Our hull has suffered as much to-days as on any day yet. We can only advance with the current; faster than that brings us foul. Our speed is not more than 1 1/2 miles per hour, if that.

Wheels and stacks have escaped, through care; but with over 20 feet above water, and less than 3 in it, without steerage-way, light winds play with us, bringing the sides and trees in rough contact. I imagine that the character of this navigation is different from what was expected. We will get through in fighting condition, but so much delayed that all the advantages of a surprise to the rebels will have been lost.

Evening. - The steamer Bayard broke her stern-post to-day, and that has caused delay. In the Pass, had a hole punched in her below water; she half filled, but was re-covered. The crooked course of the stream, and the thickly wooded shore, prevents our having more than an occasional glimpse of other vessels. Each has its position and distance assigned, but a knowledge of the whereabouts of those next can generally only be ascertained by means of a boat.

The iron-clads have the least trouble from trees or overhanging branches, and are scarcely affected by the wind.

A case of small-pox was reported by the Petrel to-day, and was immediately transferred to a returning transport, for passage to Helena and the hospital.

The shore occasionally makes down to the clear water, but much of the route is through a clearing amidst trees standing in water. I don't think we have seen a plantation in the last 8 miles; all is swamp.

March 4. - The Petrel comes in with her wheel much damaged, and without the means of repairing. I can it, but my supply was for but one vessel.

March 5. - The river is clearer, and we make better speed. If we reach the Tallahatchee this evening, which our advance may do, our total distance from Delta will be but 50 miles, not 6 miles per day. I am having an account of the number of navy radios in the expedition taken. No vessel has more than a month's supply at this date, and the Chillicothe but seven days, the Lioness thirteen, and the Fulton seven. The last reports one boiler badly burned. My first knowledge of the Petrel, Lioness, and Fulton being attached to the expedition was received after entering the Pass. They joined after reaching Coldwater, too late for me to prepare them for the expedition, which could only have been done by sending them to Memphis. We are better off than the army, however, and have a fair supply of coal. An organized party of army and navy collects beef for rations and cotton for defense. The people report rebels and batteries below,&c. Gathered some cotton to-day; much that we find is so badly baled as to be dangerous. I hope to make better speed from this time through.

Tallahatchee River, 12 miles from Coldwater, March 6, evening. - Stopped for the night, and waiting for the others to close up.

Our intelligence, received from various sources, at different places and from different people, is that Yazoo City is being fortified, 3,000 negroes doing the labor, and that a large army is there for its defense, provided with heavy guns.

The same is said of Greenwood, but I do not place the same credit in the reports concerning Greenwood.

A receipt in the possession of a man near us on the shore, for cotton for a rebel steamer, shows a naval organization amongst them. It reads in this way: