 



With this relation it can easily be verified that the two» 

 kinds of circularly polarized light are propagated with 

 different velocities, which are respectively the roots of the- 

 two equations 



2 i „ . A w *i— n 



/r — 1 — a 1 + • = U, 



and tbe combination of these two circularly polarized beams 

 leads, as usual, to a pencil of linearly polarized light, whose 

 plane of polarization is being rotated at a rate per unit 

 length 



&> = iO + — A*-) w > 

 which is 



_ n 2 bi n 2 ^ be 2 jm 



'' ~2c = 2c ~ n-: 2 -n 2 * 



This is the ordinary formula obtained by Drude. 



This formula appears very inadequate when the first 

 test of constitution is applied to it, as witness the almost 

 innumerable number of hypotheses introduced to ex- 

 plain the departures from it in the actual behaviour of 

 most substances. It does not satisfy the second test very 

 well, as the Boltzmann formula alone may be regarded as an 

 approximation to it in certain very special cases. 



2. First modified theory. — We have, however, seen that even 

 in the simple case of ordinary isotropic media the term E does 

 not completely represent the whole effect of the force on 

 the electron due to the applied field. We must, in fact, add 

 a term aP, where P is, as before, the intensity of polarization 

 induced in the medium, and a is a constant approximately 

 equal to 1/3 in numerical value. 



We are, however, still at liberty, when extending the theory 

 to optically active substances, to assume the same origin for 

 the chiral quality in the medium ; and we should then have 

 as a general form for F 



n 



F=E + aP+.6curlE, 



