430 The Theory of Aether and Electrons in the 



for the specific inductive capacity in terms of the number and 

 circumstances of the electrons.* 



Eeturning now to the case in which the dielectric is sup- 

 posed to be in motion, the equation for the polarization may be 

 written 



from this equation, Fresnel's formula for the velocity of light in 

 a moving dielectric may be deduced. For, let the axis of z be 

 taken parallel to the direction of motion of the dielectric, which 

 is supposed to be also the direction of propagation of the light ; 

 and, considering a plane -polarized wave, take the axis of x 

 parallel to the electric vector, so that the magnetic vector 

 must be parallel to the axis of y. Then equation (III) above 

 becomes 



equation (IV) becomes (assuming B equal to H, as is always 

 the case in optics), 



The equation which defines the electric induction gives 



IV* (1/4**)** + P.; 



and equations (1) and (2) give 



4arc*P x = (ft - 1) (E x - wH y ). 

 Eliminating D x , P x , and H y , we have 



-iV- + ' 



. A 



or, neglecting w~/c 2 , 



~dz*~ = 7 ~W ' ~~? dtfc '* 



Substituting E x = e n ^ , so that V denotes the velocity 



of light in the moving dielectric with respect to the fixed aether 

 we have 



* Cf. p. 211. 



t This equation was first given as a result of the theory of electrons by Lorentz 

 in the last chapter of his memoir of 1892, Arch. Neeii. xxv, p. 525. It was also 

 given by Larmor, Phil. Trans., clxxxv (1894), p. 821. 



