Nor law, nor duty bade me fight, Nor public man, nor cheering crowds,
Ah, finally we learn about the speaker's reasons for getting involved in this whole war. Basically, none of the normal reasons for joining the army, or in this case the air force, were involved.
The law didn't make him go, neither did some sense of duty (to his country). No "public man" and no "cheering crowds" did either. We're not sure who this "public man" is, but it probably refers to a politician or official of some kind, maybe even a recruiter.
Okay, so what made ("bade") him fight? We have a feeling that he's about to tell us why he really joined, but we'll have to wait…
A lonely impulse of delight Drove to this tumult in the clouds;
But we don't have to wait very long, because he tells us right now! It was some "lonely impulse of delight" that made the speaker get involved in this fighter pilot business.
Well, actually that impulse "drove" him to "this tumult in the clouds." (For rhythmic reasons, the line leaves out the "me," as in "Drove me to this tumult," but that's understood here.) In other words, some crazy impulse that was very pleasing forced the airman to get involved in this whole battlefield, or chaos ("tumult"), in the sky.
Huh. It sounds like the speaker's reasons aren't very well defined at all. A lonely impulse of delight?
Okay, let's go through this piece by piece. Lonely? Well, this describes the impulse: there's just one impulse affecting the speaker. So what about that impulse?
Well, it makes the whole business sound like a really, well, impulsive decision—hasty, not thought out, an impulse. And it's an impulse, a sensation, an idea, a feeling that is… delightful!
Now, we know the speaker calls it an impulse, but it's a bit different than, say, deciding on a whim to buy that piece of candy sitting right by the cash register at Walgreens (curse you, delicious Butterfinger!).
It's an impulse, but an impulse that is more like a calling, a powerful sense of destiny or duty. He's not just driven by pleasure, he's driven by the pleasure he feels when he thinks about signing up for the military. It's like an itch that has to be scratched (not that we're trivializing it or anything).
Meanwhile, like the first eight lines, this group of four goes together as well, and they rhyme EFEF, as our "Form and Meter" section will explain.