274 Prof. J. J. Thomson. The Resistance of [Jan. 17, 



The solutions of these equations are 



iD.-oC, = (&D 3 - C C 3 ) 



Where * 



From these equations we can at once find C 3 and D 3 , and hence the 

 screening effect of the plate ; exactly the same conclusions hold for this 

 as for the special case previously considered ; if the screening effect of 

 two plates is the same their thicknesses must be proportional to their 

 specific resistance. 



The rapidly alternating currents, which in the experiments were 

 screened by the plates, were those resulting from the electrical vibra- 

 tions which are set up when the electrical equilibrium of a system is 

 disturbed. We shall now proceed to give a somewhat detailed in- 

 vestigation of the periods of such vibrations, as the ordinary expression 

 for the time of vibration of a condenser, whose plates are connected 

 by an induction coil, is not applicable to this case, and, in addition, I 

 think the result of these investigations taken in conjunction with some 

 experiments by Hertz, will enable us to decide the vexed question as 

 to whether the currents flow like an incompressible fluid, and to show 

 that Maxwell's hypothesis on this point is correct. 



The case we shall investigate is that of a straight wire connecting 

 two spherical balls. Let us take the axis of the wire as the axis of z, 

 and let F, G, H be the components of the vector potential, the 

 electrostatic potential. 



Then 



ax 



= ~, 

 ip dy 



TT - TT' _l V d $ 



i = 1 H -- i 

 ip dz 



cZF' d& <ZH' 



where + _ + - = 0, 



ax dy dz 



and where v is a constant. According to Maxwell's theory v = 1, 

 while according to v. Helmholtz's more general theory v = &o> 2 , where 

 ID is the velocity of propagation of the electrostatic potential, and k 

 a quantity which may be determined by the equation 



