On the 3d of May, a reconnoissance in force toward Farmington was ordered. The country is uneven and difficult to penetrate, and both time and caution were necessary. Generals Paine and Palmer of Pope’s command, were detailed for this important duty. The regiments selected were the Tenth, Sixteenth, Twenty-second, Twenty-seventh, Forty-second and Fifty-first Illinois Volunteers, Tenth and Sixteenth Michigan Volunteers, Yates’ Illinois Sharpshooters, Houghtaling’s and Hercock’s batteries, and the Second Michigan cavalry. The column proceeded about five miles on the Farmington road, where they encountered the enemy’s cavalry pickets. A skirmish ensued, in which the rebels lost eight killed, and the same number of their wounded, were made prisoners. The enemy was compelled to fall back, after a second skirmish, and at 3 o’clock, p. m., the vanguard came up from a swamp they had crossed, and the fight commenced in earnest. The enemy was strongly posted on an elevated piece of ground which was flanked by a part of the force, and the rebels were obliged to fall back half a mile, yielding their former position to the Federals, who pressed them closely. The two regiments of infantry having secured a position commanding the left flank of the rebels, poured upon them such a destructive fire, that their infantry abandoned their artillerists. The latter, finding themselves forsaken, hastily withdrew their guns to a new position, from which they were soon dislodged, and fled with all speed to Corinth. General Pope’s advance was thus put in possession of Farmington. This successful movement of General Pope’s advance was a cause of great annoyance to the rebels, and on the 9th of May they came out in overwhelming force to drive him back. The enemy numbered about thirty-five thousand, under command of Bragg, Price, Van Dorn, and Ruggles. General Pope had been specially directed not to engage the enemy in force. Under these circumstances he was obliged to encounter the shock of this large body, with only a single brigade, which, however, was advantageously posted. The enemy threw forward five or six regiments, with artillery, to engage this brigade, holding their immense reserve in readiness to attack the Federal reinforcements, which they supposed would be brought on the field. After five hours of desperate resistance, General Pope withdrew his advance, with a loss of forty killed, and about one hundred and twenty wounded. The rebels, surprised by the obstinate resistance of this small force, and their sudden retreat, made no pursuit, but fell back to their own intrenchments, after having suffered a much greater loss. Three different “parallels” were constructed along the Federal lines, from the time of the first investment to the occupation of Corinth. The construction of these works compelled the rebels to fall back further upon their centre, until the last was completed.