Bannister smiled back and waved his hand gaily as the train drew slowly from the long platform. Anthony made his way back to his hotel. There he sought the seclusion afforded by the smoke-room. Writing materials were to hand. Mr. Bathurst set to work upon what he always called his “Initial Summary of Facts.” Completed he snuggled back in his chair and surveyed the epitome complacently. This is how it read. (A) Present at Hunt Ball—“_lever de rideau_,” so to speak—Alexis—Sheila—Daphne—Major Carruthers—Sir Matthew Fullgarney (probably)—Alan Warburton—and the mysterious “Mr. X.” (B) Present at “Cassandra” when compromising photograph was taken—Alexis—Daphne—Captain Willoughby——“? Mr. X.” (C) Present at Seabourne at the time of the actual tragedy—Alexis—Sheila—Daphne—Alan Warburton—Captain Willoughby——“? Mr. X.”? Is “Mr. X.” one of these? If so, which one? Or is he another person altogether? A curious point how certain names are like a certain type of decimals—they keep recurring. (D) Sheila is deliberately shrouded under Daphne’s identity and provided with her suit-case—why? Arrangements are made in _Daphne’s name_—and that luggage is deliberately substituted—again why? (E) Sheila is poisoned at a dentist’s of all places. (F) “Pinkie” and Alan Warburton are agreed that there came a lover into her life. When exactly? Crown Prince? Mr. X? (G) Whose was the mysterious correspondence referred to by “Pinkie” Kerr? Who was the ardent horticulturist that wrote concerning the beauty of the Iris? (H) Who wrote Branston’s address on the back of Alan Warburton’s visiting-card—Sheila herself, Warburton—or another? (I) Why did Sheila want the “Peacock’s Eye” on that particular day? (J) What is Lal Singh to do with the picture? Does he really fit in at all? (K) Colonel Dan drowned—Major Carruthers killed whilst motoring—Mrs. Delaney dead—Sheila murdered—is it just a line of coincidences or a _sequence of intention?_ (L) Why exactly did the murderer, murderess, or murderers return post-haste to Tranfield? What did they want if they _had_ the “Peacock’s Eye”? Anthony twisted the top of his fountain-pen round and round and smiled grimly. It was a smile that boded no good for a very clever criminal. Anthony Bathurst had formed certain conclusions. He added another heading. (M) Did Stark (E. Kingsley Stark) _know Sir Felix Warburton_? He spent another quarter of an hour or so studying his list then folded it carefully and placed it in his pocket. He looked at his watch, obtained his hat and stick from the stand outside the door of the smoke-room and sauntered to the front entrance of the hotel. The porter knew Crossley Road very well. He would assist Mr. Bathurst! Mr. Bathurst should follow the tram-lines, turn round by the “Ram and Raven,” pass the statue to Doctor Harvey, and he would see that Crossley Road was the first turning on the left. Mr. Bathurst accepted the instructions with a charming thankfulness and sallied forth.