FLAG-SHIP BLACK HAWK, June 3, 1863.

Major General U. S. GRANT;

DEAR GENERAL: Six deserters have just come in. One, who has been in the trenches, says if you were to fire more at night it would prevent the rebels from working and resting. They are moving some heavy guns to the rear, which they could not do if the artillery kept at work. I give you this information for what it is worth. We get about 15 deserters a day, who all tell the same story-shortness of food and intention to hold out ten or twenty days. Our mortar shells have given out, but I hope to have a fresh supply in a day or two. Our mortars have killed a great many cattle of all kinds, and I am sorry we have no more on hand. The gunboats, though, keep shelling in direction of the cattle-pens. All the cattle-drivers (Mexicans) have deserted us.

The rebels have made a raid upon Perkin's Landing from Tensas River. FIFTEEN hundred of them stood the fire of the gunboat Carondelet for an hour, but finally retreated. The colonel commanding at James' plantation destroyed all the stores at that place when the rebels hove in sight, though the gunboat was near at hand. The captain of the gunboat was near at hand. The captain of the gunboat thinks he behaved badly.

I have sent six 8-inch guns up the Yazoo, with men to work them, to be placed where required, and two 9-inch at Warrenton. I will send plenty of hand-grenades if you want them. I have sent some already. They work beautifully.

Nine steamers were burned by the late expedition up the Yazoo. the rebels set fire to some of them and our men could not put the fire out. Others were aground, and we had to burn them,, and others up the Sunflower were inside of a bar, and could not be got out. They were burned with a large amount of provisions. I was in hopes of presenting you with some fine transport.

I would have been over to see you the other day, but after going over Sherman's works I was so sick I had not the strength to go farther. I will be up in a day or two.

Very truly, yours, &c.,

DAVID D. PORTER,

P. S. - An intelligent black has just come in. He says they talk of cutting their way out. I have just found out where they have moved their cattle to for safety, and am going to shell them with the gunboats. There are not many troops kept opposite McClernand's front. Most of them are in front of McPherson and Sherman. Your shot and shell are killing a great many.

JUNE 3, 1863.

General GRANT:

Captain Walker has command at Haynes' Bluff, and will give any convoy required.

A deserter just came in; says they talk of cutting their way out.

PORTER.

HEADQUARTERS THIRTEENTH ARMY CORPS,
Near Vicksburg, June 3, 1863.

Major General U. S. GRANT:

The enemy opened with artillery and infantry from his works this morning, but was successfully replied to. I have ordered my artillery.