HDQRS. DEPT. OF THE GULF, NINETEENTH ARMY CORPS, Before Port Hudson, La., June 29, 1863.

GENERAL: Affairs here are progressing steadily to a favorable conclusion. The battery erected on our extreme left, at about 300 yards of the citadel, breached the parapet of the citadel, drove the enemy out of a troublesome rifle-pit, and destroyed a gallery, which is believed to have been a part of a mine. Under cover of its fire, our approach on the extreme left has been pushed up to the citadel, and General Dwight makes an attempt to enter it to-night.

The sap on General Grover's front has been pushed to within 13 feet of the ditch in the re-entrant of the priest-cap. The sap-rolled into the ditch last night.

An elite storming party has been organized, made up of about 850 volunteers from the whole force, under the command of Colonel H. W. Bige, Thirteenth Connecticut, who has been engaged some days in preparing the column for its works.

The number of deserters increases steadily. There have been 30 to-day. The beef-cattle of the garrison have all been killed, either for food or by our fire, and the salt meat has all been eaten. The men who deserted to-day after dinner have had no meat, and, were told they would get no more, and that mule meat was to be issued hereafter.

I have seen a copy of the Port Hudson Herald of the 28th, containing the news of the arrival at that place of an officer from General Joe Johnston with dispatches. General Gardner publishes a general order, of date the 27th, assuring the garrison that General Johnston will soon relieve Vicksburg, and then send re-enforcements here, and declaring his purpose to defend the place to the last extremity.

On the 18th instant a force of the enemy (stated by some of our prisoners who were released on parole to be one regiment of infantry, two of cavalry, and a battery of artillery, under the command of Colonel James P. Major, formerly of our service), captured and burned the steamers Anglo American and Sykes at Plaquemine, taking 68 prisoners, of whom 5 were citizens. The prisoners consisted mainly of some convalescents belonging to the Twenty-eight Maine.

The same force the passed down the river and Bayou La Fourche, and, avoiding Donaldsonville, struck the Opelousas Railway at Terre Bonne Station on the 20th instant, cutting off communication between Brashear City and New Orleans.

The same day they attacked and were repulsed by our forces at La Fourche Crossing, consisting of the One hundred and seventy-sixth New York and Twenty-third Connecticut, lacking two companies, which had been concentrated to meet the attack, under the command of Lieutenant Colonel Albert Stickney, Forty-seventh Massachusetts.

The attack was renewed on the afternoon of the 21st, and again repulsed in a manner very creditable to the troops engaged and to their commander. With less than 1,000 men, he drove back the greatly superior force of the enemy, who retired, leaving 53 of his dead on the field and 16 prisoners in our hands. Our loss was 8 killed and 16 wounded.

The Twenty-sixth Massachusetts, and Ninth Connecticut were sent down from New Orleans in a special train that night, and the Fifteenth Maine, which had opportunely arrived from Pensacola, followed the next morning. No further attack was made.

The steamer Saint Mary's, sent round from New Orleans, with orders from General Emory to the troops at Brashear to hold out to the last, meat at Southwest Pass the gunboat Hollyhock, returning from Berwick Bay, with the unpleasant news that the enemy, having crossed the