that is, "the shining," occurs in Homer as an epithet or surname of Helios, and is used by later writers as a real proper name for Helios (Argonautica. The Aeneid Book V) but it is more commonly known as the name of a son of Helios by the Oceanid Clymene, the wife of Merops.
The genealogy of Phaethon, however, is not the same in all writers, for some call him a son of Clymenus, the son of Helios, by Merope, or a son of Helios by Prote, or, lastly, a son of Helios by the nymph Rhode or Rhodes.
He received the significant name Phaethon from his father, and was afterwards also presumptuous and ambitious enough to request his father one day to allow him to drive the chariot of the sun across the heavens. Helios was induced by the entreaties of his son and of Clymene to yield, but the youth being too weak to check the horses, came down with his chariot, and so near to the earth, that he almost set it on fire.
Zeus, therefore, killed him with a flash of lightning, so that he fell down into the river Eridanus or the Po. His sisters, who had yoked the horses to the chariot, were metamorphosed into poplars, and their tears into amber. (Argonautica. Metamorphoses by Ovid I)
2. A son of Cephalus and Eos, was carried off by Aphrodite, who appointed him guardian of her temple. (Theogony of Hesiod 986) Apollodorus (iii) calls him a son of Tithonus, and grandson of Cephalus, and Pausanias (i. 3. § 1) a son of Cephalus and Hemera.
3. The name of one of the horses of Eos. It is also a surname of Absyrtus. (Argonautica)