Final answer:
C. Auguste Dupin employs ratiocination, going beyond conventional police methods to solve how a murderer escaped, by understanding the criminal's mindset.
Step-by-step explanation:
C. Auguste Dupin uses the method of ratiocination to figure out how the murderer left the scene through the back window. By employing a blend of intuitive reasoning and logical deduction, Dupin surpasses the conventional investigative methods used by the police. He understands the mind of the criminal and uses that insight to deduce where the murderer would not hide evidence, leading him to unravel the mystery in a way that the authorities could not.