( 381 ) 



h^ =: 0. So the coeflicient of absorption of the medium normal to the 

 bounding plane had to be 0. For metals this is not the ease, so that 

 no total reflection can occur there, as has been observed above. 



It is well known that with total reflection on perfectlj^ transparent 

 media the planes of equal phase and amplitude are normal to each 

 other for the disturbance in the second medium which is propagi\ted 

 parallel to the bounding plane. Voigt showed, that this case also 

 occurs for a disturbance, which leaves a prism of a substance which 

 absorbs light, when plane waves fall on it and the dimensions of 

 the prism are large with respect to the wave length '). 



From (6) and (7) we may derive (/•/ — ?io^) co>i a = n^ k^ ( —). 



\n k ) 



From this follows, that according as k : n increases, « differs more 



from jr : 2, with which we have got back a result of Voigt's ^). 



5. Eisenlohr') showed, that by the introduction of a complex 

 index of refraction, we arrive at Cauchy's results for metallic reflection. 



In the follo\ving way it may be shown that for metals a complex 

 quantity corresponds to the index of refraction of transparent bodies. 

 With observance of the conditions (3) and (4), (2) is a possible distur- 

 bance. In this /i and /^ are the distances from the point for which 

 (2) holds, to the plane of equal amplitude, in which the amplitude 

 is A and the plane of equal phase, in which the phase is ^'. We 

 may also write for (2) : 



Ae-V\->^-l''i~ dn{ct — q^x —q.^z—s) (11) 



because the planes of equal phase and amplitude are noi'mal to the XZ- 

 plane. The normals from the point x,z on the two above mentioned of these 

 planes are respectively (^i a- -fpj^) : VP\-Vv^ ^"<^1 {'lv^\^i^)'-V<lx^-^q^', 

 so that P= VV^'P.\Q=Vqf\q,'' 



In the same way as (11) a possible disturbance is also: 

 ylg-'/'i^'-y^2- cos {ct — q^x — q^z — s). 



The differential equations, which are supposed homogeneous and 

 linear, are therefore also satisfied by : 



yl(2— Pi^— /'2- '>^cos {ct— q^x — q^^—f') =t I sin {ct — q^x — q.-^z — s)\ 

 or by 



Ae±'H^i--'-<hT'-/>i)-='i-z+'P-i-si (12) 



For a perfectly transparent medium q)^ = p^ = 0. The velocity 

 of propagation is then v = c : V'qi^-^qj^, or c being c=2jr : T, 



1) Wied. Ann., 24, 153, 1885. 



2) Wied. Ann , 24, 150, 1885. 



3) Pogg. Ann., 104, 368, 1858- 



