In 1821 Alexis Bouvard published a book with tables of the orbits of Jupiter, Saturn and Uranus and future predictions of the orbits. The real orbit of Uranus deviated from the calculations which was the starting point of an investigation which eventually led to the discovery of Neptun.
I am wondering how he performed the calculation, which I presume is not just Keppler Orbits, but including some pertubation from the know planets (correct me if I understand that wrong). Usually nowadays you would do pertubation calculations in the Hamilton-Jacobi framework, but since Jacobi just started college in 1821 it has not been invented yet (I presume).
So anybody knows how exactly these calculation were done at that time?