John Herschel discovered NGC 6257 = h1974 on 16 May 1831 (sweep 357) and recorded "a suspicious object. It is pointed to by a faint double star nf. Doubtful whether a nebula or a vF double star, with perhaps a third star near (of course ill seen)." There is nothing at his position. It was looked for once at Birr Castle, but not found.
RNGC, CGCG and PGC identify CGCG 225-012 as NGC 6257, though this galaxy is 70 seconds of RA east of Herschel's position (and 2' north). Furthermore there isn't a reasonably bright "F double* nf" as per his description. Finally it may be too faint for JH to have picked up. So, the standard identification is very unlikely. Karl Reinmuth, in the 1926 photographic survey "Die Herschel-Nebel" was probably the first to equate CGCG 225-012 with NGC 6257, though his position was 2.5' too far southwest. In response to an email I sent, Harold Corwin took a look at the field and was unable to find a good alternate candidate (UGC 10599 doesn't match his description, either).
400/500mm - 17.5" (6/24/95): extremely faint, very small, round, 15" diameter (elongated NW-SE on the POSS). Requires averted vision but sighting certain using GSC field chart. A mag 13 star is 1.7' SW (part of collinear string of stars oriented NW-SE). Uncertain RNGC identification.
17.5" not seen in fairly poor seeing and transparency.
Notes by Steve Gottlieb