In connection with the expedition organized for the attack on Legareville and the enemy's vessels lying off that village, it is reported that the Pawnee came up the Stono this afternoon, and that the Marblehead is in the same position. All that remains to be done is to build the battery at Lady's Island, and this will be accomplished to-morrow night. The siege train to accompany this expedition passed Church Flats at 9 o'clock this morning.

The enemy's fleet at Hilton Head is reported as follows: Two steam frigates, one sloop of war, one cutter, one iron-clad, six gunboats, and ninety-eight transports.

December 24, 1863.-Since 5 p.m. of the 23rd, not a shot has been fired. During the day, there was no firing on the part of the enemy, and only an occasional shot from our batteries, directed against working parties at Cumming's Point.

There are reported inside the bar this morning the Ironside, four monitors, and the usual number of transports, gunboats, &c.

It is observed that the enemy have extensive camps on Cole's and Big Folly Islands, with large storehouses on the south end of the latter, which appear to be at least 300 feet in length, two stories high, with a cupola on top, used as a lookout and signal station.

Infantry entrenchment and a lookout and signal station can also be seen on the northeast end of Dixon's Island. No decrease of camps can be noted either on Morris or Little Folly Islands.

On the west end of Black Island the enemy have erected a two-gun battery, and on the south end of Morris Island, on Light-House Inlet, there appears to be a one-gun battery. Another battery for two guns is on the north end of Little Folly Island. All of these works bear on Secessionville.

The Marblehead remains off Legareville, and the Pawnee, having in tow a bark, came up the Stono in the evening, and anchored off Lady's Island. She subsequently changed her position, and at 7.30 p.m. was, together with the Marblehead and a supply vessel,, lying directly in front of our Parrott gun battery.

Two steam frigates, one steam sloop of war, one steam cutter, five wooden gunboats, and ninety-eight transports compose the enemy's fleet at Port Royal to-day.

December 25, 1863.-The enemy remained quiet last night until about 1 a.m., when they opened a heavy fire upon the city from Battery Cumming. After about 60 shells had been thrown, Battery Gregg and the mortar battery also joined in the bombardment, which was then carried on vigorously until 1.12 p.m., by which hour 133 shells had fallen within the limits of the city. The evening gun, which was fired from Battery Cumming as the flag was lowered at sunset, was charged with a shell which exploded in the city.

Soon after bombardment commenced, Batteries Simkins, Cheves, Rutledge, Moultrie, Marion, and the Brooke gun battery opened on Cumming's Point with vigor, but did not, as usual, succeed in checking the fire of the enemy. These batteries continued in action at intervals during the entire bombardment. Their fire, however, does not appear to have been very effective, judging from the result.

Captain [T. S.] Hale remained at his post of observation (Saint Michael's steeple) during the entire bombardment, and recorded each shot. He reports that the second shell thrown into the city struck and set on fire a building on Broad near Church street; that he called to the police at the guard-house, directing their attention to the matter (the watchman in the belfry had left when the first shell