on the night of his release, halliday slept in the room next to ours at the hotel, and all night long i heard him moaning and protesting in his sleep. undoubtedly his experience in the villa had broken his nerve, and in the morning we failed completely to extract any information from him. he would only repeat his statement about the unlimited power at the disposal of the big four, and his assurance of the vengeance which would follow if he talked.

after lunch he departed to rejoin his wife in england, but poirot and i remained behind in paris. i was all for energetic proceedings of some kind or other, and poirot's quiescence annoyed me.

"for heaven's sake, poirot," i urged, "let us be up and at them."

"admirable, mon ami, admirable! up where, and at whom? be precise, i beg of you."

"at the big four, of course."

"cela va sans dire. but how would you set about it?"

"the police," i hazarded doubtfully.

poirot smiled.

"they would accuse us of romancing. we have nothing to go upon—nothing whatever. we must wait."

"wait for what?"

"wait for them to make a move. see now, in england you all comprehend and adore la boxe. if one man does not make a move, the other must, and by permitting the adversary to make the attack one learns something about him. that is our part—to let the other side make the attack."

"you think they will?" i said doubtfully.

"i have no doubt whatever of it. to begin with, see, they try to get me out of england. that fails. then, in the dartmoor affair, we step in and save their victim from the gallows. and yesterday, once again, we interfere with their plans. assuredly, they will not leave the matter there."

as i reflected on this, there was a knock on the door. without waiting for a reply, a man stepped into the room and closed the door behind him. he was a tall, thin man, with a slightly hooked nose and a sallow complexion. he wore an overcoat buttoned up to his chin, and a soft hat well pulled down over his eyes.

"excuse me, gentlemen, for my somewhat unceremonious entry," he said in a soft voice, "but my business is of a rather unorthodox nature."

smiling, he advanced to the table and sat down by it. i was about to spring up, but poirot restrained me with a gesture.

"as you say, monsieur, your entry is somewhat unceremonious. will you kindly state your business?"

"my dear m. poirot, it is very simple. you have been annoying my friends."

"in what way?"

"come, come, monsieur poirot. you do not seriously ask me that? you know as well as i do."

"it depends, monsieur, upon who these friends of yours are."

without a word, the man drew from his pocket a cigarette case, and, opening it, took out four cigarettes and tossed them on the table. then he picked them up and returned them to his case, which he replaced in his pocket.

"aha!" said poirot, "so it is like that, is it? and what do your friends suggest?"

"they suggest, monsieur, that you should employ your talents—your very considerable talents—in the detection of legitimate crime—return to your former avocations, and solve the problems of london society ladies."

"a peaceful programme," said poirot. "and supposing i do not agree?"

the man made an eloquent gesture.

"we should regret it, of course, exceedingly," he said. "so would all the friends and admirers of the great m. hercule poirot. but regrets, however poignant, do not bring a man to life again."

"put very delicately," said poirot, nodding his head. "and supposing i—accept?"

"in that case i am empowered to offer you—compensation."

he drew out a pocket-book, and threw ten notes on the table. they were for ten thousand francs each.

"that is merely as a guarantee of our good faith," he said. "ten times that amount will be paid you."

"good god," i cried, springing up, "you dare to think—!"

"sit down, hastings," said poirot autocratically. "subdue your so beautiful and honest nature and sit down. to you, monsieur, i will say this. what is to prevent me ringing up the police and giving you into their custody, whilst my friend here prevents you from escaping?"

"by all means do so if you think it advisable," said our visitor calmly.

"oh! look here, poirot," i cried. "i can't stand this. ring up the police and have done with it."

rising swiftly, i strode to the door and stood with my back against it.

"it seems the obvious course," murmured poirot, as though debating with himself.

"but you distrust the obvious, eh?" said our visitor, smiling.

"go on, poirot," i urged.

"it will be your responsibility, mon ami."

as he lifted the receiver, the man made a sudden, cat-like jump at me. i was ready for him. in another minute we were locked together, staggering round the room. suddenly i felt him slip and falter. i pressed my advantage. he went down before me. and then, in the very flush of victory, an extraordinary thing happened. i felt myself flying forwards. head first, i crashed into the wall in a complicated heap. i was up in a minute, but the door was already closing behind my late adversary. i rushed to it and shook it, it was locked on the outside. i seized the telephone from poirot.

