Maxwell. 299 



The equations by which (f> and a have been defined are 

 equivalent to the equations 



V 2 </> - $1* = - 4^, (2) 



V 2 a - a/c 2 = - 47ri, (3) 



while the equation of conservation of electricity, 



div i + p = 

 gives 



div a + <f> = 0. (4) 



From equations (1), (2), (4), we may readily derive the equation 



divE = 47rcV; (I) 



and from (1), (3), (4), we have 



curl H = E/c 2 + 47rt, (II) 



where H or curl a denotes the magnetic force : while from (1) 

 we have 



curl E = - H. (Ill) 



The equations (I), (II), (III) are, however, the fundamental 

 equations of Maxwell's theory; and therefore the theory of 

 L. Lorenz is practically equivalent to that of Maxwell, so far 

 as concerns the propagation of electromagnetic disturbances 

 through free aether. Lorenz himself, however, does not appear 

 to have clearly perceived this ; for in his memoir he postulated 

 the presence of conducting matter throughout space, and was 

 consequently led to equations resembling those which Maxwell 

 had given for the propagation of light in metals. Observing 

 that his equations represented periodic electric currents at 

 right angles to the direction of propagation of the disturbance, 

 he suggested that all luminous vibrations might be constituted 

 by electric currents, and hence that there was " no longer any 

 reason for maintaining the hypothesis of an aether, since we 

 can admit that space contains sufficient ponderable matter to 

 enable the disturbance to be propagated." 



Lorenz was unable to derive from his equations any explana- 

 tion of the existence of refractive indices, and his theory lacks 



