As the other answers have noted, there are two similes in the first paragraph of "The Fly."
First, we learn that Mr. Woodifield:
peered out of the great, green-leather armchair by his friend the boss's desk as a baby peers out of its pram.
Second, he, like the rest of humanity:
cling[s] to our last pleasures as the tree clings to its last leaves.
In the first simile, Mr. Woodifield is likened to a baby comfortably and safely seated in a pram or baby carriage as he talks to his not-yet-retired friend—the boss.
In the second simile, the way he, an elderly man who has had a stroke, hangs on to his few remaining pleasures is compared to the way the last leaves of autumn cling to a tree: both are stubbornly past their time or season to die but also soon to fall.
In a story whose major theme is the trauma and devastation brought on by World War I, these similes are important. They show that some of those of the old generation, represented by people like Mr. Woodifield, are still sheltered by the...
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