Oil drop experiment and quantization of charge

Question

How to systematically show that the resulting charges in oil drop experiment are integers multiplied by $e$ in other word how to extract $e$ from the data?

Answer 1

To address John Rennie's comment in the comment section regarding the existence of a systematic, human-guess-independent algorithm for determining the LCM of a data series in the presence of significant experimental error and without the aid of single-electron-charged droplets to make a human-sensible guess:

a = 12.5654;
L = 400;
list = Table[a (RandomInteger[{6, 35}] + RandomReal[{-0.25, 0.25}]), {k, L}];
f[b_] := Module[{g = Nearest[b Range[L]]}, Sum[Abs[g[list[[k]]][[1]] - list[[k]]], 
{k, L}]/b];
ListPlot[list, PlotRange -> All]
Plot[f[x], {x, 6, 15}, PlotRange -> All]

There's no way a human could look at that plot of the noisy raw data and guess the LCM, but a computer can handle it just fine. Note that this is reliably indicating the LCM even though the "measurement" error is on the order of 50%. I used uniformly-distributed error, but it works with Gaussian-distributed errors just as fine.

As an interesting mathematical aside, in the absence of noise the LCM appears as the largest zero of the merit function, which has a sequence of zeros whose density of zeros tends as $(a x)^{-1}$ where $a$ is the LCM and $x$ is the guess. As $x\rightarrow 0$ the there is an oscillatory singularity, and for $x>a$, there are no further zeros.

Answer 2

If the experiment was done with sufficient accuracy, simply plotting the calculated charge values should give obvious clustering. (Two measurements per particle: mass from free fall velocity, and voltage to achieve zero velocity is how I remember the experiment, but that is from a fifty year-old memory of high-school physics... plot voltage/mass.)

R.J.Doe has a set of directions (with an amusing apocalyptic conclusion) on writing up a somewhat different version of the experiment: http://www.phys.ksu.edu/personal/cocke/classes/phys506/aasamplewriteup.htm using both a downward and upward acceleration to give three velocities per particle. I'm wondering if that might have the advantage that you would not need to depend on a previously measured value for the viscosity of air.

I see that DumpsterDoofus is expressing annoyance at a lack of effort and suggest perhaps the use of http://webphysics.davidson.edu/applets/pqp_preview/contents/pqp_errata/cd_errata_fixes/section4_5.html to generate dome "data" would mollify him. It would be more interesting to see data gathered this way than to look at his generation of data which I suspect is very much unlike what was gathered by Millikan. (I also disagree that we could not have done such data analysis without computers.)