Major Jenkins reports that the enemy are moving troops from Folly to Kiawah Island.

September 27, 1863.-There are inside the bar this morning 4 monitors, the Ironsides, two mortar-boats, 27 transports, &c., and 8 vessels off the bar of the usual class.

The enemy continue to work on Wagner and Gregg, and are still hauling timber-for stockades, it is supposed.

Moultrie, Bee, Simkins, and Haskell have been firing at various times in the past twenty-four hours, and have thrown, in all, 126 shots. The enemy did not reply.

Battery Simkins fired 47 rounds to-day, with good effect it is thought. Battery Cheves was silent, as the magazine at that post is still unfinished.

September 28, 1863.-An exchange of companies in Fort Sumter was effected last night. Captain [J. M.] Carson's company. Twenty-fifth South Carolina Volunteers, was ordered to relieve Company D, Eleventh South Carolina Volunteers, as the commander of that company was the senior officer under Major Elliott, and was reported in-competent to command the fort in case of accident to Major Elliott. Captain Carson is now the senior line officer, and is believed to be fully competent to command in an emergency. The garrison is now composed of Companies H, I, and K, Eleventh South Carolina Volunteers, and Captain Carson's company, Twenty-fifth South Carolina, Total, 267 men.

Major Elliott reports that the enemy have constructed a covered way from Battery Gregg to the sand-hills. Southern slope of one of the faces of Wagner directed on Sumter finished and merlons constructed. Major Elliott complains that the commander of the waterboat is an arrant coward, and if the boat is not seized and placed under military control, the garrison may suffer for want of water, as was the case last night.

Moultrie, Bee, and Simkins have been in occasional action since yesterday morning, firing in all 97 shots. The enemy fired but once, and then against Fort Johnson.

Thirty-three vessels were inside the bar this morning, including the Ironsides, four monitors, four gunboats, three mortar-boats, &c. One mortar-boat, a French vessel, and four others were outside.

The enemy are working to-day on Wagner and the mud battery.

At 1.45 p.m. the enemy's land batteries, distant about 2 1/3 miles from Sumter, opened on that work, directing their fire against the angle under the flag-staff. One hundred shots were fired, of which 48 struck, 16 fell short, and 36 passed over. The damage to the fort was slight, and one casualty only occurred- a negro who was slow in seeking cover.

Ninety-six shots were fired to-day from Battery Simkins with supposed good effect. As the magazine at Battery Cheves is not yet completed, there was no firing from that work to-day.

The engineers at Fort Johnson having received an additional supply of tools, the carpenter work on the bomb-proof at that work is progressing vigorously.

Dispatches from the Stono state the usual arrival and departure of transports, &c., but no troops were observed on any of them.

The fleet at Port Royal is composed of one steam frigate, two sloops of war, five gunboats, and seventy-five transports.

General Taliaferro telegraphs from Royal's that Colonel [Charles H.] Simonton, commanding in front, reports the enemy's pickets on Dixon's and Horse Islands, much reduced.