But to-day we have a dispatch from Gen. Bragg, announcing a great battle on the 19th and 20th insts. He says, “after two days’ engagement, we have driven the enemy, after a desperate resistance, from several positions; we hold the field, but the enemy still confronts us. The losses on both sides are heavy, and especially so among our officers. We have taken more than twenty guns, and 2500 prisoners.” We await the sequel—with fear and trembling, after the sad experience of Western victories. The Secretary of War thinks Longstreet’s corps had not yet reached Bragg; then why should he have commenced the attack before the reinforcements arrived? We must await further dispatches. If Bragg beats Rosecrans utterly, the consequences will be momentous. If beaten by him, he sinks to rise no more. Both generals are aware of the consequences of failure, and no doubt it is a sanguinary field. Whether it is in Georgia or over the line in Tennessee is not yet ascertained.

September 22d.—Another dispatch from Bragg, received at a late hour last night, says the victory is complete. This announcement has lifted a heavy load from the spirits of our people; and as successive dispatches come from Gov. Harris and others on the battle-field to-day, there is a great change in the recent elongated faces of many we meet in the streets. So far we learn that the enemy has been beaten back and pursued some eleven miles; that we have from 5000 to 6000 prisoners, some 40 guns, besides small arms and stores in vast quantities. But Gen. Hood, whom I saw at the department but a fortnight ago, is said to be dead! and some half dozen of our brigadier-generals have been killed and wounded. The loss of the enemy, however, has been still greater than ours. At last accounts (this morning) the battle was still raging—the enemy having made a stand (temporarily, I presume) on a ridge, to protect their retreat. They burnt many commissary stores, which they may need soon. Yet, this is from the West.

The effects of this great victory will be electrical. The whole South will be filled again with patriotic fervor, and in the North there will be a corresponding depression. Rosecrans’s position is now one of great peril; for his army, being away from the protection of gun-boats, may be utterly destroyed, and then Tennessee and Southern Kentucky may fall into our hands again. To-morrow the papers will be filled with accounts from the field of battle, and we shall have a more distinct knowledge of the magnitude of it. There must have been at least 150,000 men engaged; and no doubt the killed and wounded on both sides amounted to tens of thousands!

Surely the Government of the United States must now see the impossibility of subjugating the Southern people, spread over such a vast extent of territory; and the European governments ought now to interpose to put an end to this cruel waste of blood and treasure.

My little garden has been a great comfort to me, and has afforded vegetables every day for a month past. My potatoes, however, which occupied about half the ground, did not turn out well. There were not more than a dozen quarts—worth $10, though—in consequence of the drought in June and July; but I have abundance of tomatoes, and every week several quarts of the speckled lima bean, which I trailed up the plank fence and on the side of the wood-house—just seven hills in all. I do not think I planted more than a gill of beans; and yet I must have already pulled some ten quarts, and will get nearly as many more, which will make a yield of more than 300-fold! I shall save some of the seed. The cabbages do not head, but we use them freely when we get a little bacon. The okra flourishes finely, and gives a flavor to the soup, when we succeed in getting a shin-bone. The red peppers are flourishing luxuriantly, and the bright red pods are really beautiful. The parsnips look well, but I have not yet pulled any. I shall sow turnip seed, where the potatoes failed, for spring salad. On the whole, the little garden has compensated me for my labor in substantial returns, as well as in distraction from painful meditations during a season of calamity.

September 23d.—We have nothing additional up to three p.m. to-day; but there is an untraceable rumor on the street of some undefinable disaster somewhere, and perhaps it is the invention of the enemy. We still pause for the sequel of the battle; for Rosecrans has fallen back to a strong position; and at this distance we know not whether it be practicable to flank him or to cut his communications. It is said Gen. Breckinridge commanded only 1600 men, losing 1300 of them! Gen. Cooper and the Secretary of War have not been permitted to fill up his division; the first probably having no desire to replenish the dilapidated command of an aspiring “political general.”

A Mr. G. Preston Williams, of Eden, Chatham County, Ga., writes to the President, Sept. 7th, 1863, saying he has lost three sons in the war, freely given for independence. His fourth son is at home on furlough, but he shall not return unless the President gives up his obstinacy, and his favorites—Bragg, Pemberton, Lovell, etc. He charges the President with incapacity, if not wickedness, and says our independence would have been won ere this, but for the obstacles thrown by him in the way. He threatens revolution within a revolution, when Congress meets, unless the President reforms, which will cause him to lose his office, and perhaps his head. To which the President replies thus, in an indorsement on the envelope:

“Secretary of War.—This is referred to you without any knowledge of the writer. If it be a genuine signature, you have revealed to you a deserter, and a man who harbors him, as well as incites to desertion, and opposition to the efforts of the government for public defense. Sept. 19th, 1863.—J. D.”

The indorsement was written to-day, since hearing of Bragg’s victory.

September 24th.—A dispatch from Gen. Bragg, received to-day, three miles from Chattanooga, and dated yesterday, says the enemy occupies a strong position, and confronts him in great force, but he is sending troops round his flanks. No doubt he will cross the river as soon as possible. Only a small portion of Longstreet’s corps has been engaged, so Bragg will have a fresh force to hurl against the invader. We learn to-day that Gen. Hood is not dead, and will recover.