No time to think of that now; he was fast in the clutches of his theory. It seemed to guide him like some superior being seated at the helm of his intelligence: his private dæmon pitted against the veiled goddess! It was exciting, undoubtedly; considerably more so, for example, than taking tea with the President’s wife at Purewater. He was beginning to feel like Napoleon, disposing his battalions to right and left, advancing, retreating, reinforcing or redistributing his troops. Ah, the veiled goddess was getting what she deserved for once! At a late hour of the evening, when the Professor had become the centre of an ever-thickening crowd of fascinated observers, it suddenly came back to him that a woman had given him that original hundred franc note. A woman in the train that afternoon.... But what did he care for that? He was playing the limit at every stake; and his mind had never worked more clearly and with a more exquisite sense of complete detachment. He was in his own particular seventh heaven of lucidity. He even recalled, at the precise moment when cognizance of the fact became useful, that the doors of _Arcadie_ closed at midnight, and that he had only just time to get back if he wished to sleep with a roof over his head. As he did wish to, he pocketed his gains quietly and composedly, rose from the table and walked out of the rooms. He felt hungry, cheerful and alert. Perhaps, after all, excitement had been what he needed—pleasurable excitement, that is, not the kind occasioned by the small daily irritations of life, such as the presence of that woman in the train whose name he was still unable to remember. What he would have liked best of all would have been to sit down in one of the brightly lit cafés he was passing, before a bottle of beer and a ham sandwich; or perhaps what he had heard spoken of as a Welsh rabbit. But he did not want to sleep on a bench, for the night air was sharp; so he continued self-denyingly on his way to _Arcadie_. A sleepy boy in a dirty apron let him in, locked up after him, and led him to a small bare room on the second floor. The stairs creaked and rattled as they mounted, and the rumblings of sleep sounded through the doors of the rooms they passed. _Arcadie_ was a cramped and ramshackle construction, and the Professor hoped to heaven that his _pension_ in the hills would be more solidly built and less densely inhabited. However, for one night it didn’t matter—or so he imagined. His guide left him, and he turned on the electric light, threw down on the table the notes with which all his pockets were bulging, and began to unstrap his portmanteaux.