Lieutenant-Colonel Grier's and Captain Gibson's reports are herewith inclosed. Major Williams' (now absent with his regiment) will be forwarded as soon as it can be obtained.

The total loss inflicted on the enemy, known to be considerable, under the circumstances could not be ascertained with any precision.

I have to report the loss of 35 killed and wounded and missing, including Lieutenants McClellan, D'Wolf, and Benton, all severely wounded. Names and other details given in reports of commanders. About the same number of horses were killed and wounded, of which 22 were in the battery. Captain Gibson praises highly all his officers. The captain and the whole company, which was under my eye, appeared cool, brave, and devoted.

It is with the greatest pleasure that I can report that my command generally gave me high satisfaction.

Of my staff Lieutenant James P. Martin, acting assistant adjutant-general, Captain W. Merritt and Lieutenant Frank Beach, aides-de-camp, I must say that they did all and more than their duty with such calm bravery and judgment that I feel much pride in their association.

Very respectfully, your obedient servant,

P. ST. GEO. COOKE,

Brigadier-General, U. S. Army.

Brigadier General GEORGE STONEMAN,

Chief of Cavalry, Headquarters Army of the Potomac.

Numbers 4. Report of Lieutenant Colonel William N. Grier,

First U. S. Cavalry.

HEADQUARTERS FIRST REGIMENT CAVALRY, Camp at Williamsburg, Va., May 7, 1862.

SIR: I have the honor to make the following report of the part borne by the First Regiment U. S. Cavalry during the action between the advance guard of the army and the enemy near Williamsburg, Va., on the 4th instant:

Agreeably to orders received from Brigadier General P. St. G. Cooke I formed my regiment in close column in a small ravine to the right and a little in advance of the artillery, and about 430 yards in front of the enemy's fortifications. The nature of the ground was such as to enable it to charge at any moment in line or in column upon any cavalry or infantry the enemy might send against the battery. While holding this position the regiment was constantly subjected to a fire of shells and spherical case, which was kept up during the withdrawal of the force, which was ordered to retire, the cavalry in rear to cover the artillery. When the last squadron, composed of Companies I and K, Captains Davis and Baker, was at the entrance of the woods, the whole battery had retired, with the exception of one piece and four caissons, which were disabled by the loss of their horses. After waiting till ten horses had been hitched to the piece without being able to drag it out of the mud the horses were unhitched and the squadron retired at a walk. The squadron was again delayed in the woods, assisting our wounded to the rear, and finally was charged by a large body of the enemy's cavalry. Captain Davis, commanding the squadron, composed of 60 men, wheeled it about by fours, there being room for no larger