BOWLING GREEN, December 20, 1862.

Colonel J. P. GARESCHE,

Assistant Adjutant-General and Chief of Staff:

We are all right. Scouts out, and will lose no opportunity to find Morgan. Do not know Bruce's strength or condition. Will telegraph him.

R. S. GRANGER,

Brigadier-General.

FORT HENRY, December 20, 1862.

General ROSECRANS:

Started my cavalry yesterday up west side of Tennessee. Am just starting up in boats, with infantry and artillery, in obedience to an order from General Grant, and hope to get in rear of enemy. I take nearly 1,300 men.

W. W. LOWE,

Colonel, Commanding.

CAMP HAMILTON, December 20, 1862-11.50 a.m.

Colonel J. P. GARESCHE,

Chief of Staff:

This morning 20 rebel cavalry approached our vedettes at Brantwood, to surprise them, but were surprised themselves by 12 of Colonel Stanley's escort. One of the rebels, the officer in command, was badly wounded. They were pursued about a mile, to a strong rebel picket. One Springfield rifle and musket (cut short) was captured. The rebels wore our army overcoats; had our knapsacks in use as haversacks.

JAS. S. NEGLEY,

Brigadier-General.

HDQRS. FOURTH DIV., FOURTEENTH ARMY CORPS,
DEPARTMENT OF THE CUMBERLAND,

Camp near Nashville, December 20, 1862.

Major LYNE STARLING,

Assistant Adjutant-General:

MAJOR:I have the honor to report, for the information of the general commanding, that I left camp this morning about 8 o'clock (various causes producing an hour's delay), and marched with my whole command to Stewart's Ferry, on Stone's River. From that point Colonel Hazen, with the Nineteenth Brigade, with Colonel Minty, Fourth Michigan Cavalry, proceeded to Rural Hill, and Colonel Enyart, with part of the Fourth Ohio Cavalry, to Silver Springs. Both these officers report to me that they found no enemy, though the rebel pickets had occupied both places until Thursday last, when, it seems, they were withdrawn. No considerable force could be heard of by either, except that Colonel Minty learned, upon what seems good authority, that Scott's cavalry are stationed at Oak Grove. Colonel Minty's advance had a slight skirmish with a small force 1 1/2 miles beyond Rural Hill, without any consequence beyond the flight of the enemy. I will add that my impression is that on day before yesterday,or, perhaps, yesterday morning, the rebel forces were withdrawn from the regions we visited to-day, and that no considerable force has been there lately.

Very respectfully,

J. M. PALMER,

Brigadier-General, Commanding.