Immediately after the battle of Iuka, the rebel forces of Price and Van Dorn formed a junction, for the purpose of making another attempt upon Corinth. General Rosecrans, meanwhile, always watchful and energetic, speedily divined their plans, and at once made the requisite preparations to check their advance. Nor was the collision long deferred. On the morning of the 3rd of October, the Union forces were attacked by a body of insurgents, largely superior in numbers, (officially stated at thirty-eight thousand,) and on that day and the next was fought one of the bloodiest battles of the war, which is known as the battle of Corinth. The rebel force was commanded by Generals Price, Van Dorn, Lovell, Villipigue and Rusk. The following was the disposition of the Union troops, on the 3rd of October: General McKean with his division occupied Chewalla; General Davis with his division, occupied the line between the Memphis and Columbus road: General Hamilton, with his division, had taken position between the rebel works, on the Purdy and Hamburgh roads; and General Stanley held his division in reserve, near the old headquarters of General Grant. This disposition of the troops placed General Hamilton on the right, General McKean on the left, and General Davis in the centre. McKean had an advance of three regiments of infantry, and a section of artillery under Colonel Oliver, on the Chewalla road, beyond the enemy’s breastworks. On the morning of the 3rd, the advance under Colonel Oliver, took a strong position on a hill, near an angle in these breastworks: and at about nine o’clock they were strongly pressed by the enemy, who manœuvred to outflank them. At ten o’clock General Rosecrans was informed that Colonel Oliver was imperatively in need of reinforcements, and must yield his position unless they were furnished. The hill would be of great value to the enemy; and it was therefore necessary that the Union forces should hold possession of it; and two regiments of Colonel Davies’ brigade were sent to Colonel Oliver’s assistance. It was presently demonstrated that Brigadier-General Arthur had taken up four more regiments from McKean’s division; and Colonel Oliver’s position upon the hill was being strongly contested. An advance, leaving an interval between McArthur’s and Davies’ left, was now made upon the enemy’s breastworks; but the rebels cleverly pushed on behind Davies’ left, and, after a fierce and determined resistance, forced the brigade to a rapid retreat of nearly a thousand yards, in which movement it lost two heavy guns. Of the fighting, in this engagement, on the 3rd of October, General Rosecrans speaks thus: