in Singly and Doubly Refracting Media. 343 



If , then, for the Tith zone, and for the limit-point G 7 to the 

 right of it, we have ^—^ = 0, the whole of the particular ex- 

 cursions will, with the entry into the absorption-streak, simul- 

 taneously undergo such differences of phase ; but these reach 

 at the middle line only an insignificant maximum, and on the 

 other side of it sink again to zero. Only for (p' Q , p Q ) n does 

 2(% 7 — %) rise considerably ; it reaches, at least with very feeble 

 dispersion, at the middle line the value ±90° (corresponding 

 to ±il), and for the limit-point G 77 on the left the value ± 180° 

 (or ±il); so that here, indeed, again b~0, and therewith the 

 curve becomes real, but the sign of p f ^ in equation (11), in 

 accordance with the hypothesis, changes into its opposite. 



Forming, lastly, the resulting ratio of the vires viva? for the 

 interior of the complex zone, we can put 



BJ'» 



All the calculations can now be carried out for a substance 

 with only one inconstancy in the spectrum (n m =l), conse- 

 quently with omission of the symbol of summation. We find, 

 in the first place, for very small dispersive forces, 



sin W-X)=\/£=^, ow 2(^'- % )= a/^ 



'A n V % — \ 



(13) 



We then obtain, pursuant to the above convention : — 



Left of the middle. Right of the middle. 



" V x m -\ 



2ab = 



Designating now the expression a 2 — b 2 — 1 = N 2 — 1 as the 

 merely refractive, 2ab as the at the same time absorptive part 

 of the index of refraction n, the former diminishes as we pro- 

 ceed from the right-hand limit G/ of the absorption-streak (at 

 which it attains the value + \/.D = n / l — 1) to the middle line. 

 At this, a 2 — 6 2 ==N 2 =1, and sinks for the limit-point G" on 

 the left still more, to 1 — \/D = n // l. If, therefore, we imagine 

 the limit-points G 7 , G 77 connected with each other by a curve 



