Technically the 8mm Mauser cartridge is the 7.92x57, 7.92 being nominal bore dia (.312"). 7.7mm = .303" & 7.8mm = .307". When the official ammunition was changed from the roundnose bullet to the Spitzer it was fearedit would not be gripped firmly enough & the grooves were deepemed & diameter increased to .323 thus the S mark for Spitzer. Actual bore size for the "Army" rifle remained unchanged.
Sporting rifles of course do not necessarily follow exactly the military specs, so different sizes of bores are encountered. Not positive but I believe at this point the bores were marked in .1mm increments per the largest gage (plug) which would enter the bore the required depth.
This one with the 7.7 mark could well have been just shy of accepting the 7.8 gage & actually be closer to .307" than the .303" the mark indicates.