"is that the bureau? stop a man who is coming out. a tall man, with a buttoned-up overcoat and a soft hat. he is wanted by the police."

very few minutes elapsed before we heard a noise in the corridor outside. the key was turned and the door flung open. the manager himself stood in the doorway.

"the man—you have got him?" i cried.

"no, monsieur. no one has descended."

"you must have passed him."

"we have passed no one, monsieur. it is incredible that he can have escaped."

"you have passed some one, i think," said poirot, in his gentle voice. "one of the hotel staff, perhaps?"

"only a waiter carrying a tray, monsieur."

"ah!" said poirot, in a tone that spoke infinities.

"so that was why he wore his overcoat buttoned up to his chin," mused poirot, when we had finally got rid of the excited hotel officials.

"i'm awfully sorry, poirot," i murmured, rather crestfallen. "i thought i'd downed him all right."

"yes, that was a japanese trick, i fancy. do not distress yourself, mon ami. all went according to plan—his plan. that is what i wanted."

"what's this?" i cried, pouncing on a brown object that lay on the floor.

it was a slim pocket-book of brown leather, and had evidently fallen from our visitor's pocket during his struggle with me. it contained two receipted bills in the name of m. felix laon, and a folded-up piece of paper which made my heart beat faster. it was a half sheet of note-paper on which a few words were scrawled in pencil but they were words of supreme importance.

"the next meeting of the council will be on friday at 34 rue des echelles at 11 a.m."

it was signed with a big figure 4.

and to-day was friday, and the clock on the mantelpiece showed the hour to be 10:30.

"my god, what a chance!" i cried. "fate is playing into our hands. we must start at once—though. what stupendous luck."

"so that was why he came," murmured poirot. "i see it all now."

"see what? come on, poirot, don't stay daydreaming there."

poirot looked at me, and slowly shook his head, smiling as he did so.

"'will you walk into my parlour, said the spider to the fly?' that is your little english nursery rhyme, is it not? no, no—they are subtle—but not so subtle as hercule poirot."

"what on earth are you driving at, poirot?"

"my friend, i have been asking myself the reason of this morning's visit. did our visitor really hope to succeed in bribing me? or, alternatively, in frightening me into abandoning my task? it seemed hardly credible. why, then, did he come? and now i see the whole plan—very neat—very pretty—the ostensible reason to bribe or frighten me—the necessary struggle which he took no pains to avoid, and which should make the dropped pocket-book natural and reasonable—and finally—the pitfall! rue des echelles, 11 a.m.? i think not, mon ami! one does not catch hercule poirot as easily as that."

"good heavens," i gasped.

poirot was frowning to himself.

"there is still one thing i do not understand."

"what is that?"

"the time, hastings—the time. if they wanted to decoy me away, surely night time would be better? why this early hour? is it possible that something is about to happen this morning? something which they are anxious hercule poirot should not know about?"

he shook his head.

"we shall see. here i sit, mon ami. we do not stir out this morning. we await events here."

it was at half-past eleven exactly that the summons came. a petit bleu. poirot tore it open, then handed it to me. it was from madame olivier, the world-famous scientist, whom we had visited yesterday in connection with the halliday case. it asked us to come out to passy at once.

we obeyed the summons without an instant's delay. madame olivier received us in the same small salon. i was struck anew with the wonderful power of this woman, with her long nun's face and burning eyes—this brilliant successor of becquerel and the curies. she came to the point at once.

"messieurs, you interviewed me yesterday about the disappearance of m. halliday. i now learn that you returned to the house a second time, and asked to see my secretary, inez veroneau. she left the house with you, and has not returned here since."

"is that all, madame?"

"no, monsieur, it is not. last night the laboratory was broken into, and several valuable papers and memoranda were stolen. the thieves had a try for something more precious still, but luckily they failed to open the big safe."

"madame, these are the facts of the case. your late secretary, madame veroneau, was really the countess rossakoff, an expert thief, and it was she who was responsible for the disappearance of m. halliday. how long had she been with you?"

"five months, monsieur. what you say amazes me."

