The way in which scientists should deal with errors in observations of natural phenomena was a subject of much debate over a period of about 150 years between around 1720 and 1870. The history is well documented in numerous publications by Oscar Sheynin (also Oskar Cheinine, Л. Б. Шейнин) .
Two issues of central importance to the debate were:
- whether the mean of a series of observations provided a better estimate of the true value than a did a single "good" observation (see for example, the paper by Simpson), and
- how best to characterize the distribution of errors (see for example, the paper on Gauss and the Theory of Errors by Sheynin)
Although I have looked at several papers of Sheynin's, and tracked down some of the papers to which he refers, I have been unable to find any actual set of observations (of anything ... astronomical, geodetic, or otherwise) that dates from the period and were used in any writing on the topic either of the mean or of error distributions.
Can anyone suggest where I might locate such a data set, even if of only a handful of observations? ... It would be especially useful to me if I can find a set of repeated (i.e., resampling) observations, as opposed to a time series.
But for his death only a few weeks ago on 3 January 2024, and of which I only just learnt, I might have emailed Shenyin himself. As it stands, this forum seemed the best place to ask because of the subject of interest, although obviously SE Opendata is an alternative if my question is not considered appropriate here.