Private letters received from officers of the 15th deny in tota the report first published by the Detroit Free Press, that that regiment was placed under arrest in Indianapolis, on its way back to the seat of war. The slander had just reached the regiment. The letters aver that there was no trouble whatever, after leaving Monroe. The 15th is now in the advance of Sherman’s army, and done some gallant fighting. We have been shown also, a copy of the Memphis Appeal of May 10th, taken from the body of a dead rebel Captain, by a member of the 15th, at Resacca. Ga. The paper is perforated with thirty-eight bullet holes, probably all made with one Union bullet, which caused the rebel’s death. A Captain’s report was also taken from the body, which shows that he belonged to a Florida Company. This indicates that the Florida troops have been sent to reinforce Johnston.