The R in a circle could indicates that the barrel tubes were made by Rose Brothers of, Hales Owen,and as such could be one of their trade marks.
The 3 could be a component batch control mark some times seen when a number of lower cost guns of similar gauge/type were are manufactured at the same time. The number ensured that components for an individual gun were not mixed prior final assembly. This was necessary because in this era parts were not truly interchangeable and most required some degree of hand fitting.In such circumstances the final gun number was not added until the final assembly of barrels to locks and action.
On some more expensive custom guns the final serial # or part of was used for batch/quality control purposes.
