Francois:  Your rear 'diopter' sight is a Lyman #48-K made specifically for the Krag.  This sight required that extra holes be drilled into the Krag receiver and some wood had to be removed from the stock.  My reference source indicates this is the 2nd variation of this sight.  The elevation slide was shorter with markings going to 125.  The adjustment knobs were regarded the 'Hunter' style rather than 'Target' style.  The second variation was made from 1919 to 1947.
     It is possible that your barrel is a 1903 Springfield barrel that was shortened at the breech, re-chambered for the .30-40 cartridge, and fitted to the Krag action.  Lots of Gunsmiths did this to replace rough & pitted Krag barrels.  This would explain the absence of rear sight holes on your barrel.  A reused 1903 Springfield military barrel will have an Ordnance Bomb marking and date on the barrel behind the front sight,  There is also a notch across the bottom of the barrel for a cross pin that held the rear sight collar in place.

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