Closing Years of the Nineteenth Century. 429 



denotes the refractive index of the dielectric ; and therefore the 

 refractive index is determined in terms of the frequency by the 

 equation 



- mn z ). 



This formula is equivalent to that which Maxwell and 

 Sellmeier* had derived from the elastic-solid theory. Though 

 superficially different, the derivations are alike in their 

 essential feature, which is the assumption that the molecules 

 of the dielectric contain systems which possess free periods 

 of vibration, and which respond to the oscillations of the 

 incident light. The formula may be derived on electro- 

 magnetic principles without any explicit reference to electrons ; 

 all that is necessary is to assume that the dielectric polarization 

 has a free period of vibration.f 



When the luminous vibrations are very slow, so that n is 

 small, fjr reduces to the dielectric constant ej ; so that the. 

 theory of Lorentz leads to the expression 



e <= 



* Cf. p. 293. 



t A theory of dispersion, which, so far as its physical assumptions and results 

 are concerned, resembles that described above, was published in the same year 

 (1892) by Helmholtz, Berl. Ber., 1892, p. 1093, Ann d. Phys. xlviii (1893), 

 pp. 389, 723. In this, as in Lorentz' theory, the incident light is supposed to 

 excite sympathetic vibrations in the electric doublets which exist in the molecules 

 of transparent bodies. Helmholtz' equations were, however, derived in a different 

 way from those of Lorentz, being deduced from the Principle of Least Action. 

 The final result is, as in Lorentz' theory, represented (when the effect of damping 

 is neglected) by the Maxwell-Sellmeier formula. Helmholtz' theory was developed 

 further by Reiff, Ann. d. Phys. Iv (1895), p. 82. 



In a theory .of dispersion given by Planck, Berl. Ber., 1902, p. 470, the 

 damping of the oscillations is assumed to be due to the loss of energy by radiation : 

 so that no new constant is required in order to express it. 



Lorentz, in his lectures on the Iheory of Electrons (Leipzig, 1909), p. 141, 

 suggested that the dissipative term in the equations of motion of dielectric electrons 

 might be ascribed to the destruction of the regular vibrations of tit^electrons 

 within a molecule by the collisions of the molecule with other molecule 



Some interesting references to the ideas of Hertz on the elet.:t)magnetic 

 explanation of dispersion will be found in a memoir by Drude, Ann. d. Phys. (6) i 

 (1900), p. 437. 



+ Cf. p. 283. 



