On the 20th ultimo General Hobson left here with his command to proceed, via Mount Sterling, to the place of rendezvous, the month of Beaver, on the Big Sandy. The general commanding started from here on the 22nd ultimo, via Cincinnati, Catlettsburg, and Louisa, for the same point. Some delay was experienced at the mouth of Beaver in obtaining a sufficiency of supplies. On the 5th instant the expedition moved to attack the rebels, but after one day's march information that Morgan had entered the State through Pound Gap with nearly 3,000 men was received, and the command returned at once to the month of Beaver, whence on the day following the commanding general started in pursuit of Morgan, sending General Hobson, via river and railroad, to this place to command the forces left in this vicinity. General Hobson reached Cincinnati on the day the railroad communication, via the Kentucky Central Railroad, was cut off, and as information [was received] that Mount Sterling was in possession of the rebels and Lexington threatened, he at once proceeded to organize a force to enable him to push through here. One regiment, the One hundred and sixty-eighth Ohio, 100-days' men, was pushed forward from Covington at once, and distributed to guard the railroad as far as Cynthiana. General Hobson followed with 600 men of the One hundred and seventy-first Ohio, and attacked Morgan at Keller's Bridge, near Cynthiana, on the 11th instant; was outnumbered, surrounded, and compelled to surrender after six hours' fighting. General Burbridge, by forced marches day and night, fell upon Morgan at Mount Sterling, at daylight 9th instant, and defeated him after a very severely contested engagement lasting four hours, in which the rebel loss far exceeded ours. Over 200 of their dead were buried by our men; we had but about 25 killed. Nearly 200 prisoners captured at Mount Sterling are now here. Morgan moved rapidly to this point and entered the city at 2 p. m. 10th instant, after a slight resistance from the two companies of cavalry, all we had here to meet him. But little damage was done here, the rebels leaving for Georgetown at 7 a. m. On the afternoon of the same day General Burbridge arrived, and, obtaining fresh horses are, and at Camp Nelson for his command, moved at midnight for Paris and on Saturday night for Cynthiana, where at daylight Sunday morning he attacked Morgan, whose command, increased to nearly 2,800 men by accessions from the militia of Owen and contiguous counties, was drawn up in line of battle and confident of victory. The battle lasted about two hours, our cavalry regiments making several brilliant saber charges. The rebels broke in all directions, panic-stricken. We took 500 prisoners, killed 300, besides wounding a great number. Colonels Hanson and Garrard are in hot pursuit of a portion of Morgan's command, with which are the prisoners they captured from Hobson. It is reported here that Morgan was defeated and our prisoners released, eight miles east of Cynthiana. This report not yet confirmed.

The commanding general desires me to say that he considers the raid over. Morgan's command is wholly broken up. His men have thrown away their arms, are out of ammunition, and are being captured in small squads by our cavalry.

I have the honor to be, very respectfully, your obedient servant,

J. BATES DICKSON,

Captain and Assistant Adjutant-General.

Governor Thomas E. BRAMLETTE,

Frankfort, Ky.