William Herschel discovered NGC 3166 = H I-3 = h684, along with NGC 3169, on 19 Dec 1783 (early sweep 58). His summary description from 4 sweeps reads "cB, pL, cometic, mbM." John Herschel made 4 observations. John Herschel's first of four observations was on 13 Feb 1826 (sweep 18): "B; R; gbM; 60". The preceding of 2 [with NGC 3169]."
Édouard Stephan's observation on 18 Mar 1884, which was published in list XIII-56, is within a few arcseconds of NGC 3166 though Dreyer and Esmiol (who later re-reduced all of Stephan's positions) misidentify this entry as NGC 3165. Also Stephan's XIII-57 refers to NGC 3169, though he calls it NGC 3166 in the notes section to list XIII.
300/350mm - 13" (4/16/83): fairly bright, bright core. Forms a pair with NGC 3169.
400/500mm - 17.5" (3/23/85): bright, almost round, even concentration to a brighter core and stellar nucleus (large, low surface brightness arms not seen). The core appears brighter than NGC 3169 7.8' ENE but the duo is pretty similar. Second of three with NGC 3165 4.6' SW. Two mag 12.5 stars lie 2.6' NW and 2.8' SW of center.
Notes by Steve Gottlieb