in Singly and Doubly Refracting Media. 339 



And if again ; generally, we put 



K f IJ; me' ' 

 then comes definitively 



„»_1 = S V- (7) 



Now, to compare this expression with experience, or to bring 

 it into a more convenient form for numerical treatment, let it 

 be considered that the entire spectrum accessible to accurate 

 measurement comprises only about two octaves, and that it is 

 affected by the absorptions of the least as well as of the greatest 

 wave-lengths. Let us imagine, further, the I 2 laid down as 

 abscissae, and the individual function-values of the same, 

 namely the terms contained under the sign of summation, 

 each by itself, as ordinates. We thus obtain IT particular 

 curves ; and the total ordinate is the sum of all the particular 

 ones. Each of these part-curves runs according to a hyper- 

 bolic law ; their centre is at L ; to the right of this it rises 

 higher, to the left sinks lower, than the horizontal asymptote ; 

 and its steepness diminishes rapidly on both sides. In con- 

 sequence of this, all curves whose middle point is proportion- 

 ally distant from the boundaries of the accessible spectrum 

 exert only an approximately constant influence upon the total 

 curve obtained between them. If the influence of the ultra- 

 violet region preponderates, the curve is raised ; but if the 

 ultra-red region is the stronger, it is lowered. In both cases 

 we should have a medium with only feeble dispersion, and the 

 mean refraction-ratio of which would be either above or below 

 1, so that n % m — l = a. 



To these distant curves comes now the influence of one of 

 those whose centre falls either just within the visible spectrum 

 or at least lies sufficiently near its limits. The total curve 

 then attains the form 



2 1 ^_ D ' 



n — l = a+ , 2 



— —1 



L 2 l 



And if for a its value above given be introduced, and there- 

 fore logically a be referred to the ordinates whose middle point 

 is free from local elevation, and, lastly, L = l m , D' = T)nf n be 

 put, we get 



(n*-niXP-PJ = BnlP m ... . (8) 



and also 



{ u >l-^)(p-%"-)=m. 



Z2 



