Reports of the engagement; HDQRS. DISTRICT OF WEST TENNESSEE, Memphis, Tenn., May 4, 1864. GEN.: On the afternoon of the 2d instant the advance of Sturgis’ cavalry, 700 strong, under Lieut.-Col. Karge, Second New Jersey Cavalry, encountered a brigade of Forrest’s cavalry near Bolivar, on the south side of Hatchie. The enemy were from 800 to 1,000 strong. After a severe fight of two hours the enemy retreated across the Hatchie, destroying the bridge. They retreated through Bolivar in a southeast direction. Gen. Sturgis fears that Forrest has retreated between the Hatchie and Tennessee Rivers. He hears that the cars are running to Corinth, and that a part of Gen. Polk’s forces are below Corinth. Our losses in the action were 2 killed and 10 wounded. My latest information from Gen. Sturgis is to 7.30 o’clock yesterday morning, whence was 16 miles west of Bolivar but expected to have a large part of his cavalry force up to Bolivar by 12 o’clock yesterday. The heavy rains had so swollen the creeks as to greatly retard his movements. I am, general, your obedient servant, C. C. WASHBURN, Maj.-Gen. HDQRS. DISTRICT OF WEST TENNESSEE, Memphis, May 6, 1864. GEN.: On the 30th ultimo I sent from here 3,300 cavalry and 2,000 infantry in pursuit of Forrest, under Gen. Sturgis. On the day following [May 1st] Forrest left Jackson, Tenn., in force, retreating south. My advance met a brigade of his in the afternoon of the 2d near Bolivar, and after a sharp engagement of two hours drove them from their intrenchments with considerable loss. They retreated across the Hatchie, destroying the bridge behind them. Our loss, 2 killed, 10 wounded. Forrest with his whole force encamped on night of 2d at Purdy, and continued his retreat the day following [3d] toward Pocahontas. He crossed the Hatchie at Pocahontas on the 4th, and Sturgis was in hot pursuit. A co-operating force which I expected from Bethel to be at Purdy on the night of 30th failed me or I should have captured his whole force. The Hatchie was very high and impassable anywhere below Bolivar. I still hope to punish him severely before he gets out of reach. C. C. WASHBURN, Maj.-Gen. HDQRS. DISTRICT OF WEST TENNESSEE, Memphis, May 8, 1864. (Received 11th, 11 a. m.) Forrest is driven out of West Tennessee. My forces followed him as far as East Mississippi, but his swift horses rendered farther pursuit unavailing. There is no organized enemy in West Tennessee or Kentucky.