what is the resolution

Strombolite fishermen pick them up and take them to Messina. They then travel to Volturne. As it turns out everybody knows about their adventure because Martha had let the secret out,

"Then my uncle became a great man and I the nephew of a great man, which, at all events, is something. Hamburg gave a festival in our honor. A public meeting of the Johanneum Institution was held, at which the Professor related the whole story of his adventures, omitting only the facts in connection with the compass."