LA GRANGE, TENN., January 1, 1863.

General GRANT:

There were indications of a rebel force a few miles north of this place last night, and confirmed this morning. We are all right here. In ordering me here last night I intended to clean out this force. It may be a part of Forrest's force, but think it is only a congregation of guerrillas to the number of perhaps 1,500. No fear of Grand Junction or this place. Your dispatch of last night received. I have sent Lee his instructions at Moscow.

C. S. HAMILTON,

Brigadier-General.

LA GRANGE, January 1, 1863.

General GRANT:

Richardson's guerrillas are hovering about Somerville, 800 to 1,200 strong. Is it best for Lee to forage in the neighborhood, so that the scoundrels can't subsist there? To do that it may be necessary to burn the mills. I want to see them cleaned out.

I propose to send a couple of infantry regiments to Somerville in a few day on a foraging expedition, and see if Somerville bacon is good.

Quinby is at La Fayette. Train of cars goes there in the morning.

C. S. HAMILTON,

Brigadier-General.

HOLLY SPRINGS, MISS., January 1, 1863.

Brigadier General C. S. HAMILTON, La Grange, Tenn.:

I would forage off the neighborhood of Somerville, but destroy nothing, not even the mills. We can use all the have.

Sullivan caught up with Forrest and gave him a tremendous thrashing; captured six pieces of his artillery, killed and wounded a great many, took his baggage and several hundred prisoners. The gunboats got up and destroyed all his ferries. Dodge says that a scout brings in the news that Rosecrans had had a fight and whipped the enemy badly.

Vicksburg is not taken. Kirby Smith is re-enforcing that place with his army corps, 30,000 strong.

U. S. GRANT,

Major-General.

McPHERSON'S, January 1, 1863.

General GRANT:

The defeat of Johnston [Bragg] is good news for New Year's day. I have nothing definite from Grenada or the southeast. The scout whom I expected back from Grenada has not returned. I have sent three more, one southeast, one in south of Panola, and one toward Grenada, but it is very difficult to get good scouts here. The citizens generally don't know anything, and when they do are not to be trusted, unless corroborated from other sources. The cavalry are out every day, but thus far have got no news of the enemy's movements.

JAS. B. McPHERSON,

Major-General.