The prisoner had been arrested in consequence of the discovery, in his room, by Detective Inspector Japp ”a most brilliant officer ”of the identical phial of strychnine which had been sold at the village chemist's to the supposed Mr. Inglethorp on the day before the murder. 
The clue that solved the case was that a phial of strychnine had been sold just the day before.
The prisoner was arrested for confessing to the murder.