A rifled 32-pounder gun killed 4 artillery horses and took off the leg of Corpl. Abram S. McCorkle, of Lilly's battery, at one shot. This comprises the list of my casualties.

The roads down Walden's Ridge are very steep and rough. I am now repairing the Anderson road down the mountain on this side. Wagner's brigade is on the mountain, on the Anderson road, and Hazen's brigade is on the mountain, on the Poe road, with three regiments at Poe's. I am camped at the foot of the mountain, on the Anderson road, with parties thrown out to the vicinity of the river on all roads. Two of my regiments are at Poe's, with parties out to the river at Harrison.

I wish to get further orders. My artillery ammunition is getting short. Can you send me 200 rounds percussion-shell to Tracy City for 3-inch guns, and 200 rounds fuse-shell (Hotchkiss) and 1,000 friction-primers?

I think that the rebels have one corps off two divisions at Chattanooga and vicinity-D. H. Hill's, formerly Hardee's corps. Polk's corps is reported to be down the road toward Bridgeport. None of this information is very well founded, being made up from reports from deserters, negroes, and citizens. There is no rebel force north of the river except bushwhackers on the mountains, who try to take our couriers. I have sent a company up Walden's Ridge after them to -day. Dibrell's-formerly Starnes'-brigade is reported to be in vicinity of Smith's Cross-Roads, and Forrest, with a brigade, is said to be near Kingston.

I have taken, in the entire, 40 men and killed 2 and wounded several ; also took a train of 4 empty wagons and the mules of a battery that were grazing on the north side of the river near Chattanooga.

We shelled Chattanooga, at intervals, from 10 to 5 p. m. yesterday, silencing every battery that opened on us. But few of their guns could reach us, being mostly 12-pounder howitzers and 6-pounders rifled. They opened on us with nineteen different guns. One 32-pounder rifled gun covers all on this side. Lilly made most excellent shots, dismounting guns at 2,000 yards. He threw shells directly in their embrasures. Their parapets are very broad; appear to be at least 15 feet or more, certainly not less. Their water batteries are sunk in pits level with the ground and with the banks built up for protection, with embrasures through the banks.

It is reported that Johnston came here on the night of the 20th, bringing with him two trains of troops and superseded Bragg, who is sent to Atlanta. This I learn from an intelligent negro who came from Chattanooga yesterday, and who claims to have seen them all. The citizens state that Bragg is at Atlanta.

There appears to be a large camp-fire 5 or 6 miles in the rear of Chattanooga. A movement appears to have been made down the river last night; it sounded like cavalry. They may be coming in on our rear, on top of Walden's Ridge, by crossing the river below. A good watch should be kept at the mouth of Sequatchie Valley.

They have a steamer on the river below here, the old Paint Rock.

I am, sir, very respectfully, your obedient servant,

JOHN T. WILDER,

Colonel, Commanding.

P. S.-No changes have been reported this morning. All is quiet across the river; but few troops can be seen.

J. T. W.