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On the Thursday, Rénine did not stir out of doors. In the afternoon, he received several letters in reply to his advertisement. Then two telegrams arrived. Lastly, at three o’clock, there came a pneumatic letter, bearing the Trocadéro postmark, which seemed to be what he was expecting.

He turned up a directory, noted an address — “M. de Lourtier-Vaneau, retired colonial governor, 47 bis, Avenue Kleber” — and ran down to his car:

“Adolphe, 47 bis, Avenue Kleber.”

He was shown into a large study furnished with magnificent bookcases containing old volumes in costly bindings. M. de Lourtier-Vaneau was a man still in the prime of life, wearing a slightly grizzled beard and, by his affable manners and genuine distinction, commanding confidence and liking.

“M. de Lourtier,” said Rénine, “I have ventured to call on your excellency because I read in last year’s newspapers that you used to know one of the victims of the lady with the hatchet, Honorine Vernisset.”

“Why, of course we knew her!” cried M. de Lourtier. “My wife used to employ her as a dressmaker by the day. Poor girl!”

“M. de Lourtier, a lady of my acquaintance has disappeared as the other six victims disappeared.”

“What!” exclaimed M. de Lourtier, with a start. “But I have followed the newspapers carefully. There was nothing on the 18th of October.”

“Yes, a woman of whom I am very fond, Madame Hortense Daniel, was abducted on the 17th of October.”

“And this is the 22nd!”

“Yes; and the murder will be committed on the 24th.”

“Horrible! Horrible! It must be prevented at all costs...”

“And I shall perhaps succeed in preventing it, with your excellency’s assistance.”

“But have you been to the police?”

“No. We are faced by mysteries which are, so to speak, absolute and compact, which offer no gap through which the keenest eyes can see and which it is useless to hope to clear up by ordinary methods, such as inspection of the scenes of the crimes, police enquiries, searching for fingerprints and so on. As none of those proceedings served any good purpose in the previous cases, it would be waste of time to resort to them in a seventh, similar case. An enemy who displays such skill and subtlety would not leave behind her any of those clumsy traces which are the first things that a professional detective seizes upon.”

“Then what have you done?”

“Before taking any action, I have reflected. I gave four days to thinking the matter over.”

M. de Lourtier-Vaneau examined his visitor closely and, with a touch of irony, asked:

“And the result of your meditations...?”

“To begin with,” said Rénine, refusing to be put out of countenance, “I have submitted all these cases to a comprehensive survey, which hitherto no one else had done. This enabled me to discover their general meaning, to put aside all the tangle of embarrassing theories and, since no one was able to agree as to the motives of all this filthy business, to attribute it to the only class of persons capable of it.”

“That is to say?”

“Lunatics, your excellency.”

M. de Lourtier-Vaneau started:

“Lunatics? What an idea!”

“M. de Lourtier, the woman known as the lady with the hatchet is a madwoman.”

“But she would be locked up!”

“We don’t know that she’s not. We don’t know that she is not one of those half-mad people, apparently harmless, who are watched so slightly that they have full scope to indulge their little manias, their wild-beast instincts. Nothing could be more treacherous than these creatures. Nothing could be more crafty, more patient, more persistent, more dangerous and at the same time more absurd and more logical, more slovenly and more methodical. All these epithets, M. de Lourtier, may be applied to the doings of the lady with the hatchet. The obsession of an idea and the continual repetition of an act are characteristics of the maniac. I do not yet know the idea by which the lady with the hatchet is obsessed but I do know the act that results from it; and it is always the same. The victim is bound with precisely similar ropes. She is killed after the same number of days. She is struck by an identical blow, with the same instrument, in the same place, the middle of the forehead, producing an absolutely vertical wound. An ordinary murderer displays some variety. His trembling hand swerves aside and strikes awry. The lady with the hatchet does not tremble. It is as though she had taken measurements; and the edge of her weapon does not swerve by a hair’s breadth. Need I give you any further proofs or examine all the other details with you? Surely not. You now possess the key to the riddle; and you know as I do that only a lunatic can behave in this way, stupidly, savagely, mechanically, like a striking clock or the blade of the guillotine...”

M. de Lourtier-Vaneau nodded his head:

“Yes, that is so. One can see the whole affair from that angle... and I am beginning to believe that this is how one ought to see it. But, if we admit that this madwoman has the sort of mathematical logic which governed the murders of the six victims, I see no connection between the victims themselves. She struck at random. Why this victim rather than that?”

“Ah,” said Rénine. “Your excellency is asking me a question which I asked myself from the first moment, the question which sums up the whole problem and which cost me so much trouble to solve! Why Hortense Daniel rather than another? Among two millions of women who might have been selected, why Hortense? Why little Vernisset? Why Miss Williamson? If the affair is such as I conceived it, as a whole, that is to say, based upon the blind and fantastic logic of a madwoman, a choice was inevitably exercised. Now in what did that choice consist? What was the quality, or the defect, or the sign needed to induce the lady with the hatchet to strike? In a word, if she chose — and she must have chosen — what directed her choice?”

“Have you found the answer?”

Rénine paused and replied:

“Yes, your excellency, I have. And I could have found it at the very outset, since all that I had to do was to make a careful examination of the list of victims. But these flashes of truth are never kindled save in a brain overstimulated by effort and reflection. I stared at the list twenty times over, before that little detail took a definite shape.”

“I don’t follow you,” said M. de Lourtier-Vaneau.

“M. de Lourtier, it may be noted that, if a number of persons are brought together in any transaction, or crime, or public scandal or what not, they are almost invariably described in the same way. On this occasion, the newspapers never mentioned anything more than their surnames in speaking of Madame Ladoue, Mlle. Ardant or Mlle. Covereau. On the other hand, Mile. Vernisset and Miss Williamson were always described by their Christian names as welclass="underline" Honorine and Hermione. If the same thing had been done in the case of all the six victims, there would have been no mystery.”

“Why not?”

“Because we should at once have realized the relation existing between the six unfortunate women, as I myself suddenly realized it on comparing those two Christian names with that of Hortense Daniel. You understand now, don’t you? You see the three Christian names before your eyes...”

M. de Lourtier-Vaneau seemed to be perturbed. Turning a little pale, he said:

“What do you mean? What do you mean?”

“I mean,” continued Rénine, in a clear voice, sounding each syllable separately, “I mean that you see before your eyes three Christian names which all three begin with the same initial and which all three, by a remarkable coincidence, consist of the same number of letters, as you may prove. If you enquire at the Courbevoie laundry, where Mile. Covereau used to work, you will find that her name was Hilairie. Here again we have the same initial and the same number of letters. There is no need to seek any farther. We are sure, are we not, that the Christian names of all the victims offer the same peculiarities? And this gives us, with absolute certainty, the key to the problem which was set us. It explains the madwoman’s choice. We now know the connection between the unfortunate victims. There can be no mistake about it. It’s that and nothing else. And how this method of choosing confirms my theory! What proof of madness! Why kill these women rather than any others? Because their names begin with an H and consist of eight letters! You understand me, M. de Lourtier, do you not? The number of letters is eight. The initial letter is the eighth letter of the alphabet; and the word huit, eight, begins with an H. Always the letter H. And the impletnent used to commit the crime was a hatchet. Is your excellency prepared to tell me that the lady with the hatchet is not a madwoman?”