the Inertia of Electric Convection, 237 



displacements of electrons in the molecules, the order of 

 magnitude may be the same. 



If jz/j,'i 2 represent the energy per unit volume due to 

 electric inertia where i is the displacement current, the 

 complete equations for the magnetic induction become, for a 

 medium of specific inductive capacity K and conductivity k, 



/_, d uJKd 2 \ „ ~d?a . i 



with the two corresponding equations for b and c. 

 If a varies proportionally to e~ ipt this reduces to 



( 1 — ijipte — —j—- ) V 2<2 = "~ (Kp 2 + ±7r/ci)a. 



In non-conductors the terms involving /c disappear, and 

 a = efa x is a solution provided that 



which gives for the velocity of propagation p/q the equation 

 a 2 K ±ir P ' 



dividing by V 2 , where V is the velocity of light in vacuo, we 

 obtain for the refractive index of the medium (n) 



fJir 



n 2 KV 2 X 2 ' 



If the second term is small we find to the first approxima- 

 tion, writing n for V v'K, 



n = '' l ° + aT" + 



J. Willard Gibbs * nearly twenty years ago deduced from 

 the mere assumption that the medium possesses a fine-grained 

 structure an equation for the relation between velocity of 

 wave-propagation and wave-length which is identical with 

 the above, and it was pointed out by him that his equations 

 include the case in which the medium is endowed with 

 electric inertia. 



It seems of interest to determine the order of magnitude 

 of the quantity /// '. The coefficient of 1/X- 2 may be calculated 

 from the optical dispersion and for ordinary flint-glass is 



* American Journal of Science, vol. xxiii. p. 262 (1882). 



