M. Paul roused himself with an effort and, sitting up, his elbow resting against the sofa back, motioned his associate to a chair.

“By the way,” he asked, “what do you think of that?” He pointed to a Japanese print in a black frame that hung near the massive sideboard.

“Why,” stammered Tignol, “I—­I don’t think anything of it.”

“A rather interesting picture,” smiled the other.  “I’ve been studying it.”

“A purple sea, a blue moon, and a red fish—­it looks crazy to me,” muttered the old agent.

Coquenil laughed at this candid judgment.  “All the same, it has a bearing on our investigations.”

“Diable!”

M. Paul reached for his glasses, rubbed them deliberately and put them on.  “Papa Tignol,” he said seriously, “I have come to a conclusion about this crime, but I haven’t verified it.  I am now going to give myself an intellectual treat.”

“Wha-at?”

“I am going to prove practically whether my mind has grown rusty in the last two years.”

“I wish you’d say things so a plain man can understand ’em,” grumbled the other.

“You understand that we are in private room Number Seven, don’t you?  On the other side of that wall is private room Number Six where a man has just been shot.  We know that, don’t we?  But the man who shot him was in this room, the little hair-brushing old maid saw the pistol thrown from this window, the dog found footprints coming from this room, the murderer went out through that door into the alleyway and then into the street.  He couldn’t have gone into the corridor because the door was locked on the outside.”

“He might have gone into the corridor and locked the door after him,” objected Tignol.

Coquenil shook his head.  “He could have locked the door after him on the outside, not on the inside; but when we came in here, it was locked on the inside.  No, sir, that door to the corridor has not been used this evening.  The murderer bolted it on the inside when he entered from the alleyway and it wasn’t unbolted until I unbolted it myself.”

“Then how, in Heaven’s name——­”

“Exactly!  How could a man in this room kill a man in the next room?  That is the problem I have been working at for an hour.  And I believe I have solved it.  Listen.  Between these rooms is a solid wooden partition with no door in it—­no passageway of any kind.  Yet the man in there is dead, we’re sure of that.  The pistol was here, the bullet went there—­somehow. How did it go there? Think.”

The detective paused and looked fixedly at the wall near the heavy sideboard.  Tignol, half fascinated, stared at the same spot, and then, as a new idea took form in his brain, he blurted out:  “You mean it went through the wall?”

“Is there any other way?”

The old man laid a perplexed forefinger along his illuminated nose.  “But there is no hole—­through the wall,” he muttered.