From Tennessee — military Execution.
Chattanooga, Sept. 4.
--The enemy were signalling all night on Waldron's ridge, but everything is remarkably quiet across the river to-day.
There are no further indications of an advance on the part of Rosecrans.
The Knoxville Register has been removed to Cleveland.
Capt. J. R. Rhodes, of the 1st Confederate infantry, was shot at noon to-day, for encouraging desertions from his own company, and embezzling the money of substitutes.
He made a short speech, acknowledging the justice of the sentence, manifested but little concern, and died without a struggle.
Lt. Col. Adolph, of the same regiment, was cashiered and conscripted yesterday for having been concerned in the same offences.
[second Dispatch.]
Chattanooga, Sept. 5.
--Although the armies are in close proximity, there are no indications of an early engagement; but a slight cause may bring it on, however at any moment.
Our artillery at Driver's Ferry opened on the enemy at 6 o'clock this morning, for the purpose of ascertaining the strength of the position of the enemy's batteries.
They responded promptly, and for half an hour a lively artillery duel was kept up without injury to our side.
The discipline and health of the army are very fine.
The troops are in the best spirits.
Nothing heard from Gen. Buckner's command.
The weather is clear and warm.
[another Dispatch.]
Atlanta, Sept. 5.
--A special dispatch to the Confederacy says that Col. Morrison, of the 1st Georgia cavalry, repulsed the enemy at Diamond Gap, on the night of the 3d inst. Our loss was two wounded. The enemy's loss is not known.
The brigade fell back south of the Tennessee river.
The enemy shelled London on the 2d instant, and killed two women.
The bridge was burnt to prevent the enemy's crossing. 