From General Bragg's army.
[from our own correspondent.]
Lookout Mountain, Sept. 30.
No change has taken place in the situation of affairs since the date of my last letter, except in the extent and character of the enemy's works in and around Chattanooga, and of our own. The town is completely invested on the South side of the Tennessee river by Gen. Bragg's forces.
We hold Missionary Ridge in front of the place, Lookout Mountain and the Nashville and Chattanooga railroad on the South side, and the valley between Lookout and the Ridge.
We also command the East Tennessee railroad.
Indeed, our lines rest upon the river above and below the town, just as do those of Rosecrans.
The enemy continue to work day and night like beavers.
They are building bomb-proofs for their artillerists and their supports, and providing every other means of defence one can imagine.
Their efforts are not limited to the South side of the river, but extend also to the North side, where they have planted batteries on the heights overlooking the river and the town, and in some cases constructed traverses to protect their gunners from the cross fire of our artillery.
If we should get possession of the place, therefore, we should still be exposed to the fire of the batteries beyond the river.
The outer front line of the enemy is crescent-shaped, the two horns of the crescent resting on the curves of the river above and below the town, and is the complement to the semi-circle described by the river in their rear.
Their whole line, therefore, including the river and breastworks, assumes the form of a circle, or rather of an ellipse.
The Confederate line conforms to their exterior line, and consequently is a crescent in form.--These facts are as well known to Rosecrans as to Gen. Bragg; for the high hill in rear of the town gives the former a full view of our position, and therefore there can be no impropriety in stating them here.
Reverting to the battle, I am told by citizens of the country, who are familiar with the boundaries of Walker and Catoosa counties, that nearly the whole of the battle occurred in Catoosa county, about eight miles due west from Ringgold, and about the same distance due south from Chattanooga.
It was some four miles below the Tennessee line, and on the west side of and near to the Chickamauga, which is spelt indifferently with or without a "k." Our line ran northeast and southwest at the commencement of the struggle on Saturday; but, as our left swung round, pushing the enemy before it, its direction became east and west, extending across the valley from the Chickamauga to the foot of Missionary Ridge.
The enemy retreated down the valley, crossing the ridge through the pass at Rossville, the former home of John Ross, the Indian Chief, and thence to Chattanooga.
It is now believed that our casualties reached 12,000, an unusual proportion of which will fall under the head of comparatively slight wounds.
We lost but few prisoners, including four surgeons, who were sent back this morning, together with thirteen wounded men. The work of paroling and returning the enemy's wounded who fell into our hands still continues.
We captured fifty-three surgeons and some twenty-five or thirty chaplains, who, I understand, will not be returned until the enemy shall release such of our surgeons as are now confined in the prisons of the United States.
Lieut. Gen. Polk and Major-Gen. Hindman have been relieved of their commands by order of Gen Bragg for alleged disobedience of orders.
It is reported that Gen. Hindman was ordered to occupy a certain pass in the mountains on Friday, and thus prevent a concentration of the Federal forces, which he failed to do in time; and that Gen. Polk, who held the right, was ordered to open the fight at sunrise Sunday morning, instead of 10 o'clock, the hour at which his guns first opened.
Gov. Brown, of Georgia, arrived here yesterday, and to-day he is visiting our lines, accompanied by Gen. Bragg, Gen. McLaws, and Gen. Walker. Sallust. 