2ab 



344 On the Dispwgion of Light in Refracting Media. 



constructed according to the foregoing law N=F(A,)*, this curve 

 forms in a certain relation the continuation and complement 

 of the till now isolated branches of the real dispersion-curve; 

 its ordinates increase simultaneously with the wave-length. 



The absorptive part, on the contrary, increases from the two 

 limits to the middle ; hence everywhere the upper or the lower 

 sign only is to be used. 



Passing, finally, from quite feeble to stronger dispersive 

 forces, the consideration of equation (4) gives, on substituting 



in it - for /, and solving it according to n 2 — 1 instead of n, 



immediately : — 



It divides for the complex zone into the two following, 

 = ±V /D_x( 1 + D _|) 2 , 



m 



and gives, besides j- = v D, more complicated values for 



2(%' — %). For the middle line particularly this angle always 

 becomes less than 90°. 



That the processes here indicated never take place without 

 absorption, is scarcely surprising. We have, in the occurrence 

 of the difference of phase between the cethereal and corporeal 

 particles, an implicitly communicated coefficient of friction; and 

 the intensity of the absorption f will be exactly proportional to 



* Of course N must be distinguished from the actual Telocity- or sine- 

 ratio, v= — = ^-^ (for perpendicular incidence = a), whose difference 

 7 co sin r 



v ^—l= — Q 2 "becoming variable, must be regarded as the actual refracting 



m 

 force. Cf. I c. pp. 70, 85 ; et infra sub § 15. 



t If, after Cauchy, we put the absorption-factor of the amplitude 



equal to eP x , p= ■*- ~^7-> tne abscissa z being taken vertically, we have, 

 for D small, 



" m'p ! 2 am2( x '-x )j 



mp 2 —?np 2 > 



where d denotes the thickness passed through, and /3 is only negative. 

 I accept this fully, but conditionally — that is, rigorously retaining the 

 preceding signification, and without any connexion with the so-called 

 limit-equations. Conf. /. c. p. 69. 



