1I was dumbfounded. Up to the last, I had not been able bring myself to believe Jack Renauld guilty. I had expected a ringing proclamation of his innocence when Poirot challenged him. But now, watching him as he stood, white and limp against the wall, and hearing the damning admission fall from his lips, I doubted no longer.

2But Poirot had turned to Giraud.

3“What are your grounds for arresting him?”

4“Do you expect me to give them to you?”

5“As a matter of courtesy, yes.”

6Giraud looked at him doubtfully. He was torn between a desire to refuse rudely and the pleasure of triumphing over his adversary.

7“You think I have made a mistake, I suppose?” he sneered.

8“It would not surprise me,” replied Poirot, with a soupçon of malice.

9Giraud’s face took on a deeper tinge of red.

10“Eh bien, come in here. You shall judge for yourself.” He flung open the door of the salon, and we passed in, leaving Jack Renauld in the care of the two other men.

11“Now, M. Poirot,” said Giraud laying his hat on the table, and speaking with the utmost sarcasm, “I will treat you to a little lecture on detective work. I will show you how we moderns work.”

12“Bien!” said Poirot, composing himself to listen. “I will show you how admirably the Old Guard can listen,” and he leaned back and closed his eyes, opening them for a moment to remark. “Do not fear that I shall sleep. I will attend most carefully.”

13“Of course,” began Giraud, “I soon saw through all that Chilian tomfoolery. Two men were in it—but they were not mysterious foreigners! All that was a blind.”

14“Very creditable so far, my dear Giraud,” murmured Poirot. “Especially after that clever trick of theirs with the match and cigarette end.”

15Giraud glared, but continued:

16“A man must have been connected with the case, in order to dig the grave. There is no man who actually benefits by the crime, but there was a man who thought he would benefit. I heard of Jack Renauld’s quarrel with his father, and of the threats that he had used. The motive was established. Now as to means. Jack Renauld was in Merlinville that night. He concealed the fact—which turned suspicion into certainty. Then we found a second victim—stabbed with the same dagger. We know when that dagger was stolen. Captain Hastings here can fix the time. Jack Renauld, arriving from Cherbourg, was the only person who could have taken it. I have accounted for all the other members of the household.”

17Poirot interrupted:

18“You are wrong. There is one other person who could have taken the dagger.”

19“You refer to M. Stonor? He arrived at the front door, in an automobile which had brought him straight from Calais. Ah, believe me, I have looked into everything. M. Jack Renauld arrived by train. An hour elapsed between his arrival, and the moment he presented himself at the house. Without doubt, he saw Captain Hastings and his companion leave the shed, slipped in himself and took the dagger, stabbed his accomplice in the shed—”

20“Who was already dead!”

21Giraud shrugged his shoulders.

22“Possibly he did not observe that. He may have judged him to be sleeping. Without doubt they had a rendezvous. In any case he knew this apparent second murder would greatly complicate the case. It did.”

23“But it could not deceive M. Giraud,” murmured Poirot.

24“You mock yourself at me. But I will give you one last irrefutable proof. Madame Renauld’s story was false—a fabrication from beginning to end. We believe Madame Renauld to have loved her husband—yet she lied to shield his murderer. For whom will a woman lie? Sometimes for herself, usually for the man she loves, always for her children. That is the last—the irrefutable proof. You cannot get round it.”

25Giraud paused, flushed and triumphant. Poirot regarded him steadily.

26“That is my case,” said Giraud. “What have you to say to it?”

27“Only that there is one thing you have failed to take into account.”

28“What is that?”

29“Jack Renauld was presumably acquainted with the planning out of the golf course. He knew that the body would be discovered almost at once, when they started to dig the bunker.”

30Giraud laughed out loud.

31“But it is idiotic what you say there! He wanted the body to be found! Until it was found, he could not presume death, and would have been unable to enter into his inheritance.”

32I saw a quick flash of green in Poirot’s eyes as he rose to his feet.

33“Then why bury it?” he asked softly. “Reflect, Giraud. Since it was to Jack Renauld’s advantage that the body should be found without delay, why dig a grave at all?”

34Giraud did not reply. The question found him unprepared. He shrugged his shoulders as though to intimate that it was of no importance.

35Poirot moved towards the door. I followed him.

36“There is one more thing that you have failed to take into account,” he said over his shoulder.

37“What is that?”

38“The piece of lead piping,” said Poirot, and left the room.

39Jack Renauld still stood in the hall, with a white dumb face, but as we came out of the salon, he looked up sharply. At the same moment there was the sound of a footfall on the staircase. Mrs. Renauld was descending it. At the sight of her son, standing between the two myrmidons of the law, she stopped as though petrified.

40“Jack,” she faltered. “Jack, what is this?”

41He looked up at her, his face set.

42“They have arrested me, mother.”

43“What?”

44She uttered a piercing cry, and before any one could get to her swayed and fell heavily. We both ran to her and lifted her up. In a minute Poirot stood up again.

45“She has cut her head badly, on the corner of the stairs. I fancy there is a slight concussion also. If Giraud wants a statement from her, he will have to wait. She will probably be unconscious for at least a week.”

46Denise and Françoise had run to their mistress, and leaving her in their charge Poirot left the house. He walked with his head bent down, frowning thoughtfully at the ground. For some time I did not speak, but at last I ventured to put a question to him.

47“Do you believe then, in spite of all appearances to the contrary, that Jack Renauld may not be guilty?”

48Poirot did not answer at once, but after a long wait he said gravely:

49“I do not know, Hastings. There is just a chance of it. Of course Giraud is all wrong—wrong from beginning to end. If Jack Renauld is guilty, it is in spite of Giraud’s arguments, not because of them. And the gravest indictment against him is known only to me.”

50“What is that?” I asked, impressed.

51“If you would use your grey cells, and see the whole case clearly as I do, you too would perceive it, my friend.”

52This was what I called one of Poirot’s irritating answers. He went on, without waiting for me to speak.

53“Let us walk this way to the sea. We will sit on that little mound there, overlooking the beach, and review the case. You shall know all that I know, but I would prefer that you should come at the truth by your own efforts—not by my leading you by the hand.”

54We established ourselves on the grassy knoll as Poirot had suggested, looking out to sea. From farther along the sand, the cries of the bathers reached us faintly. The sea was of the palest blue, and the halcyon calm reminded me of the day we had arrived at Merlinville, my own good spirits, and Poirot’s suggestion that I was “fey.” What a long time seemed to have elapsed since then. And in reality it was only three days!

55“Think, my friend,” said Poirot’s voice encouragingly. “Arrange your ideas. Be methodical. Be orderly. There is the secret of success.”

56I endeavoured to obey him, casting my mind back over all the details of the case. And reluctantly it seemed to me that the only clear and possible solution was that of Giraud—which Poirot despised. I reflected anew. If there was daylight anywhere it was in the direction of Madame Daubreuil. Giraud was ignorant of her connection with the Beroldy Case. Poirot had declared the Beroldy Case to be all important. It was there I must seek. I was on the right track now. And suddenly I started as an idea of bewildering luminosity shot into my brain. Trembling I built up my hypothesis.

57“You have a little idea, I see, mon ami! Capital. We progress.”

58I sat up, and lit a pipe.

59“Poirot,” I said, “it seems to me we have been strangely remiss. I say we—although I dare say I would be nearer the mark. But you must pay the penalty of your determined secrecy. So I say again we have been strangely remiss. There is some one we have forgotten.”

60“And who is that?” inquired Poirot, with twinkling eyes.

61“Georges Conneau!”