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.

[Illustration: Fig. 5]

Let us assume that a thunder-cloud is approaching the rod, A B (Fig. 5),
from above, and that it has reached a point, D', where the distance. D'
B, is equal to the perpendicular height, D' C'. It is evident that, if
the potential at D be increased until the striking-distance be attained,
the line of discharge will be along D' C or D' B, and that the length, A
C', is under protection. Now the nearer the point D' is to D the shorter
will be the length A C' under protection; but the minimum length will be
A C, since the cloud would never descend lower than the perpendicular
distance D C.