He turned to what he considered the central feature of the case--the finding of the body in the cask--and began to separate in his mind the facts actually known about it from those assumed. Firstly, the body was in the cask when the latter reached St. Katherine’s Docks. Secondly, it could not have been put in during the journey from the rue Cardinet Goods Station. So much was certain. But the previous step in the cask’s journey was surmise. It was assumed that it had been taken from the Gare du Nord to the rue Cardinet on a horse-cart. On what was this assumption founded? Three facts. First, that it left the Gare du Nord on a horse-cart; second, that it reached the rue Cardinet in the same manner; and third, that such a vehicle would have occupied about the time the trip had actually taken. The assumption seemed reasonable, and yet. . . . He had to remember that they were up against a man of no ordinary ability, whoever he might be. Might not the cask have been taken by the first horse-cart to some adjoining house or shed where the body could have been put in, then sent by motor-lorry to some other shed near the Goods Station and there transferred to a horse-cart again? This undoubtedly seemed far-fetched and unlikely, nevertheless, the facts were not known, and, he thought, they should be. He must find the carter who brought the cask to the Goods Station. Then he would be certain where the body was put in, and therefore whether the murder was committed in London or Paris. He noted a third point. The various letters in the case--and there were several--might or might not be forgeries, and if the former, it was obviously impossible for him to say off-hand who had written them. But there was one letter which could not be a forgery--at least in a certain sense. The Le Gautier letter which Felix said he had received was done on a typewriter which could be identified. It was hardly too much to assume that the man who typed that letter was the murderer. Find the typewriter, thought La Touche, and the chances are it will lead to the guilty man. A further point struck him. If Boirac were guilty, might he not even yet give himself away? The detective recalled case after case in his own experience in which a criminal had, after the crime, done something or gone somewhere that had led to his arrest. Would it be worth while having Boirac shadowed? He considered the question carefully and finally decided to bring over two of his men for this purpose. Here, then, were four directions in which inquiries might be made, of which the first three at least promised a certain and definite result. As the train slackened speed for the capital, he felt his work was cut out for him. And then began a period of tedious and unprofitable work. He was very efficient, very thorough and very pertinacious, but the only result of all his painstaking labours was to establish more firmly than ever the truth of Boirac’s statements.