As he thought over the thing, further probabilities occurred to him. The lady would go up to her bedroom as one person and come down as another. Therefore, surely, the larger the hotel, the less chance of the transformation being observed. One of a crowd, she would go to the reception office and engage a room for a few hours’ rest, and pay for it then and there. Then, having accomplished the make-up, she would slip out, unobserved in the stream of passers-by. Yes, French felt sure he was on the right track, and, with a fresh accession of energy, he jumped to his feet, knocked out his pipe, and left the building. He called first at the South Western and made his inquiries. But here he drew blank. At the Dolphin he had no better luck, but at the Polygon he found what he wanted. After examining the records, the reception clerk there was able to recall the transaction. About midday an American lady had come in, and saying she wanted a few hours’ rest before catching the 5.26 to London, had engaged a bedroom on a quiet floor until that hour. She had registered, and French, on looking up the book, was delighted to find once more the handwriting of the lady of the cheques. It was true that on this occasion she figured as Mrs. Silas R. Clamm, of Hill Drive, Boston, Mass.; but knowing what he knew of her habits, French would have been surprised to have found a name he had seen before. At first he was delighted at so striking a confirmation of his theory, but as he pursued his inquiries his satisfaction vanished, and once more depression and exasperation swept over him. For the reception clerk could not remember anything more than the mere fact of the letting of the room, and no one else in the building remembered the woman at all. With his usual pertinacity, he questioned all who might have come in contact with her, but from none of them did he receive the slightest help. That Mrs. X had made herself up at the hotel for her impersonation stunt was clear, but unfortunately it was equally clear that she had vanished from the building without leaving any trace. The worst of the whole business was that he didn’t see what more he could do. The special clues upon which he had been building had failed him, and he felt there was now nothing for it but to fall back on the general one of the photographs. One of the portraits was excellently clear as to details, and he decided he would have an enlargement made of Mrs. X, and circulate it among the police in the hope that some member at some time might recognise the lady. Not a very hopeful method certainly, but all he had left. He took an evening train from the West Station, and a couple of hours afterwards reached his home, a thoroughly tired and disgruntled man. CHAPTER XIII MRS. FRENCH TAKES A NOTION