He followed the quays right across the town till he came to the Gare du Sud, then turning away from the river, he found himself in the Avenue du Sud. From this he worked back along the line of great avenues which had replaced the earlier fortifications, until eventually, nearly three hours after he had started, he once again turned into the Place Verte, and reached the Carillon. He ordered a room for the night, and some strong tea, after which he sat on in his secluded corner of the comfortable restaurant, and smoked a meditative cigar. His walk had done him good. His brain had cleared, and the weariness of the journey, and the chagrin of his deadlock had vanished. His thoughts returned to his problem, which he began to attack in the new. He puzzled over it for the best part of an hour, without making the slightest progress, and then he began to consider how far the ideas he had already arrived at fitted in with what he had since learned of Dangle’s movements. He had thought that the nature of the articles on Dangle’s list suggested a sea expedition. He remembered the delight with which, many years earlier, he had read _The Riddle of the Sands_, and he thought that had Dangle contemplated just such another cruise as that of the heroes of that fascinating book, he might well have got together the articles in question. But since these ideas had passed through his mind, French had learned the following fresh facts: 1. From a fortnight after obtaining the tracing, Dangle had been paying frequent visits to Antwerp. 2. He had on these occasions put up at the Carillon. 3. His last visit had followed immediately on the failure to murder Cheyne, with its almost certain result of the calling in of Scotland Yard. 4. He had on this last visit remained at the Carillon for two days, leaving about 2:00 P.M. on the Thursday, the previous day. 5. He had carried his hand-bag from the hotel, without calling for a taxi. At first French could not see that these additional facts had any bearing on his theory, but as he continued turning them over in his mind, he realized that all but one might be interpreted as tending in the same direction. 1. Dangle’s visits to Antwerp. Supposing Dangle had been planning some secret marine expedition, where, French asked himself, could he have found a more suitable base from which to make his arrangements? Antwerp was a seaport: moreover, it was a great seaport, large enough for a secret expedition to set sail from without attracting notice. It was a foreign port, away from the inquisitive notice of the British police, but, on the other hand, it was the nearest great port to London. If these considerations did not back up his theory, they at least did not conflict with it.