. r »9 



Mr. H. R. Hasse on the Equations of 



Nevertheless it is possible to construct as above the con- 

 stitutive relations necessary to complete the scheme of 

 electrodynamical equations, thus showing again that there 

 is practically no limit to the numbers of schemes of electro- 

 dynamical equations which can be deduced by means of 

 the principle of relativity alone, and that it is only by 

 means of some theory of the aether and of the consti- 

 tution of matter that we can decide between the various 

 schemes. 



II. 



The experimental evidence which has led to the formu- 

 lation of the hypothesis that optical and electrical phenomena 

 are independent of the direction of the motion of the earth 

 through the aether, contains a special group of experiments 

 which have dealt with the changes to be expected when 

 light or electricity passes through a moving medium. There 

 are three outstanding examples of this group, viz., the 

 rotation of the plane of polarization by an active medium*, 

 the double refraction due to the motion of the medium f , and 

 the electrical resistance of a moving medium J. 



The theory of the last two experiments does not present 

 any mathematical difficulties and the experimental results 

 lead to the constitutive relations given above §. On the 

 other hand, in the case of the rotation of the p>lane of 

 polarization we have to deal with a more complicated con- 

 stitutive relation, and since this case serves as a good 

 illustration of the first part of this paper, we shall deal 

 Avith it in detail. 



For the purpose of finding the absolute value of the 

 rotation of the plane of polarization, it is perhaps easier to 

 work with the equations (11) referred to axes moving with 

 the matter, so that putting 



x f = x — wt, y'=y, z'=z, t' = t . . . . (13) 

 the circuital relations take the form 



* Lord Rayleigh, Phil. Mag. 1902, p. 215. 



t Lord Rayleigh, Phil. Mag. 1902, p. 678 ; D. B. Brace, Phil. Mag. 

 vii. 1904, p. 317. 



X Trouton and Rankine, Proc. Rov. Soc. A. vol. lxxx. 1907-08, 

 p. 420. 



§ Equations (12), when B = H, since the medium is non-magnetic, 

 and p=0. 



