Tracy and a large number of the enemy. Our own exceed 150 killed and 500 wounded. The country is extremely broken, and, therefore, very difficult to operate in.

Yesterday we pushed into Port Gibson by 8 o'clock, to find the enemy gone, and all the bridges across Bayou Pierre destroyed. The bridge was rebuilt, and our troops pushed on to Willow Springs. Found the fine bridge over the north fork of Bayou Pierre destroyed. Repaired it, and by 5 o'clock this morning were in motion again. By 9 we were at Willow Springs, having met the enemy's skirmishers just beyond the bayou. Logan is now on the main road from here to Jackson, and McPherson, closely followed by McClernand, on the branch of the same road from Willow Springs.

The enemy is badly beaten, greatly demoralized, and exhausted of ammunition. The road to Vicksburg is open. All we want now are men, ammunition, and hard bread. We can subsist our horses on the country, and obtain considerable supplies for our troops.

U. S. GRANT.

HEADQUARTERS SIXTEENTH ARMY CORPS, Memphis, Tenn., May 3, 1863.

Lieutenant Colonel John A. RAWLINS, Milliken's Bend, La.:

SIR: I have the honor to report that General Dodge and his command have returned to Corinth.

General Dodge furnished to Colonel Streight 500 horses, and the latter-named officer proceeded upon his mission, pursuant to instructions already furnished to you.

I have the honor to be, sir, very respectfully, your obedient servant,
S. A. HURLBUT.

WILLOW BRANCH, MISS., may 4, 1863.

Major General U. S. GRANT, Comdg. Dept. of the Tennessee:

GENERAL: Your dispatch of this date is received. I wrote to you yesterday, directing the letter to Grand Gulf, that my corps was without the means of transportation and would be without rations to-day, except as far as it could gather them in the rear of the SEVENTEENTH Army Corps, and requesting that rations be sent out. I inter that you did not receive the communication. I repeat the request that it contains.

The teams belonging to this corps are, as you are aware, behind, and cannot be brought here unless water transportation is afforded to bring them across the river. I have sent three officers successively to look after this matter, but, of course, their efforts will avail nothing unless transports can be made available for temporary use.

I reconnoitered ahead on the Jackson road last night, and found nothing. A rebel force, variously estimated from two regiments to 10,000 men, are reported by different spectators to have passed yesterday morning, on the Jackson road, to the forks of Vicksburg and Grand Gulf roads, and to have returned a short distance, and turned to the left to cross the Big Black, at the crossing of the Vicksburg road. This counter movement, no doubt, was caused by our advance on Willow Springs.

You are aware that I have left a brigade at Port Gibson and another