MURFREESBOROUGH, June 20, 1863.

General HARTSUFF:

Morgan is reported 9 miles from Lebanon, probably on his way into Kentucky, or perhaps to Carthage. His forces reported 4,000 and one battery.

W. S. ROSECRANS,

Major-General.

CINCINNATI, OHIO, June 20, 1863.

Major General H. W. HALLECK,

General-in-Chief:

General Parke, with all his command but two brigades, joined General Grant the 14th. The two remaining brigades passed Memphis on the 15th, so that all his command is with except Edwards' battery, detained by General Asboth. I have heard nothing of the expedition sent into East Tennessee and Western Virginia. It is understood now that no considerable forces have been sent out of East Tennessee. I have nevertheless started another force to Jamestown, tenn., and will follow it up by all available force if found expedition to proceed.

A. E. BURNSIDE,

Major-General, Commanding.

SOMERSET, Ky., June 20, 1863 - 2.05 a. m.

General HARTSUFF:

Dispatch received. Will start 1,000 mounted men, under Colonel Kautz, by 6 a. m. toward Jamestown, supported by regiment of infantry and a battery.

CARTER.

SOMERSET, JUNE 20, 1863.

General STURGIS:

The news I receive through scouts from East Tennessee are so conflicting that I am at a loss to know what the rebel force there is. One puts it down as low as 7,000 to 8,000; another puts the maximum estimate at 20,000.

General Buckner passed up toward Big Creek Gap last Friday. He stated at a house on the way that he wa coming into Kentucky. The officer who accompanied him returned on Saturday without Buckner. On Wednesday the force of Pegram was at and in vicinity of Travisville. A force under Colonel Kautz left for that place at 6 this morning.

CARTER,

Brigadier-General.

NASHVILLE, June 21, 1863 - 10.30 p. m.

(Received 11 p. m.)

Lieutenant-Colonel GODDARD,

Assistant Adjutant-General;

Scout returned this afternoon from few miles beyond Silver Spring. No enemy at Silver Spring; 100 reported there day before yesterday. From best information, Captain [B. T.] Hayden, Seventh Kentucky, commanding party, was satisfied Morgan was not at Lebanon. Main force