The following article is transcribed from the New York Times, dated June 13, 1862:

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FREMONT's HEADQUARTERS, PORT REPUBLIC, Va., June 6, 1862.

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The army advanced early this morning in line of battle, but finding no enemy proceeded in column through the woods and over the country to Port Republic. Everywhere were evidences of the completeness of yesterday's success. The battle was fought at Cross Keys, and therefore takes that name. The rebel loss was greatly superior to ours. They left their dead and many wounded on the field. Not less than 500 dead were found and many wounded. Two of their guns were left behind, which we captured this morning. Capt. DUNNKA, of Gen. FREMONT's Staff, was killed Capt. GITTERMAN, of CLUSERETT's Staff, was severely wounded. No other staff officers were wounded. The rebel wounded were found in every house along the road. Ambulances, wagons, arms and clothing strewed the field. Forty of our wounded, taken prisoners, were left in a church, and were retaken. The Sixth Louisiana lost all but 30 men. The enemy retreated till midnight, and this morning their rear guard crossed the Shenandoah at this place and burnt the bridge.