NASHVILLE, November 30, 1863.

Brig. General GEORGE CROOK,

Commanding Second Cavalry Division, Huntsville, Ala.:

The following telegram is just received from Brig. General A. S. Williams, commanding at Tullahoma:

TULLAHOMA, November 30, 1863-7.30 p.m.

Roddey, with 1,000 men, without artillery or train, is reported at Salem last night, moving north. Being unencumbered, it is possible he intends striking the railroad at some unguarded point. There is no cavalry on this line for observation. Colonel Oliver, with a brigade of mounted infantry, Fifteenth Corps, is somewhere west of Stevenson. I believe the report came originally from him, but I cannot learn his whereabouts.

A. S. WILLIAMS,

Brigadier-General, Commanding.

W. S. SMITH,

Brigadier-General, Chief of Cavalry, Div. of the Miss.

STEVENSON, November 30, 1863-7.30 p.m.

General WILLIAMS,

Tullahoma:

The information has been sent to the cavalry along the Tennessee. It will probably reach General Crook in that way, if he has not received it before,as he probably has.

His headquarters are 53 miles from here on the railroad line, on Memphis road, which was to go this morning; have deferred the trip until further information is received.

The rebel cavalry are now about 50 miles from General Crook's headquarters, with fresh horses and no baggage.

SAMUEL ROSS,

Colonel, Commanding Post.

TULLAHOMA, November 30, 1863.

Brigadier-General KNIPE,

Decherd:

It is reported that Roddey, with 1,000 men,is at Salem, moving north. Has no artillery nor train. Have you heard anything?

I shall order a section of artillery to report to you from Elk River. Can you send up two companies as an escort for the artillery?

A. S. WILLIAMS,

Brigadier-General.

COLUMBIA, November 30, 1863. (Received December 3.)

Maj. General U. S. GRANT:

I examined bridge this morning. Will camp working force close by it. Am in communication with Brigadier-General Dodge. He will send me 100 mechanics. Captain Donahugh, just returned to me from General Morton's pioneer brigade, will go to Nashville to-morrow and secure everything necessary. Boom will be arranged to protect trestle-work against drift-wood. Bridge is 2 miles from town.

HENRY R. MIZNER,

Colonel, Commanding.