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Another Battle Before Richmond.

New York, June 30.

The Tribune has issued an extra, dated: "Battlefield," giving an account of two days fighting. A company of Bucktails was surrounded and captured in the retreat of our right wing. Over 125,000 men were engaged.

All civilians are ordered away from White House.

WASHINGTON, June 29.

A severe and most determined battle was fought on our right wing on Thursday and Friday, which is claimed by some of our officers as a successful strategic movement into which the enemy had unwillingly been drawn, and which will soon result in the capture of Richmond and the entire rebel army. The attack was made by the enemy in immense force, who crossed the Chickahominy near the railroad above Mechanicsville, Thursday afternoon, fought desperately, but were unable to drive our men a single rod. Though the enemy were two to our one, the only force engaged that day was McCall's division, the battle lasting from 2 to 9 p.m., when the division was ordered back.

Gen. McClellan was on the field, and expressed himself satisfied with the result.