( 379 ) 



in (2) passes info e-''^'= and rf, = 0. In lliis case r^ may be called 

 llie angle of refraction in agreement willi wlial lakes [»lacc for 

 perfectly transparent bodies. Denote it by «, then (4) passes into : 



PQcosa^=pq (5) 



Let US now pnt P = 2 .i k : )., where ?. is the wave length in the 

 air, and k the coefficient of absorption. In (2) we pnt Q=z2:i:.X^, 

 where P-j represents the wave length in the metal. Be P. : ).^ = n, then 

 we may call the index of refraction of the metal n, in agreement 

 with what happens in transparent bodies. In the same way Q = 2.t ii : ^. 

 Let us call the values of / and n, when the light propagates in the 

 metal perpendicularly to the bounding plane I-, and n^. Then in (1) 

 p z= 2jt kg : X, q=: In n„ : X. 



Introducing these values into (3) and (5), we get: 



P-n' = A-/-«/ (6) 



kn cos a ^= kg iig (7) 



In order to bring our formulae for the disturbance in the metal 

 at the bounding plane in harmony with those for the disturbance in 

 the air, we must put sin i : sin a=:).: ).^ = n or sin i = n sin a, when 

 / is the angle of incidence. It follows from (6) and (7) that both 

 the index of refraction and the coefficient of absorption depend on 

 the direction of propagation, i. e. on the direction of the normal 

 of the planes with equal phase. 



If (7) is written in the form : 



k' n' cos' a = k' {n' — sin' i) = k„' n,' . . . . (8) 



it follows from (6) and (8) that: 



2n' = - kg' + n,' -f sin' i 4- \/{kg' - n„' + sin' i)' + 4/./ k,' . . (9) 



2k' = kg' - ng' + sin' i + ]/{kg' - ng' + sin' i)' + 4»/ kg' . . (10) 



They denote in what Wtiy k and n depend on the angle which 

 the direction of the propagation of the disturbance falling on the 

 metal forms with the normal to the bounding plane '). 



For an opaque mirror of silver deposited on glass by a chemical 



1) Ketteler was the first to derive these equations, (see inter alia Pogg. Ann., 

 160, 408, 1877) which, of course, also occur in Voigt's theory. Voigt puts the 

 quantity corresponding to P equal to 2t k : A^, so that Voigt's 7ik corresponds 

 to the coefficient of absorption k introduced here. It is not correct that C.auchy 

 already gave these equations, as Drude observes (Wied. Ann. 35, 515, 1888). 

 They have not been given explicitly in this theory. This appears, indeed, from 

 the fact that Beer (Pogg. Ann., 92, 412, 1854) substitutes other relations for 

 them, which are not correct. Derivations of the principal equations were given by 

 Wernicke (Pogg. Ann. 169, 226, 1876) and Ketteler, Pogg. Ann. 160, 468, 1877. 

 See also Ketteler, Wied. Ann., 49, 512, 1893 and Theoretische Optik, p. 198, 

 g 85, Zur Geechichle der Hauptgleichungeni 



