I see a caliber marking on the rifle barrel of 7.7 mm / 57. This is a way to small a bore for the 8x57R/360 which is nominally a 9 -9.3 mm size, I forget its actual bullet size.
The military 8mm was nominally a 7.92 mm or .312" bore with grooves for either the .318 or .323S bullets. 7.7mm = .303" which likely simply the 8x57IR cut with deep grooves, not unusual on hunting rifles.
As mentioned in another thread I have an 8x58R S&S with 172.28 gauge bores (.300"). Slugging its bore revealed a groove diameter of .321" while the bore itself measured just short of the next gauge step which would have been .310" or a 156.14 gauge.
I have a Miller & Val Greiss, Munchen hammer drilling chambered 16/16/9.3x72R. It was proofed 6 13 & is marked 8.8mm / 72. 8.8mm =.346".
