I have two brigades in the position, forming a first line and half as reserves, two Michigan regiments supporting the pickets to the left and front, and four companies of Ward's brigade directly in front, ready to attack in flank any enemy approaching Hooker's left.

My battery sweeps every approach, and would materially aid an attack on Hooker's left.

The natural defenses are of little avail in our front, but are said (I have often examined the swamp) to be a reliable protection from our left to the rear. However, from the height of our left I regard it as of small avail excepting as preventing the crossing of artillery.

From the abatis, 300 yards from and nearly on a height with Hooker's redoubt, the swampy grounds extend in a semi-circle around to our left, and was the first crossed by him yesterday. I regard it as barely an impediment to the enemy. In front it is watched by four picked companies, which, with the strong Indiana marksmen, have orders to support Hooker actively.

As to myself, it is under the sweep of a battery of eight pieces, independent of a steady line of infantry in position, with equal numbers in support.

The picket line commences half a mile in our front; I should say much farther relatively in front than is Hooker's. The main line extends around to my left on the swamp, rather increasing in distance from my site on the road over which the enemy is most likely to approach, certain wood roads arriving from the upper points of the Charles City road, and circling around from the Williamsburg road, a mile or so in front of Hooker's. We are upon the enemy's pickets; we are perhaps 200 paces apart. They vary their line. We have thorough marksmen at these points, vigilant pickets, and very strong reserves-two companies on the two dangerous road which come into a lateral road some 300 paces apart, and one company on the shortest line to the Charles City road. In addition, on this short line to the new Charles City road, the one on which General Heintzelman rode out, we have a chain of small pickets, guarding also certain branches of it to said road. We hold the new Charles City road for about one-third of a mile. This road is a short 2 miles from our left. The general rode out yesterday about 1 mile on it. It is perfectly secured. On this new Charles City road the side of it toward us is forest; then comes a strip of clearing (and many road farmhouses) 300 to 400 yards wide, and then comes a belt of heavy timber bordering the arm of the White Oak Swamp. There is said to be a crossing there. The distance between the two roads is about three-quarters of a mile. The new Charles City road comes into the main one 1 1/4 miles from our pickets. The enemy's pickets seem in some force close to us, as toward Richmond, and as on the swamp between the two Charles City roads.

The only requisite to be desired is a supply of axes to make vistas for the artillery, especially toward Hooker. They cannot be obtained either from Hooker or Sumner. It is to be regretted.

In conclusion, I state it for what it is worth that between my first crossing and return over the nearest arm of the White Oak Swamp the water had diminished almost completely-more than three-quarters. I have given orders to our scouts to watch the swamp. It may be the cessation of the rain; it may be that the waters are being diverted.

Respectfully, your obedient servant,

P. KEARNY,

Brigadier-General, Commanding Division.