The decisive battle of Pittsburgh, on Monday, April 7th, terminated in the retreat of the vast army of rebels, which fell back to Corinth. During the latter part of the same week, Gen. Halleck arrived on the field to assume the chief command of the Federal Army. The success of Gen. Pope’s division at New Madrid, and at Island No. 10, placed his superb army of about twenty thousand strong, at Halleck’s disposal; and they were now ordered to join the grand army under the commander-in-chief. They were assigned position at Hamburgh, four miles above Pittsburgh Landing, fronting on the extreme left of the Federal lines. Several changes were now made in the organization of the Federal army. The divisions of Sherman and Crittenden were added to Grant’s _corps d’armée_. This gave Grant eight divisions. The reserve of Grant’s forces were composed of the divisions of Gen. Lew. Wallace, Crittenden, and McClernand; the former command of the latter being conferred upon Brig.-Gen. John A. Logan. While McClernand was placed in command of this reserve, Gen. Thomas was placed in chief command of the remaining divisions of Grant’s forces. In the field position, Grant’s forces constituted the right, Buell’s the centre, and Pope’s the left. The first advance was ordered on April 29, the entire army moving toward the common centre, Corinth. Wallace held the extreme right. McClernand moved along the lower Corinth road, to a point one and a half miles west of Monterey. Sherman moved directly for a hill commanding Monterey, and occupied it on the morning of the 30th of April. Every thing on the route indicated the haste with which the enemy had retreated, after his defeat. Gun carriages, caissons, wheels, tents, and all the apparatus of war, broken or burned, strewed the whole line of march. On the same day Gen. Wallace dispatched a force to cut the Ohio and Mobile railroad at Bethel, south of Purdy, in order to sever the rebel communication to the northward. Three battalions of cavalry, and one of infantry, under command of Col. Morgan L. Smith, executed this commission. They found the rebels in position near Purdy, in a piece of woods. While the infantry and a detachment of cavalry engaged the enemy, Colonel Dickey, with two battalions of cavalry moved to the railroad. They destroyed a bridge a hundred and twenty feet in length, and the conductor, engineer, and four others were taken prisoners. Buell struck direct from Pittsburgh Landing toward Corinth, while Pope’s division pushed forward from Hamburgh towards the lower point.