P. S.-General Jos. E. Johnston is in command in my front, and has been re-enforced this morning and again late in the afternoon. They evidently felt hard pressed when our re-enforcements arrived. They attacked General Hooker at about 8 a.m. intending to overwhelm him before estimated by the prisoners we have taken as high as 50,000 men. They have intrenchments and they are so situated we cannot make much use of our artillery. May I beg you to send me at least a division before daylight?

HEADQUARTERS THIRD CORPS, Williamsburg, Va., May 7, 1862.

GENERAL: I have the honor to make the following report of the engagement of General Hooker's and Kearny's divisions of my corps with the enemy at their intrenchments in front of Williamsburg on the 5th of May, with so much of what previously occurred as is necessary for the understanding of the operations:

On Saturday evening, May 3, the enemy in Yorktown kept up a fire of shot and shell our lines till after midnight. At the first appearance of daylight Sunday morning I heard what I took to be a heavy skirmish in the direction of Yorktown and saw a bright light. I ordered an ascension with the balloon, and Professor Lowe reported to me that the light was a burning or a vessel near the wharf off Yorktown. Subsequently I learned that the firing was caused by the explosion of small-arm cartridges and shells from a rebel magazine in the direction of Yorktown. I then got a telegram from General F. J. Porter that it was believed the enemy were abandoning Yorktown. I immediately went up in the balloon with Professor Lowe. We could not distinguish any guns or men in or around the fortifications of Yorktown and the smoke of their camps was very much diminished. In a few minutes we saw to our right a line of skirmishers advance steadily, supported by a regiment of infantry, toward the rebel works and enter them. I immediately descended, and gave to the divisions of General Kearny and Hooker to prepare to march; also to Colonel Averell's Third Pennsylvania Cavalry.

At 10 a.m. I went to general headquarters, and received orders for General F. J. Porter's division to occupy Yorktown; that the reserve cavalry and four batteries of horse artillery, under General Stoneman, would advance toward Williamsburg,and for me to support it with Hooker's division. Soon after I received orders for General Kearny's division to prepare to march.

One thousand men of General Hooker's division were on duty in the trenches, and were detained for some time by the general on duty there. Another regiment, the Seventh-first New York, was still at Cheesman's Landing. This delayed the march of the division till near 1 p.m. My headquarters accompanied this division.

Before I reached the Half-way House, where I was directed to leave a force to watch the road from Lee's Mill, I heard firing in front, and received a note from General Stoneman that he had me the enemy intrenched about 2 1/2 miles from Williamsburg,and wanted infantry to aid in carrying their works. At the Half-way house, 7 miles from Yorktown, I found the head of General Hooker's column detained by General Smith's division, which had reached that point before him,