(v1 - v2)(v2 - v3).
But this last expression is proportional to the instantaneous power
taken up in the inductive circuit, and hence the difference of the two
readings of the electrometer is proportional to the mean power taken
up in the circuit (_Phil. Mag._, 1891, 32, p. 206). Ayrton and Perry
and also P.R. Blondlot and P. Curie afterwards suggested that a single
electrometer could be constructed with two pairs of quadrants and a
duplicate needle on one stem, so as to make two readings
simultaneously and produce a deflection proportional at once to the
power being taken up in the inductive circuit.
[Illustration: FIG. 7.--Quadrant Electrometer. Dolezalek Pattern.]
Quadrant electrometers have also been designed especially for measuring
extremely small potential differences. An instrument of this kind has
been constructed by Dr. F. Dolezalek (fig. 7). The needle and quadrants
are of small size, and the electrostatic capacity is correspondingly
small. The quadrants are mounted on pillars of amber which afford a very
high insulation. The needle, a piece of paddle-shaped paper thinly
coated with silver foil, is suspended by a quartz fibre, its extreme
lightness making it possible to use a very feeble controlling force
without rendering the period of oscillation unduly great. The resistance
offered by the air to a needle of such light construction suffices to
render the motion nearly dead-beat. Throughout a wide range the
deflections are proportional to the potential difference producing them.
The needle is charged to a potential of 50 to 200 volts by means of a
dry pile or voltaic battery, or from a lighting circuit. To facilitate
the communication of the charge to the needle, the quartz fibre and its
attachments are rendered conductive by a thin film of solution of
hygroscopic salt such as calcium chloride. The lightness of the needle
enables the instrument to be moved without fear of damaging the
suspension. The upper end of the quartz fibre is rotated by a torsion
head, and a metal cover serves to screen the instrument from stray
electrostatic fields. With a quartz fibre 0.009 mm. thick and 60 mm.
long, the needle being charged to 110 volts, the period and swing of the
needle was 18 seconds. With the scale at a distance of two metres, a
deflection of 130 mm. was produced by an electromotive force of 0.1
volt. By using a quartz fibre of about half the above diameter the
sensitiveness was much increased. An instrument of this form is valuable
in measuring small alternating currents by the fall of potential
produced down a known resistance. In the same way it may be employed to
measure high potentials by measuring the fall of potential down a
fraction of a known non-inductive resistance. In this last case,
however, the capacity of the electrometer used must be small, otherwise
an error is introduced.[4]
See, in addition to references already given, A. Gray, _Absolute
Measurements in Electricity and Magnetism_ (London, 1888), vol. i. p.
254; A. Winkelmann, _Handbuch der Physik_ (Breslau, 1905), pp. 58-70,
which contains a large number of references to original papers on
electrometers. (J. A. F.)