Lt. Gen. Ulysses S. Grant pressed on with fierce fighting in Virginia, his massive Union force intent on breaking the backbone of the Confederacy on its territory. But Confederate rivals in turn exacted heavy casualties on the Union foe. On June 1, 1864, Union cavalry fighters drove back one attack by Confederate forces, which were being reinforced by more troops arriving from Richmond, Va., seat of the Confederacy. Union attempts to attack the Southern forces met with heavy casualties on the federal side. The fighting raged for days along a front stretching for miles to the Chickahominy River in Virginia. By mid-June of that year, with both sides bloodied and wearied, Grant began moves to relocate his forces in an area threatening Petersburg, Va., below Richmond.