"But what made you fix on Hempdon as the headquarters of the blackguard?" enquired Sir John.
"That was easy," remarked Malcolm Sage, polishing the thumb-nail of his left hand upon the palm of his right.
"Easy!" The exclamation burst involuntarily from the inspector.
"You supplied me with a large scale-map showing the exact spot where each of the previous maimings had taken place. I drew a square to embrace the whole. Lines drawn diagonally from corner to corner gave me the centre of gravity."
"But——" began the inspector.
Ignoring the interruption Malcolm Sage continued.
"A man committing a series of crimes from a given spot was bound to spread his operations over a fairly wide area in order to minimise the chance of discovery. The longer the period and the larger the number of comes, the greater the chance of his being located somewhere near the centre of his activities."
"Well, I'm damned!" remarked Sir John for the second time. Then suddenly turning to Inspector Wensdale, "Dammit!" he exploded, "why didn't you think of that?"
"There was, of course, the chance of his striking in another direction," continued Malcolm Sage, digging into the bowl of his pipe with a penknife, "so I placed the men in such a way that if he did so he was bound to be seen."
Inspector Wensdale continued to gaze at him, eager to hear more.