The last four syllables rang pitilessly in his ear and to the depth of his heart. He had just lost, never, never again to recover it, complete trust in that gentle voice, in these beloved eyes. There are no such things as petty insincerities; a person who has once deceived may always deceive. The perception of this natural law, the same perception which had prevented Armand from believing in Helen, was torturing Alfred at this moment. Liar! Liar! When he came to the utterance of this word, he gave forth an outbreaking of grief as he paced to and fro about his study, to which, as often of an evening, he had withdrawn. On one of the walls was displayed a long blackboard, covered with a medley of algebraical formulæ. Between the two windows stood a white wooden table constructed so as to facilitate writing in a standing position. Another low table, intended for correspondence; a bookcase filled with tall mathematical volumes; engraved likenesses of Lagrange, Fresnel, Cauchy, and Laplace; a leathern divan, and a carpet, completed the furniture of a room, the abstract, peaceful aspect of which presented a strange contrast to the disturbed countenance of the man who was walking about in it at that moment; and the contrast symbolised only too well the drama that was being enacted in the existence of a man born for study, for prolonged and painful thought, for happy labour, and constrained to action by the sudden revelation with which he had just been visited. Yes, the necessity for action was present and inevitable. To rest at the suspicion which was tormenting him at that moment was what he could not do--neither morally, without losing self-respect, nor physically, for the pain of it was too great. As he raised his head with a gesture of despair, his eyes encountered the board; he perceived the signs of his calculations traced in chalk with that absolute equality of lettering, that absence of thick and thin strokes, which imparted an appearance of incomparable lucidity to his writing. The sudden sight of this changed the current of his grief. "Let us reason out the thing," he said aloud, and involuntarily he recovered for subservience to his passion all the methodical habits contracted by his intellect. "Yes," he went on, "let us reason it out." He sat down beside his fire in an easy-chair, and, with his forehead resting upon his hands, gathered together all his thoughts, which were not long in shaping themselves to the following dilemma: