I recently read Ken Alder's "The measure of all things" about the first steps of the metric system definition. The project described in the book was the measure the meridian arc between Dunkirk and Barcelona in order to be able to define the meter (equal to one ten-millionth of the quarter meridian). When he was in Barcelona, Pierre Méchain, the astronomer in charge of this part, made different measures in different parts of the city, but one of his results was inconsistent with the others and confused (a lot) Méchain.

Almost 30 years later, in Connaissance des temp pour l'an 1831, p. 58-77 (published in 1828), J.-N. Nicollet, a member of the Bureau des Longitudes (and later known for his maps of the Mississipi river) wrote an article about Méchain's results saying (among other things) that experimental errors should be distinguished between :

  • systematic errors, due for instance to bad calibration of instruments or imperfect methods of observation
  • random errors, due for instance to fluctuations in the measurements or interpretations

So, basically, it's all about better describing the accuracy and make a clear difference between trueness and precision.

I am wondering if Nicollet was the first to make this clear distinction. Before him, who worked on this topic and may have inspired Nicollet ?

Also, I do not see many comments to Nicollet article (only an anonymous one in Philosophical magazine 1829, p.180-188 ). Was there discussions on this topic after Nicollet ? (to challenge, to fine-tune, etc...).


1 Answer 1


One year later, let me answer my own question.

If we dig a little bit, we do find comments of Nicollet's work:

And also some words in astronomers letters:

Those comments are from total rejection (The philosophical magazine) to full acceptance (Airy). Interesting to note that french comments are not focusing at all on the constant error (but more on other aspects of the Nicollet's memoir) whereas non-french do consider this point. And we see that some of the european astronomers were already aware of this question.

  • Zach for instance noticed the strange behaviour or repeating circles, and wrote a lot on it starting from 1812 https://books.google.fr/books?id=64UvZnoWFCAC
  • Gauss, when when presenting his least squares method in February 1821 at Gottingen had to describe correctly what is a random error (upon which we can apply least squares) in opposition to systematic one (upon which we cannot).
  • Friedrich Wilhelm Bessel, from Königsberg observatory, did some experiments to identify the origin of the issues, for instance in Philosophical Magazine, Vol.59, p.44, June 1822, https://books.google.fr/books?id=UzJDAQAAMAAJ
  • Piotr Sławiński, from Vilnius observatory, even proposed formulas to correct measures made with his repeating circle, Astronomische Nachrichten, n°96, p.554, https://books.google.fr/books?id=adozAQAAIAAJ

All this studies were made and published (mostly in french or english) before Nicollet's memoir. We can safely assume french astronomers knew these publications, but probably disregarded them because the repeating circle manufacturer was not the same (made by Reichenbach in Munich versus made by Lenoir in Paris). Last interesting point, Arago, working with Nicollet at Paris observatory also noticed suspicious things with Borda's repeating circle 10 years before, and even provided a relevant experimental workaround. This can be seen for instance in the minutes of the weekly Bureau des longitudes, 11st and 25th november 1818. But, he didn't go further in his analysis: no hypothesis about the origin of the problem nor any rigorus motivation of its workaround.

My personal conclusions of this story are:

  • Nicollet is definitively not the first one to make the distinction between systematic and random error (anyway, it took decades to make this distinction clear)
  • Nicollet did not invent new concepts nor apply new methods to solve Méchain's problem, he "just" (tough calculatory work though) applied some other's ideas with better data (taken from more recent stars catalogs)
  • German astronomers did very insteresting things regarding random and systematic errors, but Nicollet ignored them (volontarily, because of french astronomers mindset ?)
  • the full history of random vs. systematic error is yet to be done (at least for the french side)


for those who are really curious, the anonymous writer of the Philosophical magazine is probably Xavier von Zach.

We can assume that from a letter Zach wrote to Johann Kaspar Horner on March 1829 (same month of the publishing) stating that he sent to a journal a very critical comment of Nicollet's work. See Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, vol.18, 1873 https://books.google.fr/books?id=xDtcAAAAcAAJ


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.