Closing Years of the Nineteenth Century. 455 



and propagated parallel to the axis of 2, the electric vector being- 

 parallel to the axis of x. Thus the equations of motion reduce 

 to 



= -r -=-^- + 4n- 



For E x and P* we may substitute exponential functions of 



where n denotes the frequency of the light, and /* the quasi-index 

 of refraction of the metal : the equations then give at once 



<y _ i) (_ a?l t + pnS~^i + y ) = 47TC 2 . 



Writing v (1 - K v/ - 1) for p, so that v is inversely proportional 

 to the velocity of light in the medium, and denotes the 

 coefficient of absorption, and equating separately the real and 

 imaginary parts of the equation, we obtain 



4*0 (y- an*) 



f?n z + (y - aw 2 ) 2 



When the wave-length of the light is very large, the inertia 

 represented by the constant a has but little influence, and the 

 equations reduce to those of Maxwell's original theory* of the 

 propagation of light in metals. The formulae were experi- 

 mentally confirmed for this case by the researches of E. Hagen 

 and H. Kubensf with infra-red light ; a relation being thus 

 established between the ohmic conductivity of a metal .and 

 its optical properties with respect to light of great wave- 

 length. 



When, however, the luminous vibrations are performed 

 more rapidly, the effect of the inertia becomes predominant; and 



* Cf. p. 290. 



t Berlin Sitzungsber., 1903, pp. 269, 410; Ann. d. Phys. xi (1903), p. 873 ; 

 Phil. Mag. vii (1904), p. 157. 



