Rouletabille motioned me to follow him up a magnificent flight of stairs ending in a landing on the first floor. From this landing one could pass to the right or left wing of the chateau by a gallery opening from it. This gallery, high and wide, extended along the whole length of the building and was lit from the front of the chateau facing the north. The rooms, the windows of which looked to the south, opened out of the gallery. Professor Stangerson inhabited the left wing of the building. Mademoiselle Stangerson had her apartment in the right wing.

      We entered the gallery to the right. A narrow carpet, laid on the waxed oaken floor, which shone like glass, deadened the sound of our footsteps. Rouletabille asked me, in a low tone, to walk carefully, as we were passing the door of Mademoiselle Stangerson’s apartment. This consisted of a bed-room, an ante-room, a small bath-room, a boudoir, and a drawing-room. One could pass from one to another of these rooms without having to go by way of the gallery. The gallery continued straight to the western end of the building, where it was lit by a high window (window 2 on the plan). At about two-thirds of its length this gallery, at a right angle, joined another gallery following the course of the right wing.

      The better to follow this narrative, we shall call the gallery leading from the stairs to the eastern window, the “right” gallery and the gallery quitting it at a right angle, the “off-turning” gallery (winding gallery in the plan). It was at the meeting point of the two galleries that Rouletabille had his chamber, adjoining that of Frederic Larsan, the door of each opening on to the “off-turning” gallery, while the doors of Mademoiselle Stangerson’s apartment opened into the “right” gallery. (See the plan.)

      Rouletabille opened the door of his room and after we had passed in, carefully drew the bolt. I had not had time to glance round the place in which he had been installed, when he uttered a cry of surprise and pointed to a pair of eye-glasses on a side-table.

      “What are these doing here?” he asked.

      I should have been puzzled to answer him.

      “I wonder,” he said, “I wonder if this is what I have been searching for. I wonder if these are the eye-glasses from the presbytery!”

      He seized them eagerly, his fingers caressing the glass. Then looking at me, with an expression of terror on his face, he murmured, “Oh!—Oh!”

      He repeated the exclamation again and again, as if his thoughts had suddenly turned his brain.

      He rose and, putting his hand on my shoulder, laughed like one demented as he said:

      “Those glasses will drive me silly! Mathematically speaking the thing is possible; but humanly speaking it is impossible—or afterwards—or afterwards—”

      Two light knocks struck the door. Rouletabille opened it. A figure entered. I recognised the concierge, whom I had seen when she was being taken to the pavilion for examination. I was surprised, thinking she was still under lock and key. This woman said in a very low tone:

      “In the grove of the parquet.”

      Rouletabille replied: “Thanks.”—The woman then left. He again turned to me, his look haggard, after having carefully refastened the door, muttering some incomprehensible phrases.

      “If the thing is mathematically possible, why should it not be humanly!—And if it is humanly possible, the matter is simply awful.” I interrupted him in his soliloquy:

      “Have they set the concierges at liberty, then?” I asked.

      “Yes,” he replied, “I had them liberated, I needed people I could trust. The woman is thoroughly devoted to me, and her husband would lay down his life for me.”

      “Oho!” I said, “when will he have occasion to do it?”

      “This evening,—for this evening I expect the murderer.”

      “You expect the murderer this evening? Then you know him?”

      “I shall know him; but I should be mad to affirm, categorically, at this moment that I do know him. The mathematical idea I have of the murderer gives results so frightful, so monstrous, that I hope it is still possible that I am mistaken. I hope so, with all my heart!”

      “Five minutes ago, you did not know the murderer; how can you say that you expect him this evening?”

      “Because I know that he must come.”

      Rouletabille very slowly filled his pipe and lit it. That meant an interesting story. At that moment we heard some one walking in the gallery and passing before our door. Rouletabille listened. The sound of the footstep died away in the distance.

      “Is Frederic Larsan in his room?” I asked, pointing to the partition.

      “No,” my friend answered. “He went to Paris this morning,—still on the scent of Darzac, who also left for Paris. That matter will turn out badly. I expect that Monsieur Darzac will be arrested in the course of the next week. The worst of it is that everything seems to be in league against him,—circumstances, things, people. Not an hour passes without bringing some new evidence against him. The examining magistrate is overwhelmed by it—and blind.”

      “Frederic Larsan, however, is not a novice,” I said.

      “I thought so,” said Rouletabille, with a slightly contemptuous turn of his lips, “I fancied he was a much abler man. I had, indeed, a great admiration for him, before I got to know his method of working. It’s deplorable. He owes his reputation solely to his ability; but he lacks reasoning power,—the mathematics of his ideas are very poor.”

      I looked closely at Rouletabille and could not help smiling, on hearing this boy of eighteen talking of a man who had proved to the world that he was the finest police sleuth in Europe.

      “You smile,” he said? “you are wrong! I swear I will outwit him—and in a striking way! But I must make haste about it, for he has an enormous start on me—given him by Monsieur Robert Darzac, who is this evening going to increase it still more. Think of it!—every time the murderer comes to the chateau, Monsieur Darzac, by a strange fatality, absents himself and refuses to give any account of how he employs his time.”

      “Every time the assassin comes to the chateau!” I cried. “Has he returned then—?”

      “Yes, during that famous night when the strange phenomenon occurred.”

      I was now going to learn about the astonishing phenomenon to which Rouletabille had made allusion half an hour earlier without giving me any explanation of it. But I had learned never to press Rouletabille