CHATTANOOGA, December 20, 1864.

Major-General STEEDMAN:

The agent will send you 130 cars; all that he has. The 175 cars you took with you to Nashville have not been returned. The last of your forage, rations, and ammunition leave here this morning on board of the Kennesaw. Your cavalry march to Bridgeport to-day. Your train and cavalry cannot be sent to Decatur until two transports up the river return and General Granger releases two of the steamers that have gone with him.

A. M. MACKAY,

Lieutenant-Colonel and Chief Quartermaster.

HEADQUARTERS POST OF NASHVILLE, Nashville, Tenn., December 20, 1864.

Major BEAUMONT,
Assistant Adjutant-General, Cavalry Corps:

I am informed that between our picket-line and Brentwood Hills there are numerous bands of dismounted cavalry wandering about and committing all manner of depredations. I would respectfully suggest that some step be taken to get these men into camp and under control, that an end may be put to this evil.

I am, major, very respectfully, your obedient servant,

JNO. F. MILLER,

Brigadier-General.

WASHINGTON, December 21, 1864-12 m.

(Via Nashville, Teen.)

Major-General THOMAS:

Permit me, general, to urge the vast importance of a hot pursuit of Hood's army. Every possible sacrifice should be made, and your men for a few days will submit to any hardship and privation to accomplish the great result. If you can capture or destroy Hood's army Sherman can entirely crush out the rebel military force in all the southern States. He begins a new campaign about the 1st of January, which will have the most important results, if Hood's army can now be used up. A most vigorous pursuit on your part is therefore of vital importance to Sherman's plans. No sacrifice must be spared to attain so important an object.

H. W. HALLECK,

Major-General and Chief of Staff.

HEADQUARTERS DEPARTMENT OF THE CUMBERLAND, In the field, December 21, 1864.

Major General H. W. HALLECK,

Washington, D. C.:

Your dispatch of 12 m. this day is received. General Hood's army is being pursued as rapidly and as vigorously as it is possible for one army to pursue another. We cannot control the elements,a nd, you