The range of the 8-inch navy gun at Redoubt No. 1 was tried to-day by firing 5 shells, 3 only of which burst, and it was demonstrated that Black Island could not be reached with that gun. The large Blakely gun just mounted at Battery Ramsay was fired to-day at 1 p.m., with a charge of 40 pounds weight of powder, sabot and shell of 425 pounds weight, and 2 elevation. At the first discharge the gun burst, splitting open in eight places in rear of the first re-enforce band.

NOTE.-In a letter of the 21st instant from Colonel [Josiah] Gorgas to General Beauregard, it is suggested that an experienced artillery officer ought to have been led to reflect over the thinnes of the bronze metal at the base of the breech, and that such reflection would have led to the conviction that a heavy charge could not be fired with safety if placed within the bronze portion, i.e., the so-called air-chamber of the gun.

September 12, 1863.-Everything has been unusually quiet since yesterday morning. The enemy continue to work at Battery Gregg, and have apparently succeeded in mounting two guns at that point. The batteries on James and Sullivan's Islands kept up a slow fire on Morris Island. The Ironsides and six monitors are inside of the bar this morning, besides the usual number of gun and mortar boats, transports, &c.

Mortar fire was kept up day and night from Moultrie, Battery K, and Cheves.

About 5 p.m. the enemy opened fire on Moultrie from one of their Morris Island batteries. Only 1 shell, however, exploded in the fort, which did not do any harm. Twenty-two shots were fired at the enemy from Battery Cheves. The carriage of the 10-inch columbiad at Simkins being out of repair, there was no firing from that battery.

Major Manigault reports that an attempt was made to mount the double-banded 24-pounder rifle in gun-chamber No. 1, but from the deranged condition of the gun furnished him the attempt was unsuccessful. An artificer was immediately charged with the repair of the gun.

The enemy's fleet at Hilton Head to-day is two steam frigates, two sloops of war, eight gunboats, and fifty-four transports.

One of the enemy's wooden gunboats went up Kiawah River at 12 m., and landed some men at Wilson's, on Kiawah Island.

September 13, 1863.-The enemy still continue silent, but are working industriously at Battery Wagner, altering its shape and mounting guns.

There are inside the bar this morning the Ironsides, three mortars, and twenty-four other vessels. The other three monitors are thought to be lying behind the hulks of some of the other vessels, as they are reported not to be in the Stono River.

Mortar firing was kept up last night and to-day from Battery and Moultrie on the enemy's works on Morris Island. Seven shots only were fired from Battery Simkins. One of the shells fired from Moultrie fell into the enemy's works, and caused a great explosion, supposed to be ammunition chests.

Major [John] Jenkins telegraphs from John's Island that the enemy have established a line of communication across the marsh from Dixon's Island to Folly River, by bridging the intervening creek. A number of men can be seen crossing.