1917]
THE THEORY OF ANOMALOUS DISPERSION
491
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 v2 shall remain finite when \ = oo, and it requires that a2 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 improvement over a limited range.
It remains to consider whether a priori we have grounds for the assumption that v is finite when X = oo. 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 a2 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).
[* Similarly, the substitution of a dissipative force " dependent upon the absolute velocity of the atoms instead of upon the relative velocity of fetber and matter" (p. 489 above) appears to be the reverse of an improvement, since Maxwell's results (4) and (5) above lead to a finite v when 7i = 0, but H 4= 0 (cf. p. 490 and footnote f). W. F. S.]coefficients maybe omitted; so that (9) requires as — % = 0 and (10) then gives a2 = 0.