Lines 15–25 focus on a single, extended metaphor:
The yellow fog that rubs its back upon the window-panes,
The yellow smoke that rubs its muzzle on the window-panes,
Licked its tongue into the corners of the evening,
Lingered upon the pools that stand in drains,
Let fall upon its back the soot that falls from chimneys,
Slipped by the terrace, made a sudden leap,
And seeing that it was a soft October night,
Curled once about the house, and fell asleep.
And indeed there will be time
For the yellow smoke that slides along the street,
Rubbing its back upon the window-panes
In these lines, Prufrock, who is telling the story, uses an extended metaphor to compare the fog of the London streets to a cat. At least nine details extend the metaphor: the fog is likened to a cat rubbing its back and its face against windowpanes, licking with its tongue, lingering by pools of rainwater, letting soot fall on its back, slipping by, making a sudden leap, curling up and sleeping, and once again sliding and rubbing.
Prufrock sees the fog as alive and quietly, even stealthily, moving, as a cat might. In this series of images, the evening morphs from something "etherized" and inert, as in the first line, to a lovelier, more fluid, various, and unpredictable environment.
The sad and ironic part of all this is that if these are Prufrock's thoughts, which they are, as he walks through London, we see him as having a creative and inventive mind that engages in the world around him in a compelling and imaginative way. Tragically, when he gets too fixated on himself, as he does at the party, he loses that creative edge, making it all the worse that he seems to endlessly go to parties that are draining him of imaginative vigor.