Oil drop experiment--How was the result so accurate?

I remember while learning about Millikan's oil drop experiment and being pretty skeptical about the setup. I know that there is a lot of controversy regarding manipulation of data, but the fact is; he still got a pretty close answer. I mean, we can get the correct answer by manipulation of data if we know the answer already. If we don't all we can do is 'reduce' the error box (which Millikan purportedly did). But I'm surprised that he still got an answer close to 1% of the actual value. I personally would have expected an error of maybe even an order of magnitude for these reasons:

• Viscosity of air: The viscosity is dependent upon humidity and other factors. I know he did use the wrong value here.
• $g$: How was this known to the accuracy required for this experiment? It varies across the Earth, and besides, could it be measured to whatever accuracy using the equipment available at that time?
• Velocity of the oil drop: I don't know how fast the oil drops fell, but to me, terminal velocity looks pretty fast. How did he accurately measure the velocity? A micrometer eyepiece takes time to focus, and more time to take a reading. And anyways micrometer scales aren't that precise, are they?
• Potential difference: How did he accurately know this?
• "Selecting one drop": How was this done? If all drops had a charge as a small integral multiple of q, there should be more drops with the same charge which behave the same. How can you get rid of those?
• Densities of air/oil: Air density varies. Oil density may not be known accurately.
• Electric field: Between plates, E is not exactly constant or equal to $V/d$ There are fringing effects which may alter the value of E. IMO since the distance between the plates is comparable to the area (it look like it), fringing effects are pretty significant.
• Stokes law is only applicable for perfectly spherical bodies. Is a falling oil drop perfectly spherical?

Basically I'm skeptical of how one can get such a tiny number with 1% accuracy with all those uncertainities. Could someone convince me how he did get it so accurately? Were there any measures he took to minimise these errors (I can't find any)?

• there has been controversy in his data set selection...en.wikipedia.org/wiki/… Feb 28, 2012 at 5:41
• @VineetMenon I know that, I've mentioned it. I don't care about his reported error box, I'm just skeptical how he got such a close answer. He couldn't have chosen the data set to match the value of e as the value of e was unknown at that time. Feb 28, 2012 at 6:18

1 Answer

I vaguely remember doing a Millikan oil drop experiment in a lab in college, 60+ years ago. Here is an example. With enough measurements the statistical error can become 1%, or as precise as one wants.

So your question is basically about the systematic errors. Most of them would also follow the addition in quadrature rule, since most systematic errors themselves follow a gaussian.

I tried to find laboratory examples from students' efforts but was unsuccessful. I do not see though why the various systematic factors you list could not be within less than 1% at that time. Classical physics measurements were quite sophisticated.

• Nice link! Any idea on how the velocities were measures? Was the velocity extremely slow? Feb 28, 2012 at 6:21
• Wasn't the voltage on the plates adjusted to make the velocity zero? As I recall the drops were viewed through a crosshair. Feb 28, 2012 at 7:05
• At my time, hair lines in the scope and stop watches. The fall of the droplets could be made very slow depending on the field. Sorry not to have better memory. It was multiples of e we measured. Feb 28, 2012 at 7:09
• Yes, but part of the experiment is done without a field, right? To measure the radius of the drop? Or is it done by applying various Es and measuring velocities in each case? Feb 28, 2012 at 7:21
• If you read the instructions in the link, you will see that it is a limits method. The radius does not have to be measured explicitly. When we did the experiment the setup was readied by the lab instructor, whereas in the link instructions they are guided for calibration etc; we only had to watch for the droplets. Feb 28, 2012 at 8:00