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while Alfred Inglethorp and Miss Howard were in custody。 Now at last； I had Poirot to myself； and could relieve my still burning curiosity。
Poirot did not answer me for a moment； but at last he said：
‘‘I did not deceive you； mon ami。 At most； I permitted you to deceive yourself。''
‘‘Yes； but why？''
‘‘Well； it is difficult to explain。 You see； my friend； you have a nature so honest； and a countenance so transparent； that enfin； to conceal your feelings is impossible！ If I had told you my ideas； the very first time you saw Mr。 Alfred Inglethorp that astute gentleman would have in your so expressive idiom ‘smelt a rat'！ And then； bon jour to our chances of catching him！''
‘‘I think that I have more diplomacy than you give me credit for。''
‘‘My friend；'' besought Poirot； ‘‘I implore you； do not enrage yourself！ Your help has been of the most invaluable。 It is but the extremely beautiful nature that you have； which made me pause。''
‘‘Well；'' I grumbled； a little mollified。 ‘‘I still think you might have given me a hint。''
‘‘But I did； my friend。 Several hints。 You would not take them。 Think now； did I ever say to you that I believed John Cavendish guilty？ Did I not； on the contrary； tell you that he would almost certainly be acquitted？''
‘‘Yes； but ''
‘‘And did I not immediately afterwards speak of the difficulty of bringing the murderer to justice？ Was it not plain to you that I was speaking of two entirely different persons？''
‘‘No；'' I said； ‘‘it was not plain to me！''
‘‘Then again；'' continued Poirot； ‘‘at the beginning； did I not repeat to you several times that I didn't want Mr。 Inglethorp arrested now？ That should have conveyed something to you。''
‘‘Do you mean to say you suspected him as long ago as that？''
‘‘Yes。 To begin with； whoever else might benefit by Mrs。 Inglethorp's death； her husband would benefit the most。 There was no getting away from that。 When I went up to Styles with you that first day； I had no idea as to how the crime had been mitted； but from what I knew of Mr。 Inglethorp I fancied that it would be very hard to find anything to connect him with it。 When I arrived at the chateau； I realized at once that it was Mrs。 Inglethorp who had burnt the will； and there； by the way； you cannot plain； my friend； for I tried my best to force on you the significance of that bedroom fire in midsummer。''
‘‘Yes； yes；'' I said impatiently。 ‘‘Go on。''
‘‘Well； my friend； as I say； my views as to Mr。 Inglethorp's guilt were very much shaken。 There was； in fact； so much evidence against him that I was inclined to believe that he had not done it。''
‘‘When did you change your mind？''
‘‘When I found that the more efforts I made to clear him； the more efforts he made to get himself arrested。 Then； when I discovered that Inglethorp had nothing to do with Mrs。 Raikes and that in fact it was John Cavendish who was interested in that quarter； I was quite sure。''
‘‘But why？''
‘‘Simply this。 If it had been Inglethorp who was carrying on an intrigue with Mrs。 Raikes； his silence was perfectly prehensible。 But； when I discovered that it was known all over the village that it was John who was attracted by the farmer's pretty wife； his silence bore quite a different interpretation。 It was nonsense to pretend that he was afraid of the scandal； as no possible scandal could attach to him。 This attitude of his gave me furiously to think； and I was slowly forced to the conclusion that Alfred Inglethorp wanted to be arrested。 Eh bien！ from that moment； I was equally determined that he should not be arrested。''
‘‘Wait a minute。 I don't see why he wished to be arrested？''
‘‘Because； mon ami； it is the law of your country that a man once acquitted can never be tried again for the same offence。 Aha！ but it was clever his idea！ Assuredly； he is a man of method。 See here； he knew that in his position he was bound to be suspected； so he conceived the exceedingly clever idea of preparing a lot of manufactured evidence against himself。 He wished to be arrested。 He would then produce his irreproachable alibi and； hey presto； he was safe for life！''
‘‘But I still don't see how he managed to prove his alibi； and yet go to the chemist's shop？''
Poirot stared at me in surprise。
‘‘Is it possible？ My poor friend！ You have not yet realized that it was Miss Howard who went to the chemist's shop？''
‘‘Miss Howard？''
‘‘But； certainly。 Who else？ It was most easy for her。 She is of a good height； her voice is deep and manly； moreover； remember； she and Inglethorp are cousins； and there is a distinct resemblance between them； especially in their gait and bearing。 It was simplicity itself。 They are a clever pair！''
‘‘I am still a little fogged as to how exactly the bromide business was done；'' I remarked。
‘‘Bon！ I will reconstruct for you as far as possible。 I am inclined to think that Miss Howard was the master mind in that affair。 You remember her once mentioning that her father was a doctor？ Possibly she dispensed his medicines for him； or she may have taken the idea from one of the many books lying about when Mademoiselle Cynthia was studying for her exam。 Anyway； she was familiar with the fact that the addition of a bromide to a mixture containing strychnine would cause the precipitation of the latter。 Probably the idea came to her quite suddenly。 Mrs。 Inglethorp had a box of bromide powders； which she occasionally took at night。 What could be easier than quietly to dissolve one or more of those powders in Mrs。 Inglethorp's large sized bottle of medicine when it came from Coot's？ The risk is practically nil。 The tragedy will not take place until nearly a fortnight later。 If anyone has seen either of them touching the medicine； they will have forgotten it by that time。 Miss Howard will have engineered her quarrel； and departed from the house。 The lapse of time； and her absence； will defeat all suspicion。 Yes； it was a clever idea！ If they had left it alone； it is possible the crime might never have been brought home to them。 But they were not satisfied。 They tried to be too clever and that was their undoing。''
Poirot puffed at his tiny cigarette； his eyes fixed on the ceiling。
‘‘They arranged a plan to throw suspicion on John Cavendish； by buying strychnine at the village chemist's； and signing the register in his hand…writing。
‘‘On Monday Mrs。 Inglethorp will take the last dose of her medicine。 On Monday； therefore； at six o'clock； Alfred Inglethorp arranges to be seen by a number of people at a spot far removed from the village。 Miss Howard has previously made up a cock and bull story about him and Mrs。 Raikes to account for his holding his tongue afterwards。 At six o'clock； Miss Howard； disguised as Alfred Inglethorp； enters the chemist's shop； with her story about a dog； obtains the strychnine； and writes the name of Alfred Inglethorp in John's handwriting； which she had previously studied carefully。
‘‘But； as it will never do if John； too； can prove an alibi； she writes him an anonymous note still copying his hand…writing which takes him to a remote spot where it is exceedingly unlikely that anyone will see him。
‘‘So far；