The recent fight which Colonel Jacob had with John Morgan near Narrow Horse-shoe Bottoni, a quarter of a mile from the Cumberland lliver, and about twelve miles above Monticello, in Wayne county, was much more destructivo to the rebels than was at first supposcd. The loss in killed has been definitely ascertained to bc one hundred and fiftyseven, while the wounded are variously estimated at from 350 to 500. It is certain that ncarly every house in the neighboring valley contains disabled rebejs. Our correspondent " Eidler " gives an excellent account of this fight, but his information in some respects is incorrect, The force of 450 men had been sent out by Col. Jacob to reinforce a party of 100 who had gone on an expedition to break up a desperate band of guerillas. They were completely successful in their object, but feil in with the advance guard of Morgan's main army, when they retired in excellent order and fighting desperately. Capta W. D. Wiltsie, of the 20th Michigan Infantry, Wilson, of the 12th Kentucky Cavalry, and Searcey of the 9th Kentucky Cavalr}', led their men with great gallantry. The fight was in the open field of Coffey's, just outside of the Narrows of Horse-shoo Bottom, and was despcrately contended for against Morgan's wholo force for fifty-five minutes' after the gallant boys had previously almost destroyed Chenault's and Cluke's force, and forced them to a point of surrender, which would have been accomplished nad it not been for the tiniely aid of Morgan. A demand for an unconditiofial surrcnder was sent in to Colonel Jacob by Morgan, which having been promptly refused, he carried his wholo force to the north side of the rivcr to rcjoin his main command, and Morgan did not foei the least disposition to follow, but it is undorstood, returned to Monticello. No men could havo behaved botter than the 12th Kentucky Cavalry and the 20th Michigan Infantry. This spirited affair unquestionably prevented Morgan from efi'ecting a contemplatcd raid into our State, for prisoners state that he acknowledged that the desperate resistance at the Narrows had completely frustratcd all his plans, fST" The Medical Department have made arrngemeüts to furuish soldiers with amputated limbs, with artificial arms. It has been supplying artificial lega all the time, but anus are just introdueod, The department bas coatracted for arms at $50 apieco. The soldiers, of courso, are furnjshod free of charge.