Since Chapman's Christian names are illegible it is difficult, if not impossible to trace his connection with JW. It is not clear if Chapman even lived in London.
However, Chapman and JW may have had shared literary interests or friends in common, since Chapman's club was defined by Charles Dickens (Jr.) : 'Has for its object to secure a convenient and agreeable place of meeting for a society of gentlemen, all connected with each other by a common bond of literary or personal acquaintance. The election of members is by ballot. No ballot is valid unless twenty members actually vote; and one black ball in ten excludes. The entrance fee is £26 5s., and £1 1s. to the library fund; subscription, £10.'
Dickens (Jr.), Charles, Dickens's Dictionary of London, London, 1879