TENNESSEE CORRESPONDENCE OF THE SUN,From Chattanooga*Chattanoga, July 19th, 1862.Ed*. Sun: Were it in my power, I should be glad to keep you posted oneverything that is transpiring in thispart of the Confederacy, but the means I have of obtaining reliable information are limited, and that which comes to me for “reliable,” frequently has not a shadow of truth about it. I think, however, I am in possession of some facts which will be new and interesting to you, and for the truth of which I can vouch.Yesterday evening, an official dispatch reached this place from Col. Forest. He stated that ho attacked the enemy at Murfreesborough, with a force of 800strong, on Sunday morning, 5 o’clock ; the fight lasted nine hours, when he succeeded in burning the depot, destroying three trains of cars, and capturing 1200prisoners among which were two Brigadier Generals, lie also captured hundred horses and mnles, 400 wagons with several pieces of light artillery, and a vast amount of commissary and quartermasters stores, nearly all of which he wa3 compelled to destroy. This victory is regarded as one of the most brilliant ol the war. The dashing ColonelForest is carving out for himself a name which will stand high upon the temple offame.Yesterday, the 18th, Buell was reported at Battle Creek in person. It is supposed he went there for the purpose of reconnoitering. Perhaps he designs inarching on Chattanooga; onco hemight have done so successfully, but that time is past. If rumor can bo relied on, a knowledge of startling events will soon reach us. It is also reported here this morning in high official circles that Iho enemy have retired from and burned Huntsville.I have no local news of importance. Eince General McCowau has been in command at this post, everything seems to be* going on swimmingly. The General is regarded asja good man, and every one have the utmost confidence in his ability. Eilasstoop and xnove sideways to pass ; some*times descend a wooden ladder and again ascend one. This Cave has been, and is now, being worked for saltpetre. Mr. Pringle, who has charge of the Saltpetre Works, informs me that he has had as many as 30 hands engaged. The dirt which is obtained from the large crevices in the rock, and brought out on the backs of the laborers, is strongly impregnated, yielding as high as 7} lbs.per bushel. Oncgreat curiosity connect-ek with this wonder of nature, is the strong currents of cold air rushing from the crevices in the rock, at several places, by which some of our lamp lights were extinguished, causing us the not very pleasant reflection of a possibility of ourhaving to find our way out of the place without the assistance of a light, whichwould have been a rather difficult matter.Confederate .Letter from £ast Tennessee.Louisville, (near Knoxville,) Tenn., )July hi, 186.’. iEds Sun: All remaino as quiet here as could be expected. It now begins to be questionable whether we will have any great battle here. Our troops are bo stationed along the lino of railroad, that a strong force can soon be concentrated at any given point on the road where it may be needed.Col. Morgan continues to break the monotony in the present dearth of news. His captured Major reached Knoxville a few days ago.The government is not exactly pressinghorses, wagons, o.; but the people are selling them, knowing that the government must and will have them. There are certain localities in the Confederacy where pressing is needed. Men full of wordy patriotism, who for the sake of the good cause arc willing to talk ficm one (lay’s end to another, without furnishing but little material aid. If government agonts were to go to these men of hea vy purse and tell them wo must have some horeos, provisions, c., they would begin to realize that there is a war going on m this countrg. These remarks do not apply to East Tennessee so fully as to other portions of tho country more remote from the scene of action.We have recently had a line shower of rain here, with good prospects for more.Corn crops, iu the main, ate looking finely; and if the “Republic” is not“crushed out,” till hunger docs it, there is a probability that Jonathan will feelits keen pangs in his own maw before the work is accomplished. Darius.!From the Tennessee Hive?.Long Island, Ala., I July 18th, 1802. fEds. Sun: We arrived here on Tues-ay and reported to Gen. Heth, actingtejor General of the 2d Division of De~artment of East Tennessee, who turneda over to Brigadier General Leadbetter,jo of Bridgeport retreat notoriety) much our regret. I say regret, becausele military antecedents of this gentle-tan are not such as to inspire soldiersith any confidence in his military skillad capacity. He has the confidence ofeither soldiers or civilians hereabouts.We are encamped within one and aalf miles of the enemy. They havestrong foro6 opposite us, near and elow the mouth of Battle Creek. Their »nte are plainly visible from the summitf a mountain not far distant from our imp. Every call upon their drums are istinctly heard by us. Our pickets ring in prisoners frequently. Three on esterday, belonging to a Kentucky regi-tenfc. Their forces are variously esti-tatod at from 10,000 to 20,000.I find here Major William Gunter, for* ;erly of the 6th Alabama regiment, in )mmand of a battalion of l‘artisan Ran* ers. This gentlemen returned to his ome from Virginia last Spring after his jrm of service expired, and found his otses, oattle, o., stolen by the Yankees, his n6groes scattered through theountry, and hia family cruelly treated y the inhuman Yankeo devils. He ar-ived at home in the night, and before be break of day next morning, left and egan to rally a few daring men around lm for the purpose of annoying aud arrassing the enemy as much as pos-.ible, which he has succeeded in doing 3 a considerable extent. The Yankees ave set a price upon his head. His eeidcnce is near the line of Alabama and eanessee, opposite this place, aud dis* ant about three mil62. His family are n this side of the river.This section of our State is disgraced iy scores of tiaitore, who seize every op-ortunity of conveying intelligence of nilitary movements on this Bid© of the iver to tho enemy. And strange to say ion© of them have yet been hung, aud mt very few arrested How long shall his elate of affairs be allowed to con*inue. • *'•-/ •_: jCapt. Waddell lias been compelled toeave his command by ill-health, for ahorfc time. He visits tho 77a* m springs,loorgia.We left Major Hatch Cook at Chatta* »ooga with a battalion of llllliaid’a Le* ;ion. He was being furnished with arms.' was glad to notice while at Chattanooga.hat Capt. Humphries, Ordnance officer it that post, had on hand a good supply ,f Enfield rifles, part of a recent importation from England.News has reached us of another gak ant exploit by the bold and interprid Morgan. As I predicted iu my letter to he Sun of the loth, he turned up at a [lace little expected by the enemy. A report has also reached us, through Fed'* aral sources, that another success has attended our arms below NasWille, profitjbly at Murfreesboro’.I was mistaken in calling the railroadleading from Chattanooga to this place the Memphis and Charleston Railroad.It should have been the Chattanooga and Nashville Railroad. The former begins at Stevenson, at which place the lattertakes the direction of Nashville.I had the pleasure while at Cbatta uooga of visiting the celebrated LookoutMountain, and taking a view of the surrounding country for miles. I was wellrepaid for my trouble in climbing the mountain over a bad road, horseback, on a very hot day. The view from the summit is beautiful indeed. There is a hotel and a number of handsome cottages on the mountain. The hotel is not open,and there are no visitors, for any length of time, owing to tho troubled state of affairs.I also visited the Lookout Cave, which enters at the base of the mountain within1i