There was no firing during the night by any of the enemy's batteries, and to-day an occasional shot only was fired from Battery Gregg, which was replied to by 8 mortar shells from the Brooke gun battery on Sullivan's Island. This was the only one of our batteries in action during the entire day.

The weather was stormy and hazy, and prevented observations of the enemy's fleet, both off the harbor and at Port Royal.

The commanding general to-day organized an expedition to be composed of infantry and artillery, under command of Lieutenant Colonel Del. Kemper, for the destruction of the Federal steamers Pawnee and Marblehead, which have been reported for several days past in the Stono, off Legareville. The programme also includes the destruction of that village, and the capture of such of the enemy's forces as may be there stationed. The artillery to accompany the expedition is composed of 8-inch siege howitzers, 30 and 10 pounder Parrotts, and a few other guns of lighter caliber. It is arranged for them to open, if practicable, Christmas morning, and it is hoped the results will be commensurate with the importance of the attempt.

December 18, 1863.-The enemy were again silent last night, but at the usual hour this morning, about 11 o'clock, opened on the city from the mortar battery near Gregg with two Parrott guns. After the second shot had been fired, Batteries Marion, Rutledge, and the Brooke gun battery, on Sullivan's Island, and Batteries Simkins and Cheves, on James Island, opened vigorously on Morris Island, and compelled the enemy to close after they had fired only 5 shells. All of these shells fell short.

It is reported from the Stono that the Pawnee and the pile-driver went down the river to-day, and did not return. The Marblehead, however, still lies in the vicinity of Legareville.

The enemy signated several hours to-day from the Botany Bay Observatory, and it is thought they have a complete line of stations from Morris Island to Port Royal. All of their messages were intercepted, but none were of any importance.

Colonel Elliott, commanding Fort Sumter, reports that he penetrated this morning to that portion of the magazine used as a commissary storehouse, and that he discovered a small amount of burning material on the floor. This, however, was completely extinguished in a few moments with-buckets of water.

The following is the number of shots fired by our batteries to-day: Rutledge, 23 mortar shells; Marion, 19 mortar shells; Brooke gun battery, 34 mortar shells; Simkins, 12 mortar and 18 columbiad rifle shells; Cheves, 17 columbiad shells. No casualties are reported at any of our works.

The fleet to-day off Port Royal is as follows: Two steam frigates, two steam sloops of war, one cutter, two iron-clads, seven wooden gunboats, and ninety-three transports.

December 19, 1863.-There was but little firing during the morning and afternoon between our batteries and those of the enemy. A few shots, however, were fired from Simkins and Cheves against parties of the enemy on Morris Island.

Colonel Elliott reports that Fort Sumter was unmolested during the day, and that the engineer work at their post is progressing as usual.

A sergeant and 10 men were detailed from Company H, and 6 men from Company K, Palmetto Battalion Light Artillery, as a firing party to execute the deserter, Elisha Clark, of Company D, Palmetto Battalion Light Artillery. He was shot on James Island at meridian.