Lieutenant SLACK, Mortar Battery:

Please ask Captain Closson to send me to-day twenty boxes of spherical case and twenty boxes shells.

BRADLEY,

Lieutenant.

Received. "Report shells from mortar."

Sent. "Big rifle is just disabled by our Parrott."

Received. "How badly? Is any gun of big battery firing at it now?"

Sent. "The gun has pitched forward. No."

Received. "We are firing at the gun in ravine behind the citadel. How was that?"

Sent. "Can't see any gun mounted within 1,000 yards of the citadel. Should like to direct fire of Numbers 9 or 10; is it possible? Last mortar shell fell 70 yards short of the disabled rifle."

Received. "What do you propose to fire at with Numbers 9 or 10?"

Sent. "Two fine guns, the lowest on river bank, and now firing at our Parrotts."

Received. "You can direct the fire of Numbers 9 or a 24-pounder. Will wait for your report after each shot. What was last shot?"

Sent. "Forty yards to the right. That shell burst little short. Range first rate."

Lieutenant BRADLEY:

Cease firing for the present, and withdraw your section from the bank.

RICHARD ARNOLD,

Brigadier-General.

Sent. "Last shot but one was 50 yards to the right; last shot was splendid, only 3 yards to right. F. L. L. Cease signaling."

Sent. "F. L. L."

Received. "How was last shot from howitzer?"

Sent. "That shot touched the breastwork 8 feet to the right of the gun. F. L. L. and little lower."

Received. "And the last?"

Sent. "Had good range, but was 100 yards short."

Sent. "That burst short."

Sent. "Last shot was 100 yards to the right. This shot was capital; a fraction high. Last shot was 50 yards to the right."

Received. "It can't get any farther to the left. Where is the second rebel gun?"

Sent. "The lowest gun is 75 yards from the river; second gun is a little farther up, and 40 yards from the river."

Received. "How was that?"

Sent. "Little too high. Last shot little too high."

Received. "Are we firing at the lower or second gun?"

Sent. "Howitzer is firing at second gun; the others fire to your right of both S. O. E. very little."

Sent. "Howitzer's shell goes 6 feet over the gun every shot; last shot was too high; little too high again. Can't they, or won't they, depress that gun?"

Received. "Won't, I guess."

Received. "Was that shot any better, and that?"

Sent. "Both and forever too high."

Received. "We will vamoose now. Come again to-morrow.

Sent. "Nine a. m. will do, will it not?"

Received. "Yes; cease signaling."

OPPOSITE PORT HUDSON,

July 3--9 a. m.

The record of this day's work is so long and monotonous that I omit it. One day is almost literally the counterpart of another. The firing of our heavy batteries yesterday, under the guidance of our signals, was accurate and destructive.

(In communication with General Banks' headquarters.)

JULY 7--11 a. m.

General BANKS:

I am detaining the General Price here to take Colonel Smith back to Vicksburg. If he intends returning, pray send him at once.

PALMER,

Commodore.