While he was there he wrote a famous memoir on the magnetic compass which he submitted for the Grand Prix of the Académie des Sciences in 1777.
This 1777 paper won Coulomb a share of the prize and it contained his first work on the torsion balance [1]:-
... his simple, elegant solution to the problem of torsion in cylinders and his use of the torsion balance in physical applications were important to numerous physicists in succeeding years. ... Coulomb developed a theory of torsion in thin silk and hair threads. Here he was the first to show how the torsion suspension could provide physicists with a method of accurately measuring extremely small forces.