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 a