The proofs are from the London proofhouse of course.
"38" is the pre-rifling gauge stamp which would mean that a plug of 0.497" would pass the whole length while a plug gauge of .492 would not. "38" was typical for a 500-bore or 1/2 inch. The probability of it originally being a 38-55 is quite slim without some later modification in the U.S. of A. and without any case measurements I would guess the 38-55 brass is the parent of the formed 360(2 1/4") BPE(Black Powder Express) which would have had a bore stamp of 118.35 or 118/35. The 360 surfaced circa 1873 and there were at least 3 case lenghts:
2 1/4"
2 7/16"(the once Alexander Henry really cottoned to)
2 3/4".

A chamber cast would tell the tale as well as some of your case data. I have some 360 2 1/4" from Buffalo arms which has a 30-40 Krag headstamp and I'll check on converting 38-55.

Kind Regards,

Raimey
rse