"it is true, nevertheless. these papers, were they easy to find? or do you think an inside knowledge was shown?"

"it is rather curious that the thieves knew exactly where to look. you think inez—"

"yes, i have no doubt that it was upon her information that they acted. but what is this precious thing that the thieves failed to find? jewels?"

madame olivier shook her head with a faint smile.

"something much more precious than that, monsieur." she looked round her, then bent forward, lowering her voice. "radium, monsieur."

"radium?"

"yes, monsieur. i am now at the crux of my experiments. i possess a small portion of radium myself—more has been lent to me for the process i am at work upon. small though the actual quantity is, it comprises a large amount of the world's stock and represents a value of millions of francs."

"and where is it?"

"in its leaden case in the big safe—the safe purposely appears to be of an old and worn-out pattern, but it is really a triumph of the safe-maker's art. that is probably why the thieves were unable to open it."

"how long are you keeping this radium in your possession?"

"only for two days more, monsieur. then my experiments will be concluded."

poirot's eyes brightened.

"and inez veroneau is aware of the fact? good—then our friends will come back. not a word of me to any one, madame. but rest assured, i will save your radium for you. you have a key of the door leading from the laboratory to the garden?"

"yes, monsieur. here it is. i have a duplicate for myself. and here is the key of the garden door leading out into the alleyway between this villa and the next one."

"i thank you, madame. to-night, go to bed as usual, have no fears, and leave all to me. but not a word to any one—not to your two assistants—mademoiselle claude and monsieur henri, is it not?—particularly not a word to them."

poirot left the villa rubbing his hands in great satisfaction.

"what are we going to do now?" i asked.

"now, hastings, we are about to leave paris—for england."

"what?"

"we will pack our effects, have lunch, and drive to the gare du nord."

"but the radium?"

"i said we were going to leave for england—i did not say we were going to arrive there. reflect a moment, hastings. it is quite certain that we are being watched and followed. our enemies must believe that we are going back to england, and they certainly will not believe that unless they see us get on board the train and start."

"do you mean we are to slip off again at the last minute?"

"no, hastings. our enemies will be satisfied with nothing less than a bona fide departure."

"but the train doesn't stop until calais?"

"it will stop if it is paid to do so."

"oh, come now, poirot—surely you can't pay an express to stop—they'd refuse."

"my dear friend, have you never remarked the little handle—the signal d'arrêt—penalty for improper use, 100 francs, i think?"

"oh! you are going to pull that?"

"or rather a friend of mine, pierre combeau, will do so. then, while he is arguing with the guard, and making a big scene, and all the train is agog with interest, you and i will fade quietly away."

we duly carried out poirot's plan. pierre combeau, an old crony of poirot's, and who evidently knew my little friend's methods pretty well, fell in with the arrangements. the communication cord was pulled just as we got to the outskirts of paris. combeau "made a scene" in the most approved french fashion and poirot and i were able to leave the train without any one being interested in our departure. our first proceeding was to make a considerable change in our appearance. poirot had brought the materials for this with him in a small case. two loafers in dirty blue blouses were the result. we had dinner in an obscure hostelry, and started back to paris afterwards.

it was close on eleven o'clock when we found ourselves once more in the neighbourhood of madame olivier's villa. we looked up and down the road before slipping into the alleyway. the whole place appeared to be perfectly deserted. one thing we could be quite certain of, no one was following us.

"i do not expect them to be here yet," whispered poirot to me. "possibly they may not come until to-morrow night, but they know perfectly well that there are only two nights on which the radium will be there."

very cautiously we turned the key in the garden door. it opened noiselessly and we stepped into the garden.

and then, with complete unexpectedness, the blow fell. in a minute we were surrounded, gagged and bound. at least ten men must have been waiting for us. resistance was useless. like two helpless bundles we were lifted up and carried along. to my intense astonishment, they took us towards the house and not away from it. with a key they opened the door into the laboratory and carried us into it. one of the men stooped down before the big safe. the door of it swung open. i felt an unpleasant sensation down my spine. were they going to bundle us into it, and leave us there to asphyxiate slowly?

however, to my amazement, i saw that from the inside of the safe steps led down beneath the floor. we were thrust down this narrow way and eventually came out into a big subterranean chamber. a woman stood there, tall and imposing, with a black velvet mask covering her face. she was clearly in command of the situation by her gestures of authority. the men slung us down on the floor and left us—alone with the mysterious creature in the mask. i had no doubt who she was. this was the unknown frenchwoman—number three of the big four.

she knelt down beside us and removed the gags, but left us bound, then rising and facing us, with a sudden swift gesture she removed her mask.

it was madame olivier!

