Tom,
Your rifle is most likely an 8x57 that was converted to 8x60 after WW1 to comply with Treaty( lawful) requirements. Depending on chamber length, it also could have been chambered to 8mm/06 after arriving in the US. The H.M. is likely the touch mark of the barrel maker. Lack of markings could result from being removed before the reblue job in the US, in which case the H.M. would likely be the initials of the person doing the work. It is possible that it was a rifle put together after WW2 before the Germans were allowed to make guns again. Times were hard enough that gunsmiths built many such rifles for GIs in return for various barter items, including cigarettes. Some cleaned the markings off to avoid discovery, but most didn't bother. This would make 8x60 caliber less likely, but still possible. Your best bet would be to have a chamber cast made to determine the caliber. Your gunsmith could get a pretty good idea by checking with 8mm and 30-06 headspace gauges.
Mike
