My losses are, in killed, 5 enlisted men; in wounded, 32, of whom there are 4 officers, viz: Lieutenant Foster, Company H; Lieutenant McGill, Company F; Lieutenant Reed, Company K, and Captain Sell, Company I. Captain McCoy, Company F, was knocked over by wind from a shell, but came up the same evening.

I am, sir, your obedient servant,

STRONG VINCENT,

Colonel Eighty-third Pennsylvania Volunteers.

Captain L. LANSING,

Acting Assistant Adjutant-General.

No. 180. Report of Lieutenant Colonel Casper Trepp, First U. S. Sharpshooters.

CAMP NEAR FALMOUTH, VA., December 17, 1862.

CAPTAIN: In pursuance of an order from division headquarters, I have the honor to report the operations of my command during the 13th, 14th, 15th, and 16th instant.

On the 13th instant, I received an order to march with the division, and was assigned a place in the column in the rear of Phillips' battery. Having no further orders, I halted my regiment when that battery halted, and bivouacked for the night near it, about half a mile from the bridge over which the rest of the divisions crossed the Rappahannock.

On the 14th instant, at about 7.30 a.m., I received an order to cross the river and report immediately to General Griffin, which order was obeyed, and the regiment entered Fredericksburg at about 8 a.m.

At about noon on the 15th instant, by order of General Willcox, four companies of my regiment were sent out on picket duty, under command of Major Hastings, on the left, to connect with General Franklin's pickets and cover a space not before covered. I carefully examined the ground, and personally superintended the posting of the pickets, making perfect the connection between General Franklin's right and the block-house by the railroad. This detachment remained on the outposts until it was withdrawn, by order of General Humphreys, at about 6.30 a.m. the next day. At about 5 p.m., by order of General Griffing, I sent two companies, under Captain Seaton, on picket on the right. These remained on the outposts until 3 o'clock next morning, when they were relieved, by order of General Griffin.

On the 16th instant, by order of General Griffin, the regiment, excepting the four companies on the outposts, crossed the Rappahannock at about 6 a.m. at the upper bridge. The said four companies retired as follows: Three companies of reserves, under Major Hastings, in column, and one company, the last on the outposts, as skirmishers under Captain Marble, bringing with them a number of stragglers from different regiments. The regiment was in camp at about noon, all present.

There have been no casualties in my command during the period.

I have the honor to remain, captain, very respectfully, your obedient servant,

C. TREPP,

Lieutenant-Colonel, Commanding First U. S. Sharpshooters.

Captain C. B. MERVINE,

Assistant Adjutant-General, First Division.