Sunday morning.-Saw not troops in Chattanooga. There was some artillery at the deport (Knoxville depot), 1 miles from the river. No camps at Chattanooga; no new fortifications there. Heard at Polk's headquarters that the troops of the enemy were scattered from Shellmound to Loudon Bridge, and all on the south side of the river. Shellmound is 20 miles from Chattanooga. Could not ascertain the exact locality of the forces nor the strength at the different points. No troops have been sent south nor to Virginia. No [information] has come in. That the enemy lost about 500 deserters, and have been strengthened by new recruits a little more than 500. Forrest's cavalry is from Chattanooga to Ringgold. Wharton is in Will's Valley, southwest of Chattanooga. Bragg's and Polk's headquarters at Chattanooga. That the rebel idea is that we will cross the river near Gunterville, and go into Georgian near Rome. That the enemy has a pontoon bridge, being taken from Kelly's Ford to Chattanooga. The people seem to keep up good spirits, but are all finding fault with Bragg. The roads are bad on all the routes traveled.

The original of this statement was forward to department headquarters the morning after it was received.

GEO. H. THOMAS,

Major-General U. S. Volunteers, Commanding.

NASHVILLE, TENN., July 23, 1863.

Major General H. W. HALLECK,

General-in-Chief:

Thomas' corps near Decherd. Headquarters there. McCook's one division building bridge at Shepherdstown. Headquarters at Winchester. Cavalry headquarters at Salem. One division at Fayetteville. Crittenden's advance at Pelham. Three divisions at McMinnville. Headquarters at Manchester. Railroad open to Bridgeport and Tracy City. Supplies going forward rapidly. Pontoons will follow.

Bragg's headquarters, from latest reports, at Chattanooga. Polk's corps reported there. Hardee between that place and Shellmound. All fords of the Tennessee guarded by small forces. Pillow gone toward Rome. Strong brigade of infantry, under Bushrod [R.] Johnson, gone to Loudon Bridge. Buckner, say with 3,000 or 4,000 infantry and 1,500 cavalry, scattered over East Tennessee.

W. S. ROSECRANS,

Major-General.

CINCINNATI, July 23, 1863.

General BOYLE, Louisville:

I am much better to-day, and will try to leave here to-morrow. The information which we receive here indicates that no force is congregating for a movement into Kentucky, but yours may be the most correct.

At all events, I will hurry the force back as rapidly as possible, and will try have them there in time to make the proper disposition before the election.

A. E. BURNSIDE,

Major-General.