However under the constant pleading by Phaethon, Apollo eventually allowed the request. So one day Phaethon climbed into the chariot, which was drawn by two white horses, grasped the reins and set off across the skies. It was soon apparent that Phaethon was incapable of controlling the horses, as they galloped so high in the sky that the earth was close to freezing, then they plunged so close to the earth that the fields were burnt. Zeus soon had enough of this nonsense and sent a thunderbolt, killing the young man. His burning body fell to Earth and landed in the River Eridanus. His sisters, for having encouraged him in this foolhardy adventure, were changed into poplar trees which stood along its banks.
It's difficult now to identify which river the constellation represents; some writers claimed it was the Tigris or Euphrates, others the Nile. And Homer called it an "ocean stream". In fact, it may originally have been a mythic river, not meant to be identified with any geographical site. Eridanus might represent the Sumerian Strong River, also known as Ariadan. Or it might be one of more of any other important rivers--the Ganges, Po, Euphrates, or Nile.
The story goes that Phaethon, son of Apollo the Sun God, pestered his father to allow him to drive the celestial chariot across the skies one day. The sun was seen as carried daily on a chariot driven by Apollo. Phaethon was encouraged by his sisters and even his own mother. But Apollo always refused, knowing that his son was far from ready to assume that awesome responsibility.