The Latest News.

M'Clellan's Lines Gradually Advancing.
Union Victory on the 3d July.
Large Stories by Rebel Prisoners.
Richmond Impregnable.
Failure of Plan to Exchange Prisoners.
From McClellan's Army.

A letter to the Tribune, dated Fort Monroe, 5th, says: Beyond a few skirmishes, in which our troops gained the advantage, nothing has occurred in the neighborhood of Richmond since my last. The rebel army appears to have fallen back toward the city, and Gen. McClellan is now in a position well intrenched. The apprehension that the rebels would stretch themselves down the Peninsula, and possibly attempt to blockade with land batteries the James River, has not as yet been realized.

Our force at Yorktown is evacuating the place; most of the guns have been burst.

The rebel prisoners do not claim a victory, but confess to have failed in the object of their attack commenced on Thursday of last week, in which their loss was confessedly much greater than ours, including many officers of high rank.

A boat came through from Newberne via Norfolk and the Canal yesterday, and returned this evening.

It is rumored that Burnside with considerable force, was preparing to co-operate with McClellan. Rumors to the effect that he had advanced from Newberne were without foundation.

The statement that McClellan has been recently reinforced by 40,000 is an exaggeration.

4 P.M. — The Warner, which left Harrison's Landing at 10 o'clock this morning, has arrived.

Yesterday our pickets advanced four or five miles from the river and saw no enemy, who seem to have mysteriously disappeared. It is suggested that General Pope will see them next.

There was a brisk engagement on Thursday (3d) in which our troops drove the enemy and captured a battery without losing a man.

Gen. McClellan has advanced his lines down to the Chickahominy, and so fears are now entertained of a flank movement in that direction. By noon to-day Gen. McClellan expected to be able to bid defiance to the enemy in any shape they might choose to come.

General Casey has arrived en route for Washington.