That "S" stamp means nothing here. It is a factory internal control stamp. The gauge number 156.14 is for a land diameter of .310". The actual barrel dimensions as marked by the factory, land 7.85 mm = .309", groove diameter 8.07 mm = .318", twist rate 1 in 12.2" are consistent with the 1926 Mauser factory dimensions for 8x57, table shown by Jon Speed in "Mauser Original Oberndorf Sporting Rifles" page 275. In this table both the 8x57 and 8x60 are marked with an*. There is a footnote below. Translated it reads: "*The hunting rifles for the cartridges 8x57 and 8x60 are chambered with the throat for S-type cartridges, so these may be used too." Strict 8mm I (.318) and S (.322) dimensions were prescribed by the 1940 proof law only. Even minimum 8mm I dimensions were set up as an industry standard in 1926, same year the American SAAMI was founded. So "undersize" barrels were quite common before WW1. The 1934 DWM and 1940 RWS handbooks told: "No accidents ever happened when 8x57S loads were used in modern 98 Mauser rifles in 8x57I. If you want to use S loads in other rifles, have the neck and throat area of your barrel checked and enlarged, if necessary,by your gunsmith." To check chamber and throat there is a simple trick: Fire an 8x57I or an emasculated American 8mm Mauser load in your rifle. If a S = .322" bullet slips easily in and out of the case'a neck and does not touch the lands on loading, you may use 8x57IS factory level loads.