116 On the Refractive Indices and the Dispersion of Opaque Bodies. 



relation is implicitly contained. The discussion of this equation, 

 of which one side is an infinite series, presents some difficulties ; 

 it has been thought* sufficient to retain the first two terms of 

 this series and neglect the rest. This would be permissible, as 

 M. Christoffel has shown, if in every case the sphere of action 

 were infinitely small in comparison with the wave-length. That 

 the last assumption is not admissible, however, the discussion of 

 the incomplete equation shows ; for it yields the result that every 

 spectrum is bounded at the violet end by a visible beam of defi- 

 nite refraction. This inference is a physical absurdity, since it 

 presupposes the existence of bodies which, under any arbitrary 

 angle of incidence, totally reflect a visible beam, or completely 

 absorb it on the surface. The dispersion-formula derived from 

 the imperfect series, even if correct for large wave-lengths, can 

 offer no explanation as to what really occurs at that limit at the 

 more refrangible end of the spectrum. 



Whilst this limit with substances of weak dispersion would lie 

 very far in the ultra-violet, it sometimes appeared in the green 

 in the bodies which I investigated. With no single body of this 

 group were even traces of interference observed in the violet. 

 The reason of this phenomenon might be sought in a strong re- 

 flection of these rays at the surface, or in a strong absorption in 

 the interior; it has been shown that the latter is the preponde- 

 rating cause of the absence of interference-bands. Then they 

 always vanish gradually with increasing thickness from the 

 violet to the red end of the spectrum, and are very soon only 

 present in the yellow and red. Hence the absorption increases 

 with decreasing wave-lengths, and indeed continuously so for a cer- 

 tain position in the spectrum which is special to each substance, 

 and so quickly that on the other side of it no ray can pass 

 through a layer of the thickness of half a wave-length. 



Hence in transmitted light sufficiently thick layers of bodies of 

 preeminent dispersion always appear yellow-red or red. I have 

 sought in vain for a substance of this kind which would be trans- 

 parent with green, blue, or violet light. 



To meet any objections to these matters of fact arising from 

 the mention of apparent exceptions, I must make the following 

 remarks. 



Thin layers can be prepared in different ways which strongly 

 absorb the light and are transparent to other than yellow or red 

 light ; such layers, however, like glass coated with soot, are not to 

 be regarded as bodies, but as loosely connected apparatus of in- 

 dividual particles, and can only be quoted as exceptions if it be 

 proved generally that they possess refractive and dispersive 



* Cauchy, " Mem. sur la Disp.," and Christoffel, Pogg. Ann. vol. cxvii. 

 pp. 27-45. 



