CAMP near CARTHAGE, May 4, 1863.

General F. P. BLAIR, Comdg. Milliken's Bend:

DEAR GENERAL: You will have heard that General Grant's forces crossed below Bayou Pierre; marched on Port Gibson, where there was an engagement, which resulted in the flight of the enemy, the capture of four field guns and 500 prisoners.

In consequence of this, the enemy evacuated Grand Gulf, where General Grant was yesterday. I have an order from Grant to hurry up, cross at Grand Gulf, and hurry forward, bringing along certain provisions and wagons that will strip the road. He is evidently moving by the road on the east side of Big Black. As near as I can make the road-13 miles to Richmond, 17 miles to Smith's, 7 miles down Vidal to bridge, and 6 to Perkin's; total, 43 miles. Then it is 20 miles down river to Hard Times and 3 across in boats to Grand Gulf. Now, you know we have not wagons and boats to handle all the material needed by this army, but the whole success of this plan depends on its hardihood.

I will push ahead, and arrange to across Grand Gulf and follow Grant, wherever he may be. But some other way must be found to feed this army. I wish you would cause our old road over to Bigg's to be examined; and if it can be used on foot, we might fell trees fore and aft, and make on the logs a plank road; then, by running the Warrenton batteries, we could run steamboats up to the crevasse.

Please make all the preliminary examinations, and even commence the work, if you judge we may need it. I know we will. I did not hear the guns last night, and infer the tugs did not run the batteries. At all events, at this moment I cannot learn anything of the affairs at the river bank, as I am at Smith's, and we can only reach the river at Carthage by boats.

One DIVISION of McPherson's corps is here (McArthur's), but I shall pass it. Keep everywhere hauling stores forward, so as to reach the Mississippi at Carthage or Perkins'.

Yours, in haste,

W. T. SHERMAN.

CAMP AT PERKINS', May 4, 1863-2 p. m.

Major-General BLAIR, Comdg. Milliken's Bend:

DEAR GENERAL: I left, Steele's DIVISION last night at Dawson's plantation; staid at Smith's and rode to this point, arriving at 10. 30 a. m. Distance from Smith's, 14 miles; total distance from the Bend, 43 miles. Road tolerably good, but lumpy, from old plow furrows and ruts. All the road would become awful in a rain.

At the moment of my arrival, two barges floated by on fire; burned low. I had barely time to order a boat out, with orders, if possible, to bring a line ashore and bring them to, but the barges were so burned that the ropes could not be made fast, so the barges floated by and are lost. This is all we know of the running the blockade last night. The steamboat Empire City passed up from Grand Gulf this morning, is now at Carthage, and may have stopped the tugs and remaining barges there, but I am uneasy lest these tugs and barges have come to some bad end.

McClernand's four DIVISIONS are across the river, and two of McPherson's are also across. You will have heard of the fight at Port Gibson and evacuation of Grand Gulf. Grant's headquarters are now there, and I will go down in the Empire City this evening, and came back by daylight,