At eight o'clock this morning the battle between the Union and rebel forces at Fair Oaks, Va., was resumed, and the rebels were defeated and compelled to fall back upon Richmond.--(Docs. 17 and 92.)
General Fremont's advance brigade, under Colonel Cluseret, occupied Strasburgh without resistance. A midnight reconnaissance three miles beyond Strasburgh came upon a rope barricade and ambush of Jackson's rear-guard, and retired successfully with the loss of only three wounded. Col. Figyelmesy, of Gen. Fremont's staff, with only fifteen men, brilliantly charged and put to flight a body of cavalry commanded by Ashby in person.
The expedition sent out by General Pope on the twenty-eighth of June, under Colonel Elliott, with the Second Ohio cavalry, returned to Corinth, Mississippi, this day. By forced marches they reached the Mobile and Ohio Railroad, and although the rebels were guarding it with a force of five thousand infantry running up and down to prevent him reaching it, succeeded in destroying the track in many places, blowing up one culvert, burning the depot, locomotives, and a  train of twenty-six cars loaded with supplies, destroying ten thousand stand of small arms, three pieces of artillery, and capturing two thousand prisoners, whom he released on parole, as he had not time to march them with his cavalry.--(Docs. 49 and 76.)
The fortifications at Pig Point, Va., were destroyed to-day, together with the rebel barracks in the vicinity.--An order was issued from the War Department extending the Department of Virginia to include that part of Virginia south of the Rappahannock and east of the railroad from Fredericksburgh to Richmond, Petersburgh, and Weldon, under command of Major-Gen. McClellan. Major-Gen. Wool was assigned to the command of the Middle Department, and Major-Gen. Dix to Fortress Monroe to assume command at that point, reporting to Gen. McClellan for orders.
Yesterday the Union forces under command of Brig.-Gen. Wright succeeded in crossing from Edisto Island to Seabrook's Point, S. C., and to-day they had a skirmish with the rebel pickets in the vicinity, which resulted in the retreat of the rebels.--Official Report.