Maxwell. 293 



and the potential energy per unit volume is 



+ 



The equations of motion, derived by the process usual in 

 dynamics, are 



Consider the propagation, through the medium thus constituted, 

 of vibrations whose frequency is n, and whose velocity of pro- 

 pagation in the medium is v ; so that r\ and are harmonic 

 functions of n(t - x/v). Substituting these values in the 

 differential equations, we obtain 



1 o oil? 2 



Now, p/^ 7 has the value 1/c 2 , where c denotes the velocity of 

 light in free aether; and c/v is the refractive index ju of the 

 medium for vibrations of frequency n. So the equation, which 

 may be written 



determines the refractive index of the substance for vibrations 

 of any frequency n. The same formula was independently 

 obtained from similar considerations three years later by 

 W. Sellmeier * 



If the oscillations are very slow, the incident light being in 

 the extreme infra-red part of the spectrum, n is small, and the 

 equation gives approximately ju 2 = (p + a)jp : for such oscilla- 

 tions, each atomic particle and its shell move together as a 

 rigid body, so that the effect is the same as if the aether were 

 simply loaded by the masses of the atomic particles, its rigidity 

 remaining unaltered. 



* Ann. d. Phys. oxlv (1872), pp. 399, 520 : cxlvii (1872), pp. 386, 525. 

 Cf. also Helmholtz, Ann. d. Phys. cliv (1875), p. 582. 



