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Gen. McClellan's Army — Only Five Miles from Richmond.

McCLELLAN'S HEADQUARTERS, May 26.

The driving of the rebels from the vicinity of New Bridge by our artillery, yesterday, was followed to-day by a reconnoisance composed of the Fourth Michigan, Colonel Woodbury, and a squad of the Second Cavalry. Thirty men of the Fourth Michigan succeeded in getting between four companies of the Fifth Louisiana and a brigade of the enemy, and attacked them unexpectedly, killing about sixty, wounding fifty and capturing thirty-one. We lost one killed, one mortally wounded and a few slightly. To-day, Stoneman's brigade, together with Davidson's advanced from New Bridge up to the Chickahominy to Ellison's Mills, on Bell's Creek. Here they encountered four regiments of rebels, with nine pieces of artillery and some cavalry. The Eighth and Ninth Regiments, under Howell Cobb, were posted to resist our advance to Mechanicsville. After 150 rounds from our artillery the rebels withdrew. A portion of Davidson's brigade followed, but night coming on they encamped within six hundred yards of the enemy. At daylight the batteries on both sides opened, but the fire was too hot for the rebels and they retreated.

Deserters from Petersburg say that in consequence of lack of provisions the army at Richmond is much demoralized. Numbers are deserting daily. They have been lately on half rations. They say fully half the army would desert if they had the opportunity, but the rebels intend making a desperate resistance.

As soon as a disposition is shown by the Norfolk people to return to allegiance the port will be opened and the former status restored. No such disposition is yet manifested.

Should Richmond be captured, hundreds in Norfolk would openly declare for the Union.

Gen. Negley's brigade is encamped five miles beyond Bottom Bridge. To obtain this they were compelled to attack the rebel Stewart's brigade. Our loss was 2 killed and 6 wounded. The rebel loss is supposed to be about 50.

Contrabands from Richmond say that the inhabitants are leaving for Danville. — All capable of baring arms are compelled to remain.

A dispatch from McClellan to the War Department, says:

"There were three skirmishes to-day. — We drove the enemy from Mechanicsville, about seven miles from New Bridge. The Fourth Michigan about finished the Louisiana Tigers. Fifty prisoners were taken and fifty killed. Our loss is ten killed and wounded."

Two squadrons of the Eighth Illinois Cavalry, under Major Clendenin, were sent up the river, and destroyed the bridge of the Richmond and Fredericksburg railroad.

Mechanicsville is now occupied by the Federal troops. It is five miles from Richmond.