Laudator Temporis Acti

In most of the exorcisms recorded in the Gospels, Jesus simply drove demons away from the possessed (apopompē, "sending away"). But at Gadara (or Gerasa or Gergesa), Jesus drove the demons into a herd of pigs (epipompē, "sending to or against"). Matthew 8.30-32 (cf. Mark 5.11-13 and Luke 8.32-33):

And there was a good way off from them an herd of many swine feeding. So the devils besought him, saying, If thou cast us out, suffer us to go away into the herd of swine. And he said unto them, Go. And when they were come out, they went into the herd of swine: and, behold, the whole herd of swine ran violently down a steep place into the sea, and perished in the waters.

Richard Wünsch first used the terms apopompē and epipompē to describe these two different ways of banishing evil in "Zur Geisterbannung im Altertum," Festschrift zur Jahrhundertfeier der Universität zu Breslau = Mitteilungen der Schlesischen Gesellschaft für Volkskunde 13-14 (1911) 9-32.

Jesus performed the exorcism by epipompē in pagan territory, the Decapolis, and it so happens that there are numerous examples of epipompē in pagan literature, usually in the context of a prayer.

Eduard Fraenkel, Horace (Oxford: Clarendon Press, 1957), pp. 410-411, described the belief that underlies the most primitive form of epipompē:

This type of prayer is based on a widespread and very ancient belief. If a daemon or god is bent on harming you -- and in the early days, before the gods became humanized, that seems to have been their favorite occupation -- it will do you little good if you just cry out 'spare me' (pheidou, parce). You have to do that as a matter of form, but if you are wise you will add some more effective bait. If you are able to point to a really attractive substitute, then, perhaps, you may succeed in diverting the god from his original object, from you and yours. An obvious candidate for such a substitute is an enemy, either your country's or a personal one; but if you do not want to be so specific, you may be content with asking the daemon to prey on 'others'.

There is a good example of this primitive form of epipompē in a Vedic charm against fever, Atharvaveda 5.22.6-7 (tr. Ralph Griffith):

Fever, snake, limbless one, speak out! Keep thyself far away from us.
  Seek thou a wanton Dāst girl and strike her with thy thunderbolt.
Go, Fever, to the Mūjavans, or, farther, to the Bahlikas.
  Seek a lascivious Sara girl and seem to shake her through and through.

In another form of epipompē, you don't address the personified evil itself, but rather you ask one of the gods who are good at averting evil to send it somewhere else. This is what we see, for example, in an Orphic hymn to Artemis (36.14-17):

Come savior goddess, dear one, propitious to all your initiates, bringing good fruits from the earth and beloved Peace and fair-tressed Health; but may you send to mountain tops diseases and pains.

ἐλθέ, θεὰ σώτειρα, φίλη, μύστῃσιν ἅπασιν
εὐάντητος, ἄγουσα καλοὺς καρποὺς ἀπὸ γαίης
εἰρήνην τ' ἐρατὴν καλλιπλόκαμον θ' ὑγίειαν·
πέμποις δ' εἰς ὀρέων κεφαλὰς νούσους τε καὶ ἄλγη.

I have discussed this topic before on this blog, and now I have devoted a separate web page to it.