During a portion of the morning the enemy continued to work unmolested at Batteries Gregg and Wagner, but at 10.30 a.m. one of the Cumming's Point batteries opened on Fort Moultrie, with a few shots, which soon brought on a general engagement between that work and Batteries Cheves, Simkins, Ruledge, Moultrie, Marion, work and Batteries Cheves, Simkins, Rutledge, Moultrie, Marion, and the Broke gun battery. The firing from our side was continued slowly but steadily until about 4 p.m.

Two steamers were observed to-day off Black Island, and were fired upon by Battery, Tatom with the 4.62-inch rifled gun. It is thought one of the vessels was struck.

The following is the number of shots reported to have been fired by our batteries during the day: Fort Moultrie, 6 shots; Brooke gun battery, 17 shells; Rutledge, 59 shells; Marion, 11 shells; Simkins, 37 shells, and Cheves, 12 shells.

It is reported by the engineer in charge that the mortar batteries at Simkins are now repaired, and that the mortar magazine will soon be in the same condition.

The two-masted gunboat remains in the same position in the Stono, and the enemy are still to be seen in Legareville.

The fleet at Port Royal to-day is reported as follows: Two steam frigates, one steam sloop of war, one steam cutter, one iron-clad, seven wooden gunboats, and ninety-six transports.

December 22, 1863.-To-day there were twenty-eight vessels inside the bar, including the Ironsides four monitors, &c. Eight vessels were outside.

Just after midnight, the enemy opened on the city with one gun from Cumming's Point, and fired 4 shots at intervals of about five minutes. None of the shells exploded, and 1 of them fell short. The firing ceased at 12.20 a.m.

As usual, Simkins, Cheves, and the Sullivan's Island batteries returned the fire, and continued until the enemy closed.

During the remainder of the day all the batteries were quiet.

At 1 a.m. one of the enemy's barges was observed off Fort Sumter, taking sounding. It finally retired, however, in the direction of Morris Island.

The condition of the forts is reported to be about the same as usual, very few changes having recently been made in its arrangements.

Captain [W. G. L.] Butt, of the Twenty-third Georgia Regiment, with 6 officers and 109 men from the Nineteenth, Twenty-third, Twenty-seventh and Twenty-eighth Georgia Regiments, last night relieved Captain [T. J.] Abercrombie, of the same regiment, and 6 officers and 101 enlisted men from the Sixth, Nineteenth, Twenty-third, and Twenty-seventh Georgia Regiments, on duty in Sumter.

The two-masted gunboat is still in the Stono near Legareville, which place continues to be occupied by the enemy.

The enemy have at Port Royal to-day two steam frigates, one steam sloop of war, one steam cutter, one iron-clad, six wooden gunboats, and ninety-eight transports.

December 23, 1863.-No material change is reported in the enemy's fleet off the harbor to-day.

Last night not a shot was fired by either our or the enemy's batteries. During the day the only one of our works in action was Battery Rutledge, which fired 26 mortar shells against Cumming's Point, but failed to elicit any reply from the enemy.

At 3 p.m. a propeller transport filled with troops was observed going south. A loaded schooner was also seen going in the same direction.