( 384 ) 



cos" i + U^ 



tqf= 4 , 



2U cos i cos II 



then 



^'/' = '■"(/- f) 



From the vahie of ƒ follows also 



/ cos i \ 

 cot f i^z cos i( sin { 2 B(jt(j —— j (14) 



Further we get: 



/ cos i\ 



tg (pp — sin u tg \2Bgtg — 1. 



Be Ri : Rp = tg h, then 



?<" cos^ (i — a) 4- k^ cos' i 



tg' h = ^ ^^ .. 



n' cos' {i -|- «) + k' cos' i 



In the corresponding expression of Cauchy the value of Cos 2 h 

 is given. From the value of tg' h follows, as 



2n cos a sin' i cos i 

 CO. 2k = (1 -*, 2/,) :(!+., 2/,) , », 2k = ——^^-^— . 



According to (13) this passes into 



cos 2h =r cos K sin I 2 Bg tg ^— J (15) 



In the same wa}' becomes 



2 U sin i tq i f sin i tg i\ 



tq ((CI - (r,,) := sin u '- — - = sin u tq 2 Bq tg --^- . (16) 



^^^^' ^'^ U'—sin'tg'i 'V U J 



The expressions (14), (15), (16) have the same form as the corre- 

 sponding ones of Cauchy, only according to Lorentz's notation a^ 

 stands for U, the angle t -\- lo for u. ^) 



Just as from /, U and u the quantities Rp, Ri, (pp, and r// maj be 

 derived, which determine the reflected beam of light, U and u may 

 be calculated from i and two of these four quantities. U and u 

 depend therefore in exactly the same way on the angle of incidence 

 and the optical properties of the metal as Cauchy's corresponding 

 quantities cq and t -|- to. At the same time it appears that two constant 

 quantities suffice for the determination of the optical behaviour of metals. 

 They are here ??„ and k„, which have a definite physical meaning, 

 with Cauchy (J and t, whose meaning is not so obvious. Whatever 



1) LoRENTz, Theorie der terugkaatsing en breking, p. 166. According to Eisenlohr's 

 notation (loc cit. p. 369, 370) U = c vf , « = f -f- u. As Rp and Ri : Rp, (fj, and 

 (ji—tpp have the same form as Gauchv's equation, this holds also for i^jandy/ 



