HDQRS. NORTHERN DISTRICT, DEPT., OF THE SOUTH, Folly Island, S. C., May 28, 1864.

CAPTAIN: I have the honor to report that nothing of importance has occurred within the district since my last.

The demonstration Monday afternoon, the 23rd instant, and during the following night, was made strictly in accordance with the orders which I had the honor to be forward on the 23rd to the general commanding the department. The gun-boats in Stono Inlet, under command of Captain Duncan and Captain Gamble, co-operated with me in the most satisfactory manner,proceeding up the river as far as the bend, 1 1/2 miles north of Legareville.

The sham attack on the 22nd had induced the enemy considerably to strengthen his outposts in front of Cole's Island, and to have field pieces with them.

As will be seem from the map, the battery on Long Island and the gun-boats on Stono River north of Legareville take the enemy on the southwestern part of James Island entirely in flank and rear; besides this, the enemy received the fire of the rockets and two howitzers in front. In consequence our fire created considerable havoc among them, driving them from one piece of woods to the other. It was probably with the view of drawing the fire of our gun-boats to that point that the enemy on the 23rd for the first time opened fire from Battery Pringle. Toward evening the transfer of the troops from Long to Tiger Island, and the disembarking of troops on Battery Island, commenced. During the early part of the night boat howitzer on Secessionville Creek continued to fire from different positions. The enemy kept up a signaling through the whole night from James Island to Charleston.

I am satisfied that the sham attack of the 22nd, on James Island, and the demonstration of the 23rd,have produced the desired result, viz, to oblige the enemy to keep a larger force than my own on my front. Their pickets have in some cases been observed to be materially strengthened; more tents are visible on James Island than before, and a greater number of bathers and strollers are to be seen around Fort Johnson and at other points. Our batteries on Morris Island have thrown the usual number of shells into the city and Fort Sumter. The firing into the city has been made more lively during business hours, some 30 shots being thrown in between 9 a.m. and 2 p.m.

On the 26th instant,the enemy opened a new battery,situated to his right and rear of Fort Johnson; the guns are rifled and throw 6-inch projectiles. From this battery and Simkins 45 shells were fired at Fort Putnam on the 26th, all of which burst in and around the fort. The fire was returned by our guns without loss on our side. The enemy has also shown more fatigue parties than usual around Forts Johnson and Moultrie and Battery Simkins. Fort Sumter has been considerably repaired since our last bombardment, and Castle Pinckney is being strengthened by having a wall of sand built up around it from the outside.

As to the movements of the enemy within the harbor, I have nothing unusual to communicate. I have had no prisoners or deserters since my last report. There was some cheering heard at Secessionville on the --, but the outposts in front of Cole's Island keep as quiet and uncommunicative as before. In regard to the fort at the white house, I have to report that within a few days it will be sufficiently advanced in its structure to be garrisoned by infantry.