Vadrilling,
I didn't see photos of the markings,but two numbers(after 1912,by proof house,possible by maker at any time)typically show the bore diameter(not groove or bullet dia.)and case length.Now we seem to have several possibilties for caliber. At first,you thought it was 9.3x72R,then as Sharps4590 pointed out,the numbers fit something else( like 9x47R).In your last post,you said it is 9.3x62R.There was, for a short time a rimmed version of 9.3x62,but it is very rare and not really appropriate for the age of the drilling. You provided a measurement for dia.of the barrel,and said you measured the chamber dia.As an amateur machinist,I have found that taking inside measuremnts directly with a caliper,usually differs from those taken across a small hole gage or chambercast; sometimes by several "thousanths".If the .365" is the actual groove diameter,then it would likely be one of the many 9.3s.A 9 mm bore diameter is possible in some 9.3 barrels.On the other hand,if the .365" is bore diameter, it would fit a 9.5mm cartridge(such as the popular 9.5x47R(MB)).You haven't said how many grooves are in the barrel.Measuring a barrel with an odd number of grooves is difficult,becaues the lands and grooves are not across from the opposite land or groove.You have the drilling "in hand" and can try different cartridges, but the only way we can effectively help is with a chamber cast.
Mike