The proof mark 7.8 over 57 could fit either 8x57 IR(JR) or it could fit 8x57R/360. It wouldn't be hard to tell the difference. The IR or JR if you prefer is about a 06 head size cartridge with a rim, and the /360 is about a 30-30 head size cartridge with a rim slightly smaller than 30-30.
Mike