it was poirot's moment, every face was turned to his in eager anticipation. "you are very kind," he said, smiling. "you know, i think, that i enjoy my little lecture. i am a prosy old fellow. "this case, to my mind, has been one of the most interesting cases i have ever come across. there was nothing, you see, to go upon. there were four people, one of whom must have committed the crime but which of the four? was there anything to tell one? in the material sense--no. there were no tangible clues---no fingerprints--no incriminating papers or documents. there were only--the people themselves. "and one tangible cluethe bridge scores. "you may remember that from the beginning i showed a particular interest in those scores. they told me something about the various people who had kept them and they did more. they gave me one valuable hint. i noticed at once, in the third rubber, the figure of 1500 above the line. that figure could only represent one thing--a call of grand slam. now if a person were to make up their minds to commit a crime under these somewhat unusual circumstances (that is, during a rubber game of bridge) that person was clearly running two serious risks. the first was that the victim might cry out and the second was that even ffthe victim did not cry out some one of the other three might chance to look up at the psychological moment and actually witness the deed. "now as to the first risk, nothing could be done about it. it was a matter of a gambler's luck. but something could be done about the second. it stands to reason. that during an interesting or an exciting hand the attention of the three players would be wholly on the game, whereas during a dull hand they were more likely to be looking about them. now a bid of grand slam is always exciting. it is very often (as in this case it was) doubled. every one of the three players is playing with close attention--the declarer to get his contract, the adversaries to discard correctly and to get him down. it was, then, a distinct possibility that the murder was committed during this particular hand and i determined to find out, if i could, exactly how the bidding had gone. i soon discovered that dummy during this particular hand had been dr. roberts. i bore that in mind and approached the matter from my second anglepsychological probability. of the four suspects mrs.lorrimer struck me as by far the most likely to plan and carry out a successful murder but i could not see her as committing any crime that had to be improvised on the spur of the moment. on the other hand her manner that first evening puzzled me. it suggested either that she had committed the murder herself or that she knew who had committed it. miss meredith, major despard and dr. roberts were all psychological possibilities, though, as i have already mentioned, each of them would have committed the crime from an entirely different angle.

"i next made a second test. i got every one in turn to tell me just what they remembered of the room. from that i got some very valuable information. first of all, by far the most likely person to have noticed the dagger was dr. roberts. he was a natural observer of trifles of all kinds--what is called an observant man. of the bridge hands, however, he remembered practically nothing at all. i did not expect him to remember much, but his complete forgetfulness looked as though he had had something else on his mind all the evening. again, you see, dr. roberts was indicated.

"mrs. lorrimer i found to have a marvellous card memory, and i could well imagine that with any one of her powers of concentration a murder could easily be committed close at hand and she would never notice anything. she gave me a valuable piece of information. the grand slam was bid by dr. roberts (quite unjustifiably)--and he bid it in her suit, not his own, so that she necessarily played the hand.

"the third test, the test on which superintendent battle and i built a good deal, was the discovery of the earlier murders so as to establish a similarity of method. well, the credit for those discoveries belongs to superintendent battle, to mrs. oliver and to colonel race. discussing the matter with my friend battle, he confessed himself disappointed because there were no points of similarity between any of the three earlier crimes and that of the murder of mr. shaitana. but actually that was not true. the two murders attributed to dr. roberts, when examined closely, and from the psychological points of view and not the material one, proved to be almost exactly the same. they, too, had been what i might describe as public murders. a shaving brush boldly infected in the victim's own dressing-room while the doctor officially washes his hands after a visit. the murder of mrs. craddock under cover of a typhoid inoculation. again done quite openly--in the sight of the world, as you might say. and the reaction of the man is the same. pushed into a corner, he seizes a chance and acts at one--sheer bold audacious bluff-exactly like his play at bridge. as at bridge, so in the murder of shaitana, he took a long chance and played his cards well. the blow was perfectly struck and at exactly the right moment.

"now just at the moment that i had decided quite definitely that roberts was the man, mrs. lorrimer asked me to come and see her--and quite convincingly accused herself of the crime! i nearly believed her! for a minute or two i did believe her--and then my little grey cells reasserted their mastery. it could not beso it was not!

"but what she told me was more difficult still.

"she assured me that she had actually seen anne meredith commit the crime.

"it was not till the following morning--when i stood by a dead woman's bed--that i saw how i could still be right and mrs. lorrimer still have spoken the truth.

"anne meredith went over to the fireplace--and saw that mr. shaitana was dead! she stopped over him--perhaps stretched out her hand to the gleaming head of the jewelled pin.

"her lips part to call out, but she does not call out. she remembers shaitana's talk at dinner. perhaps he has left some record. she, anne meredith, has a motive for desiring his death. every one will say that she has killed him. she dare not call out. trembling with fear and apprehension she goes back to her seat.

"so mrs. lorrimer is right, since she, as she thought, saw the crime committed but i am right too, for actually she did not see it.

"if roberts had held his hand at this point, i doubt if we could have ever brought his crimes home to him. we might have done so-by a mixture of bluffand various ingenious devices. i would at any rate have tried.

"but he lost his nerve and once again overbid his hand. and this time the cards lay wrong for him and he came down heavily.

"no doubt he was uneasy. he knew that battle was nosing about. he foresaw the present situation going on indefinitely, the police still searching--and perhaps, by some miracle--coming on traces of his former crimes. he hit upon the brilliant idea of making mrs. lorrimer the scapegoat for the party. his practised eye guessed, no doubt, that she was ill and that her life could not be very much prolonged. how natural in those circumstances for her to choose a quick way out, and before taking it, confess to the crime! so he manages to get a sample of her handwriting--forges three identical letters and arrives at the house hot-foot in the morning with his story of the letter he has just received. his parlourmaid quite correctly is instructed to ring up the police. all he needs is a start. and he gets it. by the time the police surgeon arrives it is all over. dr. roberts is ready with his story of artificial respiration that has failed. it is all perfectly plausibleperfectly straightforward. "in all this he has no idea of throwing suspicion on anne meredith. he does not even know of her visit the night before. it is suicide and security only that he is aiming at.

"it is in fact an awkward moment for him when i ask if he is acquainted with mrs. lorrimer's handwriting. if the forgery has been detected he must save himself by saying that he has never seen her handwriting. his mind works quickly, but not quickly enough.

"from wallingford i telephone to mrs. oliver. she plays her part by lulling his suspicions and bringing him here. and then when he is congratulating himself that all is well, though not exactly in the way he has planned, the blow falls. hercule poirot springs! and so--the gambler will gather in no more tricks. he has thrown his cards upon the table. c'estfini."

there was silence. rhoda broke it with a sigh.

"what amazing luck that window-cleaner happened to be there," she said.

"luck? luck? that was not luck, mademoiselle. that was the grey cells of hercule poirot. and that reminds me " he went to the door. "come in-come in, my dear fellow. you acted your part i merveille." he returned accompanied by the window cleaner, who now held his red hair in his hand and who looked somehow a very different person. "my friend mr. gerald hemmingway, a very promising young actor." "then there was no window-cleaner?" cried rhoda. "nobody saw him?" "i saw," said poirot. "with the eyes of the mind one can see more than with the eyes of thebody. one leans back and closes the eyes-- despard said cheerfully: "let's stab him, rhoda, and see if his ghost can come back and find out who did it."