Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Let's face it: there isn't a lot of humor in Prometheus Bound. Unless, of course, you're entertained by the spectacle of a god being chained to a rock and systematically abused for the crime of bringing fire to humankind—in which case the play must be barrel of laughs.
For the rest of you, though, it's bound to be a pretty somber play.
If anything lightens the mood, it isn't humor, but rather Prometheus's intense (some would say insane) spirit of defiance against Zeus. As Prometheus hurls out insult after insult against the king of the gods, and refusal after refusal to reveal what he knows about that king's future, it's hard not to be stirred by his words.
Still, you've got to admit that Prometheus's attitude is a bit unrelenting. Take his closing lines: "the blasts/ of all the winds at once leap at one another/ in a raging display of mutual strife,/ and sea and sky are blended into one… see how unjustly I suffer!" (1085-88). Sounds pretty over-the-top to us.