Francois Arago brought the news of Oersted’s discovery of the effect of a current-carrying wire on a magnet to Paris on September 4, 1820. André-Marie Ampère and the team of Jean-Baptiste Biot and Félix Savart quickly set to work to establish a quantitative law for this effect. Their approaches were quite different. This paper describes the experiments of Biot and Savart and their results. It also briefly discusses the approach of André-Marie Ampère, who coined the name “electrodynamics” and whose fundamental formula gave the force between two infinitesimal current elements. Ampere’s formula fell into disuse after the advent of Maxwell’s field approach. Biot and Savart’s experimental law, in the modern form of the differential magnetic field due to a current element, became the standard starting point for calculating the magnetic field due to steady currents.