340 Prof. E. Ketteler on the Dispersion of Light 



The law of dispersion expressed by these equations is the 

 same as that which I have deduced from experiment, especi- 

 eiallv for sulphide of carbon, and to which, in my treatise on 

 the " Complex," I have referred all the theoretical conse- 

 quences. If in (8) we replace I by — , understanding by X the 



wave-length belonging thereto in the aether of space, and solve 

 according to n the equation thus transformed, we get, for the 

 form of the true curve of the dispersions n=f(X), the law of 

 formation 



=i»V( 1+ x-> D± vV0- D > 



(9 a) 



and for the associated internal wave-length I, on account of the 

 symmetry of equation (8), 



*-<\/F£F^V( i -£)'- d )- ■ (^ 



If we notice, finally, that the signs are unequivocally* de- 

 termined by this, that the ordinates of the curve (9 a), in di- 

 stinction from the curve (9 b), never become infinite, it shows 

 indeed the form required by experiment. It is found to be 

 \ > \ m to the right of the middle line, n > n m above the hori- 

 zontal asymptote, \<\ m to the left, and n<n m below. The 

 curve has, further, between two determinate limiting wave- 

 lengths V , V'o (the theoretic limits of the absorption-band), 

 an apparently variable interruption. Namely, for this reason 

 the refraction-ratios become complex (n / == a±b \/ — 1), a proof 

 that here the vibrations of the ^ethereal and corporeal particles 

 no longer obey the usual laws. The dispersion-force D, ex- 

 ternal and internal limiting wave-lengths (A/ , ¥ ; \" 0i l f/ ), 

 and limiting indices of refraction (n f Qy ?i // Q ) are connected with 

 ^ m , I hy the relation 



According to experiment, for sulphide of carbon as for all 

 those media to which the foregoing formula is applicable at 

 least approximately, ri* m is greater than 1 ; consequently the 

 influence of the ultra-violet absorptions is the predominant 

 one. For all these media the next most influential particular 

 curve lies within the region of the shorter wave-lengths. 

 Only the third rank, for the majority of them, does any action 

 from the ultra-red end also make itself perceptible. 



If, finally, for the nth particular curve D n be taken as = 1 

 * Herewith at once falls an objection raised by Helmholtz. 



