During the main fight skirmishing across the river went on uninterruptedly, and down at the Baltimore pike bridge assumed serious from. My right, extending from the railroad to the bridge mentioned, was under charge of Brigadier General E. B. Tyler, now supposed to be a prisoner, who, though not tried by so severe a test, met every expectation, and performed his with ability and courage. I do not now think myself seriously beaten; there was not a flank nor gun lost. The rebels captured no stores whatever, and in face of their overwhelming force, I brought off my whole command, losing probably not over 200 prisoners. My casualty list will be quite severe, but cannot possibly equal that of the enemy, as they charged several times in close lines, and with a recklessness that can be justified only upon the ground that they supposed my command consisted of raw militia. Each one of his four lines of attack presented a front greater than that of General Ricketts' division all deployed. By calculation this would give him about 18,000 men engaged on the left bank, while he had at least 2,000 more skirmishing and fighting in my front across the river.

Permit me state that in fighting I had three objects in view:

First, to keep open, if possible, the communication by rail to Harper's Ferry; second, to cover the roads to Washington and Baltimore; the last, to make the enemy develop his force. I failed in all but the last, and from what I saw it can be safely asserted that the enemy must have two corps of troops north of the Potomac. In the computation I include his column operating in the region of Hagerstown, that about Harper's Ferry, and the one which fought me yesterday.

A rebel officer dying on the field told a staff officer of General Ricketts that Lee was managing these operations in person, and would shortly have three corps about the Potomac for business against Washington and Baltimore. This circumstance is true; give it what weight you please.

I regret to add that we were able to bring off but few of our wounded, and none of our dead. The 100-days' men straggled badly, while the men of the Sixth Corps reached this place in perfect order, and covered the retreat. The Third Regiment Potomac Home Brigade, Colonel Gilpin, of Tyler's brigade, also maintained good order. I will make a more complete report, with your permission, when I receive the report of Brigadier-General Ricketts.

I wish to make honorable mention at this time of Lieutenant Colonel D. R. Clendenin, of the Eighth Illinois Cavalry, of Captain F. W. Alexander, whose battery was well served throughout the day, and of Colonel Charles Gilpin, who commanded during the fight of Frederick City, on the 7th instant, in which the enemy lost, killed and wounded, 140 men, while we lost 1 man killed and 18 wounded. The number of rebel casualties is given on the statements of citizens of Frederick.

I wish also to make honorable mention of Colonel Brown, of the One hundred and forty-ninth Ohio National Guards, who, assisted by Captain Leib, Fifth U. S. Cavalry, stubbornly held the Baltimore pike brigade, and thus kept open my line of retreat.

LEW. WALLACE,

Major-General, Commanding.

Major General H. W. HALLECK,

Chief of Staff, Washington.