(From the Norfolk Day Book, Dec. 3.)

For some days past two or three of the federal gunboats have been in the habit of running up James river five or six miles above Newport News each evening, and remaining there all night. What the object of this is unknown, unless it may have been to keep a watch on the movements of the Confederate steamer Patrick Henry. These gunboats on Sunday evening repelled this same manouvre, and on yesterday morning the Patrick Henry got under way from her position further up James river and came down. On seeing her the gunboats left immediately and put out down the river towards the blockading ships. The Patrick Henry continued her chase after them, and they ran in under the protection of the guns of the frigates Cumberland and Congress and the fort at Newport News.