I believe 35 Winchester CF is more likely the correct caliber than 9X61R Hunting. For a while, the 35 Win. enjoyed a fair amount of popularity with German/European hunters so was a known cartridge. It fits pretty well the proof data shown by the markings on the rifle. The bore diameter is shown as 8.7mm, if it had been 8.8 or 8.9 mm I would have considered a 9.3 mm nominal cartridge. The rifle is marked for a 16.2-gram copper jacketed bullet, which closely fits the 35 Win. also. While not determinative, that it has a fairly modern looking scope mounted is indicative of being used more recently than 1914, which is shown by "Dixon" as the last year 9x61R Hunting ammo was made. All this is a guess and if "Bill's" comments include dimensions from a chamber cast, the actual cartridge can be determined. An old friend made 35 Win. cases from 9.3x74R cases for his Mod. 95 Win. It was a little trouble, but good cases resulted and together with availability of .358" bullets ammo shouldn't be much of a problem. BTY this is a very nice rifle.
Mike