This is a stretch, but with so little space to stamp their logo, may be. From DAT. Very few “Smith Co” options, the only one with J, and only on listing screwdrivers.
J Barton Smith Co
1842 to 94
211 New, Philadelphia
Categories FARM TOOLS,FILES,SAWS,SCREWDRIVERS
The company made pruners, screwdrivers, and saws; Smith was listed as a file maker (without the "Co.") in an 1871 directory. They used a brand name FAVORITE on saws.
THE J.BARTON SMITH CO. PHILADA (in a circle on a saw medallian with an anchor figure)
Possibly acquired by Nicholson
Directory of American Toolmakers, pre 1900