1889.] Electrolytes and rapidly alternating Currents. 269 



III. "The Resistance of Electrolytes to the Passage of very 

 rapidly alternating Currents, with some Investigations on 

 the Times of Vibration of Electrical Systems." By J. J. 

 THOMSON, M.A., F.R.S., Cavendish Professor of Experi- 

 mental Physics, Cambridge. Received January 9, 1889. 



The electromagnetic effect of the currents induced in a conducting 

 plate by alternations in a primary electromagnetic system in its 

 neighbourhood, is, at a point on the side of the plate opposite to the 

 primary system, in the contrary direction to the electromagnetic 

 effect of the primary. Such a plate, therefore, tends to shield off 

 from a secondary systsm the induction due to the primary, the 

 diminution it produces in the current induced in the secondary 

 depending upon the conductivity and thickness of the plate and the 

 rate of reversal of the primary current. If the rate of reversal is 

 infinitely rapid, a thin plate of very badly conducting substance will 

 be sufficient to screen off from the secondary circuit all the induction 

 arising from the primary, while, if the rate is very slow, a thick plate 

 of the best conducting metal will hardly be sufficient to do this. 

 When the current in the primary is reversed a few hundred times 

 per second, a metal plate of very moderate thickness will completely 

 shield off all induction. If the thickness of the plate exceeds this 

 limit, the currents induced in the layers next the primary will shield 

 off all electromotive force from those layers which are more remote, 

 so that in these layers no currents will be formed, the induced 

 currents will thus be confined to the skin of the conductor, the thick- 

 ness of the skin varying inversely as the conductivity of the plate 

 and the rate of reversal of the current. 



In Hughes' induction balance this screening effect of metal plates 

 is made use of to compare the resistances of two metals, but with that 

 apparatus it is hardly possible to make the alternations sufficiently 

 rapid to produce appreciable effects with substances which conduct 

 so badly as electrolytes ; we can, however, by employing the vibrations 

 of electrical systems such as those used by Hertz in his recent ex- 

 periments on the rate of propagation of electrodynaraic action get 

 oscillations sufficiently rapid to make the shielding effect of moderately 

 thin plates of electrolytes quite appreciable. 



Before describing the experiments made on this point, we shall 

 consider the theory of the screening effect of a slab of a conductor 

 bounded by two parallel planes. Let us suppose that these planes are 

 represented by the equations x = 0, x = h ; let I\, G^, H x represent 

 the components parallel to the axes of x, y, z respectively of the 

 vector potential on the side of the slab on which the primary system 



