Counties, Virginia, for the officers of collector and surveyor, that all my information from these counties was very satisfactory. I have to-day received a letter from General Lockwood, in which he says the that he summoned all the magistrates of Accomac County before him; that they all took the oath of allegiance, as well as the sheriff and his deputies and clerks. He adds: "After this there was quite a rush of smaller officers to do likewise." He was to go in a day or two after Northampton and pursue the same course. He has made but a single arrest for disloyalty..

In consider the restoration of these counties to the Union complete, and if our troops were to be entirely withdrawn I am satisfied that there would be no movement against the Government. Of the 3,000 men sent from here I have brought back 3,100. There are about 1,000 left int he two counties. As soon as convenient I trust you will appoint a collector and surveyor..

I am, very respectfully, your obedient servant,.

JOHN A. DIX,.

Major-General..

HEADQUARTERS HOOKER'S DIVISION,.

Camp Baker, Lower Potomac, Maryland, December 13, 1861.

Brigadier General S. WILLIAMS,.

Assistant Adjutant-General, Army of the Potomac:.

The commander of the Second Brigade reported to me this morning that the rebels had established a battery opposite to Maryland Point, where the channel makes in close to the Virginia shore, which promised to give our transports and other vessels some little annoyance in ascending the river. Not being able to give it a personal inspection, I made application to the officer commanding the second division of the flotilla for information concerning it. In reply I learn that it is a field battery, and the one to which I have before alluded. It is a light field battery of six rifled pieces, planted on the bank of the river during the day the removed at night. It has a regiment or two, as supports, in its vicinity..

I am further informed that vessels, in order to pass up and down the river, have to pass within three-quarters of a mile of the Virginia shore, and in case it is required of them, in my opinion, some of the guns of the flotilla can with advantage exchange shots with this battery, as it is entirely exposed; they have longer range, and are not more exposed than the enemy. But for the broad river I might possibly surprise them, but to do that with steamboats is almost an absurdity; I have more confidence in being able to surprise them or even of capturing their battery..

About 2 o'clock a. m. two steamers passed from the upper to the lower flotilla, when they were saluted with two discharges from the enemy's heavy rifled gun. It fairly shook the earth on this side of the river. This was the only effect of it. Our vessels fired a few shots in answer and passed on..

I can remark no changes either in location or number of the rebel encampments..

Very respectfully, &c.,.

JOSEPH HOOKER,.

Brigadier-General, Commanding Division..