John Herschel discovered NGC 2588 = h3125 on 16 Feb 1836 and recorded "a small F cluster of st 15m; 3' diam; R; gbM; not very rich. His position and description matches this faint cluster.

400/500mm - 17.5" (3/25/95): small faint cluster consisting of 15 stars in a 2' diameter with a few additional out to 3' diameter. The stars are pretty uniform (mag 13/14) and most are arranged in a perfect "U" asterism open towards the south. Only a few stars are inside this "U".

Notes by Steve Gottlieb