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question.

Did these hours work in? On Tuesday, frankly, they did not. What about Wednesday? Could a man who was in London at 11:00 in the morning be in Brussels at 11:00 the same evening? La Touche got his Continental Bradshaw. Here it was. London depart 2:20 p.m.; Brussels arrive 10:25 p.m. That seemed all right. A traveller arriving by that train would reach the Hôtel Maximilian “about 11:00.” Then La Touche remembered that Boirac’s account of how he spent this day had not been substantiated. He had told Lefarge he had gone to his brother’s house at Malines, having forgotten that the latter was in Sweden. No confirmation of that statement was forthcoming. Neither the caretaker nor anyone else had seen the manufacturer. La Touche was not long in coming to the conclusion he had never been there at all. No, he had crossed from London by the 2:20.

Then the detective recalled the telephone. A message had been sent by Boirac from one of the cafés in the old town, asking the hotel clerk to reserve a room. That call had been received about eight o’clock. But at eight o’clock Boirac was not in the old town. He was on his journey from London.

La Touche took up his Bradshaw again. Where would a traveller by the 2:20 p.m. from Charing Cross be at eight o’clock? And then like a flash he understood. The boat arrived at Ostend at 7:30 p.m. and the Brussels train did not leave until 8:40. He had telephoned from Ostend!

So that was it! A simple plan, but how ingenious! And then La Touche remembered that Lefarge had been quite unable to confirm the statement that Boirac had dined at the café in the Boulevard Anspach, or had been present at Les Troyens in the Théâtre de la Monnaie. No. He was on the right track at last.

The Wednesday was now accounted for, but there still remained the terrible difficulty of the Tuesday. What about the café at Charenton?

And then La Touche got another of his inspirations. He had solved the Wednesday telephone trick. Could that on Tuesday be explained in the same way?

He had already noted that a traveller by the train leaving Paris at 12:00 noon and arriving at Victoria at 7:10 could just reach Waterloo Road by 7:30. Thinking again over the point, he suddenly saw the significance of the hour of the call at the carting establishment. It was late. A man wishing to do business there would have gone earlier, had he been able. But this man was not able. He had only reached the city at 7:10.

He turned back to the telephone calls. Where, he asked himself with growing excitement, would a passenger by the 12:00 noon from Paris be at 2:30? And then he was dashed with disappointment. That train did not reach Calais till 3:31 p.m., and at 2:30 it must have been running at full speed somewhere between Abbeville and Boulogne. Boirac could not have telephoned from the train. Therefore he could not have travelled by it.

La Touche had hoped to find that, adopting the same manoeuvre on each day, the manufacturer had telephoned from some station en route, presumably Calais. But that apparently was not so. At the same time, the detective could not but feel he was getting near the truth.

He looked at the time table again. The train in question reached Calais at 3:31 and the boat left at 3:45. That was a delay of 14 minutes. Would there be time, he wondered, to make two long-distance calls in 14 minutes? Hardly, he thought. He considered what he himself would do if confronted with Boirac’s problem.

And then suddenly he saw it. What could be more obvious than to go by an earlier train and to break the journey at Calais? How would this time table work?

Paris dep. 9:50 a.m. Calais arr. 1:11 p.m. Calais dep. 3:45 p.m. Victoria arr. 7:10 p.m.

If Boirac had done that he would have had over two and a half hours in Calais, which would have given him the opportunity he required. La Touche believed he had reached the solution at last.

But Boirac had been actually seen telephoning from Charenton. For a moment the detective’s spirits fell. But he felt he must be right so far. Some explanation of the difficulty would occur to him.

And it did. The waiter had believed Boirac was there on Monday. And he must have been! In some way he must have faked the telephoning. There could be nothing else for it.

Another point occurred to him. Surely, he thought, the telephone operator always mentions the name of the calling town in inter-urban calls? If Boirac had called up his office from Calais, would not the operator have said, “Calais wants you”? If so, how had the manufacturer been able to deceive his butler and chief clerk?

This was undoubtedly a difficulty. But he put it on one side as he began to think how this new theory could be tested.

First he would go again to the Charenton waiter and explain the importance of settling the day on which Boirac lunched. Perhaps the man would now be able to recall some circumstance which would make this clear. Next he would find out from François and Dufresne whether any phrase such as “Calais wants you” had been used by the telephone operator. This inquiry, he noted, must be made with great skill, so as to avoid rousing Boirac’s suspicions should either man repeat the conversation. From the telephone central at Calais, if not at Paris, he could doubtless find if calls were made from the former town to the latter at the hour in question, and he might also find that someone answering to the description of Boirac had made those calls. Finally, it might be possible at Ostend to get information about the Brussels call.

Inquiries on these points should reveal enough to either confirm or disprove his theory.

The next morning therefore saw La Touche again in the café at Charenton in conversation with the waiter.

“The point as to which day the gentleman was here has

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