520 Prof. E. Ketteler on the Dispersion of Light 



For Hgo =1 they coincide with equations (14 b). If from 

 them, in the well known manner, the dispersion-curve also for 

 the real branches be constructed, so that first of all 



is written, then, inasmuch as n\ is put = ?z^(l — D), the root 

 can be extracted, and we get 



2»o 



W(*+&'-»±>/iHM 



which differs from equation (9 a) only by this — that here n^ 

 represents an actually existing horizontal asymptote, while 

 there n m was taken as the mean ordinate of a continuously 

 curved line. Accordingly the formula in question (and with 

 it also at the same time the curve 9 b) would by the present 

 discussion be raised again above the signification of a mere ap- 

 proximative formula. Finally, the hyperbolic curves of the 

 anomalous dispersion are now executed no longer on both sides 

 of the horizontal n = l, even for a substance optico-chemically 

 simple, but of the line n=n^\ and hence the refraction-ratio 

 of all wave-lengths may (and, indeed, not improbably) exceed 

 unity. 



For the phase-changes we have the following result. We 

 obtain for the absorption-streaks of a simple substance, accord- 

 ing to equations IY., the trigonometric tangent of the phase- 

 difference 2 A by division of the two expressions (d) : thus we 

 get 



^\AD-(l + D-g) 2 

 tan2A=- — ...(e) 



or, for D small (that is, for narrow absorption-streaks), more 

 simply, 



tVM ^ 



tan2A=_ 



As we now presuppose that n^ is always greater than 1, 

 2A remains less than 90°. The difference of phase rises then 

 from the limit-point G / on the right (for X=A/ , w / >w o0 ) up 

 to a maximal value lying on the middle line itself (X=X m ), to 

 sink again to zero in the limit-point G" (for X=X // , n // <n oo ) 

 on the left of the same. In correspondence with this, the 

 values belonging to the two real branches, instead of being 0° 

 and 180°, now become the same value 2A = 0. 



