"Doctor Bryant confirmed the steward's fear that the woman was dead. As to the cause of death, naturally, he could not pronounce on that without a detailed examination.
It was at this point that a suggestion was made - by Mr Jean Dupont - that death was due to shock following on a wasp sting.
In furtherance of this hypothesis, he drew attention to a wasp that he himself had slaughtered shortly before.
"Now, that was a perfectly plausible theory, and one quite likely to be accepted.
There was the mark on the dead woman's neck, closely resembling the mark of a sting, and there was the fact that a wasp had been in the plane.
"But at that moment I was fortunate enough to look down and espy what might at first have been taken for the body of yet another wasp.
In actuality it was a native thorn with a little teased yellow-and-black silk on it.
"At this point Mr Clancy came forward and made the statement that it was a thorn shot from a blowpipe after the manner of some native tribe.
Later, as you all know, the blowpipe itself was discovered.
"By the time we reached Croydon, several ideas were working in my mind.
Once I was definitely on the firm ground, my brain began to work once more with its normal brilliance."
"Go it, M. Poirot," said Japp, with a grin. "Don't have any false modesty."
Poirot threw him a look and went on:
"One idea presented itself very strongly to me - as it did to everyone else - and that was the audacity of a crime being committed in such a manner, and the astonishing fact that nobody noticed its being done!
"There were two other points that interested me.
One was the convenient presence of the wasp.
The other was the discovery of the blowpipe.
As I remarked after the inquest to my friend Japp, why on earth did the murderer not get rid of it by passing it out through the ventilating hole in the window?
The thorn itself might be difficult to trace or identify, but a blowpipe which still retained a portion of its price label was a very different matter.
"What was the solution? Obviously, that the murderer wanted the blowpipe to be found.
"But why?
Only one answer seemed logical.
If a poisoned dart and a blowpipe were found, it would naturally be assumed that the murder had been committed by a thorn shot from a blowpipe.
Therefore, in reality the murder had not been committed that way.
"On the other hand, as medical evidence was to show, the cause of death was undoubtedly the poisoned thorn.
I shut my eyes and asked myself: 'What is the surest and most reliable way of placing a poisoned thorn in the jugular vein?'
And the answer came immediately: 'By hand.'
"And that immediately threw light on the necessity for the finding of the blowpipe.
The blowpipe inevitably conveyed the suggestion of distance.
If my theory was right, the person who killed Madame Giselle was a person who went right up to her table and bent over her.
"Was there such a person?
Yes, there were two people. The two stewards.
Either of them could go up to Madame Giselle, lean toward her, and nobody would notice anything unusual.
"Was there anyone else?
"Well, there was Mr Clancy.
He was the only person in the car who had passed immediately by Madame Giselle's seat - and I remember that it was he who had first drawn attention to the blowpipe-and-thorn theory."
Mr Clancy sprang to his feet.
"I protest!" he cried. "I protest!
This is an outrage!"
"Sit down," said Poirot. "I have not finished yet.
I have to show you all the steps by which I arrived at my conclusion.
"I had now three persons as possible suspects. Mitchell, Davis and Mr Clancy.
None of them at first sight appeared like murderers, but there was much investigation to be done.
"I next turned my mind to the possibilities of the wasp.
It was suggestive, that wasp.
To begin with, no one had noticed it until about the time coffee was served. That in itself was rather curious.
I constructed a certain theory of the crime.
The murderer presented to the world two separate solutions of the tragedy.
On the first or simplest, Madame Giselle was stung by a wasp and had succumbed to heart failure.
The success of that solution depended on whether or not the murderer was in a position to retrieve the thorn.