Since the resistance which the air or any other dielectric opposes to this breaking strain is thus limited, there must be a certain rate of fall of potential per unit length which corresponds to this resistance. It follows, therefore, that the number of equipotential surfaces per unit length can represent this limit, or rather the stress which leads to disruptive discharge. Hence we can represent this limit by a length. We can produce disruptive discharge either by approaching the electrified surfaces producing the electric field near to each other, or by increasing the quantity of electricity present upon them; for in each case we should increase the electromotive force and close up, as it were, the equipotential surfaces beyond the limit of resistance. Of course this limit of resistance varies with every dielectric; but we are now dealing only with air at ordinary pressures. It appears from the experiments of Drs. Warren De La Rue and Hugo Muller that the electromotive force determining disruptive discharge in air is about 40,000 volts per centimeter, except for very thin layers of air.
Fig. 3
If we take into consideration a flat portion of the earth's surface, A B (fig. 1), and assume a highly charged thunder-cloud, C D, floating at some finite distance above it, they would, together with the air, form an electrified system. There would be an electric field; and if we take a small portion of this system, it would be uniform. The lines, a b, a' b'...would be lines of force; and cd, c' d', c" d' ...would be equipotential planes. If the cloud gradually approached the earth's surface (Fig. 2), the field would become more intense, the equipotential surfaces would gradually close up, the tension of the air would increase until at last the limit of resistance of the air, e f, would be reached; disruptive discharge would take place, with its attendant thunder and lightning. We can let the line, e f, represent the limit of resistance of the air if the field be drawn to scale; and we can thus trace the conditions that determine disruptive discharge.
Fig. 4
If the earth-surface be not flat, but have a hill or a building, as H or L, upon it, then the lines of force and the equipotential planes will be distorted, as shown in Fig. 3. If the hill or building be so high as to make the distance H h or L l equal to e f (Fig. 2), then we shall again have disruptive discharge.
If instead of a hill or building we erect a solid rod of metal, G H, then the field will be distorted as shown in Fig. 4. Now, it is quite evident that whatever be the relative distance of the cloud and earth, or whatever be the motion of the cloud, there must be a space, g g', along which the lines of force must be longer than a' a or H H'; and hence there must be a circle described around G as a center which is less subject to disruptive discharge than the space outside the circle; and hence this area may be said to be protected by the rod, G H. The same reasoning applies to each equipotential plane; and as each circle diminishes in radius as we ascend, it follows that the rod virtually protects a cone of space whose height is the rod, and whose base is the circle described by the radius, G a. It is important to find out what this radius is.
Fig. 5