= Oil drop charge readout and calibration
<Robert Andrews Millikan>'s 1911 protocol alternated electrically driven ascent with timed descent after short-circuiting the plates; a changed ascent <speed> signalled <ion> capture.<The Isolation of an Ion, a Precision Measurement of Its Charge, and the Correction of Stokes’s Law by Robert Andrews Millikan>[pp. 352–353]{ref}
His 1913 refinements checked voltage before and after runs, calibrated optical distance and the clock, compared independent air-<dynamic viscosity> measurements, and varied <pressure> to test slip.<On the Elementary Electrical Charge and the Avogadro Constant by Robert Andrews Millikan>[pp. 112–118]{ref} His 1924 lecture describes suppressing <convection>, switching the <electric field>, neutralizing drops, and reproducing smallest observed electrical <speed> increments.<Nobel Lectures, Physics 1922–1941/The Electron and the Light-Quant from the Experimental Point of View by Robert Andrews Millikan>[Nobel Lectures, Physics 1922–1941; pp. 56–60]{ref}
<Harvey Fletcher>'s posthumous account recalls building the first oil apparatus and measuring with <Robert Andrews Millikan>; priority for suggesting oil remains uncertain.<My Work with Millikan on the Oil-Drop Experiment by Harvey Fletcher>[pp. 44–47]{ref}
To interpret the readout, keep one drop and one <electric field> polarity. Let $u_i$ be its signed upward <terminal velocity> in charge state $i$, and let $v_f>0$ be its field-off falling <speed>. Use the <linear drag> coefficient $k$ already defined in <elementary charge>, with any required <gas slip correction to Stokes drag> included. Provided the drop's <radius>, surrounding air and <electric field> remain fixed, its electrical <speed> increment is
$$
S_i=u_i+v_f,\qquad |q_i|=\frac{k}{E}S_i,\qquad
\frac{|q_i|}{|q_j|}=\frac{S_i}{S_j},\qquad
\Delta|q|=\frac{k}{E}(u_{i+1}-u_i).
$$
These relations apply while the <electric force> points upward in every state. A drop may still descend, with $u_i<0$, when that <force> is too weak to support it. A held drop has $u_i=0$ and therefore $S_i=v_f$, rather than zero electrical response. A neutral drop has $S_i=0$: its signed <terminal velocity> agrees with field-off descent. Thus neither raw upward <speed> nor the ability to hold a drop is itself a count of <Electrons>.
The ratios cancel a fixed $k/E$, even if its value is poorly known. This is why relative <charge quantization> and absolute <measurement calibration> are different questions. A changed field-off $v_f$ warns that evaporation, air motion or another change has spoiled comparison of charge states. A stable $v_f$ is useful evidence but cannot exclude every compensating change. Repeat field-off checks around a proposed jump, allow the <terminal velocity under linear drag> to settle after switching, and propagate <measurement uncertainty> in both the field-on and field-off readings. Reusing a single estimate of $v_f$ gives the different $S_i$ a shared <covariance>.
\Image[/oil-drop-charge-jump-series.png]
{title=Simulated repeated <electric charge> states and resolved charge changes of one drop}
{id=oil-drop-charge-jump-series}
{description=Original chosen noisy readings in an arbitrary reference <electric charge> $Q_*$, with four state means and their stipulated <standard uncertainties>. These are a simulation, not measurements by <Robert Andrews Millikan> or <Harvey Fletcher>. Acquisition order is not elapsed <time>; connecting lines only group observations made in the same state.}
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