FORTRESS ROSECRANS, Murfreesborough, Tenn., December 10, 1864.

GENERAL: I have the honor to report that, in obedience to your order, I proceeded on the 7th instant ot make a reconnaissance and feel the enemy in the vicinity of this post. I took with me, by your direction, seven regiments of infantry and a six-gun battery, under the and a small detachment of the Fifth Tennessee Volunteer Cavalry. One hundred and seventy-seventh, One hundred and seventy-fourth, One hundred and seventy-seventh, One hundred and seventy-eight, first Illinois volunteer Infantry, Eighth Minnesota Volunteer Infantry, and Twelfth indiana Volunteer Cavalry (dismounted). For convenience, I divided these regiments into two brigades (pro tempore), as follows: First Brigade, Colonel Thomas, of the eighth Minnesota, commanding, consisted of a six-gun battery, eighth Minnesota Volunteer Infantry, Sixty-first Illinois Volunteer Infantry, One hundred and seventy-fourth and One hundred and eighty-first Ohio Volunteer Infantry, 1,973 strong. The Second Brigade consisted of the One hundred and seventy-seventh, and One hundred and seventy-eight Ohio Volunteer Infantry, and Twelfth Indiana Volunteer Cavalry, 1,326 strong. Total strength of my infantry, artillery, and cavalry combined, 3, 325. I started on the Salem pike about 10 a. m., and threw out the detachment of the Fifth Tennessee Cavalry in advance, who struck the rebel vedette in less than half a mile after passing our pickets. The rebel cavalry fell back rapidly before my advance. I threw out a portion of the sixty-first Illinois Volunteer Infantry as skirmishers, to assist the cavalry in driving them. Upon arriving at Stone's River, two miles out, a body of about 300 rebel cavalry were discovered across the rive. I brought up a section of Captain Bundy's battery and shelled them a few minutes, when they retreated rapidly, and I crossed the bridge and continued my march.

Upon arriving at Mr. Spence's fine residence, for miles out, I learned from his accomplished lady that there were two brigades of rebel cavalry, under Generals jackson and Armstrong, at Salem a mile farther out, and that Generals Forrest and Bate, with a large force of infantry, artillery, and cavalry, were north of me, on the Wilkinson pike, three miles from Fortress Rosecrans. I deemed it best to turn my attention in that direction, but before doing so I detailed a company and sent them back with a drove of sixty fine, fat hogs, belonging to Mr. Spence, that would have fallen into the hands of the rebels if left. I proceeded north till within half a mile of the Wilkinson pike. My skirmish line encountered that of the enemy, and in a few minutes afterward they opened on me with much rapidity from a six-gun battery stationed in the edge of a wood on the opposite side of a field in my front. I at once ordered forward Captain Bundy's battery, which artillery ammunition that could be carried in the limbers of the guns, the shell and solid shot of my supply was exhausted in about thirty minutes. Finding that the enemy would not come across the field to attack me, and not being able to ascertain his strength,a nd the left of his line, extending parallel with the Wilkinson pike, was as near Fortress Rosecrans as my right i deemed it prudent not to engage them with my infantry without having the fortress in my rear, and accordingly fell back through the forest until out of sight of the enemy, and then moved by the right flank in a northeasterly direction until my