= Pausanias the Atticist lambda14; cf. Timaeus, Platonic Lexicon 994a17; a scholion to Plato, Charmides 154B [see below]; Aelius Dionysius lambda8, Hesychius lambda789, Photius lambda220 Theodoridis, Zenobius 4.89, [Diogenianus] 6.8, Gregorius 2.67 Apostolius 10.64.
The locus classicus for the phrase, apart from the Sophocles passage quoted below, is Plato, Charmides 154B (web address 1).
While one might suppose that the phrase refers to a line dusted with white chalk, and hence potentially good for making a mark on surfaces that are not white, most commentators take it as referring to a bare line, untreated with the customary red or black powder (cf. Moeris 202.24; scholion to Homer, Iliad 15.10; scholion to Plato loc.cit.). Perhaps most of the commentary is generated by changing fashions in line-chalking that rendered Plato's phrase ambiguous to the incautious reader (this seems to have led Maximus of Tyre, for one, astray (18.4)); accordingly a passage is dredged up from one of Sophocles' obscurer plays employing the phrase in a context where a white line, chalked or unchalked, would be useless against a white background. For other applications of the phrase see Libanius, Epistles 481.2; Simplicius, Commentary on Aristotle's De caelo 7.404.
[1] Sophocles fr. 330 Radt. Up to this point the entry = Photius.
[2] cf. sigma 988; Synagoge and Photius s.v. sta/qmh; Hesychius sigma1422, sigma1599.