NEAR Vicksburg, MISS., June 25, 1863-9 a. m.,

VIA MEMPHIS, June 28-11 a. m.

(Received July 1-10 p. m.)

We have authentic information from Joe Johnston. He is between Canton, Bolton, and Bridgeport, and has made no movement of importance since that of Loring's back across the Big Black. the report from the spy of General Grant, which led to the sending, out of Sherman on the 22nd instant, was a mistake, though it must have had some foundation. Our present accounts indicate 35,000 as about the limit of the total troops of Joe Johnston. No new re-enforcements from Bragg have come up, so far as we are informed. Pemberton yesterday sent out to General Grant 4 men whom he has for several months held as hostages for the slaying of Mr. White while concerned in a guerrilla fight in Western Tennessee. Their release indicates the near surrender of Vicksburg. The prisoners' statements agree with our other accounts in representing the siege at about an end. From the best intelligence we can gain, the supply of engineer officers, the labor would be much more effectively applied. On Sherman's front everything is advancing favorably. McPherson has a mine, with three trenches extending 35 feet under the great fort in his front, which is now being tapped, and will probably be exploded before my next dispatch. It is expected this will open that fort to our occupation, and as it is the key of the rebel line on the eastern side, its possession must in all probability be followed by the early submission of the town. On Ord's front a great deal has been accomplished, especially in widening the trenches, connecting them, and making it practicable to move men and artillery through them. Ord is devoting his attention particularly to Hovey's approaches, which he thinks offer perhaps the most favorable attack in our whole line, but which McClernand has left in great backwardness. A week's labor will, however, bring them into such a condition that Hovey will probably be able to crown the rebel line with his artillery.

Next to Hovey is Lauman, who has repeatedly lost pickets, and night before last had a lieutenant-colonel and 9 men captured by the enemy. Lauman is a brave man, but an ox is just as fit to command as he.

Further on, upon our extreme left, Herron continues to press on with zeal. Last night, after a brisk skirmish, he took the last rebel rifle-pits outside of their intrenchments, and captured in it a lieutenant and 9 men. His siege approaches are going forward well, under the direction of Captain Comstock, of the Engineers. In front of the town Admiral Porter has established on the point behind one of the levees a battery of three rifled guns and four smooth-bores, which bears directly on the city, and does most effective work. Ample preparation has been made in that quarter against an attempt of the garrison to escape by means of skiffs, of which we learn they are provided some two thousand or more for this purpose.

The Marine Brigade has gone on an expedition, or rather a reconnaissance, to Delhi. The enemy are endeavoring to cut off the navigation of the Mississippi. They have planted a battery of six guns on Catfish Point,, opposite Greenville, and have annoyed several boats on their way down. An expedition leaves to-day to clear them out. The troops are