From Logan's Regiment.
— The Cairo correspondent of the Chicago Times of the 2d, says:
On Friday last, 250 of Col. Logan's men performed the first duty, other than standing guard, which the regiment has done since its organization. They went some six miles up the Mississippi to look after a body of secessionists which was reported as having driven in the out-pickets of Bird's Point. No rebels were found; and what was at first supposed to be the ashes of their camp-fires turned out to be what had been made by Col. Bird's contrabands burning timber in a clearing. Two hundred and fifty of this regiment went up to Price's Landing yesterday, where they will remain. Last night 250 more were sent up to reinforce them, including the cavalry company attached to the regiment. Those at the Landing succeeded in seizing several barrels of whisky, boots, shoes and other articles intended for rebel use.
Early yesterday morning the flag steamer Memphis conveyed Gen. Grant and a portion of his staff to Paducah. They returned last night. It is surmised by many that the visit was because of the demonstrations of the rebels, and to arrange plans for concert of action between the forces at Paducah and at the various camps in this vicinity, in repelling the assault which rumor has it is to be made at Paducah.
By a rather singular run of ill-luck; all the gun-boats are at present unfit for duty. The Conestoga is reported aground at Scuffletown bar, nine miles above Evansville; the Tyler has not received all of the repairs designed to be put on her at Mound City; and the rudder of the Lexington was broken yesterday as she was coming down the river.