The electrometer and its connections are charged to a potential _V₁_ by
a battery, and the deflection _d₁_ of the needle is noted. By means of
an insulated key, the capacity of the standard condenser is added in
parallel with the electrometer system. Let _V₂_ be the potential of the
system, and _d₂_ the new deflection.
Then _CV₁_ = (_C_ + _C₁_) _V₂_,
_C_ + _C₁_ _V₁_ _d₁_
-------- = ---- = -----
_C_ _V₂_ _d₂_
_d₂_
and _C_ = _C₁_ ----------
_d₁_ − _d₂_
[Illustration: Fig. 19.]
A simple standard capacity for this purpose can be constructed of two
concentric brass tubes the diameters of which can be accurately
measured. The external cylinder _D_ (Fig. 19) is mounted on a wooden
base, which is covered with a sheet of metal or tinfoil connected to
earth. The tube _C_ is supported centrally on ebonite rods at each end.
The capacity is given approximately by the formula
$$ C = \frac {l} {2 \log_e \frac {b} {a}} $$,
where _b_ is the internal diameter of _D_, _a_ the external diameter of
_C_, and _l_ the length of the tubes.
The following method can be used in some cases with advantage. While a
testing vessel is in connection with the electrometer, a sample of
uranium is placed on the lower plate _A_. Let _d₂_ and _d₁_ be the
number of divisions passed over per second by the needle with and
without the standard capacity in connection.
_C_ + _C₁_ _d₁_
Then ---------- = ----,
_C_ _d₂_
_d₂_
and _C_ = _C₁_ ---------
_d₁_ − _d₂_
This method has the advantage that the relative capacities are expressed
in terms of the motion of the needle under the actual conditions of
measurement.
=69. Steady deflection method.= The methods of measurement previously
described depend upon the rate of angular movement of a suspended
gold-leaf or of an electrometer needle. The galvanometer can only be
employed for measurements with intensely active matter. A need, however,
has long been felt for a method in which ordinary ionization currents
can be measured by means of a steady deflection of an electrometer
needle. This is especially the case, where measurements have to be made
with active substances whose activity alters rapidly in the course of a
few minutes.
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