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.

[Illustration: 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.

[Illustration: Fig. 4]

If the earth-surface be not flat, but have a hill or a building, as H or