JACKSON, December 18, 1862.

Major-General GRANT:

As Far As I can learn the rebels are near Mifflin. My force here is so small, numbering only 1, 3000. that until the troops I have ordered in arrive I cannot move. General Brayman will be here this afternoon with 700 men and one battery. The Thirty-ninth Iowa will be here this evening. I have ordered from Union City and Trenton all the available force, say 700 men. I will attack the rebels in the morning if they do not first attack me. My preparations for defense are good. I can hold Jackson against all their force if it numbers 10,000, and meet and whip them if they are 5,000 strong.

JER. C. SULLIVAN,

Brigadier-General.

OXFORD, December 18, 1862.

General SULLIVAN:

Have you made preparations to get forces from Corinth? Don't fail to get up a force and attack the enemy. Never wait to have them attack you.

U. S. GRANT.

Major-General.

JACKSON, December 18, 1862 - 5 p. m.

General GRANT:

General Dodge telegraphs there are no cars at Corinth. I have to send train from here, and at present we have no spare engine. Will send train as soon as possible.

Want of information from Colonel Ingersoll as to direction the enemy are marching keeps me still. I have sent out another party to find their position and will move to attack them at once. A rumor is here that Ingersoll's cavalry has been whipped and dispersed; know nothing about it.

JER. C. SULLIVAN,

Brigadier-General.

JACKSON, December 18, 1862.

Major-General GRANT:

The enemy have attacked my cavalry. They have been fighting all day between Mifflin and Lexington. I will hold this post till the last.

JER. C. SULLIVAN.

JACKSON, December 18, 1862.

General GRANT:

The enemy are within 4 miles of this place. My infantry regiments have checked their advance, which seems to be cavalry.

General Dodge is moving against their flank an I will attack in front to-morrow morning.

JER. C. SULLIVAN,

Brigadier-General.