(31st). He brings information confirming that communicated in my dispatch last evening, to the effect that the rebel armies of Bragg and Kirby Smith are moving on Nashville, troops mostly moving by rail, artillery and wagon trains moving by way of Sparta, all making haste to reach the objective point before our troops can get there to oppose them. Mr. Briscoe brings so much important information touching the condition, numbers, and organization of the rebel army that I have thought best him to you. He will reach you this evening, going by way of Cave City. I send these communications to you direct, to save time. I also send copies to General Crittenden.

Very respectfully, your obedient servant,

WM. SOOY SMITH,

Brigadier-General, Commanding Fourth Division.

P. S. - A returned prisoner, S. P. Vess, formerly a guide for our troops at Wartrace, Tenn., and engaged in making up a company for Stokes' cavalry, has just come in from Sparta, which point he left a week ago last Monday night, having drugged the guard and escaped. He says that from 500 to 800 men, principally convalescents, had garrisoned Sparta, but were ordered to Murfreesborough just before he got away. He confirms the accounts already received of the rebel advance into Middle Tennessee. He says that Joe Johnston is in command, and that it is rumored that he brought re-enforcements, swelling the number of Bragg's and Kirby Smith's combined forces to from 70,000 to 90,000.

HEADQUARTERS FOURTEENTH ARMY CORPS,
Bowling Green, November 6, 1862.

Major-General WRIGHT, Cincinnati:

The southwestern part of this State has been a disturbed district all summer. It is a granary of supplies for us. I am told a regiment of infantry and two of cavalry will suffice to clear it. I propose to detach McHenry, Seventeenth Kentucky, Rousseau's division, for the infantry, and will send them down to Russellville.

W. S. ROSECRANS,

Major-General.

HEADQUARTERS,
Lexington, Ky., November 6, 1862.

Major General W. S. ROSECRANS,

Bowling Green:

General Halleck directs that all troops in Kentucky that can be spared be sent down the Mississippi without delay. To carry out these instructions efficiently, I must send all of Granger's force, with the exception of, say, five regiments. This will, of course, prevent the occupation of London and Sommerset. Do you think such occupation so important to the success of your operations as to withhold the force of Granger from the Mississippi expedition? I do not think so. They should go. Answer quick.

H. G. WRIGHT,

Major-General, Commanding.