Much thought had gone to the wording of the line. If Grell or any of his companions noticed it, Foyle felt certain that in some way or other an attempt would be made to get in touch with the baronet. He was fairly confident that the missing man needed money. He would probably not question how Fairfield knew that he was alive. If he rose to the bait there would be a catch of some sort. Whether Grell was the murderer or not, he held the key to the heart of the mystery. The superintendent emphasised this in a talk with Fairfield.

"It's a fair ruse. We're pretty certain he's hiding somewhere in London, and it's a big field unless we've got a starting-point. That's our trouble—finding a starting-point. In detective stories the hero always hits on it unerringly at once. There was one yarn in which the scratches on the back of a watch gave the clue to the temperament and history of its possessor. Now, that watch might have been borrowed or bought second-hand, or lost and restored at some time, and

the marks made by any one but its owner. That kind of subtlety is all right in print, but in real life it would put you on a false track in nineteen out of twenty cases. In ninety cases out of a hundred the obvious solution is the right one. In an investigation there may be coincidences of circumstantial evidence pointing in the wrong direction. But when you get first one coincidence, then a second, a third, and a fourth, you can be fairly sure you're on the right track. You don't add proof together. You multiply it. See here."

He drew a piece of paper towards him and rapidly scribbled upon it.

One coincidence. . . . .=0
Two coincidences. . . . .=2
Three coincidences. . . . .=6
Four coincidences. . . . .=24
Five coincidences. . . . .=120

"That's the kind of thing in terms of arithmetic. Now look at the parts in relation to each other. Grell leaves the club and gets you to lie about his absence. Coincidence number one. A man astonishingly like him is murdered in his study a short time afterwards. Coincidence number two. He is apparently dressed in Grell's clothes and has Grell's belongings in his pockets. Coincidence number three. Both Grell and his valet, Ivan Abramovitch, disappear. Coincidence number four. Ivan is found with the pearl necklace on him. Coincidence number five. Grell writes you a note, which I stole from you. Coincidence number six. You follow me? I could go on with other proofs. Grell must

know who committed this murder, and if we get hold of him we shall know."

"I see the point," confessed Fairfield. "All the same, I don't believe, even if he knows as you say, that he had a hand in it. This may be the hundreth case, you know, and there may be some satisfactory explanation of his actions."

"I quite agree. Even cumulative proof may be destroyed. I can guess what you are half thinking. You believe that I've fastened my suspicions on Grell, and that I'm determined to go through with it right or wrong. That's a common mistake people fall into in regard to police functions. In fact, it doesn't matter a bit to a police official whether he gets a conviction or not—unless, of course, he neglects an important piece of proof through gross carelessness. All he has to do is to solve a problem and to place his answer before a magistrate, and then a judge and jury to decide whether he's right or wrong. No one but a fool would attempt to bolster up a wrong answer. In this case, too, you must remember that there are finger-prints. They cannot lie. If we get the right man—Grell or any one else—there will be no question of doubt."

Fairfield tapped a cigarette on the back of his left hand and rose.