In Chapter 20, Sheppard uses a simile to describe Poirot's approach to the investigation. The simile relies on a visual image:
“You know,” I said, throwing down the pincers I was holding, “it’s extraordinarily intriguing, the whole thing. Every new development that arises is like the shake you give to a kaleidoscope—the thing changes entirely in aspect.
A kaleidoscope is an instrument, usually a tube, with beads or pieces of colored glass at one end and angled mirrors positioned around the inside. A viewer can look through the open end of the instrument and see a vivid, tessellated pattern created by reflections of reflections of the colored glass. Turning or shaking the kaleidoscope creates an entirely new pattern by changing the arrangement of the colored glass.
Sheppard conjures the image of a kaleidoscope and compares the investigation to it. Poirot is walking Sheppard through a very different investigation than the one the police have conducted. Whereas the police have sought a straightforward, objective story of what happened, Poirot is after a collection of subjective accounts. He hopes to piece together all these accounts into an objective narrative, but for now each piece of testimony is like a new arrangement of colored glass, casting an entirely different image onto the viewer's eye.
Sheppard is still trying to get away with murder at this point. He emphasizes the way in which each development changes the image in the "kaleidoscope" of the investigation. He passes himself off as merely intrigued, but it is easy to imagine that he thinks the pieces are scrambled enough to conceal the truth forever. What he does not note is that while a kaleidoscope can cast seemingly infinite patterns, there is a finite number of glass pieces resting at the bottom. Poirot's goal is to look at as many patterns as he can and deduce what really lies beneath them all. Sheppard believes that seeing more patterns opens more possibilities, but Poirot knows that each new pattern is another clue to the truth.
