To clear his brain he determined to banish all thoughts of the case for the remainder of the day. He therefore went for a stroll along the boulevards, and, after a leisurely dinner, turned his steps towards the Folies Bergères, and there passed the evening. On his way home it occurred to him that while waiting to interview M. Dufresne at the office of the Pump Construction Company he might run over to Brussels and satisfy himself as to that part of Boirac’s alibi. Accordingly, next morning saw him entrained for the Belgian capital, where he arrived about midday. He drove to the Hôtel Maximilian, lunched, and afterward made exhaustive inquiries at the office. Here he saw copies of the visitors’ returns which every Belgian hotel must furnish to the police, and satisfied himself absolutely that Boirac had been there on the date in question. As a result of Lefarge’s inquiries the clerk recollected the circumstances of the pump manufacturer’s telephone, and adhered to his previous statement in every particular. La Touche took the afternoon train for Paris considerably disappointed with the results of his journey. On the chance that the chief clerk might be back at work, he returned next day to the pump works. Again he watched till Boirac had left and again entered and asked for M. Dufresne. The same prompt clerk came forward to speak to him, and, saying that M. Dufresne had returned that morning, once more asked him to be seated while he took in his card. La Touche then suddenly remembered the girl he had so much admired, but whose existence he had forgotten since his last visit. He glanced across the room. She was there, but he could not see her face. Something had evidently gone wrong with the splendid-looking machine which she--La Touche whimsically wondered why you did not say ‘played’ or ‘drove’--and she was bending over it, apparently adjusting some screw. But he had no time to pursue his studies of female beauty. The prompt clerk was back at his side almost immediately to say that M. Dufresne could see him. He accordingly followed his guide to the chief clerk’s room. M. Dufresne was quite as ready to assist him as had been his other informants, but he could tell him nothing the detective did not already know. He repeated his statement to Lefarge almost word for word. He was sure M. Boirac had telephoned about 2.30 on the Tuesday--he unmistakably recognised his voice, and he was equally certain of the date.