The first incarnation of this enterprise was apparently Jackson & Smith.  The partners were Charles Jackson (unidentified) and William Jackson Smith (c.1821-1879).  The latter had worked for Wragg, Long & Co between 1836 and about 1843.   Jackson and Smith parted company in 1844, when Jackson, Stacey & Smith appeared.  Besides William J. Smith, the principals included Henry and William Jackson and George Stacey (also unidentified).  The firm had a New York office in Platt Street, with Charles Street as the location in Sheffield.  The firm marketed a wide range of cutlery, including pocket knives, razors, and Bowie knives (Goins, 1998¹).  It aped Joseph Rodgers & Sons and made a Norfolk Knife for the American market, which was described in The Sheffield Independent, 23 November 1844, and displayed at the League Bazaar, London, in 1845:

Its length, when shut, is 15¼ inches; when open 30½ inches; its weight 4¾ lbs, of which the silver weighs 1lb.  The handle is of pearl, with silver shields, ends and back.  The shield bears the name of the makers; and on the same side is an engraving of the American eagle, of the Cutlers’ Arms, of the City Hall, New York, and of the President’s house.  On the other side are views of Hartford, and the Palisade Rocks on the Hudson River.  On the blades are etched the Capitol, of Washington, the tomb of Kosciusko, the Columbia Bridge over the Susquehanna, the viaduct of Baltimore and the Washington Railway, and Caldwell on Lake George.  There are a variety of minor ornaments selected with care, and executed with great beauty.

Jackson, Stacey & Smith was dissolved in 1848.  William Jackson and William J. Smith next formed Jackson, Smith & Co.  This was in Union Street and Norfolk Street, though Smith continued to be based in New York.  In the General Directory … of Sheffield (1849), ‘Jackson’ is identified as William Jackson (1790-1867), the noted Sheffield surgeon.   Perhaps he regarded the firm as a vehicle for his sons, one of whom (Alfred) was a partner.  However, the enterprise apparently ceased business in about 1850.  Alfred died in 1865, aged 39.  William Jackson Smith, commercial traveller, died on 30 June 1879 (aged 58) in Sunderland.  He was buried in the General Cemetery, leaving under £800.  

^1. Goins, J  E, and Goins, C, Goins’ Encyclopedia of Cutlery Markings (Indianapolis, 1998)