1889.] Electrolytes to very rapidly alternating Currents. 279 



The right hand side is small so that ica will be small, and the equation 

 to determine it 



or *c 2 log ^tica = m 2 ^ ; ' log 





The solution of this equation is approximately 



* 2 = 



- log 



log I 27 2 m 2 a 2V - ; '- log ^iqa 

 or say <c 2 = -/Jm. 2 ; 



but /c 2 = m 2 ^, 



-n 2 



therefore ra 2 (l +/8) = ^L , 



and the velocity of propagation of the disturbance through the wire 

 is p/m or v */(].+{$). Since the imaginary part of m does not involve a, 

 and a only occurs under the logarithm, the rate at which the vibrations 

 die away will in this case be practically independent of the resistance 

 and size of the wire. Thus, unless Maxwell's theory is true, the rate 

 of propagation of a very rapidly alternating disturbance through a 

 conductor is not the same as that of the electrodynamic action through 

 the surrounding dielectric ; if ft is positive it goes faster through the 

 wire than through the dielectric, while if ft is negative it goes more 

 slowly. The rate of propagation through the wire is almost though 

 not quite independent of the size and conductivity of the wire and of 

 the rapidity of the vibrations. Thus, if it could be proved that the 

 velocity of a disturbance through a conducting wire differed appreci- 

 ably from the velocity of electrodynamic action, and that the rate at 

 which the vibrations die away did not depend upon the resistance, it 

 would be sufficient to show that Maxwell's assumption is untenable. 

 Hertz's experiments would seem to show that the rate of propagation 

 through a metallic wire is less than that of electrodynamic action 

 through the dielectric ; but I believe he has lately found that the 

 former rate increases rapidly with rapidity of the vibrations, which is 

 inconsistent with the above result, if v' and v are independent of p. 

 No experiments seem to have been made on the rate at which the 

 vibrations die away, though this would be one of the best ways of 

 distinguishing between the theories. 



