Multiple layers of dramatic irony occurs in Chapter 8, when Fix tells the consul that he thinks he has identified the bank robber from London. The consul asks him why the robber would go out of his way to get his visa checked:
“Why was this robber so anxious to prove, by the visa, that he had passed through Suez?”
The consul points out that if Fogg were the bank robber, he would probably be more likely to avoid having his paperwork checked at every possible turn. The moment is funny because of the dramatic irony: no one except for the consul (a bystander in the conflict and a stand-in for the reader) knows what they are talking about.
The first layer of dramatic irony has to do with the reason Fix thinks he has proof that Fogg is the bank robber. Fix has pumped Passepartout for information. Passepartout does not realize that Fix is trying to arrest Fogg, so he has willingly answered all Fix's questions. The reader thus sees a hitch in Fogg's plan coming before he or Passepartout do, and Passepartout comes out looking honest to a fault.
Second, Fix is wrong about who the bank robber is. The reader does not know for sure at this point that Fix is wrong, but a careful reader can deduce just what the consul does: if Fogg is the bank robber, he is not very smart about it. Fix spends the entire novel chasing Fogg around the globe, trying to arrest him, when the real robber has already been arrested. The consul voices what the reader is likely already thinking: Fogg's itinerary is very public, which is not what someone on the run would want. Fix's failure to see this problem with his investigation leads him on a wild goose chase. The ongoing dramatic irony surrounding Fix's mistake is integral to the novel's satire of industrialization, imperialism, and modernization. If the world has truly "grown smaller," and if technology has made everything more efficient, Fix should receive word that he is after the wrong man. Instead, the ability to chase a suspect around the entire world leads to 80 days of wasted time for the detective.
In Chapter 24, on his way across the Pacific Ocean, Passepartout congratulates himself on keeping his watch on London time because it now matches perfectly with the timepieces on the ship. The narration uses dramatic irony to foreshadow the end of the novel:
Passepartout was ignorant that, if the face of his watch had been divided into twenty-four hours, like the Italian clocks, he would have no reason for exultation; for the hands of his watch would then, instead of as now indicating nine o‘clock in the morning, indicate nine o’clock in the evening, that is the twenty-first hour after midnight,—precisely the difference between London time and that of the one hundred and eightieth meridian.
In this passage, the narration lets the reader in on what Passepartout doesn't know: his watch matches up with the time on the ship's chronometers because it only has numbers 1 through 12 and does not note whether it is nine o'clock a.m. or p.m. Halfway around the world from London, there is exactly a 12-hour time difference that Passepartout forgets to consider.
The dramatic irony here (the reader sees something Passepartout does not) creates suspense. The stated point of Fogg and Passepartout's journey is to travel around the world at an unprecedented pace, so time is of the utmost importance. The reader is left wondering when Passepartout will realize his mistake. The narrator saves the discovery for the end of the novel, when the reader has all but forgotten Passepartout's mistake. The reveal that Passepartout and Fogg have accounted incorrectly for the time change, and that they have in fact made the journey faster than they realized, is all the more dramatic because of the foreshadowing in Chapter 24.
Dramatic irony in this passage also contributes to the novel's critique of imperialism and Western attitudes of superiority over the entire world. Earlier in the same passage, the narration explains that Passepartout's mistake about the time is made possible by his condescending Western attitude toward the regions he has been passing through:
It will be remembered that the obstinate fellow had insisted on keeping his famous family watch at London time, and on regarding that of the countries he had passed through as quite false and unreliable.
Passepartout has kept his watch set to London time because he has a poor opinion of non-Western countries' ability to keep time. Ironically, though, he is the one who is wrong about the time. Fogg's hypothesis is that imperialism and industrialization (Western exports to the rest of the world) allow him to manage his schedule down to the minute, even factoring in chance delays. But here, Passepartout's strict Western loyalty to his watch and to London's time zone makes him worse at managing time. This moment foreshadows not only the plot twist at the end of the novel, but also the novel's ultimate conclusion that Fogg's hypothesis is only weakly supported by his journey.