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.
It appears that the poem is back to talking about the "half-deserted streets" from stanza I.
The streets are filled with a "yellow fog," which sounds really nasty, actually. This detail might allow us to take a stab at the location of the poem.
Eliot was really interested in England, and he moved there before this poem was published. The capitol of England is London, which gets really foggy. You’ve probably heard the phrase, "London fog."
So maybe we’re in London. Around the beginning of the 20th century, London was a really modern city that also had some of the roughest, seediest neighborhoods anywhere.
This fog seems pretty acrobatic. It has a "back" and a "muzzle," which sounds like either a dog or a cat. Also, it "licks" things and makes "sudden leaps." OK, definitely sounds like a cat.
The poem is comparing the quiet, sneaky, and athletic movement of the fog to a common housecat. It’s a pretty sweet image. If you’ve ever been around a cat, you know how they can sneak up on you. One moment you’re sitting on the couch, reading a book, and the next moment, something soft and furry is rubbing against your leg.
The fog is wandering around the streets like a cat wanders around a house.
Finally, the fog gets tired and "curls" around the city houses to "fall asleep" like a cat would curl around something smaller, maybe the leg of a table or chair.
One interesting detail: it’s a "soft October night," which means the poem is set in autumn.