The discrepancy between the totals consists of 13 killed and 84 wounded and missing; total 99 reported in one instance without distinguishing between officers and men. Many who were at first reported missing are now know to have been killed.

I have the honor to be, general, your most obedient servant,

N. P. BANKS,

Major-General, Commanding.

Major General H. W. HALLECK,

General-in-Chief, Washington, D. C.

HDQRS. DEPT. OF THE GULF, NINETEENTH ARMY CORPS, Before Port Hudson, La., July 6, 1863.

GENERAL: Since my dispatch of the 29th ultimo was written, the siege has been progressing rather slowly, indeed, but with all the rapidity attainable under the circumstances. Our approached are pushed up to the ditch at the citadel on our extreme left, and in front of the right priest-cap, where the assault of the 14th was made.

On the morning of the 4th, when the right sap was within 10 feet of the ditch, the enemy sprung a small mine, and extended the approach into the ditch. Both on the right and left we are now engaged in pushing mines to blow up the parapet, and the enemy is clearly counter-mining. The column of stormers is fully organized and ready. A few days more must decide this operation, and, I have no doubt, in our favor.

By the arrival of Colonel Kilby Smith yesterday, with dispatches from General Grant, I have news from the forces before Vicksburg to June 30. Affairs there are evidently in much the same condition as here. Colonel Smith was particularly struck with and remarked upon the coincidence. The most important piece of intelligence brought by the colonel is of the inactivity of Johnston's army, and of his apparent inability to raise the siege.

From the reports of General Emory, dated the 3rd and 4th instant, copies of which and my replies I have the honor to inclose, you will see that the enemy has thrown more force into the La Fourche, and is actively engaged in annoying our communications and menacing New Orleans. I have urgently requested Admiral Farragut to patrol the river, so as to prevent the success of any attempt of the enemy to cross the river, either in force or by detachments, and partially, at least, to frustrate the attempt to cut off communication with the city. I inclose a copy of my note to the admiral.

As matters stand, the enemy will do us some harm in the La Fourche and cause us considerable annoyance on the river; but I consider it certain that Port Hudson will fall before New Orleans is seriously endangered, and that the close of this operation will enable us to make short work of the other; but I cannot refrain from reflecting what would have been the condition of affairs had this command, leaving the hostile garrison of Port Hudson in our rear, marched to Vicksburg, where General Grant has already, as he states, "a very large force - much more than can be used in the investment of the rebel works." When General Emory concentrated his little command at La Fourche Crossing, to repel the enemy's advance there,there were just 400 soldiers in and around New Orleans. I think General Emory overestimates the force in the La Fourche when he puts it at 13,000, and believe that the whole force of the enemy there consists of Taylor's army, of about 4,000 men,