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Tintin goes to visit Captain Haddock and Professor Calculus at their new home in Marlinspike Hall. On the train, he reads about a team of seven explorers returning home after a two year expedition in the Andes where they discovered the tomb of the ancient Incan priest Rascar Capac, with the latter's mummy in tow. A strange man compares them to the Egyptologists who unearthed Tutankhamen's tomb and claims the same fate will befall them. Later on, Tintin attends a music hall with Haddock and is surprised to find General Alcazar, having been deposed of power and now performing as a knife thrower. Another act by a psychic also mentions the Incan expedition and claims its members are in grave danger.
Concurrent with these events, each member of the Rascar Capac expedition starts falling into a mysterious coma, one by one. Thompson and Thomson are investigating and reveal that the only clue present at each scene are fragments of crystal spheres, which apparently contained some sort of mysterious gas that caused the comas. Despite the efforts of Tintin, Haddock, and the Thompsons, they are unable to stop the attacks and finally decide to personally guard the last explorer, Professor Tarragon, an old friend of Professor Calculus, who accompanies them to the former's house. After the Rascar Capac mummy disappears from the house in a mysterious bolt of ball lightning, Tarragon claims that this is the culmination of a prophecy: Rascar Capac has "returned to his element" and will go after Tarragon personally. Despite the escort, Tarragon succumbs to the coma as well, becoming the last of the seven. To make matters worse, Professor Calculus is kidnapped after finding the mummy's bracelet.
Tintin and Haddock chase the kidnapper and manage to track him to the Pachacamac, a ship bound for Peru. Tintin also discovers that Alcazar's assistant Chiquito, one of the last descendants of the Incas is also involved. Tintin and Haddock depart for Peru to rescue Calculus, closing part 1 of the two part story that concludes in Prisoners of the Sun.
- Curse: The explorers and archaeologists all fall victim to a curse due to desecrating a tomb.
- Dangerous Windows: Two of the members of the Sanders-Hardiman expedition fall victim to crystal balls hurled through their windows. Professor Cantonneau is attacked this way just as Tintin tries to warn him not to go near the window. Dr. Midge is then placed under police guard, but the police in question are Thompson and Thomson, and they try to guard everything but the window. With predictable results.
- Fainting Seer: Mrs. Yamilah, a stage fortune teller, tries to look into the fate of a woman married to one of the explorers. She gets a glimpse into the fate of the husband and seems physically affected.
- High-Class Glass: In the previous adventure of the series, Captain Haddock had acquired a treasure through inheritance. His newfound wealth is indicated in this album by his residence in a mansion and by his new habit of wearing a monocle. Not being accustomed to them, he loses a lot of them.
- Knife-Throwing Act: General Alcazar, exiled in this book, has his own stage act. After creating a full Knife Outline around his Indian target, he asks an audience member to blindfold him. His blind throw hits right in the center of the fruit held over the target's chest.
- A Mythology Is True: In-story example. The curse of Rascar Capac is scoffed at by the rational characters. Until it turns true to the letter.
- Nightmare Sequence: Tintin and his companions all have the same nightmare: that they are visited by the Inca mummy Rascar Capac who enters their bedroom by night and then throws a crystal ball on the floor.
- No Communities Were Harmed: The story accurately depicts the French port of Saint-Nazaire. The English translation renames it Westermouth for no good reason.
- Rule of Seven: Seven cursed explorers, seven crystal balls hurled at them and and placing them in comas.