“I’m afraid the prospects are not very rosy,” he admitted. “But you never know. We’ll try to get our hands on the woman, of course, and we may find she has not spent the money. Now, sir, if there is nothing more than you can tell me, I think I shall get along to the Savoy and to those shops where she paid the cheques.” Inspector French walked slowly down Cockspur Street, his brain bemused by this unexpected development. The impersonation of Mrs. Root was easy—or, at least, comparatively easy—to understand. He could see that it would present no serious difficulties to a resourceful woman, though the application to the Southampton police was certainly staggering. But what he could not form the slightest idea of was how this woman could possibly have got hold of Mr. Duke’s diamonds. The impersonation must have actually been arranged _before_ the robbery took place, and if this were so, it pointed to a much more far-reaching crime than he had had any conception of. And there must have been more than one in it, too—unless this mysterious woman had actually committed the murder, which he found hard to believe. He smiled with satisfaction as he thought of the vistas of possible information which were opening out before him, and by which he might hope to retrieve the loss of prestige which he had suffered. Suddenly he thought of Miss Duke. Was there a connection between her and this mysterious woman? Was Mrs. Root the woman in the waterproof? Was she Miss Duke herself? Here were far-reaching questions. As he considered them, he saw that his work for the next few days was cut out for him. CHAPTER X SOME PAIRS OF BLANKETS DURING Inspector French’s brief lunch hour he continued turning over in his mind the immediate problem which Mr. Williams’s story had raised for him, namely, at what point he had best attack his new inquiry. The facts postulated a good deal of obvious detailed investigation, and he felt he should carry this through in his usual systematic way before attempting to evolve a comprehensive theory of the crime. He had first to learn what he could of the mysterious Mrs. Root, and in this connection he foresaw inquiries at Pittsburg, from the White Star people, from the Southampton police at the Savoy, and at the various firms of jewellers to whom the cheques had been made out. He had, if possible, to find the lady, or her impersonator. These things accomplished, he could turn his attention to an attempt to connect the person found with Miss Duke, or at all events with Mr. Duke’s jewels, and subsequently with the murder of Charles Gething. By the time his meal was ended he had decided that he would commence operations at the Savoy, and ten minutes later he turned into the courtyard, and making his way to the office, inquired for the manager.