•Electricity in the last quarter of the 18^th century was a difficult subject, part of what are known today as the " Baconian Sciences ". Electrical phenomena were new and exciting and many attempts were made at interpreting, quantifying and mathematising them. These attempts, even if they eventually gave birth to a sort of " Standard Model ", were rooted in the natural philosophy and in the epistemological criteria of the time.

•Coulomb was a military engineer, one of the first to have vast mathematical skills. Working on friction, he invented a very precise, if very delicate, instrument: the torsion balance. He decided to apply it to quantify electrical attractions and repulsions, assuming a strict Newtonian gravitational framework. He succeeded with repulsion, even if he just provided three measures of only one experiment (and the third, by his own admission, was rather faulty). To explain attraction, a new device was invented, and to complete the law, the numerator was (simply) added (how could he define three quantities with one instrument?). This " elementary " law at first did not help to deal with standard bodies (the history of its acceptance is itself delightful). Given the similarities with Newtonian gravity, it eventually led to applying to electrostatics the mathematical tools of celestial dynamics, and specifically (Laplace and Poisson’s) partial differential equations, the so-called pseudo-contiguous action. Was it a stable scientific acquisition ? Certainly yes, from a quantitative point of view; certainly no, from a theoretical perspective: Feynman is rather outspoken about that.