2 Prof. J. J. Thomson. On the Effect produced by [May 2. 



p. 270), I have shown that if Maxwell's theory that electricity moves 

 like a perfectly incompressible fluid is not true, the rate of propaga- 

 tion of very rapidly alternating currents along a wire placed at an 

 infinite distance from other conductors cannot be the same as the rate 

 of propagation of the electrodynamic action through the surrounding 

 dielectric. As Hertz, in his experiments on the rate of propagation 

 of electrical waves along a metal wire, found that these rates were not 

 the same, it might appear that this proved unmistakably that Max- 

 well's theory is untenable. I wish in this note to show that, assuming 

 Maxwell's theory, we can explain the smaller velocity of propagation 

 along wires found by Hertz, by taking into account the capacity of 

 the wire, if the wire is not at a very great distance from other con- 

 ductors ; in fact that the capacity of the wire produces much the same 

 effect as the " compressibility " of the electricity which is supposed 

 to exist in all theories other than Maxwell's. In the case of a " free " 

 wire in the laboratory, the electrical effects produced by the walls and 

 floors are indefinite. I shall, therefore, consider on the most general 

 theory the case of a wire surrounded by a coaxial metal cylinder, a 

 case where the electrical conditions are perfectly definite if the elec- 

 trical oscillations are very rapid. 



I shall consider the case of a cylindrical wire surrounded by a 

 cylindrical sheath of dielectric, which in its turn is surrounded by a 

 third substance, either a conductor or another dielectric. The axis of 

 the wire is taken as the axis of z, and all the variable quantities are 

 supposed to vary as e l[mz+ P t] : the notation is as nearly as possible the 

 same as the former paper. Let a be the radius of the wire, a its specific 

 resistance, b the cuter radius of the sheath of dielectric, and K its 

 specific inductive capacity; let us first suppose that this is surrounded 

 by a substance whose specific resistance is a . 



Let denote the electrostatic potential, and let 



= e^+PQAJ^iqr), in the wire, 

 = e l (^+^)(BJ (^V)+CI (t2V)), in the dielectric, 

 — e l ( mz+ P t )~DI Q (iq"r), in the outer conductor ; 



.-,2 ^2 jr>2 



where <f = in?-'— g '2 = m 2_^L, q 'n = m 2 — V 



where n>, w', w" are the velocities of propagation of the electrostatic 

 potential in the wire, sheath, and outer conductor respectively; in 

 Maxwell's theory these are all infinite, and q = q' = q" = m. 



If F, G, H are the components of the vector potential, we may 

 put 



