Mike:
Brophy's Book page 201 shows the following:
1884-New L.C. Smith Hammer Guns - 269
1885-L.C. Smith Hammer Guns - 1,950
1886-L.C. Smith Hammer Guns - 1,583
1886*L.C. Smith Hammerless Guns - 266
1887-*L.C. Smith Guns (both types January through April 268) Total estimated for the year.. - 2,165
Total L.C. Smith Guns Syracuse - 6,223
Total Guns manufactured by L.C. Smith, Syracuse, New York 15,714........includes the Baker guns produced *(9,491)
Your gun was made in 1886 or 1887 and that is probably as close as you're going to get.....even Cody would probably not get any closer, but it may be worth calling them though @ 307-578-4031. They may have some records on your gun....?....
Hunter Arms records are available after the move to Fulton, N.Y. through the Cody museum for almost every gun made in Fulton, even the Marlin built guns (L.C. Smith Gun Co.) after October 1945.
Hope this helps.....
Best,
