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Miss Chastelnau was evidently expecting us. She stood with her back to the bay window and her face in shadow. She was the same neat and restrained person who had visited us in Baker Street. Yet I sensed that her family tragedy had inspired her with anxiety rather than grief.

The sitting-room was just what I would have expected. The sun filled its chintz curtains at the window and, on a small table, stood a Chinese vase adorned with green dragon-handles. The hearth, where Holmes and I faced one another with Miss Chastelnau upright between us on a yellow settee in the Egyptian style, was lined with William De Morgan tiles portraying centaurs, the phoenix and other mythical creatures of the ancient world. I thought afterwards that the entire room was a curious shrine of the non-existent.

As succinctly as I could, because that was kinder, I explained the details of my solution to the mystery of her two missing brothers. I added that there had, of course, been no inquest as yet. What its verdict would be I could not say. Miss Chastelnau sat quite still and listened in silence. When I had finished, she thanked me with every appearance of sincerity. If she showed little emotion, it was surely because she remained in that state of shock which precedes any outbursts of grief.

“And you, Mr Holmes,” she said quietly, turning to him, “thank you for coming to see me also.”

Throughout all this, he had been sitting with his head lowered a little, as if reading the mythology of the hearth tiles. Now he was straight-backed in his chair and looking her directly in the eye.

“I fear you are in error, madam. I did not come here to see you, for that is Dr Watson’s business. I am here to see Mr Abraham Chastelnau.”

If a bomb had gone off in that ornamented and genteel room, it could not have produced a more stunned and silent aftermath than his words. I had not the first idea what he was talking about. Our hostess could only say, as if in a dream,

“I do not understand you, Mr Holmes.”

“Do you not? Then I will explain.”

“He is not here!” The desperate cry was so unlike her habitual composure that I felt the skin of my back creep with cold.

“If you mean,” said Holmes, “that he could not be here without your knowledge, I will go so far as to accept that. I beg you, however, do not torment yourself by denials until you hear what I have to say.”

She made no reply but stared at him, as if one or the other of them had gone mad. Holmes continued.

“We are asked to believe that your brother Abraham, at the allotted time of no later than 7.45 on Sunday evening, cranked up the chain of the lantern mechanism in the Old Light at Sutton Cross. At the same time, he must have wound up the clock and the governor which controls the mechanism in order that it should continue to run correctly. Somewhen soon after that, he was summoned by a gunshot from the darkened beach. We do not know precisely what happened there between your brothers but soon afterwards Roland Chastelnau died. We presume that he drowned, from whatever cause.”

“I know that, Mr Holmes,” she said with quiet reproach.

“Abraham, it appears, attempted to return to the lighthouse. That should have been straightforward enough. However, it is alleged that Roland meant to ensure, whatever happened on the beach, that his elder brother should never reach the Old Light alive. Earlier that day, he had therefore adjusted the position of the iron shutters across the glass panes of the lantern dome. No one would have gone up there to check them, for the glass was cleaned that morning. No one would have seen the direction of the beam by daylight.”

She was holding a pocket handkerchief to her mouth and her head was bowed.

“The truth, Miss Chastelnau, is best. The altered direction of the beam, shining through the darkness a little closer to King’s Lynn and further from the Boston Deeps, was surely intended to lure its victim into the estuary and the quicksands. That would explain why his body was never found. If Roland had succeeded in such a plot, he had only to return to the Old Light as the tide ebbed and adjust the shutters to their original position. Unfortunately, he himself was drowned before the ebb. The misalignment of the shutters was therefore discovered by Dr Watson and myself. That was intended to be conclusive evidence of Roland’s guilt.”

“Intended?” she cried, looking up suddenly, “I do not understand. What Dr Watson has just told me is surely the truth.”

“And I have to tell you that it is quite impossible.”

“Why?”

“For two very simple reasons. Abraham could not have wound that clock at a quarter to eight, or at any time until after nine o’clock. Look at any simple grandfather clock, which the face of this one resembles. There are two keyholes which are covered when the hour hand is between the numerals for three and four-or eight and nine. The clock cannot be wound during those periods.”

“It may have been done earlier!”

“When the mechanism of the Old Light was inspected on the following morning, the timer had run down, as it would do after eight hours. The chain would be too heavy for the man who had to crank it up again if it ran longer. Indeed, the skipper of a collier in the Deeps noted in his log at quarter past five that morning that the signal of the Old Light was no longer being transmitted.”

“What has that to do with it?” she insisted.

“It has this to do with it, Miss Chastelnau. This indication of foul play was not that the beam of light failed after five o‘clock but that it had not stopped before. Had the mechanism been wound as early as eight o’clock the previous evening, the hour hand would then cover the keyhole until after nine. Next morning, the mechanism would have stopped and the Old Light would have failed an hour and a quarter earlier than it did. Someone had returned to the Old Light and wound the mechanism an hour or more after Abraham Chastelnau went down to the sands in response to his brother’s gunshot.”

She stared at him now with a look of dread which came from trying to guess how much more he knew.

“What happened on the beach,” he continued, “may be murder, accident, or misadventure. We can only be sure that Roland drowned, from whatever cause. Abraham lived and knew his brother was lost. He returned safely to the Old Light at about nine o’clock.”

“Why was he not trapped in the river by the altered beam of light?” I asked.

“Because it had not yet been altered. Whatever the cause or the outcome of the struggle on the sands, Abraham believed that he might face trial and execution for his brother’s death. He had not a single friendly witness to prove that he was guilty only of innocent self-defence, rather than premeditated murder. No one to prove that it was not he but Roland who fired the shot which signalled the beginning of the tragedy. Afterwards, he sat alone in the barrack-room, no doubt in distress and dread. He was alive and Roland was dead. He had very probably seen two figures on the church tower, witnesses of the struggle. The sound of the sexton’s rook rifle confirmed it.”

Neither of us spoke and Holmes continued.

“Who will believe him? He sees the stern-faced officers setting out from King’s Lynn.! He sees the dock at the assizes and the black cap put on by the judge who assures him that he will be hanged by the neck until he is quite dead. Worst of all, he sees the dreadful weeks in the condemned cell, hears the hangman’s knock and imagines the last walk across the prison yard to the tall shed with its thirteen steps leading up to the waiting noose.”