How did the police discover the wife's body in "The Black Cat"?
The final lines of this chilling and rather disturbing gothic short story answer this question. The narrator, having thought that he had committed the perfect crime when he killed his wife and then stowed her body away, placing it in his cellar and walling it up so that no trace of it could be seen, is quite happy to have the police come round and investigate. After all, he feels completely safe as no trace of any murder can be found. He has been very careful to leave no clues that could be used against him. However, it is with great shock and horror that, in the cellar, he hears a terrible noise of a cat mewling behind the wall where he has placed his wife's body. Note what is revealed when the police break down that wall:
The corpse, already greatly decayed and clotted with gore, stood erect before the eyes of the spectators. Upon its head, with red extended mouth and solitary eye of fire, sat the hideous beast whose craft had seduced me into murder, and whose informing voice had consigned me to the hangman. I had walled the monster up within the tomb!
In spite of having committed the "perfect" murder, the narrator has his plans ruined through the way in which he had inadvertently walled up the cat within the tomb with his wife's body. It is when the police come round that the cat, as if it knew that the police were there, started making noise so that the police became suspicious as to what might lie behind the wall and broke it down, uncovering both the wife's body and the guilt of the narrator.