Hobbit Presentations

In one of the Hobbit chapter presentations the idea of deus ex machina came up. It is Latin for "god out of the machine" and is a plot device whereby a seemingly impossible problem is suddenly solved with the contrived and unexpected intervention of some new character, ability, or object. The group was talking about the scene where the eagles save the dwarfs from the wargs.

However, I stumbled across something today that may mean that in the Hobbit it is not technically deus ex machina at work.

Eucatastrophe is a term coined by J. R. R. Tolkien which refers to the sudden turn of events at the end of a story which result in the protagonist's well-being. He formed the word by affixing the Greek prefix eu, meaning good, to catastrophe, the word traditionally used in classically-inspired literary criticism to refer to the "unraveling" or conclusion of a drama's plot. For Tolkien, the term appears to have had a thematic meaning that went beyond its implied meaning in terms of form. 

Examples in Tolkien's work
It could be said that the climax of The Lord of the Rings is a eucatastrophe. Though victory seems assured for Sauron, the One Ring is permanently destroyed, and with it the Dark Lord and his tower. This occurs despite Frodo, the chief protagonist, giving in to the will of the Ring and claiming it for himself. Essentially, it is an ostensibly bad situation suddenly revealed to be fortunate.

Distinction between Eucatastrophe and deus ex machina
"Eucatastrophe" is often confused with deus ex machina, in that they both serve to pull the protagonist out of the proverbial (or sometimes literal) fire. The key difference is that the eucatastrophe fits within the established framework of the story, whereas the deus ex machina, the "God from the machine", suddenly and inexplicably introduces a character, force, or event that has no pre-existing narrative reference.
In Tolkien's masterpiece The Lord of the Rings, while some of the events may seem unlikely or even impossible, they still remain consistent with the overall story. The One Ring holds almost all of Sauron's power and his entire life force. If the ring is destroyed, so is Sauron. His destruction will also bring about the destruction of his stronghold, which is only held together by his power. This will in turn panic his followers, who flee or are killed in the ensuing destruction. It is a sudden, massive change that totally alters the landscape of what happened previously in the story, yet, unlike a deus ex machina, is completely consistent with the theme and story. The destruction of the One Ring event is a definitive resolution but not an incongruous one or illogical in terms of the story and setting.