( 378 ) 



ways these investigators arrive at exactly the same results. The 

 relation inter se of the mechanic theories his heen elucidated by 

 Drude^). In 1892 Lohentz^) derived the laws of the refraction of 

 light by metal prisms, which had already been given by Voigt ') 

 and Drude ^), from a few simple principles. Concerning the nature 

 of the vibrations of light no special hypothesis is introduced. This 

 investigation of Lorentz enables us to develop the theory of metallic 

 reflection in a simple way. 



2. The simplest disturbance in a metal is that represented by: 



A e~l'-'' S171 {et — q.v -\- s^. (1) 



In this .V is the distance from the bounding plane of the metal. 

 This disturbance is caused when light falls perpendicularly on the 

 metal. Here we meet with the particularity, that tlie planes of equal 

 phase determined by the goniometric factor of (1) coincide with 

 these of equal amplitude which follow from the exponential factor. 

 From the assumption that the metal is isotropic and the deviation 

 from the condition of equilibrium in the light disturbance is a vector 

 determined by homogeneous linear differential equations, Lorentz 

 derives, what other disturbances are possible in the metal. Assume 

 that the bounding plane of the metal is the FZ-plane, and that the 

 plane wave-fronts are perpendicular to the A'Z-plane. Then a distur- 

 bance is possible, represented by : 



A e~P h sin (ct-Ql^-s) (2) 



if 



P^-Q^-^p-^-rf (3) 



PQ cos («, — ((,) =pq (4) 



are satisfied. 



The planes of equal amplitude and phase are given by /j = const., 

 /, z=r const. In this /j is the distance to the plane in which the 

 amplitude is A, and 4 that to the plane in which the phase has the 

 value s. ffj and «, are the angles of the normals of the planes of 

 equal amplitude and phase with the A'^-axis. 



3. From (3) and (4j the principal equations for the propagation 

 of light in metals may be immediately obtained. If light penetrates 

 from the surroundings into the metal, then the planes of equal 

 amplitude are parallel to the bounding plane. The exponential factor 



1) Göltinger Naclirichten 1892, 366, 393. 

 8) Wied. Ann., 46, 244. 1892. 



3) Wicd. Ann., 24, Ui, 1885. 



4) Wied. Ann., 42, 666, 1891. 



