Captain Rogers immediately took possession of the telegraph office. The post-office was next visited, and a large amount of rebel correspondence secured. Five companies of infantry, and a battery of Smith’s Light Artillery, Lieutenant Willard, were sent under Major Philips down the railroad about seven miles without meeting any of the rebel troops. Pillow was reported to be advancing, and a large bridge and trestle work were burnt to prevent him from reaching Paducah and falling upon the place by surprise. A rumor became current that a large force of rebels from Tennessee were on their way down the Tennessee river in steamboats. To ascertain the facts, and to intercept their progress, the gunboat Conestoga was dispatched up the river some thirteen miles to watch the rebel movements, and to capture suspicious vessels. Although no hostile forces were seen, a steamer was discovered on Friday, which, on seeing the Conestoga, turned about, was run ashore, and the officers and crew abandoned her. It was the Jefferson, a small stern-wheel boat, loaded with a cargo of tobacco. On Saturday the Conestoga captured a fine propeller, called the John Gault, and a boat called the Pocahontas, belonging to John Bell, of Tennessee. The prizes were all safely taken to Cairo. The inhabitants of Paducah were now seized with panic, and large numbers left the town, apprehending an attack from Pillow, in which case they expected the gunboats would freely use shell. On Saturday part of Colonel Oglesby’s Eighth regiment, the Forty-first Illinois, and the American Zouave regiment, from Cape Girandeau, entered the town, increasing the forces to about 5,000 men. THE REBEL TROOPS ORDERED TO WITHDRAW FROM KENTUCKY. On the 9th of September a dispatch from General Polk to Governor Magoffin was laid before the Legislature, the substance of which was that he had occupied Columbus and Hickman, on account of reliable information that the Federal forces were about to possess those points; that he considered the safety of Western Tennessee and of the rebel army in the vicinity of Hickman and Columbus demanded their occupation, and that, as a corroboration of that information, the Federal troops had been drawn up in line on the river opposite to Columbus prior to its occupation by them, causing many of the citizens of Columbus to flee from their homes for fear of the entrance of the Federal troops. General Polk proposed substantially that the Federal and rebel forces should be simultaneously withdrawn from Kentucky, and to enter into recognizances and stipulations to respect the neutrality of the State.