ON THE SPACE PROTECTED BY A LIGHTNING-CONDUCTOR.

By WILLIAM HENRY PREECE.

[Footnote: From the _Philosophical Magazine_ for December, 1880.]


Any portion of non-conducting space disturbed by electricity is called
an electric field. At every point of this field, if a small electrified
body were placed there, there would be a certain resultant force
experienced by it dependent upon the distribution of electricity
producing the field. When we know the strength and direction of this
resultant force, we know all the properties of the field, and we can
express them numerically or delineate them graphically, Faraday (Exp.
Res., Sec. 3122 _et seq._) showed how the distribution of the forces in any
electric field can be graphically depicted by drawing lines (which he
called _lines of force_) whose direction at every point coincides with
the direction of the resultant force at that point; and Clerk-Maxwell
(Camb. Phil. Trans., 1857) showed how the magnitude of the forces can
be indicated by the way in which the lines of force are drawn. The
magnitude of the resultant force at any point of the field is a function
of the potential at that point; and this potential is measured by the
work done in producing the field. The potential at any point is, in
fact, measured by the work done in moving a unit of electricity from the
point to an infinite distance. Indeed the resultant force at any point
is directly proportional to the rate of fall of potential per unit
length along the line of force passing through that point. If there be
no fall of potential there can be no resultant force; hence if we take