Numbers 258. Report of Brigadier General Hiram Burnham U. S. Army, commanding Second Brigade, of operations June 1-10.

HDQRS. SECOND Brigadier FIRST DIV., 18TH ARMY CORPS.

Near Cold Harbor, Va., June 10, 1864.

SIR: I have the honor to submit the following report of the operations of my command from the 1st instant up to this date:

On the morning of June 1 the brigade left bivouac near New Castle and marched in the direction of Cold Harbor, near which place the enemy were encountered at about 4 p.m. Here two regiments of my command, the One hundred and eighteenth New York Volunteers and Eighth Connecticut Volunteers were drawn up in line as a support for the Third Brigade, Colonel Henry commanding, while the other two regiments were placed on the right of the brigade, the Thirteenth New Hamsphire in the first line with the Tenth New Hampshire for its support; General Martindale's division connected with my right. Just before dark an advance was ordered. My brigade, in connection with the force on its left, moved forward through the woods and up to the open field in front of the enemy. After a short halt here by order of General Brooks, I moved my command forward to support our forces which had already gained the woods in front and were hotly engaged with the enemy. In executing this movement the Thirteenth New Hampshire, Colonel A. F. Stevens, having no force on its right, encountered a heavy fire from the enemy and suffered quite severely, but behaved gallantly and moved up to an advanced position, which it held until dark, when, as it was somewhat detached from the remainder of the brigade, and in a position which did not conform to the formation of our lines, I withdrew it and placed it in the second line. The Tenth New Hamsphire, which had supported the movement of the Thirteenth, was also placed in the second line. My other two regiment, One hundred and eighteenth New York and Eighth Connecticut, advanced until they filled a space between the Fifty-eighth Pennsylvania and the troops on its left, when they were halted and pickets thrown out in their front. During the night these two regiments intrenched themselves in pursuance of orders. Shortly after dark the Tenth New Hampshire Volunteers, Lieutenant Colonel John Coughlin, was moved into a position in the open field on the right of Colonel Henry's brigade. At about 2 o'clock on the morning of the 2nd instant I changed the position of this regiment by throwing its right forward considerably and ordered Lieutenant-Colonel Coughlin to throw up a rifle-pit to protect his me, which he succeeded in doing before daylight. At the same time I placed the Thirteenth New Hampshire in the edge of the woods in rear of the Tenth New Hampshire for the double purpose of supporting that regiment and protecting our right as much as possible. At daylight, by order of General Brooks, I moved the Eighth Connecticut and One hundred and eighteenth New York to the right so that they connected with the Tenth New Hampshire and relieved a portion of Colonel Henry's brigade with them, placing them in the front line. My command remained in this position until the morning of the 3rd, strengthening the rifle-pits and keeping up a desultory firing at the enemy.