NEAR Vicksburg, July 4, 1863.

General SHERMAN:

Ord will only get off a DIVISION of his troops to-night, and balance to-morrow. Steele will get off before daylight to-morrow; I have just returned from a visit to the admiral, at Vicksburg Landing. The number of prisoners as given by the rebel is 27,000. There is much more artillery than we thought; the field-pieces are given at 128, and about 100 siege guns.

U. S. GRANT.

HEADQUARTERS EXPEDITION, Fox's, July 4, 1863.

General GRANT:

Your dispatch announcing the magnitude of the capture of Vicksburg is most gratifying; the importance of the place in our case cannot be exaggerated.

I have left Kimball's DIVISION at Haynes' Bluff, with instructions to picket at Oak Ridge. I will order General McArthur to relieve Osterhaus at the bridge to-morrow, so that Osterhaus may report to General Ord. Three bridges will be built to-morrow at Birdsong, Messinger's and the railroad crossing. To-morrow, I suppose, Ord and Steele will be up, so that next day I will cross and move in force on Bolton.

The enemy showed one gun opposite Messinger's, [near] this place; I am willing be should meet us at once, the nearer the river the better. If he declines, I will follow promptly to Clinton; then I can discover if Johnston is scattered or concentrated, when I will act accordingly. I have not yet heard if the prisoners are to be paroled here or sent north. The farmers and families out here acknowledge the magnitude of this loss, and now beg to know their face. All crops are destroyed and cattle eaten up. You will give their case your attention as soon as more important business is disposed of. At least I promise them this. I advise, then, if you find a locomotive, that you run cars out to Big Black River and make that a depot.

Please tell Wilson or [Miles D.] McAlester about the maps east of Big Black River; I am without any. I feel an intense curiosity to see Vicksburg and its people, but recognize importance of my present task, and think of nothing else. I will keep few orderlies at Osterhaus', which is now my nearest telegraph office.

W. T . SHERMAN.

CAMP AT FOX'S, July 4, 1863.

General OSTERHAUS, Railroad Bridge:

DEAR GENERAL: You are already aware that I am ordered to move across Black River to attack Johnston. I propose that Ord's corps cross at your position, mine at Messinger's, above Bridgeport, and Parke at Birdsong. You now have a bridge, and the other corps are now at the other points, and will make theirs to-morrow. The next day I want to move direct on Bolton. You will, on General Ord's arrival, report to him, and be prepared to move with him.

McPherson's corps remains at Vicksburg, of which General McArthur has three brigades. Two of these will relieve you at the Ridge, and the benefit of your knowledge of the position and surrounding country, and advise with him as to the advisability of getting a locomotive and