The story is set somewhere in the United States in a Pullman coach car.
Leacock himself was a Canadian writer, and his works were popular in the early part of the 20th century.
In the story, two men are conversing in a Pullman coach. Neither of the men recognize each other. However, each pretends otherwise. The text tells us that one of the men is wearing a "long fur-lined coat" and that he's carrying a fifty dollar suitcase.
Now, for a little bit of history. George Pullman built the first luxury coach cars in 1863. They were so popular that he commissioned more luxury cars...
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