No. 2.-reports of Brig. (Gen. James S. Negley, U. S. Army.
General Adams' command of rebel cavalry encamped at the foot of the mountain. They formed in line anld ired upon Colonel Hambright's advance, which we replied to from two pieces of artillery, which had been placed in position unobserved. They retreated through a narrow lane toward Jasper, closely pursued by a portion of Colonel Haggard's Fifth Kentucky Cavalry and Major Vynkoop's battalion of Seventh Pennsylvania Cavalry. My escort, comrmanrded by Lieutenants Wharton and Funk, led the charge with reckless daring, dashing into the midst of the enemy, using their sabers with terrible execution. The narrowness of the lane and very broken ground alone prevented the enemy from being totally destroyed. They fled in the wildest disorder, strewing the ground for miles with guns, pistols, and swords. We captured their ammunition and commissary wagons and supplies. The enemy's loss, as far as we could ascertain, was 20 killed and about the same number wounded, among whom is Major Adams, General Adams' brother. We captured 12 prisoners, including 2 commissioned officers, with a large number of horses. Our loss, which I regret to say was chiefly sustained by my escort, is 2 killed and 7 wounded; several seriously.  The troops acted with admirable efficiency. Colonel Hanibright, acting brigadier-general, with Colonel Haggard, Major Wynkoop, and Lieutenants Wharton, Funk, Sypher, and Nell, deserve special notice. Yours, very truly,
Chattanooga this morning. They report the arrival of a portion of General Adams' cavalry, who reached Chattanooga last night. This, with the statements of citizens living along the road, proves the total rout and disgraceful flight of the enemy to Chattanooga, a distance of 43 miles, without stopping. Ah attempt was made to rally in Jasper, but they cursed General Adams and rushed on with their foaming horses. Hundreds of Union men have flocked into Jasper from the mountains. The enemy, who was crossing the river at Shell Mound, retreated to Chattanooga by rail this morning. Appearances indicate that they will not defend Chattanooga. There were but two regiments at Atlanta, Ga., on Tuesday last. Colonel Starnes' regiment of cavalry avoided meeting us, and are now near Sparta. We will give them attention on our return. I trust you will be able to engage the attention of Starnes until we can overtake him. I shall push on to Chattanooga to-morrow.