“Ah! That’s a most vital point. The raison d’être of this terrible orgy of humor lies in that cryptic signature.”

Markham turned slowly.

“Does the chess player and the astronomer fulfil the conditions of your theory as well as the mathematical physicist?”

“Yes,” Vance replied. “Since the days of Philidor, Staunton and Kieseritzki, when chess was something of a fine art, the game has degenerated almost into an exact science; and during Capablanca’s régime it has become largely a matter of abstract mathematical speculation. Indeed, Maroczy, Doctor Lasker and Vidmar are all well-known mathematicians. . . . And the astronomer, who actually views the universe, may get an even more intense impression of the unimportance of this earth than the speculative physicist. Imagination runs riot through a telescope. The mere theory of existing life on distant planets tends to reduce earthly life to second’ry consideration. For hours after one has looked at Mars, for instance, and dallied with the notion that its inhabitants outnumber and surpass in intelligence our own population, one has difficulty in readjusting oneself to the petty affairs of life here on earth. Even a reading of Percival Lowell’s romantic book[35] temporarily takes away from the imaginative person all consciousness of the significance of any single planet’ry existence.”

There was a long silence. Then Markham asked:

“Why should Pardee have taken Arnesson’s black bishop that night instead of one from the club where it would not have been missed?”

“We don’t know enough of the motive to say. He may have taken it with some deliberate purpose in view.—But what evidence have you of his guilt? All the suspicions in the world would not permit you to take any step against him. Even if we knew indubitably who the murderer was, we’d be helpless. . . . I tell you, Markham, we’re facing a shrewd brain—one that figures out every move, and calculates all the possibilities. Our only hope is to create our own evidence by finding a weakness in the murderer’s combination.”

“The first thing in the morning,” declared Markham grimly, “I’m going to put Heath to work on Pardee’s alibi that night. There’ll be twenty men checking it up by noon, questioning every spectator at that chess game, and making a door-to-door canvass between the Manhattan Chess Club and the Drukker house. If we can find some one who actually saw Pardee in the vicinity of the Drukkers’ around midnight, then we’ll have a very suspicious piece of circumstantial evidence against him.”

“Yes,” agreed Vance; “that would give us a definite starting-point. Pardee would have considerable difficulty in explaining why he was six blocks away from the club during his set-to with Rubinstein at the exact hour that a black bishop was being left at Mrs. Drukker’s door. . . . Yes, yes. By all means have Heath and his minions tackle the problem. It may lead us forward.”

But the Sergeant was never called upon to check the alibi. Before nine o’clock on the following morning Markham called at Vance’s house to inform him that Pardee had committed suicide.