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We have learned a lot from experience about how to handle some of the ways we fool ourselves.
One example: Millikan measured the charge on an electron by an experiment with falling oil drops, and got an answer which we now know not to be quite right.
It's a little bit off because he had the incorrect value for the viscosity of air.
It's interesting to look at the history of measurements of the charge of an electron, after Millikan.
If you plot them as a function of time, you find that one is a little bit bigger than Millikan's, and the next one's a little bit bigger than that, and the next one's a little bit bigger than that, until finally they settle down to a number which is higher.

1.824 seconds.