The sick man closed the book, and with assumed modesty, he asked:  “Ah, well!  What do you think of my little method of induction?”

But Lecoq was too much engrossed with his own thoughts to reply to this question.  “I think,” he remarked, “that if the Duc de Sairmeuse had disappeared for two months—­the period of May’s imprisonment, all Paris would have known of it—­and so—­”

“You are dreaming,” interrupted Tabaret.  “Why with his wife and his valet de chambre for accomplices, the duke could absent himself for a year if he liked, and yet all his servants would believe him to be in the house.”

“I admit that,” said Lecoq, at last; “but unfortunately, there is one circumstance which completely upsets the theory we have built up so laboriously.”

“And what is that if you please?”

“If the man who took part in the broil at the Poivriere had been the Duc de Sairmeuse, he would have disclosed his name—­he would have declared that, having been attacked, he had only defended himself—­and his name alone would have opened the prison doors.  Instead of that, what did the prisoner do?  He attempted to kill himself.  Would a grand seigneur, like the Duc de Sairmeuse, to whom life must be a perpetual enchantment, have thought of committing suicide?”

A mocking whistle from the old Tabaret interrupted the speaker.  “You seem to have forgotten the last sentence in his biography:  ’M.  Sairmeuse leaves behind him ill-will and hatred.’  Do you know the price he might have been compelled to pay for his liberty!  No—­no more do I. To explain his presence at the Poivriere, and the presence of a woman, who was perhaps his wife, who knows what disgraceful secrets he would have been obliged to reveal?  Between shame and suicide, he chose suicide.  He wished to save his name and honor intact.”

Old Tirauclair spoke with such vehemence that even Father Absinthe was deeply impressed, although, to tell the truth, he had understood but little of the conversation.

As for Lecoq, he rose very pale, his lips trembling a little.  “You will excuse my hypocrisy, Monsieur Tabaret,” he said in an agitated voice.  “I only offered these last objections for form’s sake.  I had thought of what you now say, but I distrusted myself, and I wanted to hear you say it yourself.”  Then with an imperious gesture, he added:  “Now, I know what I have to do.”

Old Tabaret raised his hands toward heaven with every sign of intense dismay.  “Unhappy man!” he exclaimed; “do you think of going to arrest the Duc de Sairmeuse!  Poor Lecoq!  Free, this man is almost omnipotent, and you, an infinitesimal agent of police, would be shattered as easily as glass.  Take care, my boy, don’t attack the duke.  I wouldn’t be responsible for the consequences.  You might imperil your life.”

The young detective shook his head.  “Oh!  I don’t deceive myself,” said he.  “I know that the duke is far beyond my reach—­at least for the present.  But he will be in my power again, the day I learn his secret.  I don’t fear danger; but I know, that if I am to succeed, I must conceal myself, and so I will.  Yes, I will remain in the shade until I can unveil this mystery; but then I shall reappear in my true character.  And if May be really the Duc de Sairmeuse, I shall have my revenge.”