HOLLY SPRINGS, December 22, 1862.

General GRANT:

Grierson impatient to pursue enemy; has been after me several times to telegraph to you on subject. He has been ready to pursue ever since yesterday noon.

WM. S. HILLYER,

Colonel and Aide-de-Camp.

[Indorsement.]

General HAMILTON:

Let Grierson, Lee, and Fifth Ohio Cavalry push after enemy until they find him. They may travel over West Tennessee in pursuit of the enemy until it will no longer support an army.

U. S. GRANT,

Major-General.

BOLIVAR, December 22, 1862.

General M. BRAYMAN:

Sent last night by courier, at request of Colonel Morrison, the latest news. Holly Springs reported burned with it contents. Colonel McNeil, supposed of Second Illinois Cavalry, with 250 men, prisoners. Van Dorn advancing this way; reported to be within 3 miles of Grand Junction. Rebels supposed to be on Saulsbury road in force. Keep good lookout. Wires working north to Jackson and south to Grand Junction. All quiet here.

W. L. BARNUM,

Acting Assistant Adjutant-General.

CORINTH, December 22, 1862.

General GRENVILLE M. DODGE:

I returned to Corinth Saturday at 11 a. m. Have taken every precaution to defend this place against any force.

I have assumed command of forces in and about Corinth.

August MERSY,

Colonel, Commanding.

BOLIVAR, December 22, 1862.

General J. C. SULLIVAN:

General Dodge sends by courier to this post, addressed to Major General U. S. Grant, the following:

LEXINGTON, [December] 21, [1862]-2 p. m.

I have moved 24 miles; all gone north. Four hundred men and two pieces of artillery joined Forrest to-day. I will push for him to-morrow. Expect to hear from General Sullivan to-night.

Later-LEXINGTON, [December] 21, [1862]-2 p. m.

I am pushing here toward Spring Creek, as Forrest, I learn, is there. It seems to me we should get the railroad clear first.

We are getting a long distance from Corinth. I may be wrong, but it appears to me all-important that we should open your communication north.

W. L. BARNUM,

Acting Assistant Adjutant-General.