CINCINNATI, OHIO, September 24, 1862-6.45 p. m.

Major-General HALLECK, General-in-Chief:

Major General Thomas L. Crittenden has crossed Salt River with the advance of Buell's army, consisting of 12,000 men and six batteries. Nothing new regarding Bragg's movements.

H. G. WRIGHT,

Major-General, Commanding.

LOUISVILLE, September 24, 1862.

General BUELL:

Your dispatch is received. The bridge over Salt River is ready for use. The rations are sent to Brandenburg. I have 35,000 men. I am intrenched, and believe that I can hold the city. The march by way of mouth of Salt River is dangerous with new troops until you come so close that two marches will enable me to unite with you.

When you have brought Bragg to bay then I will attack him. Only let me know the route and time. But I am ready to execute any order.

W. NELSON.

HEADQUARTERS DEPARTMENT OF THE OHIO,
Cincinnati, Ohio, September 24, 1862.

Brigadier General A. J. SMITH,

Commanding U. S. Forces, Covington, Ky.:

GENERAL: Colonel G. W. Berry proposes an expedition against Falmouth and perhaps Cynthiana, which I think well of, but he requires in addition to the force now at Augusta an additional number of cavalry. Can you spare him, say, 300 of the Tenth Kentucky? If so, please send them to-night if they can be got ready, the command to report to Colonel Bradford. The quartermaster will be instructed to furnish the necessary water transportation to Augusta, Ky.

Very respectfully, your obedient servant,

H. G. WRIGHT,

Major-General, Commanding.

P. S.- Please notify the quartermaster what force you may conclude to send.

HEADQUARTERS DEPARTMENT OF THE OHIO,
Cincinnati, Ohio, September 24, 1862.

Colonel BRADFORD, Commanding at Augusta, Ky.:

COLONEL: A force of the Tenth Kentucky Cavalry will be sent to co-operate with the force under your command in an expedition against Falmouth and perhaps Cynthiana, at both of which place it is understood there are rebel troops. This cavalry which is accompanied by Colonel G. W. Berry, provost-marshal of Harrison County, is directed to report to you.

If the rebels are in strong force at or in the vicinity of Falmouth it will be unsafe them behind and proceed first to Cynthiana, as