of Light by thin Layers of Metal. 457 



g^tanc/),, q^tanijrj, 

 g 8 = tan ^g, q 3 =tan^3, 

 become 



■,_ (l-Dy + 4D a sin« (*,-&) 



„ 2 _ (l-Dy + 4D«rin 1 '(»,-^ 



"" (l-D 2 ) 2 + 4D 2 siu 2 ('f l + -f 3 )' 



«/« - ft U J - (1 _ D2)2 + 4J,, sm2 ( ^ + ^ » 



« s-%n_ft^-^ 16D 2 cos^, S in 2 f3 



««. - ?[ U «, ;- c a- (i_DY + 4D 2 8in s (t 1 + t 3 )' 



tan*===g» Id* , 



+ COS 20J 1 _,q D 3 COs2 08 , D 4 



cos 2</>j 



•«*.==|fc Id* — , 



-cosS^ 1 . o D2 cos^3 p4 

 cos 2^ 



tani- +COs( ^ + ^ ) - 1 ^ ]D2 J 

 fan s _ -co S (f 1 + ^ 3 ), l-D 2 , 



When the third medium is identical with the first, the for- 

 mulae are transformed into those given by Stokes* for this case. 

 ForD=0, 



which, taking into consideration the signification of (j> l and ty l9 

 are the usual formulae for total reflection. 



7T 



2. The limiting case e= - , from which constantly follows w = 0, 



L = 0, is, apparently, not realized in nature. Nevertheless most 

 metals approximate to it (especially the noble metals, which have 

 hitherto been the easiest to obtain in transparent layers) much 

 more than to the opposite limiting case e = 0. On the other 



* Trans, of Cambridge Phil. Soc. vol. viii. 1849. 



