( 488 ) 



and the planes of eqnal amplitude run parallel to the bounding 

 j)lane. This is necessary as it is assumed that the light enters the 

 metal from the outside. 



The planes of equal phase are represented by: 



h=lK,C-^q,Z^C (12) 



If we introduce again n^: l\-=^ cotr, then according to (10) 



Q co.ir-\-ay) 



l\ = , /'o -. (1^) 



/ stn X 



k^ slni 



'7. = -,^- (14) 



o/. Slur 



4. Let (( be the angle between the normals of the planes of 



equal amplitude and phase. The former running i)arallel to the 



bounding j)lane or the FiT-plane, « is the angle of the normal of the 



planes of equal phase with the A'-axis. Thus cos a ^= p.^ : V^p^^ -\- q,'' 



or if we introduce the values p.^ arid q., from (13) and (14) : 



S171 t 



co.s a =: Q COS (t -f- lo) : \y^ o^ cos'^ (t -]- (o) -| ~ . . (15) 



From this follows: 



* o • I — * 2 •" 



Slïl I 



o'' cos'' (t -f to) -}- 



(16) 



a' 



it being the angle of refraction cori'esi>onding to plane waves with 

 an angle of incidence / (see § 2 of the preceding paper), we get: 



/i' =: du'' i : slii^ a = a'' o^ cos'^ ((u + t) -[- ■''*''«' '* • • • (17) 



Let rhe coeflicient of absorption belonging to n be k. Normal to 

 the planes of equal amplitude the amplitude decreases over a distance 

 .K in ratio 1 to ^-^^^'-^ = ^ As q^ = i), we get according to (8) and (9) : 



2jTkiC 2jro.f 



— — nn — — {h, .sin OJ + /:„ COS O)) 



from which again follows, when cot r is substituted for /?„ : /(„ : 



k = /i-p Q sill (t -|- to) : sin r 

 or on account of (3) : 



k = o Q sin {r -{- ixï) (18) 



5. The fundamental equations follow immediately from the values 

 found for the index of refraction and the coefficient of absorption. 

 The equations (17) and (18) lead immediately to : 



n^ — P z= o' q'^ cos 2 (r + w) -L sifi- i . 

 According to (1) the second member of this equation is equal to 

 a'^ cox 2t or according to (3) to n^^ — h^^. In this way the lirst 

 fundamental equation is obtained. 



