However, one day in March, Richis sits in his salon and watches Laure walk in the garden. She disappears behind a hedge and takes a moment too long to reappear, frightening Richis. That night he has a terrible dream in which he finds Laure murdered in her bedroom. He bursts into Laure's room to find her asleep and alive, and returns to his bedroom.
The narrator is beginning to draw similarities between Richis and Grenouille with the device of the terrifying dream to incite action. Both are powerful figures, and Richis shares some of Grenouille's beliefs that the general populace is easily fooled.
Richis thinks that he never believed the rumor that the murderer had left the town, and decides that he's surely still around. Richis also thinks that the murderer has a system, as all the victims are beautiful and youthful. He decides that the victims are part of a grand plan to assemble a picture of absolute beauty, and concludes that Laure must be the crowning jewel and the murderer's final victim. Richis feels superior to the murderer having had this thought, and he sees the situation as though he and the murderer are business competitors. He vows to keep Laure alive, as he needs her to accomplish his goals.
Richis assumes that by simply meeting the murderer in intellectual fortitude, he can outsmart him. Note that Richis feels he must keep his daughter alive in order to further his own business and social climbing ventures, not for Laure's happiness or for the sake of believing she's deserving of life regardless of her usefulness.