The correct barrel specifications for the respective old and new cartridges are:
Military Patrone M/88: 7,90 mm / 8,10 mm
Military S-Patrone: 7,89 mm / 8,20 mm
Note that these are minimum specifications, with an allowed tolerance upwards.
Civilian "I" caliber, normalized in 1938 (can widely differ, may often be tighter): 7,80 mm / 8,07 mm
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Nominal civilian bullet (maximum) specifications are:
Civilian S: 8,22 mm
Civilian I: 8,08-8,09 mm
Real measurements are often different, varying from producer to producer. Also note that on an assembled cartridge, the widest bullet diameter may frequently be hidden inside the case neck.
I will try to add nominal military S-Geschoss and sS-Geschoss specifications later.
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Am adding my sources, as Nick has reminded us all:
RWS (Ed.), Werner Lampel (auct.): Schießtechnisches Handbuch für Jäger und Schützen, 2nd ed. 1940, p. 42-44
Dynamit Nobel (Ed.): Wiederladen. Ein praktisches Handbuch für Jäger und Schützen,
9th ed. 2002, p. 254 (8x57 I), p. 305-306 (8x57 IS)
DEVA (Ed.): Wiederladen - Vorbereitung und Praxis,
5th ed. 2005, p. 342 (8x57 I), p. 354 (8x57 IS)