The Theory of Anomalous Dispersion. 497 



On the assumption tbat 



V, t= (0, D) tfte-W+i-f)*, 



we get Maxwell's results * 



1 1 _p + <r <rn 2 p 2 — n 2 , 



^W~ ~W~ + ^(f^n^y^Hhi 2f ' ' W 



; 2 



2 an 2 Un 



vln E (p 2 -n 2 ) 2 + W 



(5) 



Here v is the velocity of propagation of phase, and I is the 

 distance the waves must run in order that the amplitude of 

 vibration may be reduced in the ratio e : 1. 



When we suppose that R = 0, and consequently that Z=oo, 

 (4) simplifies. If v be the velocity in aether (o-=0), and v 

 be the refractive index, 



^ = 5£ = l + *_£l- (6) 



v P P n 



For comparison with experiment, results are often con- 

 veniently expressed in terms of the wave-lengths in free 

 aether corresponding with the frequencies in question. Thus, 

 if X correspond with n and A with p, (6) may be written 



" 2 = 1+ p -^> & 



— the dispersion formula commonly named after Sellmeier. 

 It will be observed that jo, A refer to the vibrations which 

 the atoms might freely execute when the aether is maintained 

 at rest (97 = 0). 



If we suppose that n is infinitely small, or A, infinitely 

 great, 



"„ 2 =l + ^, (8) 



thus remaining finite. 



Helmholtz in his investigation also introduces a dissipative 

 force, as is necessary to avoid infinities when n==p, but one 

 differing from Maxwell's, in that it is dependent upon the 

 absolute velocity of the atoms instead of upon the relative 



* Thus in Maxwell's original statement. In my quotation of 1899 

 the sign of the second term in (4) was erroneously given as plus. 



