Very good... and you're pretty realistic about the dates.
Ketland & Adams is the last marking of the old "T. Ketland" firm. Thomas Ketland Sr. died in November of 1816, at which point his partnership with William Walker and John Adams probably dissolved. I suspect that William Walker chose to retire... he died about 18 months later and both men were in their 80s. John Adams was quite a bit younger and may have been Thomas Sr.'s brother-in-law. I've yet to be able to decipher Thomas Sr.'s will (written in a particularly difficult chancery hand) but I suspect that he left his share of the business to his oldest son, Thomas Jr., who had returned from Philadelphia with his family about a year earlier. Thus, I believe that "Ketland & Adams" is the partnership of Thomas Jr. and John Adams. They went bankrupt in 1821 so most reasonable possible dates are 1816-1821.