Definition of Allusion
In Chapter 4, Poirot chastises Linnet for taking Simon from Jackie. He alludes to a biblical story to illustrate how he understands Linnet's actions.
You have heard of King David and of the rich man who had many flocks and herds and the poor man who had one ewe lamb—and of how the rich man took the poor man’s one ewe lamb. That was something that happened, Madame.
In Chapter 11, Poirot runs into his old acquaintance Colonel Race on the steamer. This chance meeting allows Christie to allude to another Poirot novel, Cards on the Table, which was published in 1936:
Unlock with LitCharts A+Hercule Poirot had come across Colonel Race a year previously in London. They had been fellow guests at a very strange dinner party—a dinner party that had ended in death for that strange man, their host.
In Chapter 22, Poirot alludes to another Christie novel, Murder on the Orient Express:
Unlock with LitCharts A+Once, on the Orient Express, I investigated a murder. There was a little matter of a scarlet kimono. It had disappeared, and yet it must be on the train. I found it—where do you think? In my own locked suitcase! Ah! It was an impertinence, that!
In Chapter 28, Colonel Race complains to Poirot that the famous detective is "beating around the bush" by solving the mystery of the missing pearls instead of focusing on the three murders. Poirot explains his thought process to Race with a metaphor that is also an allusion to an earlier Agatha Christie novel:
Unlock with LitCharts A+Once I went professionally to an archæological expedition—and I learnt something there. In the course of an excavation, when something comes up out of the ground, everything is cleared away very carefully all around it. You take away the loose earth, and you scrape here and there with a knife until finally your object is there, all alone, ready to be drawn and photographed with no extraneous matter confusing it. That is what I have been seeking to do—clear away the extraneous matter so that we can see the truth—the naked shining truth.