William Herschel discovered NGC 4388 = H II-168 = h1244, along with NGC 4387, 4413 and 4425, on 17 Apr 1784 (sweep 199) and recorded "Two nebulae [NGC 4388 and 4387]. The most southern [NGC 4388] extended." His position is between the two galaxies. John Herschel noted "vF; E; the p of 2 [with NGC 4413], dist about 30s in RA." He didn't realize this was the same as his father's II-168, so listed it as a "nova" and included separate listings in the GC for II-168 and h1244. Dreyer combined the listings in the NGC.

300/350mm - 13.1" (5/14/83): fairly bright, very elongated E-W.

400/500mm - 17.5" (4/25/87): moderately bright, edge-on streak E-W, fairly large, brighter core, thin extensions. A faint mag 14.5 star lies 1.3' NE of center. Located 16' SE of M84 in the core of the Virgo cluster. On a line between IC 3303 8.4' WNW and NGC 4413 11.4' ESE.

600/800mm - 24" (4/28/14): fairly bright, large, edge-on 4:1 E-W, well concentrated with a mottled, very bright core. Fairly sharp light cutoff on the south side (dust lane) of the core. Faint, stellar knots are at the west and east ends of the core.

Notes by Steve Gottlieb