LETTER FROM PRIVATE.Army of tub Potomac, 1 Davis Ford, Va., Dec. 21. /Eds. Sun : Several rumors of heavy skirmishing in front of our lines, at different places has reached us within a day or two past, resulting, it is said, in suo-cess to our forces. Reconnoitering parties in large numbers are being sent out frequently by both armies; one from Hampton’s Legion on Tuesday evening last, consisting of 400 Infantry and three companies of Cavalry in the direction of Pohick church, 12 miles below Alexandria, but with what success I have not ascertained.Ihe r euerals.captured Col. Hughes, ofthe 12th Mississippi Regiment, on Wednesday last, at a house in the vicinity of Sangster’s Cross Roads.The Confederates opeHed a new battery on Sunday morning last on the Potomac, at a place called Cockpit Point. The battery was masked, and a steamtug passed along the river shelling the woods as she passed slowly along, and when near the battery, the mask was cleaned away and the battery opened on the tug putting two holes in her when she very prudently retired beyond reach of ourguns.The youth Kennedy, of company H.f 6th Alabama Regiment, for stabbing young Crowder of Company K., same Regiment, with a bowie knife in Augustlast, has been senteuced by Court Martial, to oO days hard labor, for eight hourseach day, and to be confined one hour each day in the stocks, and forfeit two months of his pay.General orders from headquarters, were read yesterday giving 80 days leave of absence to 10 privates in each company, after the 25th inst. The same alsoto two Captainsand five Lieutenants fromeach Regiment. Men of families have precedence.The weather still continues fine, and the health of the troops good. Winter quarters will soon be ready.PRIVATE.