The Army crossed the Rhine River on 1 March 1799 under the command of Jean-Baptiste Jourdan, in the order of battle below. As elements crossed the Rhine, they took the name "Army of the Danube". The crossing was completed by 7 March. After passing through the Black Forest, the Army fought two battles in quick succession, the Battle of Ostrach, on 20–21 March, and Stockach, on 25–26 March. It suffered badly in both engagements and, following the action at Stockach, withdrew to the Black Forest. Jourdan established his headquarters at Hornberg, and the Reserve cavalry and the cavalry of the Advance Guard quartered near Offenburg, where the horses could find better forage.