William Herschel discovered NGC 4413 = H II-169 = h1259, along with NGC 4387, 4388 and 4425, on 17 Apr 1784 (sweep 199). He noted "S. It may be taken into the field with other NGC 4387 and 4388]. Caroline's reduced position is 17 seconds of RA east of UGC 7538.

On 11 Apr 1825 (early sweep 3), John Herschel recorded, "eF; gbM; has 2 stars, n and n p." His position is 2.8' too far south, although the description clearly applies. Four years later he recorded it again as h1255 = NGC 4407 and simply noted "the following of 2 [with NGC 4388]. His position was marked as very uncertain or approximate but was noted as ~30 seconds following NGC 4388 (the actual RA difference is 47 sec). So, NGC 4413 = NGC 4407, with NGC 4413 the primary designation.

300/350mm - 13.1" (5/14/83): faint, small, slightly elongated, diffuse.

400/500mm - 17.5" (4/25/87): fairly faint, fairly small, slightly elongated SW-NE, slightly brighter along major axis. A mag 12 star is off the north edge 1.4' from center and a mag 11 star is 2.9' N. Located 12' ESE of NGC 4388 in the core of Virgo cluster with NGC 4425 12.7' NE.

600/800mm - 24" (4/28/14): moderately bright, fairly small, elongated 3:2 SW-NE, 0.9'x0.6'. Unusual appearance with a brighter bar and a small, bright rounder nucleus. The bar and halo are not aligned along the same axis.

Notes by Steve Gottlieb