Attempts by Descartes and Roberval to evaluate the centre of oscillation of compound pendulums

This paper re-examines the first documented attempts to establish the quantitative law of motion for a body oscillating about a fixed axis (a compound pendulum). This is quite a complex problem as weight and motion are not concentrated in a point, but are spread over a volume. Original documents by René Descartes and Gilles Personne de Roberval, who made the first contributions to solving the problem, are discussed. The two scientists had important insights into the problem which, although they were incomplete, nevertheless somehow complemented each other - at least when seen from the viewpoint of modern mechanics. Descartes was right in considering only the absolute value of the inertia forces, Roberval was right in assuming that the force of gravity should also be taken into account.