[ 496 J 



XLVII. The Theory of Anomalous Dispersion. 

 By Lord Bayleigh, O.M., F.R.S* 



IN a short note f with the above title I pointed out that 

 Maxwell as early as 1869 in a published examination 

 paper had given the appropriate formulae, thus anticipating 

 the work of Sellmeier J and Helmholtz §. It will easily be 

 understood that the German writers were unacquainted 

 with Maxwell's formulae, which indeed seem to have been 

 little known even in England. I have thought that it would 

 be of more than historical interest to examine the relation 

 between Maxwell's and Helmholtz's work. It appears that 

 the generalization attempted by the latter is nugatory, unless 

 we are prepared to accept a refractive index in the dispersive 

 medium becoming infinite with the wave-length in vacuo. 



In the aether the equation of plane waves propagated in 

 the direction of x is in Maxwell's notation 



pd 2 V /dt 2 = F>d 2 V /dx 2 , (1) 



where rj is the transverse displacement at any point x and 

 time t, p is the density and E the coefficient of elasticity. 

 Maxwell supposes " that every part of this medium is 

 connected with an atom of other matter by an attractive 

 force varying as distance, and that there is also a force of 

 resistance between the medium and the atoms varying as 

 their relative velocity, the atoms being independent of each 

 other " ; and he shows that the equations of propagation in 

 this compound medium are 



where p and a are the quantities of the medium and of the 

 atoms respectively in unit of volume, t] is the displacement 

 of the medium, and r\ + f that of the atoms, crp 2 % is the 

 attraction, and aJid^/dt is the resistance to the relative 

 motion per unit of volume. 



* Communicated by the Author. 



f Phil. Mag. vol. xlviii. p. 151 (1899) ; Scientific Papers, vol. iv. 

 p. 413. A misprint is now corrected, see (4) below. 

 X Pogg. Ann. cxliii. p. 272 (1871). 

 § Pogg. Ann. cliv. p. 582 (1874). 



