of Lightning- Conductors. 219 



To make the problem a definite one consider the following 

 case : — 



An air-condenser with plates of any size separated by a 

 distance h (height of cloud) and charged up to bursting strain 

 {\ gramme weight per square centimetre; the less strength 

 of rare air is hardly worth troubling about). Let a small 

 portion of this condenser, of area irb 2 , now discharge itself; 

 being separated from the rest after the trap-door and guard- 

 ring manner. A volume of dielectric irbVi is relieved of 



981 

 strain, and the energy of the spark is E= — -irb 2 h ergs. 



Kb 2 

 The capacity discharged is S = -j^-, and the maximum 



potential can be reckoned by putting 



= 1107* electrostatic units. 



Let the discharge pass straight down the axis of the cylin- 

 drical region of length h and radius b, and let the channel 

 occupied by it have a sectional radius a. If the path is a 

 metal rod, then a is the sectional radius of that rod. 



We have now to calculate the self-induction of such a dis- 

 charge. A discharge of this kind differs from ordinary cases 

 in having no obvious return circuit. What is happening is 

 a conduction or disruption current down the axis of the 

 cylindrical region considered, and an inverse displacement 

 current in concentric cylinders all round it. I shall assume 

 that this inverse displacement current is uniformly distributed 

 over the whole area. A conduction rush is not uniformly 

 distributed over the section of its conductor, but is concen- 

 trated by mutual induction of the parts towards the peri- 

 phery; similarly, but inversely, there will be a tendency for 

 the displacement currents to be stronger near the central 

 axis than far away ; but there is this difference, that whereas 

 in a conductor currents are able to distribute themselves how 

 they please, they will not be so free in an insulator. It is 

 not quite correct to take the distribution as uniform, but it 

 will not make very much difference probably. (That it is 

 not correct may be seen by considering the initial and final 

 stages of the dielectric. Either it is the whole of a condenser 

 that is being discharged or it is a trap-door portion. If only 

 a portion, the initial state is one of equal strain, but lines 

 from surrounding charged areas spread in laterally to all the 

 outer regions, and so finally there is an unequal distribution 



