# How can one determine the charge of $e$ in Milikan's oil drop experiment

Inspired from this answer, I have an question about Milikan's oil drop experiment:

if we have a set of data, say $q_1, q_2, ..., q_n$, since those $g_i$'s have some error bars, we cannot directly calculate the greatest common divisor of those values because they are not exact and it will probably lead to the result $1$, so we to find a value, say $e$, s.t for all $i$, $q_i \approx e \cdot k$, where $k$ is an integer, so without trial-and error (which would be really hard to do without computers) or any other assitant of a computer, how can we find such a value $e$ ?

Edit:

Considering the fact that I have asked the question How did Milikan know that oil drops would acquire only few electron charges?, the answer given to this question is, kind of, out of range.

• I'm voting to close this question as off-topic because it is asking about statistical analysis and belongs on Cross-Validated SE. – sammy gerbil Feb 6 '18 at 20:56
• @sammygerbil Then don't downvote, just flat to be migrated, Jesus! – onurcanbektas Feb 7 '18 at 4:08
• Have a look web.pa.msu.edu/courses/2003spring/PHY192/… on the how. The milikan oil drop charge measurement is a standard physics lab experiment . I vaguely remember doing it back in 1959 using a microscope. – anna v Feb 7 '18 at 4:57
• There was no computer at the lab in 1959 either. We reproduced the experiment. Pencil and paper and brain power. :) In page 10 in my link above there is a current plot measured at a student lab. in page 6 the experimental method is clearly described. – anna v Feb 7 '18 at 5:09
• There are some basic tips on p7 here. It suggests using the smallest difference as 1st estimate of $e$. This gives the closest multiple$n$ of $e$ for each data point. Then use Linear Regression $(q=en)$ to find the value of $e$ which minimises sum of squared errors (SSE). Tweaking the biggest multiples might further reduce SSE. There is also a formula for Standard Error within Linear Regression. – sammy gerbil Feb 7 '18 at 5:51