First S is not a bore size . The original barrels were .321 groove . The S bullet was .321 main body dia with a small .323 driving band . There is no need to do any " transition " , a myth made up by people who sought to explain how they fired .323 dia bullets [ not the real size ] in a .318 bore [ not the real size ] .The S ammo was designed to be fired in the original .321 bore . Since the original "forcing cone " for the 226 grain long round nose bullet was already three times longer than needed for the short 154 grain spritzer bullet , there was no need to "lengthen" the throat . They kept that chamber size for all 8mm 98's up to 1945 . A 1945 K-98k has the same chamber throat , and will chamber the old long bullet . ALL the S stamp meant was the rifle was cleared to fire S ammo . All my S marked and non S marked rifles have the same size chambers . There was only a .002 larger neck dia from the .3188 dia to the .3208 dia bullet , how many military rifles have you seen that had that tight a chamber ? There may have been 1 out of 10,000 that was too tight and needed to be reamed . The armour's S kit was a solid dummy cartridge , and a S stamp . He stamped all rifles that cleared . If by chance one did not it was sent to back for a ream . As far as accuracy ,they were more worried about barrel fouling , it was still ok . An original P-88 bullet with the hollow base bore rides good enough , even in a .323 groove barrel . BUT about 80 % of the Gew-88 rifles in Germanservice to WWI still had a .321 groove barrel , and were shot with both types of ammo . I have a nice M-95 sporter in 8x50R with a .330 groove barrel . My best accuracy [ 2.5 inch 5-shot groups at 100 yards ] is with the old Speer .323 225 grain cupped base round nose bullet .