IIeadquarters Ahmy oï tuk Potomac, ) August 6. ) The army of the Potomac ha3 again assumed the offonsive. The reoonnoisancü made yesterday under Gen. Hooker to Malveru Hill, White Uak Swamp Bridge, and in the direction of' Newmarket aud Kichmond, was in every respect a completa suecess. Tho troops loft camp about dark night bcore last, arriv ing at Malcru Ilill at 4 o'clock yesterday moruing a distance of ten miles. - Ilere they eneouutered two régimen ts of infantry and a battery posted behind cartliworks. Fire was immediately opefied on them by Oapt. ijeuson's battery, and a section of Capt. llobinaoirs. The Infautry was not engaged. The firing lastcd about threo hpUTS, when tlie rebels inglorionsly fled by tho rivcr rond to ltiuhmoud, hotly pursued by our troops, vho succeeded m taking 100 of them prisoners. Tlie loss on our sido at tbis point was three killed and eleven woundod. Captain Bemoo had his thigh brokeu by a piece ui' shell. The doctors think the leg can be saved. Licut. Col. Gamble, of the Eighth Illinois Cavalry, waaseveflj wounded n tho breast while driving in the encmy's pickets. Col. Avcrill,with 5Qp cavalry, took tbo Quaker road to Whita Oak Swamp Bridge. There they found the Tenth Virgiuia Cavalry drawn up to receive them. A charge was innuediatelv ordered, which broka the rebel liues, when they fled. Col. Averill followed them thrcc miles, taking .'JÖ prisor.ers, without losing a man. Gen. Pfeasanfon, with a forcé of cavalry, took tbc Newmarket road, on whieh a por;ion of the rebels wcrc rctreating. - He then followoJ thcm to witLiu a short distance of Newmarket, whore, mueting two brigades of rebels, he feil back, bring ing over thirty prisooers taken on the way. Newmarket ia ten miles from Riebmoad. This endecl tho operations ior the day, whou the troop went into camp on Malvern Uil!. Gen. MoOleüan, who went to tho scène of action early yesterday morning, has not returned.