The markings described denote a Gewehr 98 Military Mauser,
made by one of the German Imperial Arsenals (the Crown on the Receiver Ring, --Spandau, Erfurt, Danzig or Amberg);

The original calibre is 7,9mm"S" ( ie, .311 Bore/.323 groove).

These Sporters were "modified" from Military Surplus rifles after WW I, by Gunmakers in Belgium, Germany and England, and of course by "amateurs" in many commonwealth countries, which had "souvenired" them. Kynoch manufactured Sporting ammo (marked "7,9 or 8mm") well into the 1950s.

The rifle concerned, if still in 7,9x57 as I strongly suspect, will safely use standard "8mm" Commercial sporting ammo of US manufacture (underloaded) or Military Surplus or European Commercial 7,9mm ("8mm") ammo of the "S" variety (Both these latter have substantially higher pressure and velocities to the US " powderpuff " ammo.).

The reference to the ".318" diameter projectile refers to the older, M1888 cartridge and the Commission Gewehr 88, with its split bridge design and smaller groove dimensions (.318, then .321, Then (in the M1888/05) throat relieved to fire .323 Bullets ( the "M88-S" or M88/05, modifications).

Whilst M88 type Sporters, by Haenel, Sauer, Schilling etc. will be in the original 8x57J (.318) cartridge, any M98 actioned rifle will be in 7,9( 8)x57 JS (.323) cartridge.

BTW, in the 1920s Germany, the Sporters made from Military rifles were chambered for 8x60S, to avoid the prohibition on Military calibres in Germany (Versailles Treaty obligations).

So it would be necessary to check, (a) if the rifle has 1920s Civilian German Proof House marks, and (b) what the calibre designation with these (if any) is. If it is Belgian converted, then it will have the equivalent Belgian (Liege) Proofs ("ELG" in oval, etc) and the British converted guns will have "BP or CP" (Birmingham or London) and details of cartridge size and pressure in "Tons per sq.in". If a "Commonwealth" country conversions, there will be NO proof marks at all, other than the original German Military ones ("Imperial eagle", before serial number on both barrel and receiver, left side).

I hope this will be sufficient to work on, if not, send some photos of the receiver and the barrel shank, with any marking there-on.

Regards,
Doc AV
AV Ballistics -Forensic Services
Brisbane Australia.