Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Matter-of-Fact
Campbell's here to enlighten rather than entertain us; the stories he's discussing can do plenty of entertaining on their own (as proven by the box-office returns on sagas like Harry Potter, Star Wars, and The Hunger Games).
So he sticks to the facts and presents his evidence as objectively as possible. Campbell basically says: "Here are the myths, here's the purpose they serve, and this is what they're supposed to achieve from a standpoint of life, the universe, and everything."
The only real point where he breaks from that is when he talks about the modern world, and how we're all too obsessed with the individual to realize the oneness of the universe:
It is not society that is to guide and save the creative hero, but precisely the reverse. And so every one of us shares the supreme ordeal —carries the cross of the redeemer—not in the bright moments of his tribe's great victories, but in the silences of his personal despair. (362.1)
Beyond that, it's detachment and objectivity, the kind of tone that educators use when passing the details on to their students. It's a little dry, but it does the job… and there's too much going on in what he's discussing to get unduly cute with the tone.