The battle of Corinth, Miss., was this day fought between the Union army, under Gen. Rosecrans, and the rebel forces, under Gens. Price, Van Dorn, and Lovell. The engagement resulted in a rout of the rebels. The loss on both sides was very severe, and particularly in officers. Gen. Hackleman fell mortally wounded while leading his brigade to the charge. General Oglesby was severely wounded. Nearly a thousand prisoners, besides the wounded, were left in the hands of the Nationals.--(Doc. 127.)
At Frankfort, Kentucky, Richard Howes was inaugurated rebel Governor of that State. Gens. Bragg and Humphrey Marshall were present at the ceremonies, and made vituperative and bitter secession speeches. In the afternoon the railroad bridge leading out of the city was destroyed, and all the rebel infantry departed for the South, leaving Scott's rebel cavalry in occupation.
The Military Exemption Act passed the rebel Congress, in session at Richmond, Va. It exempts police for sections of country having dense negro population. Secures the liberty of the press, by exempting editors and such help as they require in their business; exempts employes of transportation and telegraph companies, ministers of the Gospel, physicians, shoemakers, tanners, blacksmiths, wagon-makers, millers, superintendents and employes on Government works, overseers of plantations, and one man to every five hundred head of cattle. The exemption act passed April twenty-first was repealed.--Richmond Examiner, October 6.
The Secretary of War issued an order, publicly reprimanding Capt. George H. Johnston for communicating an official report of a confidential character and for censuring his superior officers.--General Orders, No. 151.
 A large and enthusiastic meeting of citizens was held at the Cooper Institute, New York City, for the purpose of expressing sympathy with the loyalists of Alabama, Mississippi, and East-Tennessee. Speeches were made by R. N. Havens, who presided, General W. K. Strong, Colonel R. H. Shannon, and Rev. Mr. Carter, of Tennessee.
A Union gunboat ran past the rebel battery at Fort Point, Galveston, Texas, under a heavy fire, and the authorities of the town were notified that four days would be allowed for the removal of the women and children and the surrender of the town. The rebel battery was destroyed and the troops retreated to Virginia Point.--Richmond Dispatch, October 25.
A fight occurred near Bardstown, Ky., between the advance-guard of Gen. Wood's forces, under the command of Major Foster, and the rearguard of the rebel army, under Gen. Polk. The rebels were under cover of the undergrowth, from which they fired two or three volleys into the ranks of the Unionists with such effect that they became panic-stricken and fled back on the main body of the army, which, coming up, threw a few shells among the rebels and scattered them in all directions.--Cincinnati Commercial, Oct. 5.
A company of the Fifty-fourth Pennsylvania regiment, guarding the Baltimore and Ohio Railroad bridge at Paw Paw, were attacked by a superior rebel force and taken prisoners. At the same time a force of Union cavalry, under the command of Col. McReynolds, captured the encampment of the rebels, with two guns, ten wagons, and sixty horses.