"m. poirot," she said, in a low mocking tone. "the great, the wonderful, the unique m. poirot. i sent a warning to you yesterday morning. you chose to disregard it—you thought you could pit your wits against us. and now, you are here!"

there was a cold malignity about her that froze me to the marrow. it was so at variance with the burning fire of her eyes. she was mad—mad—with the madness of genius!

poirot said nothing. his jaw had dropped, and he was staring at her.

"well," she said softly, "this is the end. we cannot permit our plans to be interfered with. have you any last request to make?"

never before, or since, have i felt so near death. poirot was magnificent. he neither flinched nor paled, just stared at her with unabated interest.

"your psychology interests me enormously, madame," he said quietly. "it is a pity that i have so short a time to devote to studying it. yes, i have a request to make. a condemned man is always allowed a last smoke, i believe. i have my cigarette case on me. if you would permit—" he looked down at his bonds.

"ah, yes!" she laughed. "you would like me to untie your hands, would you not? you are clever, m. hercule poirot, i know that. i shall not untie your hands—but i will find you a cigarette."

she knelt down by him, extracted his cigarette case, took out a cigarette, and placed it between his lips.

"and now a match," she said, rising.

"it is not necessary, madame." something in his voice startled me. she, too, was arrested.

"do not move, i pray of you, madame. you will regret it if you do. are you acquainted at all with the properties of cuare? the south american indians use it as an arrow poison. a scratch with it means death. some tribes use a little blow-pipe—i, too, have a little blow-pipe constructed so as to look exactly like a cigarette. i have only to blow.... ah! you start. do not move, madame. the mechanism of this cigarette is most ingenious. one blows—and a tiny dart resembling a fishbone flies through the air—to find its mark. you do not wish to die, madame. therefore, i beg of you, release my friend hastings from his bonds. i cannot use my hands, but i can turn my head—so—you are still covered, madame. make no mistake, i beg of you."

slowly, with shaking hands, and rage and hate convulsing her face, she bent down and did his bidding. i was free. poirot's voice gave me instructions.

"your bonds will now do for the lady, hastings. that is right. is she securely fastened? then release me, i pray of you. it is a fortunate circumstance she sent away her henchmen. with a little luck we may hope to find the way out unobstructed."

in another minute, poirot stood by my side. he bowed to the lady.

"hercule poirot is not killed so easily, madame. i wish you good-night."

the gag prevented her from replying, but the murderous gleam in her eyes frightened me. i hoped devoutly that we should never fall into her power again.

three minutes later we were outside the villa, and hurriedly traversing the garden. the road outside was deserted, and we were soon clear of the neighbourhood.

then poirot broke out.

"i deserve all that that woman said to me. i am a triple imbecile, a miserable animal, thirty-six times an idiot. i was proud of myself for not falling into their trap. and it was not even meant as a trap—except exactly in the way in which i fell into it. they knew i would see through it—they counted on my seeing through it. this explains all—the ease with which they surrendered halliday—everything. madame olivier was the ruling spirit—-vera rossakoff only her lieutenant. madame needed halliday's ideas—she herself had the necessary genius to supply the gaps that perplexed him. yes, hastings, we know now who number three is—the woman who is probably the greatest scientist in the world! think of it. the brain of the east, the science of the west—and two others whose identities we do not yet know. but we must find out. to-morrow we will return to london and set about it."

"you are not going to denounce madame olivier to the police?"

"i should not be believed. that woman is one of the idols of france. and we can prove nothing. we are lucky if she does not denounce us."

"what?"

"think of it. we are found at night upon the premises with keys in our possession which she will swear she never gave us. she surprises us at the safe, and we gag and bind her and make away. have no illusions, hastings. the boot is not upon the right leg—is that how you say it?"