Theory of Anomalous Dispersion, 499 



which is finite, unless mn 2 =/3 2 . It is singular that Helm- 

 holtz makes precisely opposite statements: — "Wenn a = 0, 

 wird k = and l/c=oo ; sonst werden beide Werthe endlich 

 sein." 



The same conclusion may be deduced immediately from 

 the original equations (9), (10). For if the frequency be 

 zero and the velocity of propagation in the medium finite, all 

 the differential coefficients may be omitted ; so that (9) 

 requires <# — £ = and (10) then gives a 2 = 0. 



"Wiillner *, retaining a 2 in Helmholtz's equation, writes (14) 

 in the form 



v*=l-PX 2 +) ^ 2 , .... (16) 



applicable when there is no absorption. And he finds that 

 in many cases the facts of observation require us to suppose 

 P = Q. This is obviously the condition that v 2 shall remain 

 finite when X=oo, and it requires that a 2 in Helmholtz's 

 equation be zero. It is true that in some cases a better 

 agreement with observation may be obtained by allowing Q 

 to differ slightly from P, but this circumstance is of little 

 significance. The introduction of a new arbitrary constant 

 into an empirical formula will naturally effect some improve- 

 ment over a limited range. 



It remains to consider whether a priori we have grounds 

 for the assumption that v is finite when \=co. On the 

 electromagnetic theory this should certainly be the case. 

 Moreover, an infinite refractive index must entail complete 

 reflexion when radiation falls upon the substance, even at 

 perpendicular incidence. So far as observation goes, there 

 is no reason for thinking that dark heat is so reflected. 

 It would seem then that the introduction of a 2 is a step in 

 the wrong direction and that Helmholtz's formulae are no 

 improvement upon Maxwell's. 



It is scarcely necessary to add that the full development 

 of these ideas requires the recognition of more than one 

 resonance as admissible (Sellmeier). 



* ^Yied. Ann. xvii. p. 580; xxiii. p. 306. 



