352 BEPOET— 1893. 



It may be observed that the analysis here given would apply equally if 

 the equations just written were substituted for the fundamental equations 

 from which it started. 



13. The electrical views by means of which Drude accounts for the 

 addition of terms of this kind to the electro-magnetic equations are as 

 follows. He starts with the two circuital relations to which the equations 

 of electrodynamics have been reduced by Heaviside, Hertz, and other 

 expositors, of the types 



- cZy d/3 _ da dR dQ 



dy dz dt dy dz ' 



in which as usual («, v, lu) is total electric current, (o, /3, y) is magnetic 

 force, {a, b, c) is magnetic induction, and (P, Q, R) is electric force. To 

 these equations we would, under ordinary circumstances, add relations 

 depending on the structure of the medium, in the form for isotropic 

 media, 



(a, &, c)=/x (a, /3, y), 



Ot,^,t.)=(^^|^ + <T) (P,Q,R), 



where K is specific indactive capacity and a is specific conductivity. To 

 introduce the magnetic rotatory property, Drude proposes to modify the 

 second set of circuital relations ' on Maxwell's analytical basis, that to 

 the kinetic energy of the medium which is expressed in simple form by 

 means of the components of the magnetic force certain subsidiary terms 

 are appended ; as according to Maxwell the magnetisation is to be con- 

 sidered as a kind of molecular vortex or concealed motion (verhorgene 

 Bewegung) .' The modification which he assumes on this ground is a re- 

 placement of the second circuital relation by one of type 



keeping the other equations unaltered. 



On forming the expression for the transfer of energy per unit 

 volume of the medium, there is obtained (jieglecting, however, the magneto- 

 optic energy) the equation 



+ . . . + . . ., 



in which dr is an element of volume, and the three integrals at the end 

 are extended over the boundary of the medium, of which (Z, m, n) are the 

 direction cosines. 



For periodic vibrations there is thus no dissipation of energy except 



