Greeneville; Beatty's is at Jonesborough, and McConnell's has gone to Warm Springs to support Kirby, who is supposed to be at Asheville, N. C. No news from Kirby to-day and none from Beatty.

April 8.-10 a. m., sent General Tillson's dispatch, received 1 p. m. April 6, to Major-General Thomas by telegraph. 10.20 a. m., received report from General Beatty, at Jonesborough. He says that he can hear nothing of the enemy, but a few guerrillas; that he has sent a scout to Wytheville, Va., and that there is very little forage or subsistence about Jonesborough. 1.30 p.m., received dispatch from Mr. Latimer, he finished Swan Pond trestle yesterday evening. It is 1,393 feet long, and he cut the timbers from the woods and built it in four days, not working at night. He also says that he will the road done to Midway by Monday night and thinks he will it done to Greenville by next Friday or Saturday, about one week. 2 p. m., Lieutenant-Colonel Greenwood, assistant inspector-general, Fourth Army Corps, arrived in Greenville. He has just returned from Asheville. Kirby's brigade will reach Greenville on the on the way back about the 10th instant. He reports that Kirby reached the vicinity of Asheville, about two from the town, at noon on the 6th instant. He Colonel Greenwood with a few mounted men dashed into the edge of the town and captured five rebels, a mule wagon and teams of mules. The enemy could be seen forming a line of battle in the far part of the town and he returned to Kirby's brigade where it had halted, about a mile and a half outside of the town. Colonel Greenwood reported that there were about 400 troops and six guns only in the place. Colonel Kirby, judging from the reports that he heard, was of the opinion that there were 1,000 or 1,500 men in Asheville, and 400 cavalry on his left flank and 700 on his right, so he refused to enter the town. He had instructions not to lose in any engagement unless he could make enough by it to pay for the loss. The enemy came out of town with a very small line of battle and fired a few shots from their skirmish line; also brought out two guns and fired a few rounds. During the night Colonel Kirby withdrew from in front of Asheville and commenced to march back for Greeneville.

April 9.- Nothing new to-day. The telegraph is completed this evening to within twelve miles of Jonesborough; will be completed to that place by noon on the 11th. The railroad is completed to-day as far as Midway Station.

April 10.-10 a. m., received news by telegraph of the surrender of Lee and the Army of Northern Virginia to General Grant. 11 a. m., the advance of Colonel Kirby's brigade arrives from Asheville. Major Steele, aide-de-camp, who accompanied Colonel K[irby], reports that citizens and deserters from the rebels report that General Stoneman was on the railroad near Salisbury, N. C., on the 2nd instant, tearing up the road and advancing on that place; also that Colonel Lyon's [Love's] Legion, consisting of 800 infantry, 400 Indians, one four-gun battery, and about 450 cavalry, were stationed at Quallatown, N. C., preparing for a raid on the Knoxville and Chattanooga Railroad at Loudon or Charleston. This information was at once telegraphed to General Thomas. Refugees who have just come in from Asheville report that there were about 400 men and five guns in that place when Colonel Kirby was before it. The railroad construction corps is working up in this direction as rapidly as possible.

April 11.-Nothing of importance to-day. 9 a. m., commenced to rain. 1 p. m., telegraph wire is up as far as Jonesborough. General