NASHVILLE, TENN., October 4, 1863-9 p.m. [Received 1.30 p.m.,5th.]

Major THOMAS T. ECKERT,

Washington, D. C.:

Portion of Wheeler's force cut wire at daylight this morning near Fosterville. Main force moving in direction of Murfreesborough; suppose they will attack it to-day. I think it can be held, but the force is small. Railroad little damaged.

SAM. BRUCH,

Assistant Superintendent Military Telegraph.

WAR DEPARTMENT, October 4, 1863-11.30 a.m.

Major-General ROSECRANS, Chattanooga, Tenn.:

Yours of yesterday received. If we can hold Chattanooga and East Tennessee, I think the rebellion must dwindle and die. I think you and Burnside can do this, and hence doing so is your main object. Of course, to greatly damage or destroy the enemy in your front would be a greater object, because it would include the former, and more; but it is not so certainly within your power. I understand the main body of the enemy is very near you-so near that you could "board at home," so to speak, and menace or attack him any day. Would not the doing of this be your best mode of counteracting his raids on your communications? But this is not an order. I intend doing something like what you suggest whenever the case shall appear ripe enough to have it accepted in the true understanding, rather than as a confession of weakness and fear.

A. LINCOLN.

CHATTANOOGA, TENN., October 4, 1863-1 p.m. [Received 10.45 p.m.,8th.]

Major General H. W. HALLECK,

General-in-Chief:

Following dispatches were sent to General Burnside:

At 11, September 30:

Since my dispatch of yesterday to General Halleck [copy sent to you] a considerable force of the enemy is reported opposite Washington. I rely on you to protect my left flank. It is obvious they should not be allowed to separate us.

At 12 midnight, same day:

The mass of rebel cavalry has crossed the river above Washington, and you will have to close up your force and cut them off. We have sent ours, and you will have to close with them.

On October 2:

We have reliable information that the rebel cavalry have not only gone into Tennessee, but to Pikeville. We now need and want all the assistance you can give us, to pursue, harass, and destroy them. Your prompt assistance is desired.

This morning I received the following:

KNOXVILLE, TENN., October 4, 1863.

Is there any truth in the crossing of the enemy's cavalry at Cotton Port, which you reported?