"Swear by the River Styx"

Charon carries souls across the river Styx
Public DomainCharon carries souls across the river Styx - Credit: Alexander Dmitrievich Litovchenko
In Greek mythology, the River Styx formed the boundary between earth and the Underworld.  The gods were bound by the Styx and swore oaths on it.  According to some versions, Styx had miraculous powers and could make someone invulnerable. Achilles was famously dipped in the river, making him invincible with the exception of his heel, by which his mother had held him. It was believed that placing a coin in the mouth of the deceased would enable them to pay the toll for the ferry across the river, easing their entry to the Underworld. 

Styx was adopted into Christian mythology in works such as The Divine Comedy and Paradise Lost. Dante made Styx the fifth circle of Hell, where the wrathful and sullen are punished by being drowned in the muddy waters for eternity.