MEMPHIS, TENN., May 23, 1863-11. 30 a. m.

Honorable E. M. STANTON,

Secretary of War:

The following dispatch has just been received at these headquarters, and is forwarded as requested:

REAR OF Vicksburg, May 20, 1863-6 a. m.

General Grant has won a great and momentous victory over the rebels under Pemberton, on the Jackson and Vicksburg road, at Baker's Creek, on the 16th instant. Pemberton had a most formidable position on the crest of a wooded hill, over which the road passes longitudinally. He had above 25,000 men. The battle began at 11 a. m. and was gained at 4 p. m. Its brunt was borne by Hovey's DIVISION, of McClernand's corps, and by Logan's and Crocker's [DIVISION], of McPherson's. Hovey attacked the hill, and held a great part of it till 2 p. m., when, having lost 1,600 men, he was succeeded by Boomer's and Holmes' brigades, of Crocker's DIVISION, by which the conflict was ended in that part of the field. Boomer lost 500 men. Logan operated on the right, and cut off the enemy's direct retreat, so that he was compelled to escape by his right flank through the woods. Logan lost 400 killed and wounded. We took about 2,000 prisoners.

On the 17th, advancing to the Big Black, we fought Pemberton again at his bridge head, and captured 3,000 more prisoners. He fought in rifle-pits, protected by a difficult bayou full of abatis. Lawler's brigade, of McClernand's corps, charged the rifle-pits magnificently, and took more prisoners than their own numbers. Pemberton burned his brigade, and returned to Vicksburg with only three cannon out of sixty that he had taken out.

Building four bridges to the Big Black, General Grant arrived before the town on the evening of the 18th, and now holds it closely invested. He had opened a line of supplies via Chickasaw Bayou, having cut the town off from Haynes' Bluff, which is abandoned by the day yesterday. Steele won, and holds the upper bluffs and the enemy's upper water batteries, and gets water from the Mississippi.

Sherman's corps lost yesterday 500 killed and wounded. McPherson, who holds the center, lost little, as did McClernand, who holds the left.

The gunboats kept the enemy alert during the night, and probably the town will be carried to-day. There are from 15,000 to 20,000 men in it. Pemberton fights with the greater obstinacy, because his people believe he has sold their cause. Joe Johnston went into the town, but we have not heard of him since.

C. A. DANA.

Honorable E. M. STANTON,

Secretary of War.

S. A. HURLBUT,

Major-General.

BEHIND Vicksburg, May 23, 1863-9 a. m.,

VIA MEMPHIS, May 29-3 p. m. (Received June 1-3. 50 a. M.)

The town was assaulted yesterday. The order required the columns to move by every road at 10 a. m. precisely, but they did not all get started at the same hour. The attempt failed, but without heavy loss. At 2 p. m. McClernand reported that he was in possession of two forts of the rebel line, was hard pressed, and in great need of re-enforcements. Not doubting that he had really succeeded in taking and holding the works he pretended to hold, General Grant ordered J. G. Lauman's DIVISION, of McPherson's corps, to his support, and at the same time McPherson and Sherman both made new attacks. McClernand's report was false, as he held not a single fort, and the result was disastrous. Lauman's DIVISION was pushed by McClernand to his front and suffered heavily. Colonel G. B. Boomer, Twenty sixth Missouri, among the killed.

Ransom's brigade, on McPherson's right, lost 25 per cent. of its strength, including Colonels G. Nevins and T. W. Humphrey killed, and