JDW, I think from the examples I have seen, and I am going from memory, not my notes and records , that the very first guns in Marathon and Lisle were marked W. H. Baker. Earliest ones seemed to have no serial numbers, and there were quite a few conversions from muzzle loaders. Serial numbered guns went up to serial number 250 [roughly] for the double guns.
Then the Baker/Smith partnership took over in Syracuse about 1877, 1878 and 1879 and the guns were marked W. H. Baker and Co. This marking on the doubles continued through about serial 1700 when Baker and Smith parted ways [about early 1880].
After that date and serial numbers continued and the guns were marked L.C. Smith, Maker on the rib, and Baker Pat. usually on the side. That double gun was produced by Smith until about 1883 or 1884 when Smith developed the Brown designed double.
When dealing with serial numbers and putting them into years, one often finds an out of sequence number that does not fit the general understanding. Until the earliest records are found , if they do even exist, all of this is by observation of guns, ads, articles, etc.
Given the above , your F Grade gun was probably made in the very earliest 1880s. But, being a special gun, probably many lower grade guns, with higher serial numbers , went out the door before the F Grade. Also, we find that Baker Gun and Forging Company, for instance, had a many month supply of finished guns in warehousing, waiting to be sold and shipped. So sometimes completion dates and selling dates were quite far apart.
