The point being that if it wasn't on an "A"base case, it wouldn't be 7.7x60R, and since someone else owned it, it would be difficult to make a chambercast.On the other hand, it wouldn't be hard to get the owner to allow measuring the head dia., and rimrecess depth. This could only exclude 7.7x60R, not show it is the caliber.
After further reflection and no additional information,I have come to the opinion that the rifle is likely chambered for a nominal 8mm cartridge. 7.7mm is often the bore diameter marked for 8mm barrels,along with 7.8 and sometimes 7.6mm.I believe the marking reported in the original posting is not the name of the cartridge, but the proof mark, showing bore(not groove or bullet)diameter and case length. If this is the case, it is likely chambered for a cartridge known as 8x62R Vierordt no 102. This cartridge is one of the several 8mm cartridges based on the British 360 Express case, which was adopted by the Germans and used for such cartridges as 8x57R/360 and 9.3x72R.Measurment of the chamber in the casehead area could also disprove my theory and exclude the 8x62R Vierordt.If I am correct, the diameter should be around .429" + a couple thousanths.