Barnes was one of the leading British chess masters at the time of Paul Morphy's visit to the UK in 1858.
Barnes had the happy fortune of having the best record against Paul Morphy during the latter's visit, winning eight games and losing nineteen (Brace 1977).
The only tournament he played in was London in 1862, where he finished in the middle of the field (Hooper & Whyld 1992), (Golombek 1976:148).
A much more dubious variation named for him is Barnes Defence, 1.e4 f6 which he played against Anderssen and Morphy, beating the latter.
This biographical article relating to an English chess figure is a stub.