That would be the name of the gunmaker, the firm in charge of "setting up" the arm. If I had to guess, J Smith was probably Joseph Smith in business from 1851-1895. The firm is listed as a Gun and Pistol maker in Birmingham and also a gun lock/barrel maker. The firm had premises at 28 Loveday Street,1851-1859 then 28 & 29 Loveday Street, 1860-1895 which was in the Birmingham Gun Quarter.