Optical Activity of Isotropic Media. 469 



appears to have a fundamental bearing on the explanation of 

 the real cause of the phenomenon. 



There are two decisive tests which can be applied to the 

 results of any theory; the formula it furnishes for the specific 

 rotation of any substance must indicate clearly the depend- 

 ence of this quantity on the density and aggregate constitu- 

 tion of that substance, and. also on the frequency of the light 

 used. The second test is probably the more fundamental, as 

 there are probable actions of an entirely foreign nature which 

 •may mask the application of the first. 



I need not here enter into the particular form in which 

 the first test is to be applied, as I have examined the question 

 thoroughly in previous communications*. 



The usual empirical formula found necessary to express 

 the dependence of the rotation co on the frequency n of the 

 .light used, is one suggested by Boltzmann, 



© = A>i 2 + B>i 4 + 



According to Landoltj, however, this formula, although 

 fairly satisfactory in most cases, is not applicable to all of 

 them. The formula suggested by Lommel, 



An 2 



appears, however, to suit all cases so far known. 



Now let us examine the three theories and the formulae 

 deduced from them. In all the various branches of the 

 theory the all important relation is that connecting the electric 

 force E with the electric flux density D, a relation which 

 depends essentially on the constitution of the medium. It 

 is, as usual, obtained, after Drude, by a statistical analysis 

 of the motions of the contained electrons, to which the part 

 of the electric flux due to the presence of the medium is due. 

 These electrons are supposed to be connected to the mole- 

 cules of the medium by quasi-elastic forces, and resisted in 

 their motion by frictional forces proportional to their velocity. 

 In the present discussion we shall, however, neglect the 

 latter forces, so that the equations of motion of the electrons 

 are of a type 



m(x +)) r 2 <v) = eF Ti 



wherein (x, i/, z) are the component displacements of the 

 electron from its position of rest, m is its mass, and e the 



* Livens, Phil. Mag. June, September 1913. 



t 'Das Optische Drehungsvermogeri ' (Brunswick, 1898), p. 126. 



J 



