( 487 ) 



from the snrroimding medinm to tlie metal. Assume plane waxes to 

 fall on the metal. The vector of light in the refracted i-ay is then 

 determined by : 



( t X COS r -\- z sin r ) 



< Asm2jrl- (//„ + /a-,,) . ... (6) 



In this X is the wave-length in the air ^). The phase is determined 

 with respect to a point in the bonnding plane. 



With the aid of (4) and (5) equation (6) |)asses into 



It .coé-'" A- zi<Ln ie-'~:(J j 



2^--—^ ("oH-"^-o) ... (7) 



(7) satisfies also the differential equations for the vector of light 

 in the metal which nre supposed homogeneous and linear, if the sine 

 is replaced by a cosine. 



If the arc occurring in (7) is called <f, also 



^4 cos (f — I A sill (f ^) 



satisfies. 



The light-vector in the metal can therefore be represented by 



-Hi'-'} 



Je-2^« Xe (8) 



In this: 



a ■=: I o.v sin co — z sin i ■ I [- o.v cos (_o A- z sin i I — . (0) 



f . . cos x\n^ f , . _ si)i x\ k^ 

 b ■=. ( Q,v cos o) -\- z sin i ) j qx sin co — ~ sin i 1 — . (10) 



V <^ J ^ \ O J '^ 



3. From (8) follows, that the planes of equal amplitude are 

 represented by : 



a-=p^x -\- q^zz=C (II) 



In this is, according to (9) 



. sin X n^ . . cos x k^^ 



q, ^z — sin i -j- sin i . 



^' a X^ a X 



As from (3) follows 



/?„ : /."(, =: cot X , we ha\e q^-=z 0. 



1) LoRENTz showed that, also when a complex index of refraction is introduced, 

 at the bounding plane the values of tlie liglil vector in the two media harmonize. 



Cf. Theorie der tcrugkaatsing en breking, 1S7G, p. 100. 



-) It appears from § 5 of the previous paper (loc. cit. p. 381), that if the index 

 of refraction is pul ^/j ± < Ay, tliis expression is ^ cos' ip + < J. sm ^. 



