[1] Cf. Siemens's account of the use of this furnace for experimental
purposes in _British Association Report_ for 1882.
ELECTROMETER, an instrument for measuring difference of potential, which
operates by means of electrostatic force and gives the measurement
either in arbitrary or in absolute units (see UNITS, PHYSICAL). In the
last case the instrument is called an absolute electrometer. Lord Kelvin
has classified electrometers into (1) Repulsion, (2) Attracted disk, and
(3) Symmetrical electrometers (see W. Thomson, _Brit. Assoc. Report_,
1867, or _Reprinted Papers on Electrostatics and Magnetization_, p.
261).
_Repulsion Electrometers._--The simplest form of repulsion electrometer
is W. Henley's pith ball electrometer (_Phil. Trans._, 1772, 63, p. 359)
in which the repulsion of a straw ending in a pith ball from a fixed
stem is indicated on a graduated arc (see ELECTROSCOPE). A double pith
ball repulsion electrometer was employed by T. Cavallo in 1777.
It may be pointed out that such an arrangement is not merely an
arbitrary electrometer, but may become an absolute electrometer within
certain rough limits. Let two spherical pith balls of radius r and
weight W, covered with gold-leaf so as to be conducting, be suspended
by parallel silk threads of length l so as just to touch each other.
If then the balls are both charged to a potential V they will repel
each other, and the threads will stand out at an angle 2[theta], which
can be observed on a protractor. Since the electrical repulsion of the
balls is equal to C^2V^24l^2 sin^2[theta] dynes, where C = r is the
capacity of either ball, and this force is balanced by the restoring
force due to their weight, Wg dynes, where g is the acceleration of
gravity, it is easy to show that we have
2l sin [theta] [root](Wg tan [theta])
V = -------------------------------------
r
as an expression for their common potential V, provided that the balls
are small and their distance sufficiently great not sensibly to
disturb the uniformity of electric charge upon them. Observation of
[theta] with measurement of the value of l and r reckoned in
centimetres and W in grammes gives us the potential difference of the
balls in absolute C.G.S. or electrostatic units. The gold-leaf
electroscope invented by Abraham Bennet (see ELECTROSCOPE) can in like
manner, by the addition of a scale to observe the divergence of the
gold-leaves, be made a repulsion electrometer.
[Illustration: FIG. 1.--Snow-Harris's Disk Electrometer.]
_Attracted Disk Electrometers._--A form of attracted disk absolute
electrometer was devised by A. Volta. It consisted of a plane conducting
plate forming one pan of a balance which was suspended over another
insulated plate which could be electrified. The attraction between the
two plates was balanced by a weight put in the opposite pan. A similar
electric balance was subsequently devised by Sir W. Snow-Harris,[1] one
of whose instruments is shown in fig. 1. C is an insulated disk over
which is suspended another disk attached to the arm of a balance. A
weight is put in the opposite scale pan and a measured charge of
electricity is given to the disk C just sufficient to tip over the
balance. Snow-Harris found that this charge varied as the square root of
the weight in the opposite pan, thus showing that the attraction
between the disks at given distance apart varies as the square of their
difference of potential.
The most important improvements in connexion with electrometers are due,
however, to Lord Kelvin, who introduced the guard plate and used gravity
or the torsion of a wire as a means for evaluating the electrical
forces.
[Illustration: FIG. 2.--Kelvin's Portable Electrometer.]
[Illustration: FIG. 3.]
His portable electrometer is shown in fig. 2. H H (see fig. 3) is a
plane disk of metal called the guard plate, fixed to the inner coating
of a small Leyden jar (see fig. 2). At F a square hole is cut out of H
H, and into this fits loosely without touching, like a trap door, a
square piece of aluminium foil having a projecting tail, which carries
at its end a stirrup L, crossed by a fine hair (see fig. 3). The
square piece of aluminium is pivoted round a horizontal stretched
wire. If then another horizontal disk G is placed over the disk H H
and a difference of potential made between G and H H, the movable
aluminium trap door F will be attracted by the fixed plate G. Matters
are so arranged by giving a torsion to the wire carrying the aluminium
disk F that for a certain potential difference between the plates H
and G, the movable part F comes into a definite sighted position,
which is observed by means of a small lens. The plate G (see fig. 2)
is moved up and down, parallel to itself, by means of a screw. In
using the instrument the conductor, whose potential is to be tested,
is connected to the plate G. Let this potential be denoted by V, and
let v be the potential of the guard plate and the aluminium flap. This
last potential is maintained constant by guard plate and flap being
part of the interior coating of a charged Leyden jar. Since the
distribution of electricity may be considered to be constant over the
surface S of the attracted disk, the mechanical force f on it is given
by the expression,[2]
S(V - v)^2
f = ----------,
8[pi]d^2
where d is the distance between the two plates. If this distance is
varied until the attracted disk comes into a definite sighted position
as seen by observing the end of the index through the lens, then since
the force f is constant, being due to the torque applied by the wire
for a definite angle of twist, it follows that the difference of
potential of the two plates varies as their distance. If then two
experiments are made, first with the upper plate connected to earth,
and secondly, connected to the object being tested, we get an
expression for the potential V of this conductor in the form