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Interesting that this had been rated high in importance by WP:Scotland & WP:Physics, but unrated by WP:Geology until today. I’ll take the liberty of rating it for WP:Geology, as mid, on the basis that:
However it is an important development which filled in a very significant specific knowledge area – how the gravitational attraction resulting from large masses of earth was initially detected. It served as the basis for the science which subsequently developed to measure the density of the planets & detection of mascons.
An argument could be made that the importance of this article is “low” – the argument would go that this is an interesting piece of historical trivia that is only useful in instructing beginning students by providing them the insight that gravitation can be measured & giving them an example of the scientific method in practice. However pivotal discoveries & turning points in scientific understanding are arguably noteworthy.
As always on Wikipedia, comments are welcomed if you think I got this wrong.
The experiment will find the mean density of the Earth. The basic theory relies on the fact that a sphere of any density distribution can be replaced by a point mass at the centre, of the same total mass. The only requirement is that the density distribution is a function only of the distance from the centre of the sphere; it must be symmetric. (This is true for any inverse-square law.) A nearby mass not lying inside the perfect sphere, or gaussian surface, can be considered as a mass separate to the Earth. The idea of replacement by a point mass was known by the early 1700s ... Leonard Euler I suspect.22.214.171.124 (talk) —Preceding undated comment added 08:25, 4 November 2015 (UTC)